Handbook of Residual Stress and Steel Deformation

© 2002 ASM International. All Rights Reserved. Handbook of Residual Stress and Deformation of Steel (#06700G)

Handbook of Residual Stress and Deformation of Steel

Edited by G. Totten M. Howes T. Inoue

Materials Park, Ohio 44073-0002 www.asminternational.org

www.asminternational.org



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2001040042 ISBN: 0-87170-729-2 SAN: 204-7586 ASM International威 Materials Park, OH 44073-0002 www.asminternational.org Printed in the United States of America

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Contributors I. Alexandru Faculty of Materials Technical University of Iasi Romania

T. Inoue Department of Energy Conversion Science Graduate School of Energy Science Kyoto University, Japan

H. Bhadeshia Department of Materials Science and Metallurgy University of Cambridge, UK

D.-Y. Ju Saitama Institute of Technology Saitama, Japan

V. Bulancea Faculty of Materials Technical University of Iasi Romania V.V. Dobrivecher Ukraine National Academy of Science Institute of Engineering Thermophysics Kiev, Ukraine T. Ericsson Linko¨pings Tekniska Ho¨gskola IKP Linko¨ping, Sweden F.D. Fischer Vorstand des Institutes fu¨r Mechanik Montanuniversita¨t Loeben Loeben, Germany A.V. Fomin Leading Research Scientist Institute Russian Academy of Sciences Moscow, Russia K. Funatani Nihon Parkerizing Co. Ltd. Nagoya, Japan Bo Gong Department of Metallurgy & Materials Science University of Toronto, Canada J. Grum Faculty of Mechanical Engineering University of Ljubljana, Slovenia A.Y. Hassan Director/Dean, School of Mechanical Engineering Universiti Sains Malaysia, Malaysia K. Heess Karl Heess GmbH Lampertheim, Germany F.T. Hoffmann ITW Bremen Bremen, Germany R. Hoffmann ITW Bremen Bremen, Germany

N.I. Kobasko Ukraine National Academy of Science Institute of Engineering Thermophysics Kiev, Ukraine Z. Kolozsva´ry S.C. Plasmaterm S.A. Tg-Mures, Romania A.I. Kovalev Surface Phenomena Research Group CNIICHERMET Moscow, Russia J. Kritzler Metal Improvement Company, Inc. Unna, Germany K.-H. Lang Institut fu¨f Werkstoffkunde 1 Universita¨t Karlsruhe (TH), Germany R.W. Lewis Department of Mechanical Engineering University College of Swansea, UK D. Lo¨he Institut fu¨f Werkstoffkunde 1 Universita¨t Karlsruhe (TH), Germany J. Lu Universite de Technologie de Troyes Trayes Cedex, France T. Lu¨bben ITW Bremen Bremen, Germany M.V. Medvedev Research Scientist Institute Russian Academy of Sciences Moscow, Russia V.P. Mishina Surface Phenomena Research Group CNIICHERMET Moscow, Russia V.S. Morganyuk Ukraine National Academy of Science Institute of Engineering Thermophysics Kiev, Ukraine iii

M. Narazaki Utsunomiya University Tochigi, Japan J. Pan School of Materials Science and Engineering Shanghai Jiao Tong University Shanghai, P.R. China P. Ramakrishnan Department of Metallurgical Engineering and Materials Science Indian Institute of Technology Bombay, India I.A. Razumovsky Leading Research Scientist Institute Russian Academy of Sciences Moscow, Russia T. Re´ti Bańki Dona´t Polytechnic Budapest, Hungary C. Ruud Pennsylvania State University University Park, PA USA G. Schleinzer Vorstand des Institutes fu¨r Mechanik Montanuniversita¨t Leoben Leoben, Germany B. Scholtes Institut fu¨r Werkstofftechnik Universita¨t Kassel, Germany K.N. Seetharamu School of Mechanical Engineering Universiti Sains Malaysia, Malayasia G.E. Totten G.E. Totten & Associates Inc. Stony Point, NY USA O.Vo¨hringer Institut fu¨f Werkstoffkunde 1 Universita¨t Karlsruhe (TH), Germany D.L. Wainstein Surface Phenomena Research Group CNIICHERMET Moscow, Russia H.W. Walton Consultant Forest City, NC USA Z. Wang Department of Metallurgy & Materials Science University of Toronto, Canada


G.M. Webster Union Carbide Corporation Tarrytown, NY USA W. Wu¨bbenhorst Metal Improvement Company, Inc. Unna, Germany


V.V. Zabilsky Physical Technical Institute, Ural Branch of RAS Ijevsk, Russia

iv

W. Zinn Institut fu¨r Werkstofftechnik Universita¨t Kassel, Germany



Contents Preface ........................................................................... vi

Residual Stress During Hardening Processes

Effect of Materials and Processing

Residual Stresses in Carburized, Carbonitrided, and Case-Hardened Components ........................................ 189 T. Re´ti

Material Factors .................................................................. 3 H.K.D.H. Bhadeshia

Residual Stresses in Nitriding............................................... 209 Z. Kolozsva´ry

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem ..........11 J. Lu

Induction Hardening.......................................................... 220 J. Grum

Residual Stresses and Fatigue Behavior.....................................27 D. Lo¨he, K.-H. Lang, and O. Vo¨hringer

Hardening by Reheating and Quenching .................................. 248 M. Narazaki, G.E. Totten, and G.M. Webster

Stability of Residual Stresses .................................................54 D. Lo¨he and O. Vo¨hringer

Metallo-Thermo-Mechanics–Application to Quenching ................ 296 T. Inoue Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling...................................... 312 N.I. Kobasko, V.S. Morganyuk and V.V. Dobrivecher

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking.............................................70 A.I. Kovalev, V.P. Mishina, D.L. Wainstein, and V.V. Zabilsky

Effect of Cryogenic Cooling on Residual Stresses, Structure, and Substructure ........................................................... 331 Ioan Alexandru and Vasile Bulancea

Measurement and Prediction of Residual Stress and Distortion Deflection Methods to Estimate Residual Stress ...........................89 H. Walton

Inducing Compressive Stresses through Controlled Shot Peening .... 345 J. Kritzler and W. Wu¨bbenhorst

Measurement of Residual Stresses ...........................................99 C. Ruud

Residual Stress Formation During Manufacturing Processes Residual Stress Formation during Casting ................................ 361 R.W. Lewis, K.N. Seetharamu and A.Y. Hassan

Stress Determination in Coatings........................................... 118 J.Albert Sue and Gary S. Schajer

Residual Stress Formation during Casting: Continuous and Centrifugal Casting Processes........................ 372 D.-Y. Ju

Methods for Determination of Inhomogeneous Residual Stress Fields ................................................................ 125 I.A. Razumovsky, M.V. Medvedev, and A.V. Fomin Residual Stress Formation in the Shaping of Materials

Residual Stress Formation Processes during Welding and Joining.... 391 W. Zinn and B. Scholtes

Residual Stress in the Forming of Materials.............................. 141 Z. Wang and B. Gong

Residual Stresses in Powder-Metal Processing........................... 397 P. Ramakrishnan Residual Stress Formation and Distortion of Rail Steel................. 424 F.D. Fischer and G. Schleinzer

The Effect of Final Shaping Prior to Heat Treatment ................... 150 T. Ericsson

Residual Stresses during Gear Manufacture .............................. 437 K. Funatani

Factors Affecting Final Part Shaping ...................................... 159 P. Jiansheng

Metric Conversion Guide .................................................. 459 Effects of Process Equipment Design...................................... 183 F.T. Hoffmann, T. Lu¨bben, R. Hoffmann, and K. Heeß

Index ........................................................................... 465 v



Preface Control of steel deformation is one of the most common concerns within the metals processing industry. Numerous surveys have been conducted by various organizations in recent years to assess the critical needs of the industry. In nearly every survey that has been conducted, distortion is either the greatest or second greatest concern among the steel heat treating community. Steel distortion control will exhibit tremendous effects on the profitability of the commercial enterprise. Therefore, it is not surprising that the ability to understand the overall distortion process and to be able to design solutions to this problem typically rank very high on these same surveys. In view of the enormous visibility and importance of steel deformation problems, the editors decided to put together an engineering handbook on steel deformation. To address this subject properly, contributing factors to overall steel deformation problems, including material effects, machining, heating and cooling, must be examined. This handbook contains 27 articles, divided into five sections: Effect of Materials and Processing, Measurement and Prediction of Residual Stress and Distortion, Residual Stress Formation in the Shaping of Materials, Residual Stress During Hardening Processes, and Residual Stress Formation During Manufacturing Processes. There are five articles in the section Effect of Materials and Processing. “Material Factors” discusses the effects of various material properties such as thermal properties and the interactions of residual stresses on the transformation products formed and steel deformation during fabrication. Transformation plasticity is discussed in some detail along with the use of modeling to better understand these processes. “Prestress Engineering of Structural Material” provides a global design approach to understanding the effects of residual stress generated during surface engineering manufacturing processes such as PVD and CVD on the material properties obtained. Some of the topics discussed in this chapter include developments in the measurements of residual stresses, advanced mechanical surface treatments, and modeling of fatigue behavior taking residual stresses into consideration. The effect of residual stresses on fatigue behavior is discussed in detail in the next article. Examples of topics discussed include stability of residual stresses, some aspects of fatigue in

steels, influence of residual stresses on cyclic deformation behavior, influence of residual stresses on crack initiation and propagation, and effect of residual stresses on S-N curves; an overview of modeling of the effect of residual stresses on fatigue behavior is provided. The next article provides an overview of the stability and relaxation behavior of macro and micro residual stresses in steel due to thermal and mechanical treatments. This discussion includes relaxation of residual stresses by annealing, residual stress relaxation by uniaxial deformation, and relaxation by cyclic deformation. Hydrogen embrittlement of metals, as well as other types of brittle fracture, result from nucleation and development of micro-cracks caused by internal stresses. The last article in this section provides an overview of the effect of residual stress on hydrogen embrittlement and stress corrosion cracking (SCC) of steel. This discussion includes the effect of hydrogen on structure and transformation of steel, types of hydrogen embrittlement, delayed fracture in steel, crack initiation and growth, SCC of low alloy steels, crack initiation and growth mechanism of SCC processes, methods of estimating sensitivity to SCC, effect of alloying elements on resistance to SCC, and the role of structure and thermal processing in SCC. In the section Measurement and Prediction of Residual Stress and Distortion, the first article describes a number of simple, inexpensive deflection (dissection) methods used to estimate residual stress of various types of components. The methods include Almen strip; Navy C-Ring; plate or bar slitting and deflection; tube slitting and opening; and bending of bars, H-beams, and channels. The next article provides an overview of residual stress measurement methods. Topics include residual stresses arising from various manufacturing processes, measurement methods including strain measuring technique, post-stress relaxation measurement, sectioning and material removal methods. In addition, strain measurement methods such as x-ray and neutron diffraction, ultrasonic, birefringent and laser, optical gages, brittle coatings, Barkhausen noise, and chemical coatings are discussed. Semidestructive methods such as blind hole drilling and ring coring are discussed. Measurement of residual stresses in coatings and thin films is important because their influence on mechanical and physical properties affect component service performance. “Stress Devi

termination in Coatings” provides a guide for measuring residual macrostress in coatings, Specific topics include origin of residual stresses in coatings and residual stress measurement methods including the deflection method, x-ray diffraction, and hole-drilling. A comparison of these methods is provided. The last article in this section provides a detailed review of methods used to measure and subsequent data analysis of inhomogeneous residual stress fields. This discussion includes residual stress as an inverse problem of experimental mechanics, indicator crack method of measuring residual stress, arbitrary cut-out indicator method, and experimental methods and equipment including photoelastic coating method, and optical interferometry. Although this is a relatively rigorous numerical discussion, practical examples also are provided. Residual Stress Formation in the Shaping of Materials contains four articles. The first article covers residual stress in the steel forming processes. The steel forming processes included are cold forming such as wire drawing, and hot forming such as extrusion, rolling, and forging. The effects of residual stresses involved in these processes are reviewed, and specific topics include residual stress in cold metal forming such as bending of sheet, drawing of wire, rod, and tube, and residual stresses in deep drawn cup, sunk tubes, and radial forging products. The effect of final shaping prior to heat treatment on residual stress formation is discussed in the next article. The effects of shaping processes including grinding, milling, turning, shot peening, and straightening on residual stress are discussed. Also discussed is distortion after final part shaping and experimental and computational studies of these processes. The next article provides a practical overview of the factors affecting residual stress and distortion during final part shaping. Included are discussions of influence of component shape on heat treatment distortion, the effect of crosssection size and asymmetry, effect of heat treating procedure and machining process on final component shape, effect of sequence of heat treating and machining, influence of machining allowance and stress relieving procedure, influence of residual stresses caused by cutting, methods of manufacturing blanks and effect of original structure, hot-rolled steels or forgings and effect of banded segregation and carbide segregation, influence of heat treating methods, the effect of heating including the rules of heating,


quenching and system design, tempering, and equipment and racking. A more focused, but practical, discussion on the effect of process equipment design on distortion follows. Subjects that are covered include distortion generating process equipment, methods that may be used to minimize equipmentrelated distortion, quench system design, and press quenching. Residual Stress During Hardening Processes contains eight articles. The first article provides a detailed discussion on the residual stresses in carburized, carbonitrided, and case-hardened components. Topics include process considerations for carburized and carbonitrided components, transformations and stress evolution in carburized and case-hardened components, effect of heat treating operations on residual stress distribution, relationship between residual stresses and properties of carburized parts and modeling and prediction of residual stress field. The article on residual stresses in steel nitriding includes a discussion of nitrided layer structure as a function of nitriding process, residual stresses in nitrided layers, influence of residual stresses on fatigue behavior of nitrided steel components, and modeling and prediction of residual stresses in nitrided steel components. The article on residual stress formation in induction hardening processes include an overview of the induction hardening process and steels used for this process, magnetic flux concentrators, conditions in induction heating and quenching of machine parts, residual stress surface profiles after induction surface hardening, stress profiles in the machine part in the loaded state, workpiece distortion in induction surface hardening, induction surface hardening of gear wheels, fatigue strength of materials, and residual stresses after induction surface hardening and finish grinding. The next article provides an overview of residual stresses and distortion resulting from reheating and quenching. Topics include phase transformation during heat treating including steel transformations, TTT and CCT diagrams, metallurgical crystal structure, estimation of volumetric change due to steel transformation upon quenching, cooling of steel with and without metallurgical transformation, tempering, basic distortion mechanism, relief of residual stresses, material movement due to thermal gradients during heating and cooling, material, component and process effects, retained austenite, quench severity and uniformity and process design effects on distortion, quench distortion and cracking, quenchant selection, measurement and evaluation of quenching power, estimation of heat transfer coefficient, wetting behavior and nonuniform quenching, surface conditions, and quench process modeling and simulation of residual stress and distortion after quenching. A detailed approach to modeling and simulation of residual stress and distortion applied to quench processing follows. This discussion is based on a metallo-thermo-mechanics approach, and topics discussed include an overview of


metallo-thermo-mechanics and numerical simulation methodology with practical examples. In the article on the control of residual stress formation and steel deformation during rapid heating and cooling, a particular emphasis is on intensive quenching. This is the first detailed, article-length discussion of this old, but littleknown technology in the western world. Topics include mathematical model for calculation of thermal and stress-strain state, computation of stress-strain state, possibility of predicting hardening cracks, predicting the deformation of bearing rings during hardening, thermal stresses formed in carburized steel products due to excessive cooling rates, generalization of computational and experimental results for heating and cooling of parts with different geometries and thermal and physical fundamentals of processing of high-strength materials. An often contradictory subject is the cryogenic processing of steels, and the detailed overview of the effect of cryogenic cooling on residual stress is presented here. Specific topics include role of residual stresses within martensitic transformation at cryogenic temperatures, evaluation of residual stresses after cryogenic cooling, influence of cryogenic cooling on residual stresses and dimensional stability of steels, and influence of cryogenic cooling on the structure and substructure of steels. The practical use of controlled shot peening to induce compressive residual stresses is described in detail next. This discussion includes a historic overview of shot peening, elementary processes of shot peening, workpiece and material process parameters, process monitoring, process optimization, x-ray diffraction, and industrial examples. In Residual Stress Formation During Manufacturing Processes, the first article includes an extensive discussion of residual stress and deformation problems arising from the casting process, and modeling of residual stress formation during casting. Discussion includes finite element analysis of heat flow during casting, formulation of the elasto-viscoplastic stress model, and deformation of a solidifying material. The next article describes residual stress formation during the casting process, and it includes continuous and centrifugal casting. Topics discussed include inelastic behavior and unified constitutive theory of metallic material in solidification, analytical method of the thermal-mechanical problem for the casting process, residual stress formation during semicontinuous casting, residual stress formation during centrifugal casting, and residual stress formation during strip casting by the twin-roll method. The origin and assessment of residual stresses during welding or brazing is discussed next. Welding residual stresses are discussed including residual stresses due to shrinkage, quenching, and phase transformations. Characteristic residual stress distributions in brazed components is also discussed. The article “Residual Stresses in Powder Metal Processing” is divided into two parts. The vii

first part describes manufacturing of ferrous P/ M parts including powder characteristics, compaction in rigid dies, isostatic compaction, sintering, heat treatment of P/M parts, hot pressing, roll compaction, powder forging, metal injection molding, spray forming, warm compaction, and rapid prototyping. The second part discusses residual stresses in P/M processing including powder production, compaction of metal powders, sintering of metal powders, pressure sintering and hot isostatic pressing, heat treatment of P/M parts, and microstructural development and properties. “Residual Stress Formation and Distortion of Rail Steel” covers the cooling process including the cooling boundary conditions and heat transfer, residual stress state analysis, weight and friction—the rail end problem, experimental results; roller straightening including residual stresses in unused roller-straightened rails, behavior of rail steel under plastic deformation, simulation of roller straightening; and rails in service including residual stresses due to welding and residual stress formation in rolling contact. The last article provides a detailed description of residual stress formation during hypoid gear manufacture. It includes an overview of residual stress formation in carburized and hardened work, profiles and peak magnitudes of residual stresses, measurement methods including the Sach’s hole-drilling method, x-ray and neutron diffraction, influence of steel properties on residual stresses, influence of carburizing process parameters on residual stress formation, benefits of residual stresses on fatigue strength, and the effects of hardness, case depth, intergranular oxidation, influence of shot peening, change of residual stresses during fatigue, and distortion of carburized and hardened steels. The preparation of a text of this scope was a tremendous task. The editors are deeply indebted to many colleagues for their patience, support, and assistance; without them this text would not have been possible. Special thanks go to the ASM staff who often labor in the background but who are vital members of the team. Particularly, thanks go to Veronica Flint and Carol Terman of ASM International for their help and encouragement. Very special thanks go to our families for their seemingly unending support. Without their understanding and encouragement, this project would never have been completed. George E. Totten, Ph.D., FASM Editor G.E. Totten & Associates Inc. Stony Point, NY USA Prof. Maurice A.H. Howes, Ph.D. (Retired) Editor Worcestershire, England Prof. Tatsuo Inoue, Ph.D., FASM Editor Department of Energy Conversion Science Faculty of Energy Science Kyoto University Kyoto, Japan

Handbook of Residual Stress and Deformation of Steel G. Totten, M. Howes, T. Inoue, editors, p3-10 DOI: 10.1361/hrsd2002p003

Copyright © 2002 ASM International® All rights reserved. www.asminternational.org

Material Factors H.K.D.H. Bhadeshia, University of Cambridge

RESIDUAL STRESSES are a consequence of interactions among time, temperature, deformation, and microstructure (Fig. 1). Material or material-related characteristics that influence the development of residual stress include thermal conductivity, heat capacity, thermal expansivity, elastic modulus and Poisson’s ratio, plasticity, thermodynamics and kinetics of transformations, mechanisms of transformations, and transformation plasticity. Many general statements can be made about the role of material factors in the evolution of residual stress. Spatial variations in temperature give rise to nonuniform thermal strains, the effect of which becomes exaggerated when the material is elastically stiff and has a high yield strength. A large thermal conductivity helps reduce residual stress by reducing temperature gradients (Ref 2). The dissipation or absorption of heat depends not only on the external environment of the component but also on internally generated heat—for example, during adiabatic deformation or due to the latent heat of transformation. Similarly, the plastic strain distribution in the component depends both on the constitutive properties and on how the shape deformations due to phase transformations compensate for the development of stress. The fundamental material properties are, of course, temperature dependent. Table 1 illustrates how several key properties might vary with temperature (Ref 3). Some of these properties, which can to some extent be estimated quantitatively, are discussed in detail in the sec-

tions that follow; others such as elastic modulus and thermal conductivity still have to be measured for individual alloys.

Heat Capacity The dominant contribution to specific heat capacity comes from lattice vibrations (phonons), since the majority of free electrons are prevented from participation in heat absorption by the Pauli exclusion principle. However, for iron and its alloys, a further important contribution comes from magnetic changes. The net specific heat capacity can therefore be factorized into three components:

冦 T 冧C

CP{T } ⳱ C LV

TD

1

Ⳮ CeT Ⳮ C Pl{T }

where C LV{TD /T} is the Debye specific heat function and TD is the Debye temperature. The funcTable 1

Physical properties that affect the development of residual stress in steels Temperature, C (F)

Property

Phase(a)

Elastic modulus, GPa

c ␣ⳭP ␣b ␣⬘

Poisson ratio

c ␣ⳭP ␣b ␣⬘ c ␣ⳭP ␣b ␣⬘

Thermal expansivity, Kⳮ1

Time, temperature

1. Thermal stress

6. Latent heat

Stress, strain

4. Heat of deformation 5. Stressinduced transformation

2. Temperaturedependent phase transformations

3. Transformation strain Microstructure

Fig. 1

The coupling of temperature, stress, and microstructure. Source: Ref 1

(Eq 1)

tion C1 corrects C LV{TD /T} to a specific heat at constant pressure. Ce is the electronic specific heat coefficient, and C lP is the component of the specific heat capacity due to magnetism. Figure 2 illustrates the data for ferrite and austenite in pure iron. Whereas it is well known that ferrite undergoes a paramagnetic to ferromagnetic transition on cooling below 1042.15 K, the magnetic properties of austenite are seen from Fig. 2 to be of some consequence in determining the heat capacity. There are two coexisting electron states of austenite, one of which is ferromagnetic with a Curie temperature of 1800 K and the other of which is antiferromagnetic with a Neél temperature of 55 to 80 K (Ref 4). The balance between these states changes with temperature, giving rise to corresponding changes in heat capacity. The data in Fig. 2 are for pure iron, but there is now sufficient understanding of the components of heat capacity to enable similar estimates for iron alloys, using internationally available computer programs and thermodynamic data-

Thermal conductivity, W/m • K

c ␣ⳭP ␣b ␣⬘

Specific heat capacity, 10ⳮ6 J/m3 • K

c ␣ⳭP ␣b ␣⬘

Yield strength, MPa

c ␣ⳭP ␣b ␣⬘

0 (32)

200 210 210 200 0.291 0.280 0.280 0.280

15.0 49.0 49.0 43.1 4.15 3.78 3.78 3.76 190 360 440 1600

300 (570)

175 193 193 185

600 (1110)

150 165 165 168

0.309 0.296 0.296 0.296 2.1 ⳯ 10ⳮ5 1.4 ⳯ 10ⳮ5 1.4 ⳯ 10ⳮ5 1.3 ⳯ 10ⳮ5 18.0 41.7 41.7 36.7 4.40 4.46 4.46 4.45 110 230 330 1480

(a) ␣, P, ␣b, and ␣⬘ represent allotriomorphic ferrite, pearlite, bainite, and martensite, respectively. Source: Ref 3

0.327 0.310 0.310 0.310

21.7 34.3 34.3 30.1 4.67 5.09 5.09 5.07 30 140 140 1260

800 (1470)

124 120 120 ... 0.345 0.325 0.325 ...

25.1 27.0 27.0 ... 4.90 5.74 5.74 ... 20 30 30 ...

4 / Effect of Materials and Processing bases (Ref 6). After all, changes in fundamental thermodynamic quantities such as enthalpy and entropy are derived from heat capacity data. It is surprising that this capability has not yet been exploited in any calculation of residual stress, even though the methodology is widely available.

Expansion Coefficient and Density Table 1 shows that the expansion coefficient of austenite is larger than that of ferrite; this might be considered surprising given the lower density of ferrite. However, the behavior is again

c0 c1 V cm{T } ⳱ (1 ⳮ y)V m {T } Ⳮ y V m {T }

30 Heat capacity, CP, J mol 1K1

V cm0 ⳱ 6.695(1 Ⳮ 2.043 ⳯ 10ⳮ5T Ⳮ 1.52 ⳯ 10ⳮ8T 2) V cm1 ⳱ 7.216(1 Ⳮ 2.043 ⳯ 10ⳮ5T Ⳮ 1.52 ⳯ 10ⳮ8T 2)

40

20

V am{T } ⳱ 7.061(1 Ⳮ 2.043 ⳯ 10ⳮ5T Ⳮ 1.52 ⳯ 10ⳮ8T 2)

Austenite 10 0 75 Ferrite

50

25 0

a reflection of the two coexisting electronic states of austenite (c0 and c1), each with a thermal expansion coefficient that is identical to that of ferrite. The c0 component has the lower molar volume and is the antiferromagnetic form, whereas the denser c1 form is ferromagnetic. The relative proportion of atoms in the c0 and c1 states changes with temperature, so that the apparent expansion coefficient of austenite as a whole, as detected experimentally, is much larger than that of ferrite (Fig. 3). The molar volumes (in cm3 /mol) of c0, c1, c, and ␣ over the temperature range of 300 to 1775 K are:

0

300

600

900

1200

1500 1800

Temperature, K

where y is the fraction of atoms of austenite in the c1 state, the details of which can be found elsewhere (Ref 4, 5). These data are for pure iron, but thermodynamic data can be used to assess how the expansion coefficients would change with alloying, since there are quite sophisticated treatments of the effect of solute elements on the magnetic and other components of the free energies of iron. Note that the “two electronic states” picture of austenite is a simplification of the real scenario, but first-principles calculations (Ref 7), which

Specific heat capacities of ferrite and austenite in pure iron, as a function of temperature. The thin lines represent the combined contributions of the phonons and electrons, whereas the thicker lines also include the magnetic terms. The dashed vertical lines represent the Curie, ␣ → c, and c → d transitions. d-ferrite is simply an alternative historical name for high temperature ␣. Source: Ref 5

deal with higher levels of complexity, are not yet applicable to practical alloys.

Plastic Deformation The familiar mechanisms of plastic deformation are slip, mechanical twinning, and creep. Phase transformations also cause permanent deformation (Ref 8–11). In steels, austenite can decompose into a large variety of microstructures that are distinguished by the atomic mechanism of transformation (Fig. 4). In a displacive transformation, the change in crystal structure is achieved by a deformation of the parent structure. A reconstructive transformation is one in which the change in structure is achieved by a flow of matter, which occurs in such a way that strains are minimized. All the transformations cause changes in shape (Fig. 5a), which for reconstructive transformations simply reflects the change in density. For displacive transformations, the shape change is an invariant-plane strain (IPS), that is, a combination of a shear on the invariant plane and a dilatation normal to that plane. The strain energy associated with a constrained IPS is minimized when the product phase has a thin-plate shape. This is why Widmansta¨tten ferrite, bainite, acicular ferrite, and martensite in steels grow in the form of plates. The distinguishing features of a variety of deformation modes are compared in Table 2, and Table 3 describes the shape deformations. The permanent strain caused by any transformation is called transformation plasticity. A

Fig. 2

Displacive Reconstructive

Invariant-plane strain shape deformation with large shear component. No iron or substitutional solute diffusion. Thin plate shape

Diffusion of all atoms during nucleation and growth. Sluggish below about 850 K

8.0 γ

α

δ

7.8

Allotriomorphic ferrite

Volume, cm3 mol1

7.6

Vγ1

7.4

Widmanstätten ferrite Carbon diffusion during paraequilibrium nucleation and growth

Idiomorphic ferrite

Vα

Bainite and acicular ferrite

7.2

Vγ

Massive ferrite

7.0

No change in bulk composition

Carbon diffusion during paraequilibrium nucleation. No diffusion during growth

6.8

Vγ0 6.6

0

300

600

900

1200

1500 1800

Temperature, K

Fig. 3

Molar volumes of the various forms of iron. Source: Ref 5

Fig. 4

Pearlite

Martensite

Cooperative growth of ferrite and cementite

Diffusionless nucleation and growth

Transformation products of austenite. Source: Ref 12

Material Factors / 5 phase change in a stress-free material is usually triggered by heat treatment, when the parent phase passes through an equilibrium transformation temperature. Alternatively, the application of a stress in isothermal conditions can trigger transformation in circumstances where it would not otherwise occur. Unusual effects can occur when stress and temperature work together. The transformation may occur at remarkably low stresses or at very small deviations from the equilibrium temperature. This is why even minute stresses can greatly influence the development of microstructure, and vice versa. It is not surprising that transformation plasticity can be obtained at stresses that are much smaller than the conventional yield stress of the parent phase.

Transformations, Residual Stresses, and Related Phenomena The strains due to phase transformations can alter the state of residual stress or strain. It is well known that the martensitic transformation of the carburized surface of a steel component puts the surface under compression. It is argued that this is because of the expansion at the surface due to formation of the lower-density martensite from austenite.

Phase transformation can also compensate for stress. Greenwood and Johnson (Ref 13, 14) showed that when a phase change is accompanied by a change in volume, the tensile strain expected when transformation occurs under the influence of a tensile stress r is given by: e ⳱

5 DV r 6 V rY

(Eq 2)

where rY is the yield stress of the weaker phase and DV/V is the transformation volume strain. The role of shear strains associated with transformation has been emphasized in later work by Magee and Paxton (Ref 15, 16), and subsequently by Fischer (Ref 17), Leblond et al. (Ref 18–22), Olson (Ref 23), and Bhadeshia et al. (Ref 24). Not only does transformation affect stress, but the latter modifies the development of microstructure. The microstructure tends to be more organized when transformation occurs in a stress’s parent phase, because the stress favors the formation of certain orientations relative to others. This is illustrated schematically in Fig. 5(b) to (d). These aspects will now be discussed in more detail, because transformation plasticity can radically alter the state of residual stress.

Table 2

Reconstructive

α

Displacive

γ Single crystal

Causes permanent change in shape Invariant-plane strain shape changewith a large shear component Changes crystallographic orientation Changes lattice type Can lead to a density change

Table 3

Allotriomorphic ferrite Idiomorphic ferrite Pearlite Widmansta¨tten ferrite Bainite Acicular ferrite Martensite Cementite plates Mechanical twins (␣) Annealing twins (c)

Slip deformation

Mechanical twinning

Displacive transformation

Reconstructive transformation

Yes Yes No No No

Yes Yes Yes No No

Yes Yes Yes Yes Yes

Yes No Yes Yes Yes

Shape change due to transformation

Transformation

(a)

Displacive transformations can be regarded as modes of plastic deformation. Just as a combination of a plane and a direction constitutes a deformation system for slip or twinning, the habit plane and displacement vector of the invariant-plane strain accompanying displacive transformation completely describe the deformation system responsible for transformation plasticity. The displacement vector describes the sense of the macroscopic displacements accompanying transformation and, along with the habit plane indices, also contains information about the magnitude of the shear component and dilatational component of the displacements. Typical data for the deformation systems associated with transformations are listed in Table 4. Note that reconstructive transformations involve only a volume change together with diffusional mass flow, so it is not appropriate to regard them as deformation systems in the present context. Given the cubic crystal structure, and the fact that habit planes tend to be irrational, there will in general be 24 of these systems per austenite grain, and they may operate simultaneously to varying extents. Of course, unlike ordinary slip,

Characteristics of different modes of deformation

Characteristic

α

Deformation System

Shape change (a)

s(b)

d(b)

Morphology

Volume change Volume change Volume change Invariant-plane strain Invariant-plane strain Invariant-plane strain Invariant-plane strain Invariant-plane strain? Invariant-plane strain

0.00 0.00 0.00 0.36 0.22 0.22 0.24 0.21? 1/冪2 0.00

0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.16? 0.00 0.00

Irregular Equiaxed, faceted Spherical colonies Thin plates Thin plates Thin plates Thin plates Thin plates Thin plates Faceted

(a) An invariant-plane strain here implies a large shear component as well as a dilatational strain normal to the habit plane. (b) s and d refer to the shear and dilatational strains, respectively. The values stated are approximate and will vary slightly as a function of lattice parameters and the details of crystallography.

(b)

(c)

(d)

Shape changes accompanying unconstrained transformations. Note that the horizontal scale bars are all the same length. (a) The two kinds of shape changes that occur when a single crystal of austenite transforms to a single crystal of ferrite, as a function of the mechanism of transformation. (b) Polycrystalline sample of austenite. (c) Polycrystalline sample of austenite that has partially transformed by a displacive transformation mechanism into a random set of ferrite plates. (d) Polycrystalline sample of austenite that has partially transformed by a displacive transformation mechanism into an organized set of ferrite plates.

Fig. 5

Table 4

Deformation systems associated with transformations

Phase

Habit plane indices

Displacement vector

m

(0.363 0.854 0.373)

[0.195 0.607 0.771]

0.185

Bainite

(0.325 0.778 0.537)

[0.159 0.510 0.845]

0.27

Widmansta¨tten ferrite

(0.506 0.452 0.735)

[0.867 0.414 0.277]

0.36

Martensite

Note: Typical habit plane and displacement directions for low-alloy steels. The indices all refer to the austenite phase. Note that the indices stated are approximate, since the habit plane and displacement direction are usually irrational. The displacement vector does not quite lie in the habit plane because the dilatational strain is directed normal to the habit plane. The magnitude of the displacement is given by m, which is the total displacement including the shear and the dilatational components.

6 / Effect of Materials and Processing the different deformation systems within an austenite grain cannot intersect, except in special circumstances where intervariant transformations are possible, as is the case with some shape-memory alloys. It follows that the ordiσN σA (applied tensile stress)

τmax τ d

Resolution of the applied stress, rA. The normal stress, rN, and the shear stress, s, both act on the habit plane. The vector d is the direction along which lie the shear displacements of the shape deformation. smax is the maximum shear stress on the habit plane, but s is given by resolving smax along d. Note that d differs slightly from the displacement vector of the IPS, which includes a dilatational component in addition to the shear.

Fig. 6

Table 5 Typical values of the mechanical driving force coefficients ⵲DG/⵲r, J/(mol MPa)

Nature of stress

Uniaxial tension Uniaxial compression Elastic crack tip (a)

ⳮ0.86 ⳮ0.58 ⳮ1.42

Tensile + Compression 0

Mechanical Driving Force The interaction of an applied elastic stress with a phase change can occur in two ways: 1. The stress can alter the driving force for the transformation. 2. The stress can change the appearance of the microstructure by favoring the formation of those variants which best comply with the applied stress. For reconstructive transformations, only the hydrostatic component of stress can interact with

Hydrostatic compression Stress (below austenite yield strength)

Indication of how the transformation-start temperature (for Widmansta¨tten ferrite, bainite, acicular ferrite, or martensite) should vary as a function of the nature and magnitude of an applied stress whose magnitude is less than that of the yield stress.

Fig. 7

Table 6 Sensitivity of transformation-start temperatures in steels to applied stress Phase

Nature of stress

Martensite Bainite Eutectoid Martensite

Pressure Pressure Pressure Tensile

Source: Ref 32

Sensitivity, K/MPa

ⳮ0.06 ⳮ0.09 ⳮ0.011 Ⳮ0.06

1000 Free energy, J mol1

Change in bainite-start temperature

(a) The stress state for the crack tip is multiaxial, but the coefficient is calculated by expressing the stress in terms of the von Mises equivalent tensile stress. Source: Ref 32

nary notion of work hardening does not apply. Work hardening nevertheless manifests itself via a different mechanism, in which the stability of the austenite increases as it becomes ever more finely divided. The Taylor/von Mises criterion (Ref 25, 26) states that in any given crystal, a minimum of five independent slip systems is necessary to produce an arbitrary shape change. A crystal in a polycrystalline aggregate has to accommodate the arbitrary deformations of neighboring grains. Therefore, a polycrystalline material is brittle unless each grain contains at least five independent slip systems. Similar logic can be applied to the crystallographic variants of a phase generated by displacive transformation. The habit plane is predicted theoretically (Ref 27, 28) and found experimentally (Ref 29) to have irrational indices. This means that there exist, in principle, 24 possible variants of the habit plane per grain of austenite (that is, 24 independent deformation systems). Given this large number of transformation variants available per grain, the Taylor criterion leads to the conclusion that transformation plasticity can cause, or accommodate, any externally imposed, arbitrary shape change—assuming that a sufficient quantity of parent phase is available. It follows that polycrystalline samples can remain intact at grain boundaries when transformation plasticity is the sole mode of deformation.

the volume change. The corresponding interaction with displacive transformations is much larger because of the shear component of the IPS. For displacive transformations, the influence of stress on the transformation can be expressed as a mechanical driving force (DGmech), which is the work done by the external stress in producing the macroscopic shape deformation (Ref 30, 31): DGmech ⳱ rNd Ⳮ ss

(Eq 3)

where rN is the normal stress on the habit plane and s is the component of the shear stress on the habit plane that is parallel to the direction along which the shear displacements of the shape deformation occur (Fig. 6). The strains d and s are the dilatational and shear components, respectively, of the shape deformation. Some typical values of the mechanical driving force terms are given in Table 5. Given a free choice of some 12 to 24 crystallographic variants of the transformation product in each grain of austenite, the work done by the shear stress is always expected to be positive, whereas that due to the dilatational component depends on the sign of rN. For steels, this latter component is relatively small. Any observed consequences of stress must therefore reflect the dominant role of the shear component unless the stress is purely hydrostatic. Since the shear stress remains positive irrespective of whether the sample is pulled in tension or uniaxially compressed, and since the shear component of the shape change is large, a uniaxial stress will always cause a temperature increase for displacive transformations in steels. Hydrostatic stress, on the other hand, has no deviatoric components and consequently interacts only with the dilatational component of the shape change. Thus, hydrostatic compression is expected and found to lead to a decrease in the transformation temperature (Fig. 7); some data (Ref 32) on the sensitivity of the transformation temperature to applied stress are presented in Table 6.

Limits to Stress-Assisted Transformation

Chemical 0 Mechanical

1000 Total 2000 300

400

500

600

700

800

900

Temperature, °C Typical magnitudes of the chemical and mechanical driving forces for stress-affected transformation. The mechanical driving force is estimated for an applied stress that is equal to the yield stress of austenite. Since this yield stress becomes small at high temperatures, the contribution of the mechanical driving force also decreases. Therefore, transformation becomes impossible as the temperature exceeds about 700 C (1290 F).

Fig. 8

At temperatures close to that at which the equilibrium transformation occurs, an applied stress can assist reaction when the chemical driving force is insufficient to achieve the change on its own. There must exist a point, however, when the applied stress simply cannot provide enough mechanical driving force to complement the chemical term to give a driving force large enough to induce transformation. After all, the magnitude of the stress that can be applied is limited by the yield point of the parent phase. Thus, there are limits to what can be achieved by the application of stress as a stimulus to transformation (Fig. 8).

Material Factors / 7

Residual stresses are often introduced unintentionally during fabrication—for example, during welding or heat treatment. A few elegant experiments illustrate how phase transformations interact with the buildup of residual stress. Using bainitic, martensitic, and stable austenitic steels, Jones and Alberry (Ref 33, 34) demostrated that transformation plasticity during the cooling of a uniaxially constrained sample from the austenite phase field acts to relieve the buildup of thermal stress as the sample cools. By contrast, the nontransforming austenitic steel exhibited a continuous increase in residual stress with decreasing temperature, as might be expected from the thermal contraction of a constrained sample. When the steels were transformed to bainite or martensite, the transformation strain compen-

500 AISI 316 9CrMo 2CrMo Austenite YS

400 Stress, MPa

300 200 100 0 –100

0

200

400

600

800

1000 1200 1400

Temperature, °C (a)

Stress

Plastic strain in austenite Transformation finished

Stress due to thermal contraction of austenite

0

Stress due to thermal contraction of ferrite

Transformation begins

sated for any thermal contraction strains that arose during cooling. Significant residual stresses were therefore found to build up only after transformation was completed and the specimens approached ambient temperature (Fig. 9). The experiments contain other revealing features. The thermal expansion coefficient of austenite (1.8 ⳯ 10ⳮ6 /K) is much larger than that of ferrite (1.18 ⳯ 10ⳮ6 /K), and yet the slope of the line prior to transformation is smaller when compared with that after transformation is complete (Fig. 9). This is because the austenite yields to accommodate the thermal contraction, which is possible because the yield strength of the austenite is reduced at elevated temperatures. Ferrite is strong at low temperatures, so the slope of the stress/temperature curve (after transformation is complete) is steeper and consistent with the magnitude of thermal contraction strains. Interpretation of experimental data of the kind illustrated in Fig. 9 is difficult in the region of the stress/temperature curve where transformation occurs. The popular view that the volume change due to transformation is the major component of transformation plasticity is probably incorrect for displacive transformations such as bainite or martensite. The shape change due to transformation has a shear component that is much larger than the dilatational term (Table 3). Admittedly, this shear component should, on average, cancel out in a fine-grained polycrystalline sample containing plates in many orientations (Fig. 5c). However, the very nature of the stress effect is to favor the formation of selected variants, in which case the shear component rapidly begins to dominate the transformation plasticity (Fig. 5d). Bulk transformation strain, %

Transformation under Constraint: Residual Stress

3 75 MPa compressive stress 2

εR

1 0

2

0

100

200

300

400

500

600

Transformation time, s (b)

Temperature

(a) Plot of residual stress versus temperature for a martensitic (9CrMo), bainitic (2CrMo), and austenitic steel (AISI 316). Adapted from Ref 33, 34. (b) Interpretation of the Jones and Alberry experiments. The thermal expansion coefficient of austenite is much larger than that of ferrite.

Fig. 9

Anisotropic Strain and Transformation Plasticity When an unstressed polycrystalline sample of austenite is transformed to plates of ferrite, the shear caused as each randomly oriented plate forms is canceled on a macroscopic scale; only the volume expansion is observed experimentally. However, if the plates do not form at random—for example, when certain variants are favored because they comply better with the external stress—the shear strains are no longer canceled out. Transformation will then lead to highly anisotropic strains, as illustrated in Fig. 11. Naturally, any anisotropy will be greatest for displacive rather than reconstructive transformations, given that the former involve large shear strains.

Modeling Anisotropic Transformation Strains

εL

1

The residual stress at ambient temperature is larger when the austenite finishes transformation at a high temperature. This is because thermal contraction strains can no longer be compensated by transformation plasticity once the austenite has decomposed. Low transformation temperatures help minimize residual stresses. High-strength welding alloys used for making submarine hulls therefore have transformation temperatures of less than about 250 C (480 F). Figure 10 illustrates one kind of distortion found in welds, measured in terms of the angle h through which the unconstrained plates rotate as they cool. Table 7 shows how the distortion depends on the temperature at which the majority of the transformation is completed, for two manual metal arc welds deposited with a 60 Vjoint preparation in a multipass fabrication involving about 11 layers, with two beads per layer to complete the joint. The distortion is clearly larger for the case where the transformation is exhausted at the higher temperature.

Development of anisotropic transformation strain when bainite forms under the influence of a constant, elastic applied compressive stress. Note that the shear strain associated with the formation of one plate is about 26%, with a volume change of about 3%. The potential for anisotropy is therefore much greater than illustrated here.

Fig. 11

Consider a distribution of bainite variants along all radial directions in a circle with the compression axis as its diameter (Ref 35, 36). The circle is divided into 18 equal segments (i ⳱ 1 → 18), each segment representing a particular orientation of bainite habit plane. The choice of 18 segments is convenient and arbitrary. The compression axis of the sample is taken to be the z direction, the x and y directions

Table 7 Chemical composition, calculated transformation temperature range (DT ), and measured distortion (h) for two manual metal arc, multipass weld deposits Composition, wt% C

θ

Fig. 10

Distortion caused by welding two plates that were originally flat

0.06 0.06

Si

Mn

Ni

Mo

Cr

DT, C(F)

h

0.5 0.3

0.9 1.6

... 1.7

... 0.4

... 0.35

802–400 (1476–750) 422–350 (792–660)

14.5 8

Source: H.K.D.H. Bhadeshia and L.-E. Svensson, unpublished data, 1994

8 / Effect of Materials and Processing being radially orientated; the unit vectors x, y, and z define the orthonormal basis X of the sample, giving a corresponding reciprocal basis X *. The shear and dilatational components of the IPS accompanying the growth of bainite are approximately s ⳱ 0.22 and d ⳱ 0.03. Thus, the 3 ⳯ 3 deformation matrix describing the shape deformation is given by: P⳱

冢

1 Ⳮ fse1 p1 Ⳮ f dp1 p1 fse2 p1 Ⳮ f dp2 p1 fse3 p1 Ⳮ f dp3 p1 fse1 p2 Ⳮ f dp1 p2 1 Ⳮ fse2 p2 Ⳮ f dp2 p2 fse3 p2 Ⳮ f dp3 p2

冣

冤冥

e1 p1 P ⳱ I Ⳮ fs e2 ( p1 p2 p3) Ⳮ f d p2 ( p1 p2 p3) e3 p3

where I is a 3 ⳯ 3 identity matrix. A further reduction of notation is achieved using the MacKenzie and Bowles notation (Ref 27): (XPiX ) ⳱ I Ⳮ fis[X;ei]( pi ;X *) Ⳮ fid[X;pi]( pi; X *)

(Eq 4)

where the subscript i identifies a particular segment of interest and X and X *, respectively, represent the real and reciprocal bases of the coordinate system in which the deformation is described. The notation due to MacKenzie and Bowles (Ref 27) is discussed in detail in Ref 35. The components of the shear direction and the dilatation direction are given by: [X;ei] ⳱ fi[ⳮcos(hi) 0 sin(hi)] [X; pi] ⳱ fi[sin(hi) 0 cos(hi)]

120

180

0

210

(a)

Ui ⳱

330

where ␾ is the angle between the shear direction and the direction of the shear component of the applied stress as resolved onto the habit plane. To facilitate a two-dimensional analysis, the value of ␾i is taken to be zero. A positive value of Ui adds to the chemical driving force (DG ac ⳱ G c ⳮ G a) for transformation; a negative value thus opposes transformation. Using these values of interaction energies, the model can be modified so that the segments transform in an order of decreasing Ui. There is, however, a further complication. The effect of stress should be largest when the interaction energy is large compared with the chemical driving force. To allow for this, the volume fraction fi of each segment θ 90

60

150

30

180

0

210

300 270

r [s sin 2hI cos ␾i Ⳮ d(1 Ⳮ cos 2hi)] 2

120 30

兿 (X Pi X ) [1 0 0] i⳱1

where (x⬘ ⳮ 1) and (z⬘ ⳮ 1) give the strains along the x and z directions. These are assumed to be equal to radial and longitudinal strains eR and eL, respectively. It is expected that those segments that comply best with the applied stress transform most rapidly, whereas the others do so at a lower rate, or not at all. This can to some extent be incorporated into the model by calculating the energy change Ui as the stress interacts with the shape deformation of a particular variant (i). Patel and Cohen’s method (Ref 30) gives:

60

150

240

兿 (X Pi X ) [0 0 1] i⳱1 18

[X; x⬘] ⳱

where p is the unit normal to the habit plane and e is the unit direction along which the shear occurs. This can be written more succinctly as:

θ 90

18

[X; z⬘] ⳱

whereas a unit vector along x changes to

fse1 p3 Ⳮ f dp1 p3 fse2 p3 Ⳮ f dp2 p3 1 Ⳮ fse3 p3 Ⳮ f dp3 p3

冤冥

where hi represents the orientation of the habit plane of variant i and fi is the volume fraction of bainite located in segment i. A unit vector along the z direction changes to a new vector z⬘ given by:

330 240

(b)

300 270

Transformation behavior inherent in the model (Ref 36). The dots illustrate the area fraction of each segment, which in the calculations is scaled according to the value of Ui Ⳮ DG ␣c. (a) Zero stress. All segments have equal area fraction, and the order in which they transform is irrelevant. (b) Applied stress of 40 MPa and DG ␣c ⳱ 400 J/ mol. The area fractions of the segments are no longer equal. The segments in which the distance of the dot from the origin is largest transform first.

Fig. 12

can be scaled according to the value of Ui Ⳮ DG ac. Note that for the model calculations, the transformation occurs with the most favored variants growing first (Fig. 12). The model thus exaggerates the effect of stress, since in reality, for the sort of stress levels considered experimentally, no variant is likely to be entirely suppressed. In addition, the grains in a polycrystalline sample are “randomly” oriented, so that perfect compliance with the applied stress is impossible. Nevertheless, the trends revealed by the model are expected to be correct. The experimental data that need explaining, and their interpretation in terms of the model are summarized in Fig. 13 and may be stated as follows: ● Without any stress, in a random polycrystal-

line sample, the transformation strains are isotropic. This is easily understood since the shear components of randomly oriented plates tend to cancel out (Fig. 13a). ● The application of the small stress at a high transformation temperature (that is, a small chemical driving force) causes the development of anisotropic strains, the transverse strain first being negative and then positive (Fig. 13b). The same effect is observed for a large stress and low temperature (that is, a large driving force). The model explains this effect when it is assumed that the favored variants form first, but that the stress is not large enough to suppress the eventual formation of other variants. The signs of eL and eR are always opposite for the favored variants, but are identical for the rest of the variants. Therefore, the transverse strain is initially negative but then becomes positive as transformation progresses. The low-stress/hightemperature situation is equivalent to the high-stress/low-temperature case because in both of these circumstances, variants that are not favored cannot be suppressed. In the former case the stress is too small for suppression, whereas in the latter case the chemical driving force is too large to permit suppression. ● When a large stress is applied at a high temperature, the favored variants dominate. Therefore, the strains are always of opposite sign (Fig. 13c). The model is thus capable of qualitatively explaining all the essential features of the formation of bainite under the influence of a small tensile stress. A uniaxial compressive stress (as used in the experiments described below) simply causes a reversal of the signs of the longitudinal and transverse stresses; there is also a minor effect from the unfavorable interaction between the compressive stress and the dilatational component of the IPS shape deformation. The most interesting conclusion to emerge from comparison of the model with experimental data is that transformation under the influence of a mild stress occurs sequentially. Variants that comply with the applied stress grow first, fol-

Material Factors / 9 lowed by those that do not. This also carries the implication that the interaction of the stress is with the growth process (that is, the IPS shape deformation) rather than the strain field of the nucleus, which is likely to be different. It is worth noting that there are similar results for martensite: most favored variants grow first in the sequence of transformation under stress (Ref 15, 24).

Summary Many of the thermal properties of steels—for example, heat capacity, thermal expansion coefficients, and latent heats of transformation— are remarkably well understood. Indeed, commercially available thermodynamic databases and programs can be used to estimate these quantities as a function of temperature and chemical composition. This capability has not been exploited in the analysis of residual stresses, even though phase diagram calculations using the same software are now routine in industry and academia. Other properties, such as elastic modulus, are

not yet calculable in the same manner. It may be the case that they are insensitive to alloying, but that remains to be demonstrated in the context of residual stress analysis. There is little doubt that transformations in steel play a major role in the development of residual stresses. For reconstructive transformations (for example, pearlite), it is the difference in density between the parent and product phases that contributes to transformation plasticity. The plasticity can be much larger for displacive transformations (Widmansta¨tten ferrite, bainite, martensite) because of the large shear component of the shape deformation when these transformation products form. These are quite sophisticated effects which, with few exceptions, are not incorporated in most residual stress analyses.

3. 4. 5. 6. 7. 8.

REFERENCES 9. 1. T. Inoue and Z. Wang, Mater. Sci. Technol., Vol 1, 1985, p 845–850 2. P.W. Fuerschbach, in The Metal Science of Joining, M.J. Cieslak, J.H. Perepezko, S.

10. 11. 12.

L T

+ L, T Strain

Strain

+

0

13.

0

14.

Transformation time

15. 16.

Equivalent time

(a)

17. L

+

18.

+

T

Strain

Strain

L 0

T

0

19.

20. 21. Equivalent time

Transformation time (b)

22. L

L

23.

+ Strain

Strain

+

0

T

Transformation time

24.

0 T

25. Equivalent time

26.

(c)

27. Schematic of the reported variations (Ref 24) in longitudinal and radial strains during the isothermal formation of bainite under the influence of a tensile load, presented alongside predictions (Ref 36) from the crystallographic/thermodynamic model. The stresses are all intended to be below the austenite yield strength, and the data in this case refer to uniaxial tension. (a) Zero stress, any temperature. (b) Small stress, low temperature. (c) Small stress, high temperature; or large stress, low temperature.

Fig. 13

28.

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10 / Effect of Materials and Processing 29. A.B. Greninger and A.R. Troiano, Trans. Amer. Inst. Min. Metall. Eng., Vol 140, 1940, p 307–336 30. J.R. Patel and M. Cohen, Acta Metall., Vol 1, 1953, p 531–538 31. L. Delaey and H. Warlimont, in Shape Memory Effects in Alloys, J. Perkins, Ed., TMS-AIME, Plenum Press, 1975, p 89–114

32. S. Denis, E. Gautier, A. Simon, and G. Beck, Mater. Sci. Technol., Vol 1, 1985, p 805–814 33. W.K.C. Jones and P.J. Alberry, Ferritic Steels for Fast Reactor Steam Generators, British Nuclear Engineering Society, 1977, p 1–4 34. W.K.C. Jones and P.J. Alberry, Residual

Stresses in Welded Constructions, Welding Institute, 1977, Paper 2 35. H.K.D.H. Bhadeshia, Worked Examples in the Geometry of Crystals, Institute of Metals, 1987 36. A. Matsuzaki, H.K.D.H. Bhadeshia, and H. Harada, Acta Metall. Mater., Vol 42, 1994, p 1081–1090



Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem J. Lu, LASMIS, Universite´ de Technologie de Troyes, France

ALL MANUFACTURING PROCESSES introduce residual stress into mechanical parts, which influences its fatigue behavior, fracture strength, and even its corrosion resistance. Few metalworking methods exist that do not produce new stresses. The role of residual stress is, therefore, very important when designing mechanical parts. Over the last few years, an increasing number of studies have been carried out to understand the effects of residual stress on mechanical performance. This article attempts to present a global approach to including residual stress in expected fatigue life calculations, and the possibility of introducing it into mechanical engineering design offices. The definitions and origins of residual stress according to production methods are first presented. Then, shown are the problems involved in correctly adapting these modeling techniques for use in design offices and the industrial consequences of taking residual stress into account on quality assurance control procedures. This article deals mainly with residual stress measurement techniques and the overall necessity to combine destructive (incremental hole-drilling method) and nondestructive (x-ray and neutron diffraction) methods in order to precisely evaluate the residual stress distribution. Some new results concerning optical methods are also discussed. Shown, too, are the beneficial and harmful effects of residual stress on the resistance of structures or industrial components, depending on whether they are tensile or compressive. The different models used to predict residual stress induced by different types of processing are then presented. The last section shows the effect of residual stress on fatigue behavior. A model based on the finite element method (FEM) for predicting the relaxation of residual stresses is presented. Finally, prediction of fatigue life, taking residual stress into account, using FEM is discussed. A new approach to concurrent engineering applied to the design of mechanical components with residual and applied stress consideration is presented.

Residual stress is usually defined as the stress that remains in mechanical parts that are not subjected to any outside stresses. Residual stress exists in practically all rigid parts, whether metallic or not (wood, polymer, glass, ceramic, etc). It is the result of the metallurgical and mechanical history of each point in the part and the part as a whole during its manufacture. In the case of structural materials, surface engineering can lead indirectly to the innovation of genuinely new materials based on conventional materials. The frustrating slowness of some of these developments reflects not only difficulties in scaling up laboratory techniques, but also general conservation in the engineering industries and a reluctance to change established habits. One of the factors that contributes to slowing the pace is that the current approach to surface engineering directly correlates performance to processing parameters; designers are left without the tools needed to optimize and take into account modified or prestressed surfaces for a particular application, and the processors are left without appropriate goals for surface properties. The recent European Network of Surface and Prestress Engineering and Design (ENSPED) project led by the University of Technology of Troyes and funded by the European Union is one of the contributions currently being made to the development of such tools. The aim is to develop a project with a hard core of about 18 partners representing a balanced selection of Europe’s major industries, such as SNECMA; European Aeronautic, Defense and Space (EADS); ABB; Siemens; Volvo; Fiat; British Aerospace; Robert Bosch; Hydro Aluminum; Wartisla; and so on. It is based on building a bridge between the fields of surface modification and prestress processing in materials engineering and computeraided design in mechanical engineering in order to find an appropriate way of approaching this interdisciplinary area. The members of the project will focus on the field of prestress processing. The main goal of the prestress engineering approach is the optimization of residual stress for

an objective mechanical behavior of the material and structure. Under this approach, the residual stress must not be considered as a parameter that only depends on the material processing conditions, but must also be considered as a parameter that can be optimized. There is an increasing interest in how the state of residual stress affects the mechanical properties of a material and its structure. The failure of a structure or a mechanical component is not only due to external loads. Residual stress is an important parameter in this respect. All manufacturing processes, for example, introduce a new state of residual stress. This can have a positive effect, such as increasing the fatigue limit in the case of surface compressive stress, or it can have a negative effect, such as decreasing the stress corrosion behavior of a material in the case of tensile residual stress. Basic and applied research in the field of residual stress has been stepped up in the last few years. Residual stress is taken into account in advanced design in the aerospace, automotive, and nuclear industries. Even the microelectronics industry is starting to take residual stress into account for the dimensional stability of electronic packaging. The introduction of advanced materials has also contributed to the development of knowledge in the field of residual stress. In fact, many new materials are multimaterials, for example, metal-matrix composites, plasma-sprayed coating, physical vapor deposition (PVD), and chemical vapor deposition (CVD) coatings, which contain residual stress as a result of the thermal and mechanical incompatibilities of the different phases of the material or structure. Figure 1 shows the different fields of research in which residual stress is taken into account and its relevance for industrial applications. Three main fields must be developed for a global approach of prestress engineering: measurement techniques for the quality control and processing analysis, processing parameter optimization and processing modeling, and modern design tool for

12 / Effect of Materials and Processing the life cycle simulation with residual stress consideration.

Origins of Residual Stress In general, macroscopic residual stress can be induced due to: ● Nonhomogeneous plastic flow under the ac-

● ● ● ● ●

tion of external treatment (shot peening, autofretting, roller burnishing, hammer peening, shock laser treatment) Nonhomogeneous plastic deformation during nonuniform heating or cooling (ordinary quenching, molding of plastics) Structural deformation from metalworking (heat treatment) Heterogeneity of a chemical or crystallographic order (nitriding or case hardening) Various surface treatments (enameling, nickel plating, chrome plating, PVD and CVD coating) Differences in expansion coefficients and mechanical incompatibility of the different components of composites (composites with a metallic and organic matrix, ceramic coatings)

Table 1 shows the different origins of residual stress for metalworking operations usually carried out in the industry. To produce an industrial part, one or several of the techniques listed in the table can be used. To calculate the residual stress existing in a part, the source of the stress must be identified first. Residual Stress Measurement Techniques in Global Approach and Quality Assurance. Over the last few decades, various quantitative and qualitative techniques have been developed (Ref 1). These techniques are used for the processing optimization and quality control of material. In general, a distinction must be made between destructive and nondestructive methods.

The first series of methods is based on destroying the state of equilibrium in the mechanical component. The residual stress is then evaluated from its relaxation. However, it is only possible to measure the consequences of stress relaxation and not the relaxation itself (displacement, fracture, strain). In most cases, the change in strain is selected as the parameter to be studied. The following procedure is used: 1. Creation of a new stress state by machining or layer removal 2. Detection of the local change in stress by measuring the strain or displacement 3. Calculation of the residual stress as a function of the strain measured using the elastic theory (analytical approach or numerical calculations such as FEM) During the recent years, the incremental holedrilling method is extensively used. It is sensitive to the first kind of residual stress, that is, the macroscopic residual stress. The principle of this technique is simple. It involves monitoring the change in strain when a hole is drilled in a component with residual stress. These strain measurements can be related to the original residual stress distribution in the analyzed sample at the hole location. The relationship between the strain and the residual stress can be calculated with the calibration coefficients Ain and Bin. The general approach used to determine the Ain and Bin FEM is detailed in Ref 2. Recently, the high sensitivity moire´ interferometer and incremental hole-drilling method for residual stress measurement has been developed. The theoretical development of a combined method is introduced in Ref 3 and 4. The relationship between the threedimensional surface displacements produced by introducing a blind hole and the corresponding residual stress is established by employing the existing theoretical solution containing a set of undetermined coefficients. The coefficients are calibrated by the three-dimensional finite ele-

Quality control

Manufacturing

Measurement technique

Prestress process development and modeling

Take residual stress into account in integrated design

Relaxation of residual stress

Dimensional stability

Fig. 1

Effect of residual stress on behaviors

New design

Mechanical design

Main research fields and industrial application fields in which residual stress is taken into account

ment method. The in-plane surface displacements Ux and Uy and out-of-plane surface displacement Uz produced by the relaxation of residual stresses are obtained using moire´ interferometry and Twyman-Green interferometry, respectively. Figure 2 shows three-dimensional displacement as a function of the drilling depth. The main advantage of this technique is the possibility of studying the residual stress with an inplane stress gradient (Ref 5). It is also possible to study composite materials (Ref 6). In this case, the through thickness residual stress distribution was evaluated ply by ply in a carbon fiber/epoxy composite. Figure 3 shows an example of residual stress determined by using this technique. Recently, this method was used (Ref 7) to study the Plastic Ball Grid Array (PBGA) package, which is a cost-effective surface-mounting package with a high-density interconnection, low profiles, and light weight. It is currently used in many electronic products, including portable telecommunication and computing products. A typical structure in a PBGA package consists of four layers: a plastic molding compound, a silicon chip, a chip-attach adhesive layer, and an organic chip carrier. Due to the coefficient of thermal expansion mismatch between the silicon chip, the plastic compound, and the organic chip carrier, considerable residual stresses are developed in the package during the assembly process. The process-induced residual stress can play a significant role in the reliability of electronic components and packages. Since a PBGA package is small and the surface layer is made of a plastic material, it has proved very difficult to use other existing methods of residual stress measurement. In this research work, a practical method has been developed to determine residual stress for electronic packaging. In this method, blind holes are drilled into the specimens, and relationships are established between the released surface displacement and the corresponding residual stress by introducing a set of calibration coefficients. A multilayer three-dimensional FEM is established to determine the relevant calibration coefficients. The surface displacements are measured accurately in a small region around the hole. For a practical PBGA package, the tensile residual stress is determined in both the plastic molding compound and the glass/epoxy laminate chip carrier. The method is accurate, simple, convenient, and practical. More applications in the field of electronic products are anticipated. The x-ray diffraction and neutron diffraction methods are based on the measurement of lattice strains by studying variations in the lattice spacing of the polycrystalline material. The first method measures the residual strain on the surface of the material, and the second measures the residual strain within a volume of the sample. Diffraction techniques can be used to study all three types. The peak shift method is sensitive to the first two, whereas line broadening is sensitive to the second and third types. These techniques have been used to measure the first type

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 13 of residual stress in different phases of advanced materials, such as metal-matrix composites (in matrix and in reinforcement) (Ref 8, 9). Residual stress can be incorporated into the design of mechanical components. Although this leads to a better knowledge of the fatigue life of parts and reduces the safety coefficient at the design stage, it also poses a host of new problems on a quality assurance level. All statistical controls are only applied today to a few critical components in the aeronautical and nuclear industries; this practice could easily become

Fig. 2

widespread. Rapid ways of checking the residual stress must therefore be developed. The methods used industrially (x-ray diffraction and the incremental hole method) will not be sufficient in the future. Other nondestructive testing (NDT) techniques (ultrasound, magnetic methods, acoustic emission) are presently being developed. But as they currently stand, these techniques use physical parameters that depend not only on the residual stress present in the parts, but also on microstructural changes. In the near future, NDT techniques will be applied at the same time as

Three-dimensional displacements measured for different hole depth by a combination of optical methods and the incremental hole-drilling method in a shot peened sample. Champ, field

Table 1

the reference techniques. Figure 4 proposes a residual stress inspection plan. Other new techniques, such as neutron diffraction and optical method, will be introduced in industry. A detailed analysis of different techniques of measurement is out of the scope of this article.

Modeling of Process The experimental techniques developed previously can contribute to the development of a residual stress prediction model. The results calculated by the model make it easier to take the residual stress into account during the mechanical design. The residual stress induced by the thermal processing is extensively treated in the other articles of this Handbook. Only some examples concerning the mechanical surface treatments and the comparison between the numerical simulation and experimental validation are presented briefly. Two kinds of models can be mentioned: analytical models and numerical models. In this case, mechanical surface treatment models were developed for shot peening (Ref 10) and cold rolling (Ref 11), while several finite element codes were used or developed for welding, grinding, heat treatment (quenching), and thermal cutting (Ref 12, 13). The results show good correlation between the prediction of the model and the experimental results. But it can also be seen that three-dimensional calculations are necessary to obtain good results in all directions. If a two-dimensional calculation is used, the residual stress evaluation correlates well in one direction only. So, in the future, three-dimensional calculations will be of greater significance for real case modeling (Ref 13). In the case of shot peening, a three-dimensional finite element dynamic model was developed to obtain a better description of the shotpeening process and to introduce this approach into the component design (Ref 14). With the

Main origins of residual stress resulting from different manufacturing processes

Process

Casting Shot peening, hammer peening, roller burnishing, laser shock treatment, bending, rolling, chasing, forging, straightening, extrusion Grinding, turning, milling, drilling, boring

Mechanical

Thermal

Structural

No Heterogeneous plastic deformation between the core and surface of the part Plastic deformation due to the removal of chips No No

Temperature gradient during cooling No

Phase transformation Depends on the material

Temperature gradient due to heating during machining Temperature gradient Temperature gradient

Phase transformation during machining if the temperature is sufficiently high No Change of volume due to a phase change

No

Thermal incompatibility

Welding Brazing Electroplating

Shrinkage Mechanical incompatibility Mechanical incompatibility

Temperature gradient Thermal incompatibility Mechanical incompatibility

Thermal spraying (plasma, laser, HVOF)

Mechanical incompatibility, microcracking Mechanical incompatibility Mechanical incompatibility

Thermal incompatibility, temperature gradient Mechanical incompatibility Mechanical incompatibility

New chemical component with volume modification Microstructural change (HAZ) New phase at interface Composition of plating depending on bath used Change of phase in plating

Quenching without a phase transformation Surface quenching with a phase change (induction, EB, laser, plasma, classical methods) Case hardening, nitriding

PVD, CVD Composite

EB, electron beam; HVOF, high-velocity oxygen fuel; HAZ, heat-affected zone

Change of phase No

14 / Effect of Materials and Processing help of three-dimensional modeling, the enormous influence of shot interaction is verified by simulating simultaneous impacts. This simulation is very similar to the industrial process. Results of the residual stress obtained by the simulation are closer to the experimental results, if a three-dimensional FEM is used (Fig. 5). The higher the coverage rate, the lower the intensity of the stress. This study shows how FEM can be used to model shot peening and determine the associated residual stress field. The results obtained for both a single impact and several impacts follow the general distribution of measured residual stress fields. This type

of analysis seems promising for studying the repercussions of a large number of parameters. However, these methods are only efficient when a maximum number of experimentally measured parameters can be introduced. They also need to be improved if they are to take most phenomena into account. The proposed models could be completed by analyzing the influence of the type of contact, the direction of the shot during the impact, behavior of the material, and so on. It could then be possible to introduce the residual stress field into metal parts in order to study their behavior, using numerical simulation, for several types of mechanical and fatigue life tests.

70 60

Average per lamina fibers Average in two laminas of fibers

Average per lamina of epoxy Average in two laminas of epoxy

50 40 Residual stress, MPa

30 20 10 0

112.5

225

337.5

450

562.5

675

787.5

900

–10 –20

Effect of Residual Stress on the Mechanical Strength of Materials Generality. When a part is subjected to a field of elastic residual stresses characterized by a tensor rR, on which is superposed a field of service stresses defined by the tensor rS, the real stress to which the part is subjected is characterized by the tensor rR Ⳮ rS (Fig. 6). If the residual stresses are added to the service stresses (residual tensile stress, for example), the part is locally overloaded due to residual stress. If, on the contrary, an appropriate finishing operation (shot peening or roller burnishing, for example) is used to introduce residual compressive stress, the part is relieved of some of the load locally and the mechanical performance of the materials is increased as a result. Figure 7 shows the properties of materials that are influenced by residual stress. In the subsequent section, several quantitative examples of the effect of residual stress are given. Influence on the Fatigue Strength (Initiation Crack Phase). Residual stress plays an extremely important role with respect to the fatigue strength of materials. It can be considered to be a mean or static stress superimposed on the cyclic stress. As the mean stress rm increases, the fatigue strength decreases. This is demonstrated in the Haigh and Goodman diagrams.

–30

y –40 –50 Hole depth, µm

Fig. 3

σR

Residual stress distribution in the half-thickness of a carbon fiber/epoxy composite

σS σR + σ S

M

I M

Mechanical components manufacturing lines

Continuous control using NDE techniques (US, magnetic, AE)

Fig. 6

Superposing of residual stress and service stress

100

Good quality

50

Defect Assembly of parts

Statistical analysis of results

Residual stress, MPa

0 Measurement of the residual stress distribution through the thickness of the part using conventional techniques (x-ray, hole drilling)

0.10

0.20

0.30

Fatigue

0.40

⫺50 ⫺100

Corrosion under tensile stress

⫺150 ⫺200

Residual stress

⫺250 ⫺300

Breaking

srr L = 0.3 mm szz L = 0.3 mm

Friction

Tensile strength

⫺350 ⫺400 Improvement of process Residual stress inspection plan for the purposes of quality assurance. NDE, nondestructive evaluation; US, ultrasonic; AE, acoustic emission

Fig. 4

⫺450 Depth, mm Modeling of the residual stress distribution induced by shot peening using the 3-D finite element method

Fig. 5

Dimensional stability

Fig. 7

Interfacial bond strength of coating

Effect of residual stress on the performance of materials

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 15 leads to a tangential residual stress equal to or slightly greater than the longitudinal stress. The thickness of the material subjected to residual compressive stress is in the same order of magnitude as the layer transformed during treatment (Ref 15). Fatigue tests were carried out by the French Technical Center for Mechanical Industry (CETIM) on 36 mm diameter XC42 steel cy-

Quenching treatment, after induction heating, introduces very high residual compressive stress into the hardened layer, which results from the increase in volume of the martensitic structure with respect to the ferrito-pearlitic structure (this applied to the treatment of annealed steel, for example). In induction-quenched cylindrical bars, the residual stress on the surface usually Table 2

Effect of quenching conditions and residual stress on fatigue strength

Type and depth of treatment at 45 HRC, mm (in.)

Surface hardness, HRC

Residual stress stabilized at the fatigue limit, MPa (ksi)

Fatigue limit after 5 ⴒ 106 cycles, MPa (ksi) rm

ra

A, induction 2.7 (0.11)

55–56

596 (87)

584 (85)

B, induction 4.2 (0.17)

55–56

623 (90)

610 (88)

C, induction 4.7 (0.19) D, water quenched after through heating without stress-relieving annealing 3.5 (0.14)

54–59 60–61

670 (97) 780 (113)

660 (96) 750 (109)

Longitudinal stress

Transverse stress

ⳮ128 (ⳮ19) ⳮ243 (ⳮ35) ⳮ273 (ⳮ40) ⳮ341 (ⳮ49) ⳮ655 (ⳮ95) ⳮ863 (ⳮ125) ⳮ777 (ⳮ113)

ⳮ468 (ⳮ68) ⳮ571 (ⳮ83) ⳮ583 (ⳮ85) ⳮ676 (ⳮ98) ⳮ603 (ⳮ87) ⳮ1132 (ⳮ164) ⳮ1156 (ⳮ168)

Source: Ref 16

Sample type

6

σ2.10, MPa

State

Crack initiation site

σBX, MPa

As welded

207

–40

Post weld heat treated

207

–37

Shot peened

392

–519

Weld toe

1 Multipass

Fig. 8

Effect of residual stress on the fatigue strength of E690 welded joints. rRX, residual stress perpendicular to the fillet (rRX); rRI, principal maximum residual stress evaluated at a depth of 0.1 mm below the surface. Source:

Ref 17

r Ⳮ rR ⳱ rf* 10−6 ZAT D.T. (40-75 mm) ZAT B.S. (40 mm)

Nontreated metal

da/dN, m/s

10−7

10−8

Rs = 0.1 E36Z

10−9

5

10

20

30

40

50

60

70

80

∆K, MPa m

Fig. 9 Ref 18

lindrical bars, quenched after induction heating, and subjected to repeated bending stress (Ref 16). The results obtained are presented in Table 2. It can be seen that the higher the residual compressive stress, the greater the fatigue strength. The resulting gain in fatigue strength produced by the residual stress can be as much as 50% of the fatigue strength of the base material treated. Figure 8 shows the effect of residual stress on the fatigue strength of welded HLE (E690) steel joints (Ref 17). Three cases are show: as-welded (residual tensile stress), stress relieved (no residual stress), and shot peened (residual compressive stress). A marked increase in the fatigue strength was observed in the case of shot peening. Influence on Fatigue Failure (Propagation Phase) and Brittle Fracture (Ref 13, 18, 19). In the case of welded assemblies, the presence of welding defects at the weld toe and the geometric profile of the latter generally lead to a limited period of crack initiation. The cracking phase must be considered by taking into account the residual stress field induced by the welding operation. The decisive influence of the residual stress field on the crack propagation speed has been demonstrated (Ref 18). Figure 9 shows the results of cracking as a function of the residual stress. Relieving residual stress by heat treatment changes the crack propagation speed considerably when the stress is high. In the case of a brittle fracture, cleavage starts in a grain when the local stress reaches a critical value of rf* and it generally propagates without difficulty in the adjacent grains by producing a brittle fracture. The tensile residual stress rR, in addition to the applied stress r, initiates this type of failure for low loads, such that:

Effect of a residual stress-relieving treatment on the cracking speed in the HAZ (butt-welded assembly of an E36Z steel). ZAT D.T., HAZ of the heat treated sample; ZAT D.T., HAZ of the as-welded sample. Source:

Once cracking has been initiated, the applied stress alone can be enough to allow propagation to continue at a high speed. Failure is therefore very sudden. Residual stresses that facilitate the initiation of brittle fracture by cleavage are therefore very dangerous for steels under load at low temperature. This is why the stress relieving of welded joints is also recommended. Grain slips come up against inclusions and create concentrated stresses at their interface that lead to fracture of either the interface or the inclusion. Cavities then appear for a critical initiation stress and grow by plastic deformation of the matrix until their coalescence leads to ductile fracture at least on a microscopic level. The speed at which the cavity grows is not only proportional to the plastic deformation speed but also to the degree of triaxial state of the stresses and to the ratio of the mean stress to the ultimate stress. Coalescence is a plastic instability phenomenon that no doubt occurs for a critical cavity size. Tensile residual stress not only facilitates the initiation of cavities but, by increasing the mean stress, also accelerates growth. These two effects combine to decrease the critical elon-

16 / Effect of Materials and Processing gation of ductile fracture. However, this is only important if the ductility is already very low in the absence of residual stresses, since plastic deformation can eliminate them. Effect on Stress Corrosion (Ref 20, 21). Stress corrosion is a mechanical and chemical cracking phenomenon that can lead to failure under the combined effect of tensile stress and a corrosive environment. Cracking is generally transcrystalline and can appear on all types of materials, such as aluminum alloys, steels, copper, titanium and magnesium. The introduction of residual compressive stress can considerably increase the fatigue life of parts subjected to stress corrosion. Tests carried out on magnesium test specimens placed under stress in a salt solution gave the following results:

used, can remain in the coatings and in the substrates. They are of several types: microstresses in the grain, produced during cooling, and macrostresses affecting the entire coating. Macrostresses are created not only by cooling but also by the difference in temperature between the substrate, the sprayed layer, and the outside surface. The differential contraction thus produced between the various materials, due to the difference in physical and mechanical properties, determines the stresses in the coating and the coating-substrate interface. These stresses therefore influence the mechanical and thermomechanical behavior of the coated parts. In order to appreciate the quality of a coating, three types of damage to parts in service can be considered:

● Ground test specimen: failure after two min-

● The coating deteriorates rapidly. ● The properties of the substrate are modified

utes ● Shot peened test specimen: no cracking after 12 days under the same conditions The tests conducted by W.H. Friske show that the fatigue life is 1000 times greater for a shotpeened 304 grade stainless steel part than it is for a non-shot-peened part (Ref 20). Tests carried out by CETIM on Z6CN18.9 stainless steel produced similar results (Ref 21). Effect on Adhesion of Coatings (Ref 22– 25). Most coatings are produced for a specific reason, particularly to improve the corrosion and wear resistance of the base material, or to provide a thermal barrier for use at high temperature. But this is only achieved if the coating adheres to the substrate correctly. Adhesion therefore indicates correct preparation of the surfaces to be coated and the quality of the coating operation. The last few years have seen the appearance of plasma-spraying techniques, both at atmospheric pressure and at reduced pressure. These processes offer a high degree of flexibility for coatings in critical areas. However, high residual stress, inherent to the coating method

σR Kc

7 6

300

200

4 3

100

2 1 0


Kc, MPa m

5

0

–1 –2

TT

STT

–100

Influence of heat treatment on the residual stress and the toughness of the interface: case of plasma-sprayed coatings at atmospheric pressure. TT, heat treated; STT, as-sprayed

Fig. 10

by the coating.

● The damage is common to both materials. It

is located at the interface and jeopardizes both the adhesion and the fatigue life. C. Richard et al. have shown that decreasing the residual stress by thermal treatment of the coating considerably improves adhesion at the interface (Ref 23). Figure 10 illustrates the effect of residual stress. It can be seen that the apparent toughness of the interface is improved by 100% when heat treatment is applied. There is a high level of residual tensile stress in the test specimen without heat treatment. When the level of residual tensile stress increases, the true toughness of the coating decreases. An increase in the residual compressive stress produces the opposite effect. Influence of Residual Stress on the Tensile Strength, Friction, Wear and Dimensional Stability. The effect of residual stress on the tensile strength is obvious, particularly in structures made of composite materials or when the prestressed layer is very thick compared with the thickness of the parts. In composites, residual stress is produced as a result of the thermal and mechanical incompatibility of the reinforcements and matrix. This can influence the macroscopic properties of composites under tensile or compressive stress (Ref 26). Little research has been carried out on the effect of residual stress on friction and wear properties. Their role is often masked by other parameters. The increase of hardness during treatment and changes in the toughness and adhesion of antiwear coatings due to residual stress can considerably affect the resistance to friction. Up until the present, this effect has been integrated into the global parameter of adhesion. In the future, work will be carried out to try to determine the real effect of residual stress. The problem of dimensional stability has been known for a long time. When a part is machined that contains residual stress produced by heat treatment or welding, the shape of the part can change after operation due to the relaxation of residual stress. This is why stress-relieving treatments are frequently used to avoid this type of

defect. Reference 27 gives a very methodical approach to defining the criteria and processes relating to relieving stress in welded structures. The same type of reflection can be applied to other types of parts.

Taking Residual Stress into Account when Calculating the Expected Fatigue Life In the previous section, the different effects of residual stress on the mechanical strength of structures and materials were mentioned. Although the ability to quantitatively estimate the fatigue life taking residual stress into account is just beginning, it is still too early to extend these predictions to other types of stress that are far more complex and involve physical and chemical phenomena. Statistics show that failures of a purely mechanical origin are mainly due to fatigue. It is for the reasons indicated previously that this article only addresses problems concerning the prediction of fatigue life. Two articles (H. P. Lieurade and A. Pellissier-Tanon) in Ref 13 deal with the question of predicting the effect of residual stress on crack propagation phase. Although, they concern welded structures, the concepts developed in these two references can be applied to other types of structures. By limiting the approach to prediction of the fatigue life to the fatigue cracking initiation stage, the problem of predicting the fatigue life of mechanical components subjected to a high cycle fatigue can be analyzed. Calculating the Effect of Residual Stress on the Fatigue Strength. Based on the experimental results mentioned previously, it would seem that a linear relationship of the Goodman type can be used to take residual stress into account: ra ⳱ rD ⳮ

rD (rm Ⳮ rR) Rm

(Eq 1)

where ra is the amplitude of admissible stress, rm is the mean fatigue stress, rD is the purely reverse tensile fatigue limit, Rm is the true rupture strength, and rR is the residual stress measured in the direction of the applied service stress. The numerous studies mentioned in Ref 28 show that the effect of residual stress is greater when the properties of the materials are high. If we try to represent the development of ra according to the residual stress rR by an equation of the following type: ra ⳱ rD ⳮ ␣ ⳯ rR

(Eq 2)

the experimental results generally show that ␣ increases with the strength of the material; for example, in the case of machining stresses in an XC38 grade steel, Syren et al. found: ● ␣ ⳱ 0 in the annealed state ● ␣ ⳱ 0.27 when quenched and tempered ● ␣ ⳱ 0.4 when quenched

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 17 Unfortunately, these results are in contradiction with an equation of the Goodman type. In Eq 2, the coefficient ␣ is none other than what is usually called the endurance ratio: ␣⳱

rD Rm

This parameter decreases as the rupture strength of steels increases. This apparent contradiction is probably explained by the fact that the residual stress relaxation phenomenon has not been taken into account. The value of the residual stress rR to be introduced into equation of type 1 or 2 mentioned previously, must correspond to the stabilized fatigue stress, or the coefficient of influence will include the relaxation process. The article by D. Lo¨he and O. Voehinger in this Handbook presents a large number of results concerning the relaxation of residual stress under mechanical and thermal loading. References 29 and 30 provide the information on the relaxation mechanism of residual fatigue stress as a function of

800 A B Repeated C bending tests D Repeated tension test

700

σa, MPa

600 500 400 300 200 100 0 0

1000 σm, MPa

2000

Use of Haigh diagrams to take longitudinal residual stress into account (XC42 steel quenched after induction heating). A through D represent results of repeated bending tests; X, repeated tension test. Table 2 presents fatigue test results that correspond to A to D.

Fig. 11

τa, MPa A B Repeated C bending tests D Repeated tension test

400

200 100

0

100

200

300

400

Pmax, MPa Use of the Dang Van criterion to take residual stress into account (XC42 grade steel quenched after induction heating). A through D represent repeated bending test; X, repeated tension test.

Fig. 12

salt ⳱ f (A, B Pmhp, C Palt )

where Pmhp is the mean hydrostatic pressure, salt is the amplitude of octahedral shearing or amplitude of the maximum shearing, and Palt is the amplitude of hydrostatic pressure. An example can be given as follows: E salt ⳱ A Ⳮ B PD mhp Ⳮ C Palt

300

⫺200 ⫺100

the cyclic behavior of the materials. However, Syren’s results show that relaxation is much greater when the mechanical properties are lower. When these experimental results are used with the residual stress measured after carrying out a fatigue test, and therefore stabilized, it is sometimes possible to use an equation such as Eq 2. In the case of the fatigue bending test on cylindrical XC42 steel bars quenched after induction heating (Table 2), the fatigue test results for the different treatments correspond perfectly to the Haigh diagram, provided any possible influence of transverse residual stress on the fatigue stress is ignored (Fig. 11). It is not possible, however, to extend these results to all materials and to the different manufacturing processes that introduce residual stress. Also, preliminary tests are needed to validate the methodology. The use of residual stress in calculations based on endurance diagrams of the Haigh or Goodman type usually only allows for an estimation of the increase in fatigue strength as a function of the residual stress. Secondly, this approach only allows for the combination of uniaxial stresses. Yet the residual stresses produced by the various manufacturing methods used to make the part are always multiaxial. The stresses on the surface are biaxial while those inside the part are triaxial. Depending on the area in which the fatigue crack is initiated (on or below the surface), the biaxial or triaxial stresses need to be included when calculating the fatigue life. This raises the problem of choosing a multiaxial fatigue stress criterion. A simplified approach based on an endurance diagram can therefore only be an approximation. The test carried out by the CETIM (Ref 16) shows that the traditional Mises and Tresca criteria can only be used in the presence of higher mean or residual stress. In this case, it is preferable to use criteria (Ref 31) that include the amplitude of octahedral shearing (socta) or the maximum shearing (sa) and maximum hydrostatic pressure (Pmax), as indicated here:

(Eq 3)

where A, B, C, D, and E are material constants. If Dsalt is taken on the maximum shearing plane, D ⳱ E ⳱ l and B ⳱ C, the result is the Dang Van criterion (Ref 32). If Dsalt is taken on the octahedral shearing plane, when D ⳱ E ⳱ 1 and B ⳱ C, the Crossland criterion results (Ref 33); when D ⳱ E ⳱ 1 and C ⳱ 0, the Sines criterion (Ref 34); and when D ⳱ E ⳱ 1 and B ⬆ C, the Kakuno criterion (Ref 35). This type of development can be continued to

invent new “criteria,” but it leads to complications because of the increasing number of parameters that need to be determined. Even with a linear relationship of the Dang Van type, two Wo¨hler curves have to be determined to obtain at least the two points needed to produce the diagram. If additional constants are added, the test plane will be even greater, which means that the criterion cannot be used in industry. As a result, the criterion to be used must be simplified as much as possible. This case deals with radial loading problems (r1 ⳱ K1 r2 ⳱ K2 r3), and a relationship of Eq 3 is sufficient. To simplify matters further, the Crossland or Dang Van criterion can be used. In the case of combined and out-of-phase loading, new criteria have been developed to take the out-of-phase effect into account (Ref 36–39). But as yet, these criteria have not been validated in a study in which combined and out-ofphase residual stresses have been taken into account. When the fatigue stress is complex, it is also very difficult to calculate the expected residual stress relaxation. When fatigue cracks are initiated on the surface, the stresses to be taken into account are biaxial; this gives the following for the Crossland or Dang Van criterion: socta ⳱ sa ⳱ Pmax ⳱

冪2 3

冢r 1a Ⳮ r 2a ⳮ r r 冣 2

2

1a 2a

r1a 2 1 (r1a Ⳮ r2a Ⳮ r1m Ⳮ r2m Ⳮ r1R Ⳮ r2R) 3

where r1a, r2a represent the amplitude of the main reversed fatigue stresses (r1a ⬎ r2a); r1m, r2m represent the average value of the main fatigue stresses; and r1R, r2R are the residual stress values measured in the two main directions (stabilized values). To use the multiaxial fatigue criteria, the reference curve for the material being considered is needed, just as it is when using the Goodman or Haigh diagram. Reference 16 shows that the use of Crossland or Dang Van criteria takes the increase in the bending fatigue strength into account perfectly as a function of the residual stress introduced by the various treatment conditions (Fig. 12). When the multiaxial aspect is brought into the picture, the method that consists in introducing residual stress into the calculation in the same way as a mean stress, therefore, seems to give satisfaction. The whole problem lies in defining the residual stresses to be included in the calculation. Taking residual stress into account is essential for correct prediction of the fatigue limit. Figure 13 shows the important role played by compressive residual stress. If it is not taken into account, the fatigue strength is underestimated (Fig. 13a). If the residual stress measured or calculated is used without taking relaxation of the residual stress into account, the fatigue strength is over-

18 / Effect of Materials and Processing estimated (Fig. 13b). The correct method consists in calculating the fatigue strength after taking relaxation into account (Fig. 13c). In order to correctly evaluate the effect of residual stress, various problems must be solved: ● Measuring methods must be available to de-

τa, MPa

τa, MPa

(a)

τa, MPa

σR

Pmax

Fig. 13

termine residual stress in the critical zone. A large range of measuring methods currently exists and it is possible to take measurements (Ref 1) in most of the cases studied, particularly as a result of development of the x-ray method and the incremental hole method. ● When a complete measurement profile is

Relaxation des σR

Pmax

Initial (b)

Pmax

(c)

Illustration of the different methods used to take residual stress into account

τa, MPa (Surface)

Xian CETIM

–300

–200

–100

0

100

200

300

400

500

Pmax, MPa (Surface)

Fig. 14

Fatigue results for a 45SCD6 steel treated under different conditions in a Dang Van diagram, taking the residual stress on the surface into account. Xian, results obtained by Xi’an Jiaotong University; CETIM, results obtained

by CETIM

τa, MPa

available of the residual stress in the surface layer in which the fatigue crack is initiated, the profile sometimes has high stress gradients. It is then difficult to know what stress value to choose—the surface stress or the stress peak that is often slightly below the surface (in the case of shot peening, for example). To make a correct calculation, it would be necessary to use calculation methods that take the stress gradient into account and make the calculation not only for a single point, but for a sufficient thickness of the material (thickness of critical layer) for it to be representative of the basic volume in which the fatigue damage process occurred (Ref 31). Figures 14 and 15 give an example of processing of our results (details can be found in Ref 29) in the case of the fatigue of a shot-peened spring steel. Figure 14 shows the fatigue results on a Dang Van diagram, taking both the residual stress and its relaxation into account. A fairly good correlation can be observed. This indicates that a multiaxial fatigue criterion taking the hydrostatic pressure into account can be used to predict the fatigue strength in the presence of residual stress. Since, in this case, the crack initiation zones are below the surface, calculations were made for different critical layer depths. Figure 15 shows the results obtained for a critical layer depth of 100 lm. Better alignment of the experimental points was observed. This example illustrates the possibility of improving the calculation precision by using the critical layer thickness approach. It is particularly relevant in the case of notched parts. It has long been known that residual stresses are not stable when they are subjected to fatigue loading. To calculate the expected fatigue life, precise information is therefore needed in order to introduce stable residual stress values into the calculation presented previously, that is, the stress values that are really likely to be present in the part during the best part of its lifetime. The stress must therefore be measured on a part already under cyclic loading or relaxation of the residual stress estimated according to expe-

600 500

350 With Without

400

σA Consideration ±600 MPa

200

τa, MPa

300 Xian CETIM

300 ±550 MPa 2 × 106 5 × 106

100 250 –300

–200

–100

0

100

200

300

400

500

0

Fatigue results for a 45SCD6 steel treated under different conditions in a Dang Van diagram, taking the residual stress into account using the “critical layer” approach. Xian, results obtained by Xi’an Jiaotong University; CETIM, results obtained by CETIM

50

100

150

200

Pmax, MPa

Pmax, MPa

Fig. 15

107

240

Prediction of the fatigue life using the Dang Van criterion for a shot-peened 35NCD16 steel, without taking residual stress into account

Fig. 16

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 19 rience or modeling. In Ref 29 and 30, a complete model was presented using FEM to determine the stabilized residual stress after fatigue loading. This estimation of the residual stress can then be used to calculate the fatigue life of a part, taking residual stress into account. Despite the initial definition of the Dang Van criterion, which proposes that it only be used in cases of fatigue strength with an unlimited number of cycles, an attempt was made to extend this criterion to include a limited fatigue life with a very large number of cycles (more than 2 ⳯ 106) (Ref 40). Figure 16 shows an example of the fatigue life estimated by calculation. First, a fatigue strength diagram of the Dang Van type was defined according to the fatigue life obtained from a series of fatigue life contours. Then the residual stress relaxation was calculated using FEM (Ref 29). Finally, the stabilized residual stress was introduced into the diagram. In this example, in the case of a loading of Ⳳ550 MPa, the point corresponding to loading is inside the limit of the fatigue life at 107 cycles. No failure occurs. For a loading of Ⳳ600 MPa, the point corresponding to loading including the residual stress is between the line corresponding to 5 ⳯ 106 cycles and that of 2 ⳯ 106 cycles. Failure therefore

τalt

2

1

2 Hardening effect

1

3 Roughness increase

1 3

Pmax

Fig. 17

Illustration of the effect of the surface finish and strain hardening on the fatigue strength

Role of hardening and residual stress

Fatigue life increasing, %

20 Role of residual stress 10

0 Role of superficial hardening –10 20

30

40

50

HRC Effect of the resistance of the base metal on the increase in the fatigue strength after shotpeening treatment, distinguishing between the effect of strain hardening and that of residual stress

Fig. 18

● A new roughness that changes the local stress

concentration

● Additional strain hardening of the surface due

to plasticizing

● A new metallurgical structure of the surface

layers Figure 17 shows the effect of the surface finish and strain hardening on the fatigue strength of materials. It can be seen that an increase in the roughness decreases the safety area, and strain hardening increases the safety area, provided it does not damage the material. In the case of thermal or thermochemical surface treatments (induction quenching, case hardening, etc.), for example, it is necessary to take the new fatigue strength of the treated layer into account in the calculation. The problem is more complex in the case of residual stress introduced by plastic deformation (pre-straining, machining, shot peening, roller burnishing), since it is more difficult to distinguish between the influence of residual stresses and residual microstresses present in the grains of the deformed material and that of strain hardening of the material. Evans (Ref 41) made this distinction in the case of shot peening; to do so, he carried out three types of fatigue tests on materials with various mechanical properties: ● Fatigue tests on a non-shot-peened material ● Fatigue tests on a shot-peened material ● Fatigue tests on a shot-peened material, but

with a mean test stress rm, which compensated for the surface residual stress. In this type of test, the effect of the macroscopic residual stress is cancelled out and the fatigue strength obtained only depends on the increase in the mechanical properties of the plastically deformed material and the residual microstresses distributed throughout the material. The results obtained are presented in Fig. 18.

40

30

occurs between 2 and 5 million cycles. The tests give an average fatigue life for the previously mentioned loading in the order of 3.5 million cycles. This example shows that, if the cyclic properties of the material are correctly known, it is possible to predict the fatigue strength of the material in the presence of residual stress. However, it should not be forgotten that other factors must also be taken into account in calculating the fatigue life—the introduction of residual stress is often accompanied by other changes in parameters that have an influence on the fatigue strength. In particular, these include:

It can be observed that, for materials with low resistance, the increase in the fatigue strength is mainly due to surface strain hardening. On the other hand, for highly resistant materials, it is mainly the influence of the residual stress that governs the fatigue strength. When materials have low elastic limits, the stresses introduced by shot peening relax much more easily than they do when the elastic limit is high. This test only shows a general tendency and does not ex-

actly show what the author is trying to demonstrate, since in the two types of tests for the same material, the ratio of R(rmin /rmax) is modified. As has been shown, the residual stress relaxation changes when the R ratio is varied (Ref 29). The real contribution of each factor will therefore be different from that indicated in Fig. 18. It can thus be seen that taking residual stress into account in the calculation requires a serious examination of the different parameters involved. When reliable results are needed, fatigue tests will no doubt need to be carried out on the part or the structure concerned. However, modeling enables the variation in the different parameters to be rapidly simulated in order to find an optimal solution. Partial Summary. The previous results show that it is now possible to take residual stress into account in calculations designed to predict the fatigue life using a global approach. This must take the relaxation of residual fatigue stress into account, as well as the other effects (strain hardening, hardness) introduced by the manufacturing method used. A multiaxial fatigue criterion that can integrate both the problem of residual stress and the effect of the stress gradient applied to a zone in the presence of stress concentration has been developed, that is, the Crossland or Dang Van criterion. It is used for a stabilized state of residual stress, averaged out for a basic volume of damage (thickness of critical layer), and applied within a network of contours that represents the fatigue life. In the future, tests will be carried out to validate this type of criterion in the case of combined stresses on notched parts in the presence of residual stress.

Incorporating the Notion of Residual Stress into the Design Office Incorporating the notion of residual stress into the design office must be gradual and can be divided up into several phases. Today, very few industrial sectors consider the residual stress parameter directly. In technical specifications, requirements are included that are often closely related to residual stress without actually naming it. An Almen intensity must be guaranteed in the case of shot peening, for example, a roller-burnishing load, a machining procedure or a minimum treated thickness in the case of thermal or thermochemical treatment, and a maximum dimensioning tolerance in the case of a machined or welded part. In the first phase of incorporation, a semiquantitative notion can be used to evaluate the increase in performance in terms of fatigue life or fatigue strength. A few examples can be presented. Table 3 gives an example of the effectiveness of shot peening in increasing the fatigue life of different types of mechanical parts, and Fig. 19 shows the beneficial role played by roller burnishing on the fatigue strength of spherical graphite cast iron crankshafts. Figure 20 shows

20 / Effect of Materials and Processing

of residual stresses is realized in the first series of fatigue cycles.

The cyclic behaviors of material are very im-

Table 3 Increase in the fatigue life of various mechanical components as a result of shot peening Type of part

Type of stress

Spindles Shafts Gear box Crankshafts Aircraft coupling rods Driving rods Cam springs Helical springs Torque rods Universal joint shaft Gear wheel Tank chain Weld Valve Rocker arm

Increase in the fatigue life (%)

Reverse bending Torsional Fatigue life tests in service Fatigue life tests in service Tensile compression Tensile compression Dynamic stress Fatigue life in service Dynamic stress Reverse bending Fatigue life tests Fatigue life tests Fatigue life tests Fatigue life tests Fatigue life tests

400–1900 700 80 3000, but highly variable 105 45 100–340 3500 140–600 350 130 1100 200 700 320

250 200 Alternated stress

150

0 100 0

50 Repeated stress

0 70

S-

G 70

S-

G 70

S-

G 40

S-

G 40

70

S-

G

S-

G

llin g

g

t

en

m

ng

in

ro

n

en

io

ce

rfa

su

ct

r

di

at

re

tri

pe

fe

ot

du

in

sh

ni

tt

ou

c

ni

ni

te

io

ith

w

By using the cyclic behaviors of material, a simplified method to calculate residual stress relaxation has been proposed in the first section. Secondly, a method to predict fatigue life by taking the stabilized residual stresses into account is presented. This design tool is based on the FEM. It has been applied to shot-peened 35NCD16 grade steel. The different fatigue parameters often used in material research are studied. On the other hand, an experimental investigation about this material had been done by Bignonnet (Ref 42). The results of the study show that this design tool on fatigue developed by the Laboratory of Mechanical Systems Engineering (LASMIS) (Ref 43) is able to take into account different loading parameters. The residual stresses, however, can be relaxed by the deliberate application of thermal or mechanical energy. They will be especially relaxed when the structure is subject to cyclic loading. The relaxation phenomenon depends on a complex interaction of a number of factors, such as the applied stress amplitude, the number of cycles of loading, the state of initial residual stresses, and the nature, origin, and mechanical properties of the material. In this article, only relaxation during cyclic loading and the influence of the stable residual stresses on the fatigue life are studied. In only a few cases are the residual stresses systematically analyzed using measurement of the residual stress state during and after fatigue testing. This is usually a difficult, time-consuming task. Several fatigue tests under tensile and torsion loading with different stress amplitudes have been done. A numerical method for the prediction of the residual stress distribution during and after fatigue has been developed. Finite element software is used for incorporating cyclic plasticity into the calculation. A simplified method to calculate stabilized residual stresses was proposed.

stresses relax with the increase of the number of cycles up to a stabilized state of cyclic properties.

● For a cyclic hardening material, the relaxation

Maximum admissible stress, MPa

Example of Integrated Design Tool

● For a cyclic softening material, the residual

According to a mechanical approach, we can make the following general predictions (Ref 30):

Fig. 19

Effectiveness of roller burnishing in increasing the fatigue strength

Thermal treatment by electron beam, R = 0.1 TT by CO2 laser, R = 0.1 TT by CO2 laser, R = –1 TT by laser shock, R = 0.1

Treatment or process

a horizontal comparison of gains to be expected in terms of fatigue strength from various surface treatments. The results presented here are not at all exhaustive and are taken from a limited bibliography. However, this figure should not be taken as a reference, since the geometry of the test specimens differs for each type of treatment. In certain cases, this parameter can have an important effect on the gain achieved. Each industrial sector must carry out this type of comparison for the treatments and materials used in order to help engineers design their products more effectively. The second phase consists of predicting the fatigue life using the notions developed in the previous paragraph. The third phase is the development of integrated tools for taking the residual stress into account. The following paragraph presents an example of such a design tool on fatigue for three-dimensional components.

ST by nitriding R = 0.1 TT by induction R = 0.1 TS carburizing R = 0.1 ST by surface rolling R = 0.1 200% ST by surface rolling R = 0.1 ST by shot peening R = 0.1 0

Fig. 20

25

50 Increase, %

75

Beneficial effect of various surface treatments on the fatigue strength (maximum gain reported in the literature). TT, thermal treatment; ST, surface treatment

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 21 portant in the prediction of residual stress relaxation. They make it possible to calculate the residual stress state for a corresponded number of cycles. Then, a method to predict fatigue life while taking these stabilized residual stresses into account is presented. The fatigue criterion under multiaxial stresses is used. After the relaxation, the residual stresses can be combined directly with the cyclic loading. They change the value of the mean stresses and influence the fatigue life. As a result, a design tool on fatigue for threedimensional components, FATIGUE3D, has been developed in the laboratory of LASMIS

Calculation of residual stresses

Outside solicitation, cyclic loading

(Ref 43). It can take the residual stresses into account when calculating the fatigue life of a structure. It is based on the FEM. With this tool, an iso-colored image of distribution of fatigue life or safety factor can be obtained. These methods mentioned above are applied to shot-peened 35NCD16 grade steel. The different fatigue parameters often used in material research are studied. A comparison with the experimental results has been carried out (Ref 43). Basic Steps for the Calculation. Figure 21 shows the elementary steps of the calculation of fatigue life while taking into account the residual stresses. First, the initial state of the residual stresses

Introduction of initial field of residual stresses

Measurement of residual stresses

Prediction of residual stress

Cyclic behaviors of material

Fatigue, 3D

Mechanical properties of material

Distribution of fatigue life, safety factor, and admissible residual stress

Fig. 21

Basic steps of calculation while taking into account the residual stresses

τ

S

N1

Example and Results N1

N

Fig. 22

P

Principle of calculating fatigue life

τ

s = OM/OM ′

M N-cycles M′

O

Fig. 23

can be obtained by the measurement method or by the simulation of surface treatment. Then, this initial field of residual stresses can be introduced by FEM using ABAQUS (Ref 44, 45). Furthermore, a stabilized field of residual stresses can be predicted after an elastic-plastic calculation, in which the cyclic behaviors of material are used. This stabilized field of residual stresses after relaxation must be taken into account when calculating the fatigue life. At last, with the help of a design tool on fatigue, FATIGUE3D, the distribution of fatigue life and that of the safety factor on fatigue can be obtained. Principle and Basic Function. According to the criteria of fatigue under multiaxial loading, the fatigue life changes along with two parameters. One of them is maximum static pressure; another is equivalent octahedral stress. Therefore, two stress-number of cycles (S-N) curves are needed under simple cases (for example, bending or torsion). With these two curves, a line can be determined for a certain number of cycles (life) in the stress plane P ⳮ s (Fig. 22). A different fatigue life is represented by a different line. If there is a complex stress state, it gives a point in the plane P ⳮ s. Respectively, the line to which this point is nearest represents the fatigue life of that stress state. In this way, the fatigue life for any complex stress state and for any part of a component can be predicted. A distribution of the fatigue life is helpful for the designer. On the other hand, the safety factor on fatigue is another interesting parameter for the designer. FATIGUE3D provides a distribution of the safety factor. In Fig. 23, N-cycles are the designed life and M⬘ is the point given by the stress state. The safety factor on fatigue is defined as S ⳱ OM/OM⬘.

P Principle of calculating the safety factor on fatigue

Fig. 24

Three-dimensional mesh

Material and Geometry. The shot-peening process is a widely used technique because it can produce a field of residual stress on the surface of a part. These stresses are compressive and will improve the properties on fatigue. As an example, a shot-peened part made of 35NCD16 grade steel (0.35% carbon, 3.7% chromium, 0.3% molybdenum and having tensile properties of: a yield strength of 1000 MPa, an ultimate tensile strength of 1100 MPa, and an elongation of 17.5%) is studied. Many results of fatigue experiments are available regarding tension compression and torsion loading (Ref 44). The geometry of the part is defined from the real geometry so that the testing results can be compared. It is similar to the fatigue test sample, only the numerical values (radius, length) vary for tension compression or torsion loading. The difficulty is to define a thin mesh near the surface (0.2–0.4 mm, or 0.008–0.016 in.) where the residual stresses are introduced while maintaining a normal mesh in other zones. Figure 24 shows the three-dimensional mesh of the part. Introduction of the Initial Field of Residual

22 / Effect of Materials and Processing 100

100 Axial stresses under tensile loading

–100

Measurement Calculated

–200

Tangential stresses under tensile loading

0 Residual stresses, MPa

Residual stresses, MPa

0

–300 –400 –500


–100 –200 –300 –400 –500

–600 –600 0.05

0

0.10

0.15

0.20

0.25

0.30

0

0.05

0.10

0.20

0.25

0.30

0.4

0.5

0.6

100

100 Axial stresses under torsion loading

–100



0.15 Depth, mm

Depth, mm


–200 –300 –400 –500 –600

Tangential stresses under torsion loading Measurement Calculated

–100 –200 –300 –400 –500 –600

–700 0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

Depth, mm

Fig. 25

0.3 Depth, mm

Initial distribution of the residual stresses

Stress. The initial residual stress distribution is calculated from the residual stresses measured by the x-ray diffraction method in the upper layer where initial stresses are introduced by surface treatment. In depth, the stresses are calculated for the structural equilibrium. Figure 25 shows the comparison of initial residual stresses between the calculation and the experiment. Prediction of the Residual Stress Relaxation. In order to predict the relaxation of the residual stresses, a simplified method proposed by Lu et al. has been used (Ref 30). It supposes that the relaxation of the residual stresses depends on

elastic-plastic properties of material, because the plastic deformation is the main cause of the relaxation. So, the cyclic behaviors of material are very important for the prediction of the residual stresses. However, they can be measured by experiment. Figure 26 shows the cyclic behaviors of 35NCD16 grade steel, a cyclic softening material. When the stabilized residual stresses are calculated, the behavior corresponding to NR /2 is used. After an elastic-plastic calculation with FEM, the relaxation of the residual stresses un-

Rec(MPa) = 920 – 55,14 log N 1 cycle 2 3 15 50 150

∆σ/2, MPa

1000 900

NR/2

800 700 600

35 NCD 16 (Rm (UTS) = 110 MPa)

0.5

0.75

N, cycles 1 2 3 15 50 150 NR/2

Re(Y.S.), MPa 940 920 910 870 830 800 660

1

∆εt/2, %

Fig. 26

0.2

The cyclic behavior of 35NCD16 grade steel. Re, yield stress; R ec, cyclic yield stress as a function of number of cycles; Det, axial plastic strain range during cyclic loading

der the cyclic loading can be obtained. Part of the results and their comparison with the test values have been shown in Fig. 27. In the case of the traction-compression loading, two loading levels were calculated. The same level for torsion loading with two different cycle numbers was also analyzed. Figure 28 shows the stabilized residual stresses for different traction-compression load levels that are used in the prediction of the fatigue life. Unfortunately, it is impossible to compare with the experiment results. Prediction of the Fatigue Life. For predicting the fatigue life under a complex stress state, it is necessary to have two S-N curves. One is for simple traction or traction compression; another is for alternated torsion. These curves are basic data of a material, and they can be obtained by experimental method. Using the program FATIGUE3D, a design tool on fatigue developed in the LASMIS laboratory, a distribution of fatigue life and a distribution of safety factor for a structure can be obtained. In this example, the fatigue life under traction-compression cyclic loading and torsion loading has been calculated. The stabilized residual stresses play a role as static load. Figure 29 shows the results of fatigue life and their comparison with the experimental results. It is very clear that the proposed method is available. Prediction of Admissible Residual Stress. In this approach, a calculation method has been developed that can predict the admissible residual stress for a given fatigue life. This tool can

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 23 100

100 103 cycles, traction compression 550 MPa

⫺100

102 cycles, traction compression 700 MPa

0

Axial measurement Axial calculated Tangential measurement Tangential calculated



0

⫺200 ⫺300 ⫺400


–100 –200 –300 –400

⫺500

–500 0

0.10

0.05

0.15

0.20

0.25

0.30

0

0.05

0.10

0.15

Depth, mm

105 cycles, torsion 380 MPa



–100 –200 –300 –400


0 –100 –200 –300 –400 –500 –600

–500 0

0.1

0.2

0.3

0.4

0.5

0

0.1

Fig. 27

life. In other zones, tensile residual stress is admissible. The fatigue life can then be used to deduce a stabilized residual stress. An example of defining the quenching conditions according to the residual stress field obtained before relaxation is analyzed. An inverse technique designed to obtain the quenching conditions is then developed (Ref 46, 47). In this technique, it is necessary to simulate quenching using the FEM. To simulate quench-

100 Tangential residual stress, MPa

100 Traction-compression 550 MPa 600 MPa 620 MPa 650 MPa 700 MPa

–200

–300

Traction-compression 550 MPa 600 MPa 620 MPa 650 MPa 700 MPa

0 –100 –200 –300 –400 –500

0.05

0.10

0.15 Depth, mm

Fig. 28

0.3

0.4

0.5

The relaxation results of the residual stresses

be used during the design phase to evaluate whether or not residual compressive stress needs to be introduced. The computer code also indicates the level of the residual stress and the zone in which it needs to be introduced. In this way, the treatment condition during the mechanical design phase can be defined. Figure 30 shows a map of the prestress zone indicated for a notch sample. It can be seen that in the high stress concentration area, residual compressive stress must be introduced to obtain a predetermined fatigue

0

0.2

Depth, mm

Depth, mm

Axial residual stresses, MPa

0.30

102 cycles, torsion 380 MPa 100


0

–100

0.25

200

100

0

0.20

Depth, mm

0.20

0.25

0.30

0

0.05

0.10

0.15 Depth, mm

The stabilized residual stresses under different traction-compression loading cases

0.20

0.25

0.30

ing under different conditions, the physical and mechanical data of the material need to be known. Generally speaking, these parameters depend on the temperature, but the surface heattransfer coefficient depends not only on the temperature, but also the sample geometry, the quenchant, and the quenching temperature. In order to solve the problem, it is considered that there is no change in any of the quenching parameters or the sample geometry. Only the quenching temperature changes. Quenching at different temperatures was carried out. This gives the variation of the surface heat-transfer coefficient as a function of the temperature for each quenching temperature. It should be mentioned that numerical methods alone are not sufficient to obtain the heat-transfer coefficient. The temperature must be measured during quenching. Since the heat-transfer-coefficient curve is known, the parameters of these curves as a function of the quenching temperature can be defined. Once this coefficient is known, quenching can be modeled at different temperatures. The quenching temperature in the case of water quenching varies between 20 and 80 ⬚C (68 and 176 ⬚F). The lower the quenching temperature, the higher the level of the residual stress field introduced. Initially, the residual stress field obtained was found to be lower than at 20 ⬚C (68 ⬚F) and higher than at

750 Without residual stresses Experimental Numerical

700 650 600 550 500

Without residual stresses Experimental Numerical

420 400 380 360 340 320

450 105

Fig. 29

440 Torsion load, MPa

Traction-compressionn load, MPa


106 107 Fatigue life N cycles

300 105

106 107 Fatigue life N cycles

Summary

Results of fatigue life

S11

Value –2.24E+02 –4.24E+01 +1.39E+02 +3.20E+02 +5.01E+02 +6.82E+02

1 3 2

Fig. 30

Prediction of admissible residual stress (or the prestressed area) for a notched sample under bending loading, using the finite element method

Mechanical component development

Introduction of a surface and prestress treatment

Optimization of geometry according to the choice of manufacturing process No Stress analysis by a finite element method Adjustment of a finite element model

Is fatigue life in accordance with specifications?

Yes Stop

Experimental checking of stress: rapid prototyping

No

Fig. 31

Are results coherent?

Yes

80 ⬚C (176 ⬚F). After this condition has been verified, the quenching temperature can be determined by varying the quenching temperature during simulation. After each simulation, the calculated residual stress field is compared to that obtained from the fatigue life. A limit condition can be defined to improve the precision of the results. When comparing the residual stress fields, the hydrostatic pressure was used at each point.

Fatigue life estimation

Various connections between residual stress-integrated design and other sectors that use the concurrent engineering approach

Residual stress plays a very important role with respect to the different properties of materials. The gain obtained from the presence of residual stress can be enormous. This article attempts to show the effects of residual stress through the example of fatigue strength. Here, it has been shown that it is now possible to predict the fatigue strength of materials, taking residual stress into account. The results of this study show that it is possible to predict the residual stress relaxation and fatigue life, with consideration of the influence of residual stress by the FEM. It has been found that the calculated results of fatigue life at surface agree very well with experimental results. Although the author is not in a position to provide the same type of calculation tools for other properties, such as corrosion resistance and the adhesion of coatings, it is now reasonable to expect that the notion of residual stress will be gradually introduced into the design stage of mechanical parts. Numerical modeling of the behavior beforehand saves a considerable amount of time because of the reduction in the number of experimental tests required. These tests are often very long and costly, but they have proved to be indispensable. The problem of taking residual stress into account at the design stage will become more and more critical with the development of new materials (multimaterials, etc.) and new treatments (combined treatments, etc.) With the development of different experimental and numerical techniques, it is now possible to introduce residual stress into the design office for the integrated design of mechanical components, thus offering a new concurrent engineering approach applied to the design of mechanical components taking residual and applied stress into consideration. Figure 31 shows the different connections between residual stress-integrated design and other sectors that use the concurrent engineering approach. A mechanical component designer can simulate dynamic characteristics, material processing, and product life. Consideration of residual stress is becoming increasingly important for two reasons: the introduction of multimaterials that induce residual stress, and the need for the designer to reduce the weight of components in order to remain competitive. Basic research has brought a better understanding of the phenomena relating to residual stress. The main aim is to develop an integrated qual-

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 25 ity control tool. For industrial applications, future developments are necessary: Measurement techniques

grant Brite-EuRam, BRRT-CT98–5090, ENSPED project), and the National Science Foundation of China (two bases project) is acknowledged.

● Improvement of ultrasonic and magnetic

measurement methods ● Integration of the portable optical method for strain measurement in destructive techniques Processing and materials ● Development for the industrialization of new

prestress processes: ultrasonic shot peening, laser shock, surface nanocrystallization, and so on. ● Optimization of residual stress in advanced materials: functional gradient coating system, for example, plasma spray coating, PVD, CVD, or diamond-like carbon (DLC) coating; metal-matrix composite; electronic packaging; intermetallic materials Modeling ● Development of advanced tools for the pre-

diction of initial residual stress in various processes: forging, casting, machining, welding, plasma spray coating, composite processing, electronic packaging manufacturing, mechanical surface treatment ● Integration of the residual stress modeling method into a global life design (3-D) and the creation of optimization codes for the design of mechanical components using the concurrent engineering approach With the recent progress in the field of research and development, it is now possible to introduce a new area of research: prestress engineering of structural materials (PESM or PRESMA). In the near future, the mechanical engineer will be able to use these tools in a prestressed concrete approach to civil engineering. The ENSPED program in Europe is an excellent example of the cooperation of industrial and research partners. Using this new approach, the fatigue behavior and mechanical behavior of new materials can be considerably improved, increasing two- or threefold in some cases. In fact, many failures occur in the area close to the surface. Improving the mechanical behavior is often only necessary on the surface (fatigue, fretting fatigue, wear, stress corrosion). As a result, this type of approach can be expected to develop very quickly in order to introduce adequate prestressing treatment in the area indicated by the advanced design tool. ACKNOWLEDGMENTS The author is grateful to all the people at LASMIS working in the field of residual stress for their help during the preparation of this paper: Prof. J.L. Chaboche, Dr. D. Retraint, Dr. E. Rouhaud, Dr. X.L. Gong, Dr. L. Couturier, Dr. R. Akrache, Dr. Z. Wu, Dr. S. Rasouli Yazdi, Mr. A. Milley, Mr. D. Deslaf, Mr. B. Guelorget, Mr. A. Voinier, Mr. F. Belahcene, Mr. K. Gong. Financial support from the European Union (under

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Residual Stresses and Fatigue Behavior D. Lo¨he, K.-H. Lang, O. Vo¨hringer University of Karlsruhe, Germany

COMPONENTS MAY FAIL DURING SERVICE in very different ways. Important aspects are: ● Onset of plastic deformation or exceeding of

allowable plastic deformation

● Crack initiation or exceeding of allowable

crack length

● Unstable crack propagation that results in

fracture of the component

● Instability such as buckling, which may result

in elastic or plastic collapse and, hence, catastrophic failure In practice, failure of a component is almost always determined by the interaction of several external parameters, such as unexpected high static and/or cyclic loads, friction, thermal energy, oxidation, corrosion, and so forth. On the other hand, the component itself may contribute to premature failure, if there is confusion of the component material, wrong heat treatment, surface decarburization, and so forth. The residual stress state in a component may be one of the most important parameters influencing its service behavior, particularly regarding high-strength material states. Residual stresses may reduce yield or elastic collapse loads and may promote corrosion cracking (Ref 1, 2). With respect to fatigue, which is the topic of this article, residual stresses may alter the cyclic deformation behavior, promote or retard crack initiation, accelerate or decelerate crack propagation, and may be beneficial or detrimental to finite fatigue life and the endurance limit. It is important to realize that in a component locally very high amounts of residual stresses may exist. For example, in a spring steel up to ⳮ2000 MPa compressive residual stresses may be produced by a combined warm and stress peening process (Ref 3). In practice, no component is free of micro residual stresses. Almost all components have macro residual stresses to a certain extent. Only a small number of components exist where macro residual stresses are negligible, for example after a suitable stress relaxation heat treatment. The reasons for residual stress formation in components are treated in other articles in this Handbook. The most important ones are the various manufacturing processes. The fundamental

mechanisms of residual stress formation are inhomogeneous plastic deformation caused by mechanical, thermomechanical, or thermal attack and the development of constraint between different constituents of a component such as phases or coatings during the formation of the constituents (e.g., during the coating process) and/or during cooling from a higher process temperature (e.g., the sintering temperature). Manufacturing processes not only result in the formation of definite macro residual stress states, but may also effect other changes of the component state close to its surface: ● Formation of a specific topography ● Work-hardening or (in very hard material

states) work-softening processes and hence alteration of the micro residual stress state ● Phase transformation ● Crack initiation All these processes may change the fatigue behavior of a given component. It is hardly possible to completely separate these influences, even though this is very important for the understanding of the existing relationships.

Residual Stress Stability of Residual Stresses. For the assessment of the influence of residual stresses on fatigue behavior, the stability of the residual stress state is of utmost importance. The reader is referred to the article “Stability of Residual Stresses” in this Handbook, which deals with the relaxation of residual stresses due to monotonic or cycling loading or due to thermal energy. It is shown there that the micro residual stress state is more stable against mechanically and thermally induced relaxation than the macro residual stress state. On the other hand, it is also proved that during fatigue the micro residual stress state of a given steel may be changed by cyclic hardening and/or cyclic softening processes, which are closely related to cyclic plastic deformations. Hence, during fatigue loading of a component with locally varying macro as well as micro residual stress states, complex interactions of the macro residual stress state with the cyclic loading stresses and the micro residual stress state

with work-hardening and/or work-softening processes occur. In both cases, the amount of cyclic plastic deformation is the most important parameter. Since during fatigue loadings that result in technically relevant lifetimes or in infinite life, the cyclic plastic deformations decrease with increasing hardness, it is generally expected that the influence of macro residual stresses is lower in low-strength steels than in high-strength steels. Comparison between Loading Stresses and Residual Stresses. Since the alteration of the micro residual stress state caused by manufacturing processes changes the local hardness within a component and hence the local strength, it is convenient to comprise the corresponding influence on the fatigue behavior of the component as a change of the local fatigue resistance of the steel used for the component. On the other hand, stable macro residual stresses are static stresses and may be regarded as locally varying mean stresses. However, it is important to realize that there are definite differences between loading mean stresses and residual stresses: ● Loading mean stresses exist as a consequence

of acting external forces, moments, pressure and/or internal pressure, and eventually temperature gradients. Residual stresses exist as a consequence of inhomogeneous plastic deformation and/or as a consequence of constraints between different constituents of a component. ● Distribution and sign of loading mean stresses depend on the external loading, the geometry of the component, the elastic-plastic deformation behavior of the material (if maximum loading stresses exceed the yield strength or the cyclic yield strength), and on thermophysical material properties (if temperature gradients exist). Distribution and sign of residual stresses depend on the amount and extension of inhomogeneous plastic deformation in relation to the whole component volume, on the interaction of mechanically and/or thermally driven deformation during manufacturing processes, on the strength of the material state, and/or on the volume fraction, the elastic as well as the


Stress amplitude (σa), MPa

thermophysical properties of the constituents of the component that impose constraint on each other. ● Loading mean stresses are in equilibrium with external forces and moments. Residual stresses are in equilibrium with themselves regarding balance of forces and moments with relation to any sectional area and axis, respectively. The latter is also true for thermally induced loading stresses. ● Loading mean stresses may be changed and finally disappear, if external loadings and/or

Nf Ni Ns

Number of cycles, N

Fig. 1

Wo¨hler curves for slip band formation (Ns), microcrack initiation (Ni), and failure (Nf). Source:

Plastic strain amplitude (εa,p), %

Ref 5

0.4 0.3 0.2 0.1 0 1

10

102

103

104

105


Some Aspects of Fatigue of Steels

Plastic strain amplitude versus number of cycles of normalized AISI 4140 steel. Source: Ref 6–8

The fatigue behavior of metallic materials is characterized by different processes. Generally, it contains four successive stages A, B, C, and D:

0.15 Inhomogeneous softening

Homogeneous hardening

0.10

0.05

01

10 102 Number of cycles, N

Cyclic deformation curve and development of inhomogeneous strain distribution during cyclic softening of normalized AISI 4140 steel. Source: Ref 6–8

Fig. 3

The interaction of the residual stress state with the cyclic loading stresses determines the fatigue behavior of components. The following sections of this article discuss the consequences of this interaction on cyclic deformation behavior, on crack initiation and crack propagation, as well as on the fatigue life and on the endurance limit. Throughout this article, no special account is given for multiaxial loading or residual stress states and equivalent stresses are not used. Instead, this article considers simple loading states and those components of the residual stress state—which is of course always multiaxial— that are relevant for the interaction of the cyclic loading and the residual stress state under consideration. With regard to notched specimens— in which a multiaxial stress state always exists upon mechanical loading—the treatment is based almost entirely on nominal stresses and stress amplitudes. Hence, the fatigue strengths and the cyclic loadings corresponding to finite fatigue lives given in this article are nominal stress amplitudes. First of all, the section “Some Aspects of Fatigue of Steels” introduces some basic definitions and relations of fatigue. This is done here rather briefly. The phenomenon and the processes of the fatigue of steels are presented in general and in detail in Volume 19 of the ASM Handbook (Ref 4).

106

Number of cycles, N

Fig. 2

if existing temperature gradients are changed and finally removed. Residual stresses may be changed and eventually disappear by thermally and/or mechanically induced relaxation. ● Loading mean stresses are not influenced by cyclic plastic deformation in stress-controlled loading, unless stress gradients become very high—for example in the root of sharp notches, where mean stress redistribution may occur. Residual stresses always relax, if the cyclic loading exceeds certain threshold values (see the article “Stability of Residual Stresses” in this Handbook).

● Stage A: Cyclic deformation with work-hard-

ening or/and work-softening effects in the total volume (homogeneous loading such as push-pull of smooth specimens) or in the highest loaded regions (inhomogeneous loading such as bending, torsion, or any loading of notched components) and development of persistent slip bands at the surface ● Stage B: Microcrack initiation and propagation. Normal evolution of a macrocrack in the surface region ● Stage C: Stable macrocrack propagation connected with changes in the state of the material in the crack tip plastic zone

● Stage D: Unstable crack propagation and fail-

ure An example of the consequences of these fatigue stages is shown in Fig. 1 in an S-N diagram (Wo¨hler diagram) for the plain carbon steel SAE 1020 (German grade C 20), which presents experimental results for persistent slip band formation (ra /log Ns curve), microcrack initiation (ra /log Ni curve), and failure (ra /log Nf curve) (Ref 5). Cyclic Deformation Behavior. Investigations on the cyclic deformation behavior in stage A using computerized servohydraulic test systems enable the determination of the complete stress/total-strain response at distinct numbers of cycles that yields to hysteresis loops. In a stress-controlled test, the plastic strain amplitude ea,p plotted versus log N results in a cyclic deformation curve that corresponds to the microstructural changes in the material during cyclic loading. Decreasing (increasing) ea,p values with an increasing number of cycles N are typical for a cyclic work-hardening (work-softening) behavior. Characteristic cyclic deformation curves of the low-alloy steel AISI 4140 (German grade 42 CrMo 4) in a normalized state are shown in Fig. 2. During stress-controlled push-pull tests with R ⳱ rmin/rmax ⳮ1 and ra RP0.2, the plastic strain amplitudes systematically change with the stress amplitudes applied. In the initial stage of cyclic loading, a quasi-linear elastic behavior is found. This stage is followed by a period of increasing ea,p values due to cyclically induced work-softening effects that are connected with inhomogeneous deformation processes caused by fatigue Lu¨ders bands. This can be proved with photoelastic investigations. A typical result obtained for this steel is presented in Fig. 3. Plastically deformed areas appertaining to the individual stages of inhomogeneous cyclic deformation were registered photographically and marked as hatched areas on the specimens that are allied to the cyclic deformation curve. Similar macroscopic softening effects occur in all normalized states of plain carbon steels and low-alloy steels with carbon contents below 0.6 wt% (Ref 6–8). The quasi-linear elastic period shortens and the extent of cyclic work softening grows simultaneously with increasing stress amplitude ra. After reaching a maximum of softening, the materials behavior is mainly characterized by work hardening, and the ea,p values decrease with increasing number of cycles. At the end of the specimen’s life, the plastic strain amplitude increases again, however fictitiously as a consequence of changes in the compliance of the specimens due to crack propagation. The plot of ra versus ea,t at N ⳱ Nf /2, the so-called cyclic stress-strain curve, of this steel is presented in Fig. 4 together with the monotonic-stress/totalstrain curve at nearly the same strain rate e˙ . In the elastic-plastic range, the cyclic curve is lower than the monotonic curve due to the work softening. The cyclic stress-strain curves of plain

Residual Stresses and Fatigue Behavior / 29

Monotonic: ε• 0.4 × 101s1

400 300

Cyclic: ε• 0.3 × 101s1 N = Nf/2

200 100 0 0

0.1 0.3 0.2 Total strain (εt) or total strain amplitude (εa,t), %

Monotonic stress-strain curve and cyclic stressstrain curve at Nf /2 of normalized AISI 4140 steel at nearly the same strain rates. Source: Ref 6–8


Fig. 4

0.8 wt% C

0.45

400

0.22

300

0.01 200

100 0

0.1

0.2

0.3

Plastic strain amplitude (a,p), %

810

750

0.2 0.1

700

600

500

0

Fig. 6 6–8

σa = 850 MPa

0.3

1

10

102 103 104 Number of cycles, N

105

• ε (one) × 101s1

800

Cyclic: ε• 0.6 × 101s1 N = Nf/2

600 400 200 0

0

2

4

6

8

10

Total strain (εt) or total strain amplitude (εa,t), % Monotonic stress-strain curve and cyclic stressstrain curve at Nf /2 of quenched-and-tempered AISI 4140 steel at nearly the same strain rates. Source: Ref 6–8

Fig. 7

Fig. 5 Cyclic stress-strain curves of plain carbon steels with the indicated carbon contents (wt%) in normalized conditions. Ref 8–10

0.4

Monotonic:

1000

0.4


0.5

Stress (σ) or stress amplitude (σa), MPa

500

ments is characterized by a continuous increase of the plastic strain amplitude that lasts up to failure. The cyclic softening sets in after an incubation number of cycles Ni, which depend on the applied loading amplitude. Figure 6 shows the cyclic deformation curves ea,p versus log N at different stress amplitudes for AISI 4140 tempered at 570 C. As a consequence of this cyclic deformation behavior, the cyclic stress-strain curves of quenched-and-tempered steels proceed below the monotonic curves (see Fig. 7). In this material state, the cyclic softening is caused by an inhomogeneous deformation behavior. The plastic deformation develops localized in distinct zones and remains localized in these zones up to failure. Figure 8 shows results from photoelastic investigation carried out on quenched-and-tempered AISI 4140. In the plastically deformed zones, the cyclic softening is caused by a rearrangement of the dislocations to energetically more favorable dislocation structures such as cell structures. As a consequence, the stored strain energy and the hardness decrease. Within these plastically deformed zones, microcrack initiation and propagation occur (Ref 6–8). Crack Initiation. The plastic strains generated by a cyclical loading lead to the formation of microcracks in the material after a certain

0.3

0.2

σa = 750 MPa Inhomogeneous softening

0.1

0 10

106

Plastic strain amplitude versus number of cycles of quenched-and-tempered AISI 4140 steel. Ref

number of cycles. These fatigue cracks usually develop at the surface. Only in special cases— for example, very heterogeneous materials such as case-hardened steel—or at special loading conditions—such as Hertzian pressure—fatigue cracks may initiate below the surface. The first microscopic cracks can appear in a very early stage of the cyclic loading. Depending on the loading conditions and the material, microcracks can already be detected after 0.1 to 10% of the lifetime and number of cycles to failure, respectively. In ductile materials, changes of the surface structure precede fatigue crack initiation. Fatigue slip bands (persistent slip bands, PSBs), which often are connected to extrusions and intrusions, arise from irreversible gliding. These persistent slip bands are often places in which first fatigue cracks initiate. The crack initiation at persistent slip bands often is typically for lower to middle loading amplitudes. At higher amplitudes, cracks may also initiate at grain boundaries. Crack initiation and the first phase of crack propagation in ductile materials are controlled by shear stresses. Within the first grain layers, the cracks grow at an angle of 45 to the load axis. This phase is called stage I crack growth. After reaching a certain length, the cracks become the socalled stage II cracks. Further propagation of theses cracks is controlled by normal stresses. Stage II cracks grow approximately rectangular to the load axis. In brittle materials, crack initiation is often observed at inclusions and other defects. Crack Propagation. To describe the stress and strain field in front of a crack tip the loading details and the geometry of a cracked specimen or component must be considered. If the plastic zone in front of a crack tip is small in comparison with the dimensions of the specimens or components, the linear elastic fracture mechanics are applicable, and the local loading conditions in front of the crack tip can be described by the stress intensity factor, K. Therefore, Paris, Gomez, and Anderson (Ref 11) considered the stress intensity factor as a driving force for the propagation of a crack and suggested a crack growth equation in the form: da ⳱ C • (dK)m dN


Stress (σ) or stress amplitude (σa), MPa

carbon steels with 0.01, 0.22, 0.45, and 0.80 wt% C (German grade Ck 01, Ck 22, Ck 45, and C 80) in normalized conditions, determined from cyclic deformation curves at N ⳱ Nf /2, are drawn up in Fig. 5. With increasing carbon content and pearlite content, respectively, an increasing stress amplitude at ea,p ⳱ constant occurs due to a phase-hardening mechanism (Ref 8–10). The cyclic deformation behavior of quenchedand-tempered steels in stress-controlled experi-

102

103

104

Number of cycles, N Cyclic deformation curve and development of inhomogeneous strain distribution during cyclic softening of quenched-and-tempered AISI 4140 steel. Source: Ref 6–8

Fig. 8

(Eq 1)

where da/dN is the crack growth rate, DK the range of the mode I stress intensity factor, and C and m are constants (Ref 12). With this equation, which is the well-known Paris law, it is possible to describe the crack propagation in the midrange of the crack growth rate. Figure 9 shows the qualitative features of the crack growth behavior in a double logarithmic plot of the growth rate versus the range of the stress intensity factor for experiments with constant stress range Dr ⳱ rmax ⳮ rmin. Distinct curves are observed for different mean stresses rm or values of R ⳱ rmin /rmax, respectively. The lower parts of the curves exhibit a threshold value of DK below which crack growth is essentially arrested. Typically, the crack growth

Crack growth rate, log da/dN


R1 R2 R3 Stress intensity factor range, log ∆K

Fig. 9

Crack propagation rate versus stress intensity factor range for stress ratio values R1 R2 R3

rate in this region is below 10ⳮ8 mm/cycle. The upper parts of the curves represent the crack growth behavior as the Kmax values approach the critical stress intensity factor KIc, which marks the onset of unstable crack propagation. Then the crack growth rate increases boundlessly. The Paris law does not represent the complete crack growth curves shown in Fig. 9. The upper part of the curves depends on KIc, and the lower part on the threshold value DKth. Therefore, several complementations were suggested. An equation that incorporates all of the features of crack growth curves has been used by NASA (Ref 13). It has the form:

Quantitatively, the following relationships are valid: ea,p ⳱ ef • N ⳮa f

and ea,e ⳱ rf /E • N ⳮb f

(Eq 6)

with ef the fatigue ductility coefficient, rf the fatigue strength coefficient, ␣ the fatigue ductility exponent, b the fatigue strength exponent, and E the Young’s modulus. Rearrangement of both equations yields to: ea,p • N fⳮa ⳱ constant

da C • (1 ⳮ R)m • DKn • (DK ⳮ DKth)p ⳱ dN [(1 ⳮ R) • KIc ⳮ DK]q

(Eq 5)

(Eq 7)

and (Eq 2) ea,e • E • N ⳮb ⳱ ra • N ⳮb ⳱ constant f f

log σa log σf log Rm β log Rf

log Ns

Strain amplitude (εa)

Fig. 10

log Ne log Nf

Stress Wo¨hler curve (S-N curve)

εf

σ f/ E

E N N Number of cycles to failure, Nf

Fig. 11

Total strain Wo¨hler curve

This equation is able to account for the threshold effect, the R ratio effect, and the final instability effect. By suitable choice of the exponents, this equation can accept a number of different variants of crack propagation laws. For m ⳱ p ⳱ q ⳱ 0, for example, the Paris law is obtained. The concepts of linear elastic fracture mechanics and the use of the stress intensity factor are limited to cases in which small-scale yielding develops at the crack tip. Moreover, the applicability of Eq 1 and 2 is restricted to sufficiently long macroscopic cracks. Short cracks can grow at smaller ranges of the stress intensity factor as DKth. At comparable DK values, they can exhibit clearly higher crack growth rates than long cracks (Ref 14). Lifetime Behavior. The lifetime behavior of steels is commonly described in an S-N diagram (Wo¨hler diagram) (Ref 15), where the loading amplitude is plotted versus the number of cycles to failure in double logarithmic scaling. For stress-controlled fatigue tests, the S-N curve is frequently described by three straight lines (see Fig. 10). In the range of the quasi-static strength Rm (Nf Ns) and the fatigue strength Rf(N N0f ), the endurable stress amplitude is constant and given by the ultimate strength Rm and the fatigue strength Rf, respectively. In the range of finite life (Ns Nf Ne), the Basquin relation (Ref 16):

Fatigue strength, Rf

ra ⳱ rf • N ⳮb f

often describes the lifetime behavior satisfactorily. rf is the fatigue strength coefficient and b the fatigue strength exponent. In the case of total-strain-controlled fatigue tests the ea,t values in the total strain Wo¨hler curve (Fig. 11) can be separated into the elastic and plastic parts:

Re Goodman 0

Rf

Gerber

ea,t ⳱ ea,e Ⳮ ea,p Re Mean stress σm

Fig. 12

Endurance limit versus mean stress

(Eq 3)

Rm

(Eq 4)

From experience it is known that both parts extend exponentially from the number of cycles to failure Nf, which means that the plots log ea,e versus log Nf and log ea,p versus log Nf are linear.

(Eq 8)

which are the well-known relationships from Coffin-Manson (Ref 17, 18) (Eq 7) and Basquin (Eq 8). Tensile mean stresses promote crack initiation and accelerate crack propagation. Therefore, the fatigue strength Rf decreases with increasing mean stresses. This correlation is normally represented in a Smith (Ref 19) or in a Haigh (Ref 20) diagram. As an example of such fatigue strength diagrams, Fig. 12 shows a Haigh diagram. The fatigue strength Rf is plotted versus the mean stress rm. The Goodman approximation (Ref 21): Rf ⳱ R0f • (1 ⳮ rm /Rm)

(Eq 9)

which represents a straight line between the fatigue strength R0f at rm ⳱ 0 and the tensile strength Rm, is frequently used to estimate fatigue strength. For practical use, the allowable stresses are restricted by the demand that macroscopically no plastic deformation should occur. This restriction leads to a straight line connecting the yield strength Re at both axes. Through this, the allowable stress amplitudes lie in the hatched area in Fig. 12. The slope of the Goodman straight line is often also described as mean stress sensitivity M ⳱ R0f • rm /Rm. The Goodman approximation normally leads to conservative estimations. Often, the Gerber parabola (Ref 22): Rf ⳱ R0f • [1 ⳮ (rm /Rm)2]

(Eq 10)

is used as a nonconservative estimation of the fatigue strength. Mostly, experimental results range between the Goodman and the Gerber approximations. In the range of infinite lifetime, the influence of mean stresses can be described by damage parameters. Two frequently used damage parameters are the one proposed by Smith, Watson, and Topper (Ref 23): PSWT ⳱ 冪(ra Ⳮ rm) • ea,t • E

(Eq 11)

and the one proposed by Ostergren (Ref 24):

Residual Stresses and Fatigue Behavior / 31 (Eq 12)

ra and rm are the imposed stress amplitude and mean stress, respectively, ea,t and ea,p are the resulting total strain amplitude and plastic strain amplitude, respectively, and E is the Young’s modulus. Normally, for ea,t and ea,p the values at half of the lifetime are used.

Influence of Residual Stresses on the Cyclic Deformation Behavior

0.4 σa in MPa Unpeened Shot peened

0.3

380

0.15

10

102

103

104

105

106

Number of cycles, N

0.4 σa in MPa

450

Unpeened Shot peened

0.3

550

600 0.05

400 375 350 350 400 275

0 1

10

(b)


1.0 900 0.8

105


10

σa in MPa Unpeened 800 Shot peened

750 700

0.2

500 400 550 600

0

(c)

10


105

σa in MPa Unrolled 0.03 Deep rolled

600 650 550 600

0.02

500 0.01

550 500

0 102 103 104 Number of cycles, N

10

(b)

105

106

Cyclic deformation curves for stress-controlled push-pull loading of (a) normalized and (b) nitrocarburized specimens of the SAE 1045 steel in unpeened and deep-rolled conditions. Source: Ref 27

Fig. 14

0.10 Untreated 0.08 Shot peened 0.06 Deep rolled

0.04 0.02 0

106

Cyclic deformation curves for stress controlled push-pull loading of (a) normalized, (b) quenched-and-tempered (730 C/2 h), and (c) quenchedand-tempered (570 C/2 h) smooth specimens of the steel AISI 4140 in unpeened and shot peened conditions. Source: Ref 25, 26

Fig. 13

106

0.04

1 1

105

106

0.6 0.4

500 450

1 450

550

0

0.2 0.1

σa in MPa Unrolled Deep rolled

510

0.10

(a) Plastic strain amplitude (εa,p), %

0

(a) Plastic strain amplitude (εa,p), %

600

1

325 300 250

0.1

1


0.20

350

0.2



Characteristic Examples. The influence of macro and micro residual stresses on the cyclic deformation behavior can be studied very well after mechanical surface treatments, for example

by shot peening or deep rolling. Characteristic cyclic deformation curves for stress-controlled push-pull loading of different heat treated smooth specimens of the steel AISI 4140 (German grade 42 CrMo 4) are compared in Fig. 13 in unpeened and in shot peened conditions with compressive residual stresses at the surface (Ref 25, 26). In the normalized state (Fig. 13a), the onset of cyclic deformation is different in both conditions, since the shot peened specimens with surface compressive residual stresses rrs ⳱


POST ⳱ 冪(ra Ⳮ rm) • ea,p • E

10


104

105

Cyclic deformation curves of different mechanically surface treated materials for stress-controlled push-pull loading in the low-cycle fatigue (LCF) regime of the plain carbon SAE 1045 steel. Stress amplitude ra ⳱ 350 MPa, Almen intensity I ⳱ 0.120 mm A, rolling pressure p ⳱ 150 bar; surface residual stresses: shot peening rrs ⳮ500 MPa, deep rolling, approximately ⳮ600/ –350 MPa. Source: Ref 28, 29

Fig. 15

ⳮ400 MPa show cyclic softening from the first cycle and higher plastic strain amplitudes during the first cycles for stress amplitudes ra between 250 and 350 MPa. After a certain number of cycles, the opposite tendency can be detected and the plastic strain amplitudes of the shot peened conditions are smaller than those of the unpeened material states. However, for the same ra values the plastic strain amplitudes of both conditions approach another at relatively high numbers of cycles. Corresponding results for a quenchedand-tempered (730 C/2 h) AISI 4140 steel are presented in Fig. 13(b). In the unpeened condition, the characteristic cyclic deformation behavior of quenched-and-tempered steels occurs with a quasi-elastic incubation period, which is followed by cyclic softening until crack initiation. After shot peening that generates surface compressive residual stresses rrs ⳱ ⳮ410 MPa, the onset of cyclic softening is shifted to smaller numbers of cycles. Furthermore, it is interesting to note that for identical stress amplitudes and comparable numbers of cycles, the higher plastic strain amplitudes are always measured for the shot peened specimens. Figure 13(c) shows a compilation of cyclic deformation curves for another quenched-and-tempered (570 C/2 h) AISI 4140 steel with a higher strength compared with the steel condition in Fig. 13(b). In this case, the shot peened condition that has surface compressive residual stresses rrs ⳱ ⳮ530 MPa is characterized for all investigated ra values by small measurable plastic strain amplitudes during the first cycle that diminish or disappear first of all with an increasing number of cycles. After a subsequent regime of quasi-elastic behavior, cyclic softening, which yields to lower plastic strain amplitudes and larger numbers of cycles to failure in comparison with the unpeened conditions, is dominant. The effect of deep rolling on the behavior of the cyclic deformation curves is presented in Fig. 14(a) for the normalized plain carbon steel SAE 1045 (German grade Ck 45) (Ref 27). At comparable stress amplitudes essentially smaller plastic strain amplitudes are measured in the deep-rolled condition. In this materials state, the cyclic softening effects are extremely restricted, but continue during the whole lifetime until crack initiation. As a consequence of the smaller plastic strain amplitudes at identical stress amplitudes, higher numbers of cycles to failure are observed for the deep-rolled condition compared with the normalized ones. Figure 14(b) shows the influence of deep rolling in the case of a nitrocarburized SAE 1045 steel. Due to the different microstructures in the near-surface areas of the specimens, the same stress amplitudes yield plastic strain amplitudes that are five times smaller than those of the normalized state. The deep-rolling process modifies the cyclic deformation curves of the nitrocarburized specimens in a manner similar to the normalized specimens. However, the reduction of the plastic strain amplitudes is much less pronounced. Figure 15 shows plastic strain amplitudes as a function of the number of cycles plotted for

Cyclic stress-strain curves of deep-rolled AISI 304 (rolling pressure 150 bar, surface residual stresses r ⳮ350 MPa) using compact as well as hollow specimens with different percentages of strain-hardened layers compared with an untreated state and a shot peened condition (rrs ⳮ450 MPa). Source: Ref 28, 29

damage is clearly correlated with plastic strain amplitude, the benefit of mechanical surface treatments becomes obvious. The influence of mechanical surface treatments on cyclic plasticity can be summarized in cyclic stress-strain curves, which correlate stress amplitudes and plastic strain amplitudes for, for example, half the number of cycles to failure (see the section “Cyclic Deformation Behavior”). Figure 16, as an example, shows data for an austenitic AISI 304 steel in shot peened as well as deep-rolled conditions compared with untreated specimens (Ref 28, 29). Effects of mechanical surface treatments are more distinct with a higher ratio between the area of affected surface layer and the cross section of the specimen. In the case presented here, hollow thin-walled specimens were prepared from compact specimens for analysis. As shown in Fig. 16, cyclic yield strength considerably increases compared with compact specimens, if only the fatigue behavior of the surface layers of mechanically surface treated components is investigated. If residual stresses are present in the root of notched specimen, marked changes always occur in the initial parts of the notch root cyclic deformation curves (ea,p /log N curves) and in the notch root cyclic mean strain curves (em /log N curves) that depend on the sign and the magnitude of the residual stresses. Characteristic examples are presented in Fig. 17 for normalized

True plastic strain amplitude (εa,p), %

True plastic strain amplitude (εa,p), %

32 / Effect of Materials and Processing push-pull loading with the stress amplitudes indicated for a normalized SAE 1045 steel (Ref 28, 29). Results for annealed as well as for shot peened or deep-rolled conditions are shown. One can clearly see that both mechanical surface treatments considerably diminish the plastic strain amplitudes. Due to the thicker affected surface layer in the case mentioned first, the effect for deep-rolled states is more pronounced than for shot peened states. Because fatigue


700 600 500

Deep rolled (1 mm wall thickness) Deep rolled (0.5 mm wall thickness) Deep rolled (0.3 mm wall thickness)

400 300 200

Untreated Deep rolled Shot peened

100 0 0

0.1 0.2 0.3 0.4 Plastic strain amplitude (εa,p), %

0.5

Fig. 16

rs l

0.4

σn,a in MPa σrs = 15 MPa σrs = 490 MPa

0.3 220 0.2

240 200

220 175

0.1

150

0 1

10

102

170 150 190

103

104

105

106

0.06 σn,a = 200 MPa 0.04 σrs = 710 MPa 460

0.02

320 0 1

10

102

103

104

105

106

Number of cycles, N

(a)

Number of cycles, N 0.06

0.30

σn,a in MPa

220

190

170

150

0.15

0.00

Plastic mean strain (εm), %


(a)

σn,a = 200 MPa

0.04

0.02 460

σrs = 710 MPa 0.2 1

0.15 1 (b)

10

102

103

104

105

106

(b)

10

102

103

104

105

106

Number of cycles, N

Number of cycles, N

True plastic strain amplitude (a) and plastic mean strain versus number of cycles (b) for stress-controlled push-pull loading of normalized notched specimens (notch factor Kt ⳱ 3.0) of the SAE 1045 steel in unpeened and shot peened conditions. Source: Ref 30, 31

Fig. 17

320

0

True plastic strain amplitude (a) and plastic mean strain versus number of cycles (b) for stress-controlled push-pull loading of quenched-and-tempered (400 C/2 h) notched specimens (notch factor Kt ⳱ 3.0) of the SAE 1045 steel in cut-milled and shot peened conditions with different surface residual stresses. Source: Ref 30, 31

Fig. 18

specimens and in Fig. 18 for quenched-and-tempered specimens of SAE 1045 with a notch factor Kt ⳱ 3.0 that were investigated in push-pull tests (Ref 30, 31). Figure 17(a) compares the cyclic deformation curves of material states with very low residual stresses (produced by milling and subsequent annealing) with rather high residual stresses (produced by shot peening). In both conditions plastic deformation occurs in the first cycle at nominal stress amplitudes rn,a above 150 MPa. The annealed state yields continuous cyclic softening for all investigated rn,a values. Contrarily, the initial plastic strain amplitudes of the shot peened condition that are much less dependent on the stress amplitude compared to the milled and annealed state are reduced during the first cycles. This is a result of residual stress relaxation that is the more pronounced the higher the nominal stress amplitude is (see the following section “Evaluation of Experimental Results”). The consequences are smaller effective stress amplitudes and smaller ea,p values in the following cycles. Hence, the observed cyclic work hardening is fictitious. However, at higher numbers of cycles, cyclic softening occurs with lower ea,p values than in the unpeened condition. On the other hand, as can be seen from Fig. 17(b), the shot peening notch root residual stresses have an influence on the initial parts of the mean strain curves that were determined for different nominal stress amplitudes (Ref 30, 31). As a consequence of the cyclic deformation induced relaxation of the compressive residual stresses in the notch, the initial parts of the em / log N curves show negative plastic mean strains, where the magnitudes of em increase with increasing nominal stress amplitude. The minima of em are shifted to lower numbers of cycles with increasing rn,a values. However, from the minima of em at approximately 5% of the number of cycles to failure, the em /log N curves show increasing mean strains for all nominal stress amplitudes. Simultaneously, a decrease of the tensile compliance in the hysteresis loops that intensifies with an increasing number of cycles is observed. By that, the compressive compliance is approximately constant. This finding proves that this increase of the mean strains with the number of cycles is caused by an increase of the number of microcracks and/or the growth of microcracks. These sections are indicated by dashed lines in the em /log N curves of Fig. 17(b). The true plastic strain amplitudes in the cyclic deformation curves of the quenched-and-tempered (400 C/2 h) specimens in Fig. 18(a) are influenced by the magnitude of the notch root residual stresses, but not by their sign (Ref 30, 31). All investigated conditions in Fig. 18(a) show for the initial cycles fictitious cyclic-workhardening effects due to the relaxation of residual stresses rrs of the surface layers (rrs ⳱ 460 MPa and ⳮ320 MPa produced by upcut milling as well as ⳮ710 MPa by shot peening). Up to N ⳱ 20 cycles, increasing magnitudes of the compressive residual stresses cause higher negative mean strains. However, positive milling re-


0 σn,a = 220 MPa 200 σn,a = 150 MPa

400


0.20 250

σa in MPa

0.16 125 0.12 150 0.08 350 0.04

200

100

0 1

102

10

(a) 3

10

102

103

104

105

106

Number of cycles, N (a)

105

106

125

250 9 350 15

σa in MPa

102

10

400 450 103

104

105

106

Number of cycles, N

Plastic strain amplitude (a) and plastic mean strain versus number of cycles (b) for axial stress-controlled cyclic loading with mean stress rm ⳱ 300 MPa for specimens of the normalized SAE 1045 steel. Source: Ref 32

Fig. 20

σn,a = 200 MPa

rs

300

100

300 600 900 0

(b)

1

10

102

103

104

105

106

Number of cycles, N

Residual stress relaxation during stress-controlled push-pull loading of notched specimens (notch factor Kt ⳱ 3.0) for (a) normalized SAE 1045 in shot peened conditions and (b) quenched-and-tempered (400 C/2 h) SAE 1045 in cut-milled and shot peened conditions. Source: Ref 30, 31

Fig. 19

Ratio of cycles N/Nf, %

0

A Untreated B Deep rolled

80 60 40 20 0

A

B

C

C Shot peened Macrocracks (>750 µm) Short cracks (200-750 µm) Microcracks (>200 µm) No damage marks

Influence of mechanical surface treatments on the damage evolution of the push-pull loaded austenitic steel AISI 304. ra ⳱ 320 MPa; R ⳱ ⳮ1; A, Nf ⳱ 3859; B, Nf ⳱ 4445; C, Nf ⳱ 20,265. Source: Ref 28

Fig. 21

plastic strain of notched specimens (see Fig. 18b). A study of the residual stress effects on the cyclic deformation behavior seems to be possible by their simulation by applied mean stresses, which are homogeneously distributed over the cross section of the specimen. An example is presented in Fig. 20 for smooth, normalized SAE 1045 steel specimens that were stress-controlled loaded in push-pull tests with a constant mean stress of rm ⳱ ⳮ300 MPa (Ref 32). The cyclic deformation curves at stress amplitudes ra ⳱ 125 and 150 MPa in Fig. 20(a) show first of all a quasi-elastic incubation interval, followed by considerable cyclic softening within some cycles. Subsequently, within some further cycles, cyclic work hardening occurs to such an extent that extremely low plastic strain amplitudes result. For ra ⱖ 200 MPa, the compressive stress peak | rm ⳮ ra |, which is higher than the yield strength, induces plastic deformation in the first cycle. This procedure is followed by a rapid cyclic work hardening in such a manner that at cycles above 100 extremely low ea,p values are observed. As a consequence of the constant compressive mean stress, the specimens shorten for all investigated stress amplitudes, as proved by Fig. 20(b). For ra ⱖ 200 MPa, the mean strains increase considerably and continuously. However, for ra 200 MPa the ea,p values saturate above 20 cycles.

200

3

(b) 1

104

150

100

0

21

600

103

Number of cycles, N

1

0

Residual stress (σl ), MPa

stricted mean free path of the mobile dislocations in the work-hardened surface layers. In hardened as well as in quenched-and-tempered at low temperature conditions, the changes in the cyclic deformation behavior result not only from surface hardening or softening effects, but also from the more stable residual stresses as can be seen in Fig. 19(b) for notch root residual stresses of the quenched and tempered (400 C/ 2 h) SAE 1045 steel under the loading conditions of Fig. 18(a) (Ref 30, 31). The consequences are a considerable influence of the residual stresses on the cyclic behavior, especially with regard to the development of mean


rs


sidual stresses yield to positive mean strains. The increases in the plastic mean strains that appear for the numbers of cycles above the minimum of em are caused also by microcracks as described previously. Evaluation of Experimental Results. In relatively soft material states, as for example in normalized as well as in quenched-and-tempered at high-temperature conditions, the consequences of mechanical surface treatments by shot peening or deep rolling on the cyclic deformation behavior are mainly caused by near-surface micro residual stresses, that is, work hardening of the surface layers, because the macro residual stresses are relaxed very soon by cyclic plastic deformation (see the article “Stability of Residual Stresses” in this Handbook). This relaxation of macro residual stresses is shown in Fig. 19(a) for shot peening residual stresses in the notch root of a normalized SAE 1045 steel (Ref 30, 31) under the loading conditions of Fig. 17(a). The dislocation structures in the ferrite after the mechanical surface treatment are not stable and change during cyclic loading in energetically more favorable arrangements. The formation of typical fatigue-induced dislocation structures is combined with cyclic softening effects as presented in Fig. 13(a), 14(a), and 17(a). The small plastic strain amplitudes of the shot peened or deep-rolled conditions and the resulting increase in fatigue life are caused by the re-

Influence of Residual Stresses on the Crack Initiation Characteristic Examples. Crack initiation occurs as a consequence of microstructural changes in metallic materials during cyclic loading. Different mechanisms are responsible for their formation (e.g., Ref 33). If it is accepted that for given materials states at comparable load amplitudes increasing amounts of plastic strain amplitudes lead to decreasing numbers of cycles to crack initiation Ni, it follows that residual stresses may extend, shorten, or leave unchanged the number of cycles to crack initiation. However, experimental investigations concerning the influence of macro and micro residual stresses on crack initiation are scarce. This is due to the difficulties connected with the observation of the formation and the propagation of small cracks. A recently published investigation gives a report on the influence of mechanical surface treatments on crack initiation and crack propagation in push-pull loading of steels (Ref 28). In untreated materials, crack initiation normally takes place at positions of high localized slip, for example, at extrusions and intrusions that are connected with persistent slip bands. However, as shown in Fig. 21 in shot peened and deep-rolled conditions of the austenitic steel AISI 304, crack formation occurs later than in the untreated state due to the consequence of numerous obstacles for slip (dislocations, grain and twin boundaries) in the work-hardened surface layer that impede localized slip. In these surface-work-hardened

34 / Effect of Materials and Processing conditions, no persistent slip band is observed at all. Furthermore, crack propagation is slower than in the untreated state due to the effect of microstructure and compressive residual stresses. Similar results are found in Ref 28 for the normalized steel SAE 1045, in Ref 34 for the plain carbon steel SAE 1080, and in Ref 35 and 36 for a high-strength spring steel AISI 6150 (German grade 50 CrV 4). However, as reported in Ref 1, the crack initiation time of shot peened specimens is sometimes shorter than that of unpeened specimens despite increased lifetimes. One example is given in Fig. 22 for the quenched-and-tempered steel SAE 1045 in the case of bending fatigue tests in seawater (Ref 37). With the exception of high stress amplitudes, the cracks are formed earlier in shot peened specimens than in ground ones. This finding is attributed to an enhanced crack initiation at micronotches resulting from shot peening, which is obviously supported by corrosion pittings in the case of seawater environment. However, the number of cycles to failure of the shot peened conditions are higher than that of ground conditions. Residual stresses may have a remarkable influence on the location of crack initiation. In the case of bending fatigue, for example, cracks may start below the surface, if the magnitude of the


800

compressive residual stresses near the surface is high enough. Characteristic results are presented in Fig. 23 for shot peened bending specimens in a hardened state of the steel SAE 1045 with the bending fatigue strength Rf ⳱ 960 MPa after shot peening with the shot size d ⳱ 0.3 mm and Rf ⳱ 1050 MPa with d ⳱ 0.6 mm, respectively (Ref 38, 39). For stress amplitudes ra Rf, crack initiation was observed directly at the surface. However for ra Rf, subsurface cracks occurred as shown in Fig. 24. If the centers of the rosettes on the scanning electron micrographs (SEMs) are considered to be the crack initiation points, it is obvious that the crack initiation depth increases with decreasing stress amplitude (Ref 39). At stress amplitudes that result in a fatigue life Nf above 107 cycles, crack initiation is located approximately 0.3 mm below the surface. These findings stimulated the development of a concept of the local fatigue strength (see the paragraphs on experimental results in the section “Influence of Residual Stresses on S-N curves” in this article). Evaluation of Experimental Results. The definition of the number of cycles to crack initiation Ni and particularly the establishment of the affiliated crack length is of decisive meaning for the evaluation of the influence of different parameters on Ni from experimental results from

(a) Fracture Crack initiation

600

200 µm (b)

400

200 µm

200 Shot peened

(c)

Ground 0 104


107

Stress amplitude versus number of cycles to crack initiation and to failure of a quenchedand-tempered SAE 1045 steel under bending fatigue loading in seawater. Source: Ref 37

200 µm (d) 200 µm

200 µm

Distance from surface, mm

0.4

200 µm

0.2 Site of macrocrack initiation

However, decreasing Ni values are observed, if in the surface area: ● The roughness is increased, for example, by

shot peening

● Tool marks or material overlaps from shot

peening or deep rolling exist

● Tensile macro residual stresses occur that fa-

vor interface cracks between matrix and hard second phases. In this context, an investigation of the fatigue crack initiation in double-edge notch specimens of SAE 1080 steel with a fine-grained, spheroidized microstructure shows considerable effects of the macro residual stresses (Ref 34). In a press-fitted condition, large compressive residual macro stresses occur that remained relatively stable throughout the fatigue life and thus greatly increased the numbers of cycles to crack initiation Ni. With reference to the Basquin-relationship, Ni is estimated from the following relationship:

冢r⬘ ⳮ (r

2ra a

1/b;

Ⳮ r )冣 rs

(Eq 13)

where Ni is defined as the number of cycles at a crack length of a ⳱ 0.1 mm, rrs is the macro residual stress, ra is the applied stress amplitude, and r⬘i ⳱ 2315 MPa and bi ⳱ ⳮ0.197 are material constants.

200 µm

Shot size 0.3 mm Shot size 0.6 mm

1000 1200 Stress amplitude (σa), MPa

Influence of Residual Stresses on the Crack Propagation

(g)

1400

Crack initiation sites versus stress amplitude of a hardened SAE 1045 steel in different shot peened conditions. Source: Ref 38, 39

Fig. 23

stresses

● Is smoothed by polishing or deep rolling

(f)

0.3

800

face treatment

● Bears additional compressive macro residual

i

(e)

0

● Becomes work hardened by mechanical sur-

Ni ⳱

Fig. 22

0.1

literature. If the corresponding crack length amounts to only some grain diameters, then Ni is determined by shear-stress-controlled processes in stage I of crack propagation. However, if crack lengths of several hundred microns appear (stage II of crack propagation), Ni will be determined by normal-stress-controlled processes. In the last case, stable macro residual stresses may have a considerable influence on the Ni values. The experimental results achieved until now for crack formation directly at the surface with an appropriate consideration of the Ni definition show increasing numbers of cycles to crack initiation, if the surface area:

Scanning electron micrographs of fractured specimens of hardened and shot peened SAE 1045 at different stress amplitudes. (a) ra ⳱ 1300 MPa. (b) ra ⳱ 1250 MPa. (c) ra ⳱ 1200 MPa. (d) ra ⳱ 1100 MPa. (e) ra ⳱ 1000 MPa. (f) ra ⳱ 950 MPa. (g) ra ⳱ 900 MPa. Source: Ref 39

Fig. 24

Characteristic Examples. During cyclic loading, the lifetime of components is determined significantly by the stage of crack propagation, especially in the case of existing macro residual stresses. Crack propagation as a consequence of fatigue loading without mean stresses can be described, with the exception of the crack initiation and the near-fracture stage, by the Paris equation (see Eq 1):

Residual Stresses and Fatigue Behavior / 35 da ⳱ C(DK)m dN

(Eq 14)

where DK is the stress intensity range and C and m are constants. Mean stresses are taken into account by the Foreman equation: da C(DK)m ⳱ dN (1 ⳮ R)Kc ⳮ DK

200

rs

0

200

Crack propagation rate (da/dN), mm/cycle

(Eq 15)

where R is the stress ratio and Kc is the stress intensity factor for plane stress. Both relationships are valid for crack propagation in materials states without macro residual stresses. However,

Residual stress (σy ), MPa

these descriptions imply that a propagating crack itself is surrounded by a typical residual stress field as shown in Fig. 25(a) for a high-strength structural steel of the European grade S690QL1 (Ref 40, 41). A crack was produced by cyclic loading up to a stress intensity range of DKI ⳱ 47.4 MPa 冪m. The distribution of the macro re-

10−4

As received

10−5

10−6

Autofrettaged

0

0.2

0.4

0.6

0.8

1.0

Ratio a/W

Crack propagation rate da/dN versus ratio a/ W in an autofrettaged and an untreated tube of the SAE 4337 steel. Source: Ref 43

Fig. 27

400 12

8 4 0 4 8 Distance from crack tip, mm

(a)

12 10 150 bar Crack propagation rate (da/dN), mm/cycle

rs

Residual stress (σy ), MPa

200

0

200

8 4 0 4 8 Distance from crack tip, mm

Residual stress component rrsy versus distance from crack tip of the steel S690QL1 after a mode I base load of DK ⳱ 47.4 MPa 冪m (a) and an overload of DK ⳱ 94.8 MPa 冪m (b). Source: Ref 40, 41

10−2 λ=2

10−3 10−4

λ=3

10−5

8

4

0

4

8

75 bar

6

225 bar

4 2 300 bar 0

1 2 Crack length (a), mm

3

Fatigue crack propagation rates da/dN in annealed and with different rolling pressures deep-rolled steel AISI 304. Stress amplitude ra ⳱ 320 MPa, surface residual stresses rrs ⳮ200 MPa (75 bar), ⳮ350 MPa (150 bar), ⳮ400 MPa (225 bar), and ⳮ300 MPa (300 bar). Source: Ref 29

Fig. 28

Fig. 25

12

10−3

10−4

Stress relieved

As welded

10−5

10−6

5

10

20

30 40

60 80

Stress intensity range (∆K), MPa m

Crack length (aol), mm

Crack propagation rate da/dN versus crack length a0l for overloads with k ⳱ 2 and 3. Source: Ref 40, 41

Fig. 26

Untreated

12


12 (b)

10−6

8

0

400


10−3

Crack propagation rate da/dN versus stress intensity range DK in the heat-affected zone of EN S355 steel in an as-welded condition and after a stressrelief heat treatment. Source: Ref 44

Fig. 29

sidual stress component rrs y , which acts perpendicular to the crack flanks, shows maximum compressive residual stresses of approximately ⳮ350 MPa at the crack tip. The alteration of this distribution after application of 20 overload cycles with an overload ratio k ⳱ 2 (DKI ⳱ 94.8 MPa 冪m) is given in Fig. 25(b). In front of the crack tip, a larger maximum value and a larger area with compressive residual stresses compared with Fig. 25(a) are developed. The influence of different overload cycles on the crack propagation rate is shown in Fig. 26 for k ⳱ 2 and 3. For both overload ratios, a delayed retardation of crack propagation occurs that is more pronounced for k ⳱ 3 than for k ⳱ 2 due to the effect of overload-induced compressive residual stresses. Thus, by sufficiently high overloads, crack arrest can be produced (Ref 42). If a crack propagates into a macro residual stress field, the crack propagation behavior can be considerably influenced by magnitude and distribution of the residual stresses. This is shown in Fig. 27, in which crack propagation rates within an autofrettaged tube of SAE 4337 steel are compared with those in the untreated material (Ref 43). As a consequence of the autofrettaging process, a triaxial residual stress state is created with very high compressive residual stresses near the inner surface of the tube. In agreement with Eq 14, loading with a constant stress intensity range results in a constant crack propagation rate in residual-stress-free tubes. However, if the crack propagates through the compressive residual stress field at the inner surface of the autofrettaged tube, considerably smaller crack propagation rates occur. Crack velocity is influenced by work hardening as well as by residual stresses in mechanically treated surface layers. This is demonstrated in Fig. 28 for differently surface-rolled AISI 304 stainless steel. The crack propagation rate da/ dN, which was determined by analyzing striations on cracked surfaces, increases with increasing rolling pressure and is considerably diminished compared with untreated specimens (Ref 29). Finally, the influence of welding residual stresses at the steel European grade EN S355 is compared with the behavior of the same steel in a stress-relieved condition in Fig. 29 in a da/dN versus DK diagram (Ref 44). The crack propagation rate in the heat-affected zone is considerably lower in the as-welded state than in the stress-relieved state due to the distribution of welding compressive residual stresses. Evaluation of Experimental Results. For practical purposes, it is very important to know that crack propagation through residual stress fields can be modeled quantitatively by introducing an effective stress intensity range DKeff. This can be seen in Fig. 30, which shows crack propagation rates da/dN in welded and unwelded specimens of SAE 1019 steel (Ref 45). Exactly at the welding seam, tensile residual stresses of about 340 MPa exist that disappear in a distance of 10 mm. Figure 30 presents crack propagation rates in the unwelded base material

10−3 0.1 0 0.5 1.0 10−4

0.2

R = 0.4

2.0

10−5

10−6

6

10

20

30

40 50 60



(a)

10−3

R=0 0.5

10−4

10−5

10−6

1.0

2.0 ˚ 6

10

20

30

40 50 60

(Eq 16)

If the influence of the residual stress contribution on Kop is known, DKeff can be estimated and used to predict the fatigue crack growth. Thus, the double logarithmical plot of the crack propagation rate da/dN versus the effective stress intensity range DKeff in Fig. 30(c) shows that all measured data points form a narrow scatter band. In welded specimens, the (da/dN)/DK relations are completely changed (e.g., Fig. 30a and b). Obviously, for small DK values the crack propagation behavior is entirely controlled by the welding residual stress state, which leads to identical crack propagation rates irrespective of the R ratio. However, outside the volume areas

Nominal stress amplitude (σn,a), MPa


DKeff ⳱ Kmax ⳮ Kop


(b)

10−3

10−4

10−5

10−6

6

10

20

30

300 Upcut milling σrs = –234 MPa 200

Downcut milling σrs = 242 MPa

kt = 2.5 η=5 0 104

105 106 107 Number of cycles to failure, Nf

Alternating bending S-N curves of notched specimens of normalized plain carbon SAE 1045 steel after annealing, downcut milling and upcut milling. Source: Ref 47–49

Fig. 31

10−3

10−4

10−5

10−6

6

10

20

30

40 50 60

Effective stress intensity range (∆Keff), MPa m

(d) Crack propagation rate da/dN versus stress intensity range DK in the base material (a) and (c) and versus effective stress intensity range DKeff (b) and (d) in the welded zone of the SAE 1019 steel. Source: Ref 45

Fig. 30

300

200

η=1

η = 0.4 η = 0.1

kt = 1.7, η = 2

kt = 2.5, η = 5 100

kt = 4.4, η = 15

kt = 2.5, η = 2

Smooth Notched 0 750 500 250

0

250

500

750

rs

Surface residual stress (σl ), MPa Alternating bending fatigue strength of milled smooth and notched specimens of normalized plain carbon SAE 1045 steel versus surface residual stress. Source: Ref 47–52

Fig. 32

with high tensile residual stresses, individual curves for each R value used are observed. For R ⳱ ⳮ (pulsating compression), first increasing and then decreasing crack propagation rates are observed indicating the influence of the tensile residual stress field. However, also in this case, the crack propagation behavior can be described by a single, relatively narrow scatter band if the influence of the welding residual stresses on the DK values appearing at the crack tip is taken into account (see Fig. 30d). In this way, the crack propagation behavior in macro residual stress fields can be quantitatively described if crack propagation data of macro residual-stress-free materials are available and the residual stress distribution is known.

Influence of Residual Stresses on S-N Curves Characteristic Examples Low-Strength Steel. Figure 31 shows S-N curves for alternating bending of normalized SAE 1045 steel (German grade Ck 45) (Ref 47– 49). The notched specimens had a stress-concentration factor kt ⳱ 2.5. The stress gradient at the notch root dr/dz related to the maximum stress r (normalized stress gradient g): g⳱

Annealed σrs = 0 MPa

100

40 50 60

Effective stress intensity range (∆Keff), MPa m

(c) Crack propagation rate (da/dN), mm/cycle

as a function of DK for different stress ratios R. As expected, with increasing R values, higher crack propagation rates are observed. It is important to note that a mode I crack can only grow during that portion of loading cycle where the crack is open. This portion is influenced by the R value itself and the near-crack-tip residual stress distribution. The effective stress intensity range can be determined quantitatively as the difference between the maximum stress intensity and the stress intensity where the crack opens:

Bending fatigue strength (Rf), MPa



1 dr rˆ dz

冷z⳱0

(Eq 17)

was 5 mmⳮ1. All data are nominal stress amplitudes and are valid for a failure probability of 50%. The bending fatigue strength was evaluated at an ultimate number of cycles Nu ⳱ 107. By downcut milling and upcut milling, surface residual stresses of 242 and ⳮ234 MPa, respectively, were generated. The corresponding S-N curves are almost identical. A third batch of specimens was annealed 2 h at 700 C after downcut milling. The annealing results in a reduction of bending fatigue life and bending fatigue strength (Ref 47–49). The alternating bending fatigue strengths of milled smooth and notched specimens with different geometries are plotted in Fig. 32 as a function of the surface residual stresses (Ref 46–52). Again, all data are given for a failure probability of 50%, and the bending fatigue strengths are nominal stress amplitudes at Nu ⳱ 107. With increasing stress-concentration factor and decreasing stress gradient, the bending fatigue strength decreases. The influence of the stressconcentration factor is clearly visible from a comparison of the specimens with the same value g ⳱ 2 mmⳮ1, but different values kt ⳱ 1.7 and 2.5, respectively. On the other hand, the increase of g from 2 to 5 mmⳮ1 at specimens with kt ⳱ 2.5 results in a significant increase of bending fatigue strength. It is also interesting to note that specimens with kt ⳱ 4.4, g ⳱ 15 have a somewhat higher strength than specimens with


300 280 260

Deep rolled

240 220 200 180 104


320 280

rs

260 240 220 200 180 104

1000

Deep rolled

300



(a)

2 • 20 µm, 30 m/s 500 2 • 6 µm, 15 m/s 0 2 • 3 µm, 15 m/s

500


0

0.1 0.2 Distance from surface, mm

(b)


600 500 400 σrs = 221 MPa

300 200 100 0 104

19

kt = 1.7 η=2

602


Alternating bending S-N curves of notched specimens made from quenched-and-tempered (60 C/2 h) plain carbon SAE 1045 steel after different grinding processes. Source: Ref 47–49

Fig. 34

Depth distribution of the residual stress in notched specimens made from quenched-andtempered (600 C/2 h) plain carbon SAE 1045 steel by different grinding processes with the indicated two steps of final feed and cutting speed. Source: Ref 47–49

Fig. 35


S-N curves of specimens made from normalized plain carbon SAE 1015 steel in the asheat-treated state and after an additional deep rolling for (a) push-pull loading and (b) rotating bending. After Ref 53

Fig. 33

with rather small and with compressive surface residual stresses yield identical fatigue behavior. It should be noted that the surface layer bearing compressive residual stresses is rather small. Contrarily, the generation of tensile residual stresses causes a significant decrease of bending fatigue strength and a rather small decrease of finite fatigue life, which obviously vanishes at high stress amplitudes. The alternating bending fatigue strength of ground smooth and notched specimen with different geometries made of the same material state is plotted in Fig. 36 as a function of the surface residual stresses (Ref 47–52). Similar to Fig. 32, the influences of the stress-concentration factor and the normalized stress gradient are clearly discernible. However, contrary to the normalized steel there is distinct reduction of the bending fatigue strength with increasing tensile residual stress, this being more pronounced in the comparison of smooth specimens with notched specimens. In the range of compressive residual stresses covered, the influence of residual stress on bending fatigue strength is rather small. The S-N curves of smooth specimens in the ground state and after an additional shot peening are compared in Fig. 37(a) (Ref 47–49). There is a distinct increase of the bending fatigue strength by shot peening, but a rather small in-

400 η = 0.4

Smooth 300

η = 0.1

kt = 1.7 Notched

η=2

200

100

0 500

η=5

kt = 2.5

250

η=2 0

250

500

750

rs Surface residual stress (σl ), MPa

Alternating bending fatigue strength of ground smooth and notched specimens made from quenched-and-tempered plain carbon SAE 1045 steel versus surface residual stress. Source: Ref 47–52

Fig. 36


320

machining procedures. After correction of the data points given in Fig. 32 to the same hardness, it turns out that the bending fatigue strength is hardly changed or slightly diminished at most, if the residual stresses change from compressive to tensile (Ref 49). S-N curves for push-pull loading of smooth specimens made from normalized SAE 1015 steel (German grade Ck 15) in the as-heat-treated state and after an additional deep rolling are shown in Fig. 33(a) (Ref 53). Again, the fatigue behavior in the range of finite fatigue life and the fatigue strength do not differ much. Figure 33(b) shows a plot of S-N curves for rotating bending of the same material states. Now, by deep rolling finite fatigue life is increased by one order of magnitude or more, and the bending fatigue strength is increased significantly. Medium-Strength Steel. Figure 34 shows SN curves that were determined in alternating bending on notched specimens of quenched-andtempered (600 C/2 h) SAE 1045 steel (Ref 47– 49). All data are valid for a failure probability of 50% and Nu ⳱ 107. Three batches of specimens were manufactured by grinding. The grinding parameters (final feed, cutting speed) and the resulting depth distributions of residual stresses are given in Fig. 35 (Ref 47–49). Specimens

600 500

Shot peened

400 300 Ground 200 100 0 104


(a) Nominal stress amplitude (σn,a), MPa


kt ⳱ 2.5, g ⳱ 2 mmⳮ1. However, with regard to the residual stress state, there is no significant influence on the bending fatigue strength, even though the range of residual stresses covered comes to more than 1000 MPa regarding specimens with kt ⳱ 4.4, g ⳱ 15 mmⳮ1. Careful inspection of the hardness of the specimens tested shows that a positive slope of the lines in Fig. 32 is not related to the changing (macro) residual stress state, but to different hardness of the specimen and, hence, differences in the micro residual stress state produced by different

600 500

Shot peened

400 Milled 300 200

Ground

100 0 104

(b)


Alternating bending S-N curves of specimens made from quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel. (a) Smooth specimens after grinding and after additional shot peening. (b) Notched specimens after milling, grinding, and grinding with additional shot peening. Source: Ref 47–49

Fig. 37


400 Smooth η = 0.4

300

grinding. Again, in the range of finite fatigue life, the influence of the different manufacturing processes is almost negligible. The relative increase of the bending fatigue strength by shot peening is more pronounced compared with smooth specimens. It is interesting to note that milled specimens have a higher bending fatigue strength than ground ones, even though they have lower compressive residual stresses (ⳮ159

200 Notched kt = 1.7 η=2

100 0 750 500 250

0

250

500

750

rs

Maximum residual stress (σl ), MPa Alternating bending fatigue strength of quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel versus surface residual stress evaluated from Fig. 36 and 37

Fig. 38



fluence on finite fatigue life. Figure 37(b) compares S-N curves of notched specimens which were milled, ground, and shot peened after

800

600

400

Notched

Smooth

200

0

0

1000

2000 3000 4000 Deep-rolling force, N

5000

Bending fatigue strength smooth and notched specimens made from quenched-and-tempered SAE 5135 steel versus deep-rolling force. After Ref 57

Alternating bending S-N curves of smooth specimens made from blank-hardened AISI 5115 steel in the as-blank-hardened and with different conditions shot peened states including one with a subsequently electropolished surface. 1, as-blank-hardened; 2, shot velocity v ⳱ 23 m/s, coverage c ⳱ 100%, mean diameter of the shot d ⳱ 0.6 mm; 3, v ⳱ 53 m/s, c ⳱ 100%, d ⳱ 0.3 mm; 4, v ⳱ 53 m/s, c ⳱ 100%, d ⳱ 0.6 mm; 5, v ⳱ 81 m/s, c ⳱ 600%, d ⳱ 0.6 mm; 6, v ⳱ 53 m/s, c ⳱ 100%, d ⳱ 0.6 mm, 100 lm surface layer electrolytically removed. After Ref 54–56

Fig. 39


Fig. 41

600 σrs = 400 MPa

500 400

9

300 200

923

100 0 104

kt = 1.7 η=2 105 106 107 Number of cycles to failure, Nf

Alternating bending S-N curves of notched specimens made from quenched plain carbon SAE 1045 steel after different grinding processes. Source: Ref 47–49

Fig. 42

1000

1

200


0 200

rs

rs


400

3 4 5

400 600 800

1000 0

0.1 0.2 0.3 0.4 Distance from surface, mm

0.5

Depth distribution of the residual stress in specimens made from blank-hardened AISI 5115 steel in the as-blank-hardened (1) and in different conditions of the shot peened state (3), (4), and (5) corresponding to Fig. 39. After Ref 54–56

Fig. 40

2 • 15 µm, 30 m/s 500 2 • 9 µm, 15 m/s 0 2 • 3 µm, 15 m/s 500

0

0.1 0.2 Distance from surface, mm

Depth distribution of the residual stresses in notched specimens made from quenched plain carbon SAE 1045 steel and ground with the two steps of final feed and cutting speed indicated. Source: Ref 47–49

Fig. 43

MPa) at the surface than the latter ones (ⳮ221 MPa). Figure 38 shows plots of the alternating bending fatigue strengths evaluated from Fig. 37 as a function of the surface residual stresses. The arrows mark the shift in bending fatigue strengths and surface residual stresses produced by shot peening. Additionally, data points of ground specimens with negligible or tensile residual stresses shown in Fig. 36 are included. In the case of notched specimens, all data points lie on a common line with the slope ⳮ0.154 except for ground specimens with compressive residual stresses at the surface. Regarding smooth specimens, the influence of tensile residual stresses on the bending fatigue strength is much more pronounced than the influence of compressive residual stresses. Figure 39 shows S-N curves for alternating bending of smooth specimens (g ⳱ 1 mmⳮ1) of blank-hardened AISI 5115 steel (German grade 16 MnCr 5) determined in the unpeened and various shot peened states including one with electrolytically removed surface layer (Ref 54– 56). The corresponding depth distributions of residual stresses are given in Fig. 40. From the comparison of both figures, it becomes clear that the surface residual stress is not a suitable parameter for the assessment of the influence of the various treatments on the fatigue behavior. The influence of the deep-rolling force on the rotating bending fatigue strength of smooth and notched specimens made from quenched-andtempered SAE 5135 steel (German grade 37 CrS 4) is shown in Fig. 41 (Ref 57). In both cases, a maximum of the fatigue strength occurs at a certain force. However, the increase of the fatigue strength of notched specimens (kt ⳱ 2) by deep rolling is much more pronounced than that of smooth specimens. In the end, the optimal bending fatigue strength of notched specimens— which is a nominal stress amplitude—is higher than the bending fatigue strength of smooth specimens. High-Strength Steels. S-N curves for alternating bending of notched specimens of quenched SAE 1045 steel in differently ground conditions are compared in Fig. 42 (Ref 47–49). The grinding parameters (final feed, cutting speed) and the resulting depth distributions of residual stresses are given in Fig. 43. Similar to ground quenched-and-tempered specimens, the fatigue behavior of specimens with very small or compressive residual stresses (which have a very small penetration depth) hardly differ. Tensile residual stresses, however, not only cause a strong reduction of bending fatigue strength, but also of finite fatigue life. In Fig. 44, the bending fatigue strength that was evaluated from Fig. 42 and corresponding data from tests on smooth specimens are plotted as a function of the surface residual stresses. The negative influence of tensile residual stresses on the bending fatigue strength of smooth specimens is even more pronounced compared to notched specimens. The influence of compressive residual stresses generated by grinding is


800 Smooth η = 0.4

600 400

200 0 –1000

Notched kt = 1.7 η=2

–500

0

500

fatigue life, which comes up to one and a half orders of magnitude at high stress amplitudes. The S-N curves of notched specimens of the same steel state after grinding and after additional shot peening with shot of different hardness are shown in Fig. 45(b). Compared to smooth specimens, shot peening produces a much stronger increase of the bending fatigue strength. Again, there is also a remarkable in-



much smaller than the influence of tensile stresses. In Fig. 45(a), the S-N curves of smooth specimens in the ground state and after additional shot peening are compared (Ref 46–49). Similar to quenched-and-tempered specimens (see Fig. 37), shot peening produces a significant increase of the bending fatigue strength. Contrary to the results of the medium-strength steel, however, there is also a very pronounced increase of finite

1000

800 Smooth η = 0.4

600

400

Evaluation of Experimental Results

Ground Shot peened Milled

200


0 –1000

–500

0

500

1000

rs

Surface residual stress (σl ), MPa

1500

rs


Fig. 44 Alternating bending fatigue strength of ground smooth and notched specimens of quenched plain carbon SAE 1045 steel versus surface residual stress. Source: Ref 47–49

Alternating bending fatigue strength of smooth and notched specimens made from quenched plain carbon SAE 1045 steel with different surface conditions versus surface residual stress

Fig. 46

Ratio ∆Rf/∆Rh, MPa/µm

900

Shot peened

800 700 Ground 600

10 4

1 500 400 104

200

400

600

800

Surface hardness, HV 5 105 106 107 Number of cycles to failure, Nf

(a)

Changes of alternating bending fatigue strength DRf relative to changes of surface roughness height DR h versus surface hardness HV 5 for different heat treated SAE 1045 and AISI 5115 steels. After Ref 58, 59

Fig. 47

1000 900

0 54–58 HRC

800 700 600 500 400 104

46–50 HRC Shot peened Milled Ground 105 106 107 Number of cycles to failure, Nf

(b) Alternating bending S-N curves of specimens made from quenched plain carbon SAE 1045 steel. (a) Smooth specimens after grinding and after additional shot peening. (b) Notched specimens after grinding, milling, and grinding with additional shot peening with shot of the indicated hardness. Source: Ref 46–49

Fig. 45

rs


SAE 1045 AISI 5115

40



100 1000

crease of finite fatigue life. Additionally, the SN curve of milled specimen is included. Finite fatigue life and bending fatigue strength of these specimens are lower compared to shot-peened ones, even though they contain very high surface compressive residual stresses of ⳮ1200 MPa. In Fig. 46, the bending fatigue strength data already plotted in Fig. 44 are complemented by data evaluated from Fig. 45. The arrows mark the shift in bending fatigue strengths and surface residual stresses produced by shot peening. Similar to the discussion of Fig. 39 and 40, it becomes obvious that the magnitude of surface residual stress is not a suitable parameter for the assessment of the influence of shot-peening-induced residual stresses on the fatigue strength.

σn,a = 360 MPa

200

325

400

280 200

600

185 0

1

10

102 103 104 105 106 107 Number of cycles, N

Surface residual stress in notched (kt ⳱ 1.7) upcut milled specimens made from normalized plain carbon SAE 1045 steel during alternating bending fatigue at different nominal loading amplitudes versus number of cycles. Source: Ref 49

Fig. 48

Low-Strength Steels. Regarding Fig. 31 to 33, different machining processes or process parameters were applied to the specimens investigated producing different surface topographies. In Fig. 47, the ratio DRf /DRh, which gives the change of the alternating bending fatigue strength of differently treated SAE 1045 and AISI 5115 steels per lm increase of roughness height is plotted as a function of the hardness at the surface (Ref 58, 59). As is well known from many other investigations, the susceptibility of the bending fatigue strength to roughness increases with increasing hardness. For the steel states investigated, a value of 2 MPa/lm can serve as a guide. Since the roughness height of the specimens did not vary by more than 2 lm, the results plotted in Fig. 31 and 32 are hardly influenced by surface topography. It should be kept in mind, however, that a large increase of surface roughness will significantly decrease the fatigue strength even in low-strength material states. In low-strength steels, cyclic plasticity appears if the cyclic loading approaches the fatigue strength. Extensive cyclic plasticity occurs in the range of finite fatigue life, being combined with cyclic softening and/or hardening processes (see the section “Some Aspects of Fatigue of Steels” in this article). Cyclic plasticity results in macro residual stress relaxation, which is more rapid the higher the cyclic loading is (see the article “Stability of Residual Stresses” in this Handbook). Figure 48 (Ref 49) shows the relaxation of the surface residual stresses during alternating bending fatigue in notched upcut milled specimen made from normalized SAE 1045 steel starting at an initial value of ⳮ590 MPa. The bending fatigue strength amounts to 190 MPa (see Fig. 32). During loading with an amplitude of 185 MPa just below the fatigue limit, the change of the macro residual stresses is almost negligible. During all other fatigue loadings, extensive residual stress relaxation occurs. Therefore, almost no influence of macro residual stresses is found in Fig. 31 and 32 (Ref 47–52). The amount of cyclic plasticity, which occurs during cyclic loading resulting in a given finite

40 / Effect of Materials and Processing fatigue life or which corresponds to the fatigue limit, decreases with increasing strength of the steel. This results in decreasing residual stress relaxation rates and finally in stable macro residual stresses. On the other hand, in a low-strength steel, local work hardening may occur during manufacturing processes such as milling, turning, or grinding. In other words, the micro residual stress state is changed, mainly by the increase of the dislocation density. As discussed in the article “Stability of Residual Stresses” in this Handbook, the resistance of the micro residual stress state against cyclic relaxation is much higher compared to that of the macro residual stress state. So one may assume that macro residual stresses that exist in a part of a component that has undergone work hardening by manufacturing processes are more stable than expected from the basic strength of the material. Looking at Fig. 32, this relationship may be responsible for the small reduction of the bending fatigue strength by tensile residual stresses that occurs in some of the specimen series investigated. A much more important consequence of the change of the micro residual stress state by local work hardening is the direct alteration of the local fatigue behavior. Increasing strength reduces the local cyclic plastic deformation at a given external loading, thus increasing the number of

cycles to crack initiation and decreasing the propagation rate of short cracks (Ref 60, 61). Therefore, as is evident from Fig. 31, a residual stress relief heat treatment that eliminates the machining-induced work hardening reduces the finite fatigue life and the fatigue limit of normalized SAE 1045 steel. At rather high loading amplitudes, this influence vanishes because then the cyclic deformation behavior is almost entirely governed by cyclic softening and hardening processes during the fatigue loading (see the section “Cyclic Deformation Behavior” in this article) irrespective of initial variations of the local work-hardening state. A smaller influence of the micro residual stress state appears in Fig. 33(a) and a somewhat stronger one in Fig. 33(b). Here, it becomes clear that even in a rather soft material state such as normalized SAE 1015 steel, an improvement of the fatigue behavior can be obtained from local work hardening. In this case, the depth of the surface layer of the smooth specimens influenced by deep rolling is relatively large compared to the milled specimens, which are the basis of Fig. 31 and 32. Nevertheless, push-pull loading (Fig. 33a) without stress gradient reveals a small influence of deep rolling, because of two major effects. First, the crack initiation site may be shifted below the work-hardened zone. Then, the small increase of the fatigue strength mirrors the benefit of omitting surface effects (such as spec-

600

Smooth η = 0.4 σn,a = 200 MPa

rs

2


Ratio ∆Rf/∆HV 5

3

Rh = 3 µm 1

Rh = 15 µm 0 0

200

400

600

800

1000

Surface hardness, HV 5

400 Notched kt = 1.7, η = 2 σn,a = 150 MPa

200

kt • σn,a = 255 MPa

0 0

Changes of alternating bending fatigue strength DRf relative to changes of surface hardness DHV 5 versus surface hardness HV 5 for different surface roughnesses heights Rh. After Ref 58, 59

1

10

Fig. 49

600

η=2

kt = 2.5

η=5

1.5

kt = 1.7

400

200

200

0 0

0

200

400

106 107

1

10

102

103

104

105

106

Number of cycles, N 600

rs Surface residual stress (σl ), MPa

Fatigue notch factor kf of specimens made from quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel versus surface residual stress. Source: Ref 47–49

Fig. 50

105

Notched σn,a = 350 MPa kt = 1.7 η=2 kt • σn,a = 595 MPa

η=2 1.0 400

104

Smooth η = 0.4 σn,a = 400 MPa

rs

2.0

103

(a) Surface residual stress (σl ), MPa

Fatigue notch factor, kf

2.5

102

Number of cycles, N

(b) Surface residual stress in smooth and notched specimens made from quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel versus number of cycles (a) at a lifetime of approximately 2 ⳯ 106 cycles and (b) at a lifetime of approximately 105 cycles. Source: Ref 47–49

Fig. 51

imen roughness, corrosion, oxidation) on the crack initiation. Secondly, if crack initiation occurs at the surface, the influence of the workhardened zone may also be rather small, because—at a given loading—a stress redistribution may occur from the softer core region of the specimen to the work-hardened zone. This effect is combined with cyclic plasticity in the core region and, hence, with rather high loading amplitudes. The first effect predominates in the range of the fatigue limit, where cyclic plasticity is small, and the second one in the range of finite fatigue life. On the other hand, during rotating bending (Fig. 33b) with a distinct stress gradient, crack initiation always occurs at the surface. If the work-hardened zone is thick enough, there is no stress redistribution from the core region— which is then purely elastically loaded—to the work-hardened zone. Again, at very high loading amplitudes, the cyclic softening/hardening processes produced by the cyclic loading itself push the influence of the initial work-hardening state into background. In Fig. 49, the ratio DRf /DHV, which gives the increase of alternating bending fatigue strength per unit hardness, is plotted as a function of the hardness itself (Ref 58, 59). The diagram shows that the sensitivity of the fatigue strength to the hardness decreases with increasing hardness. Taking into account that the resistance of the macro residual stress state against cyclic relaxation is low in low-strength steels, it becomes clear from Fig. 49 that—besides the change of the surface topography—the alteration of the micro residual stress state is the governing parameter for the assessment of the influence of machining on the fatigue behavior of components made from low-strength steel. Medium-Strength Steel. A detrimental effect of tensile grinding residual stresses appears in Fig. 34 and 36 on alternating bending fatigue strength, being more pronounced for smooth than for notched specimens. Therefore, the fatigue notch factor decreases with increasing residual stress, as shown in Fig. 50. There is relaxation of surface residual stresses during bending fatigue loadings of smooth and notched specimens, which results in lifetimes of approximately 2 million cycles, as shown by Fig. 51(a). The stress relaxation in the notched specimens is significantly more pronounced than in smooth ones. An elastic estimation of the stress in the notch root r* ⳱ kt • rn,a yields a much higher value than the stress amplitude in the smooth specimens. Even though r* is only an upper bound for the true stress at the notch root, it becomes clear that it is the higher local cyclic loading in notched specimens that causes the stronger cyclic stress relaxation and, hence, the smaller residual stress sensitivity of the bending fatigue strength compared to smooth specimens. Regarding the relatively high loadings indicated in Fig. 51(b), stress relaxation in notched specimen is almost complete at the end of fatigue life, and therefore only a small influence of initial macro residual stresses on fatigue life at high loadings is expected. This is shown in Fig. 34.

Residual Stresses and Fatigue Behavior / 41 According to Fig. 34 and 36, the beneficial effect of compressive grinding residual stresses on bending fatigue strength is small regarding smooth and almost negligible regarding notched specimens. Again, the smaller effect in notched specimens is due to a stronger residual stress relaxation. However, during cyclic loading corresponding to the fatigue limit, a considerable portion of the initial residual stresses is retained to the ultimate number of cycles even in notched specimens. Therefore, and in view of the small penetration depth of the compressive residual stresses ( 20 lm, see Fig. 35), one would assume that the crack initiation site is shifted below the surface. However, this could not be proved unambiguously in either smooth or notched specimens (Ref 49). Therefore, it is thought that very thin surface zones bearing compressive residual stresses do not retard the initiation and early growth of microcracks. Regarding smooth specimens in Fig. 38, a smaller effect of compressive residual stresses produced by grinding or shot peening appears compared to tensile grinding residual stresses, even though crack initiation occurred always at the surface. The small influence of compressive

rs


0

σn,a = 400 MPa

–500

N 107 Before loading

–1000

–1500 0

0.1

0.2

0.3

0.4

0.5

Distance from surface, mm Residual stress of smooth ground and additional shot peened specimens made from quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel before loading and after 107 cycles versus distance from surface. Source: Ref 46–49

Fig. 52

rs


0 σn,a = 460 MPa

N ≥ 103 σn,a = 300 MPa

–500

N ≥ 107 Before loading

–1000

–1500 0

0.1

0.2

0.3

0.4

0.5

Distance from surface, mm Residual stress of notched ground and additional shot peened specimens made from quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel before and after loading at different nominal stress amplitudes versus distance from surface. Source: Ref 46–49

Fig. 53

grinding residual stresses was already attributed to their small penetration depth. Contrarily, as evident from Fig. 40, compressive residual stresses generated by shot peening have a rather large penetration depth. However, since the bending fatigue strength of shot peened specimens (414 MPa) is much higher than that of specimens with tensile grinding residual stresses (195 MPa), also the residual stress relaxation is more pronounced during corresponding cyclic loadings. As shown in Fig. 52, residual stresses relax significantly during fatigue loading, which does not cause failure within 107 cycles. Furthermore, the surface roughness of the shot peened specimens (Rh ⳱ 35.6 lm) was much higher than that of ground specimens (Rh ⳱ 6.5 lm) (Ref 46–49). If the bending fatigue strength of shot peened specimens is corrected for the high surface roughness by means of Fig. 47 and is plotted in Fig. 38 at the surface residual stress remaining after 107 cycles (see Fig. 52), one gets a data point that lies significantly above the extrapolated relationship between bending fatigue strength and tensile residual stresses. The relationship between bending fatigue strength and surface residual stresses of notched specimens (Fig. 38) is described by a straight line except for specimens with compressive grinding residual stresses as already discussed. In all cases, crack initiation occurred at the surface of the specimens that failed. Since the extrapolated straight lines for smooth and notched specimens cross at a tensile surface residual stress of approximately 750 MPa the fatigue notch factor approaches a unity with increasing tensile residual stress (see the paragraphs on medium-strength steel in the section “Haigh Diagram” in this article). Again, different residual stress relaxation plays an important role. As shown in Fig. 51(a) (Ref 49), and discussed previously, the residual stress relaxation in a smooth specimen loaded just above the fatigue limit, which failed after 2 million cycles, is significantly smaller than in a notched specimen that failed after approximately the same number of cycles. Figure 53 proves that residual stress relaxation is even more significant up to a distance of 100 lm from the surface during fatigue loading of shot peened notched specimens, which did not fail up to 107 cycles. During fatigue loading resulting in a fatigue life of approximately 104 cycles, residual stress relaxation is almost complete. Therefore, no influence of macro residual stresses appears in the low-cycle fatigue range (see Fig. 37b). From Fig. 51(a) and 53, it follows that at the fatigue limit, the residual stress relaxation in shot peened notched specimens with compressive tensile residual stresses is more pronounced than in ground notched specimens with tensile residual stresses. For this comparison, in Fig 51(a) only the stress relaxation up to the appearance of a crack (arrow at 5 ⳯ 105 cycles) may be regarded, because the final relaxation is influenced by crack propagation and does not exist in Fig. 53. Furthermore, the surface roughness of shot peened notched specimens (Rh ⳱ 18.0

lm) was larger than that of ground specimens (Rh ⳱ 5.5 lm). Therefore, the question arises why the data points of shot peened specimens do not fall below the solid line drawn in Fig. 38. Careful inspection of microhardness distribution and the width of x-ray interference lines as a function of the distance from the surface show that—compared to grinding—shot peening produces a more intense work hardening which, in addition, penetrates into a larger depth. The same holds for smooth specimens. The work hardening reduces cyclic plasticity and retards crack initiation. Hence, it becomes clear that the bending fatigue strength of medium strength steel is strongly influenced by both the micro and the macro residual stress states and their stability against cyclic loading. However, in the low-cycle fatigue (LCF) range, the macro residual stress state is unstable and the influence of the (more stable) micro residual stress state vanishes in view of the strong cyclic-softening processes occurring during this loading condition (see the section “Cyclic Deformation Behavior” in this article). Therefore, neither an influence of the macro residual stress state nor an influence of the micro residual stress state appears in Fig. 37 at high loading amplitudes. Figure 40 shows that rather different depth distributions of compressive residual stresses can be produced in smooth specimens (g ⳱ 1 mmⳮ1) made from a medium-strength steel by shot peening with different peening parameters (see also the article “Stability of Residual Stresses” in this Handbook). To understand the influence of the surface roughness, the work hardening and the macro residual stress state produced by shot peening on the resulting bending fatigue behavior it is necessary to discuss crack initiation and crack propagation separately, and this is done in the section “Propagating and Nonpropagating Cracks” in this article. Some relationships, however, should be pointed out here. The highest bending fatigue strength (curve 6 in Fig. 39) was determined for specimens shot peened according to curve 4 in Fig. 40. Then, a 100 lm thick surface zone was electrolytically removed, shifting the maximum compressive residual stresses to the surface and reducing the surface roughness. The smooth surface (Rh ⳱ 3 lm) and the work hardening of the surface zone oppose crack initiation. The relatively high compressive residual stresses at the surface hinder microcrack propagation. This influence outweighs the larger maximum and the greater penetration depth of the compressive residual stresses according to curve 5. In this shot peening state, a higher surface roughness (Rh ⳱ 43.8 lm) and a lower work hardening at the surface result in crack initiation at a lower stress amplitude, and the lower surface compressive residual stresses offer less resistance to early microcrack propagation. On the other hand, in the range of finite fatigue life, there is almost no advantage of the electropolished state 6 compared to the initial shot peened state 4 and a clear disadvantage compared to state 5. Here, the higher number of cycles to crack initiation (state 6) is

42 / Effect of Materials and Processing almost compensated (state 4) or overbalanced (state 5) by a slower rate of crack propagation due to the larger penetration depth and—in the case of state 5—the higher amount of the compressive residual stresses. Since the surface roughness, the surface work-hardening state and the surface residual stress state (see Fig. 40) of the material states 2 to 5 do not differ much, they have similar resistance to crack initiation at the surface. Hence, the different fatigue strength appearing in Fig. 39 is determined by the appertaining resistance to microcrack propagation, which, in turn, depends on the depth distribution of the compressive residual stresses. This is discussed in more detail in the section “Propagating and Nonpropagating Cracks” in this article. A very interesting example of the interaction of changing surface roughness as well as micro and macro residual stress state in a mediumstrength steel are given in Fig. 41. The strong increase of the rotating bending fatigue strength of notched specimens by deep rolling is clearly attributed to the generation of micro- and macrostresses with a rather large penetration depth. It is interesting to note that the resistance to microcrack initiation is hardly influenced by the deeprolling treatment (Ref 57), and the increasing bending fatigue strength is almost entirely combined with an increasing resistance to micro-

Fatigue notch factor, kf

2.5

2.0

kt = 1.7 η=2 1.5

1.0 500

0

500

1000

rs

Surface residual stress (σl ), MPa Fatigue notch factor kf of specimens made from quenched plain carbon SAE 1045 steel versus surface residual stress. Source: Ref 47–49

Fig. 54

rs


0 Before loading σn,a = 750 MPa

–500

N ≥ 107 –1000

–1500 0


0.5

Residual stress of smooth ground and additional shot peened specimens made from quenched plain carbon SAE 1045 steel before loading and after 107 cycles versus distance from surface. Source: Ref 46–49

Fig. 55

crack propagation, resulting in crack arrest at stress amplitudes increasing with the deep-rolling force. At relatively high forces, however, the bending fatigue strength decreases, because then the impairment of the surface zone by the strong increase of the surface roughness and microcracking as well as an unfavorable residual stress state at the surface enhances the formation of rather long initial cracks that only arrest at reduced stress amplitudes. The bending fatigue strength of smooth specimens increases only weakly with increasing rolling force. Regarding the maximum value, an increase of only 15% is achieved, compared to 120% in the case of notched specimens. Since the stress gradient is rather small in smooth specimens, there is some speculation (Ref 56, 57) that the crack initiation site is shifted below the surface by deep rolling. Then, the small increase of the fatigue strength mirrors the benefit of omitting surface effects (such as specimen roughness, corrosion, oxidation) and the effect of a decreasing local stress amplitude on the crack initiation. This mechanism is discussed in detail in the section “Haigh Diagram” in this article. At high rolling forces, however, the crack initiation occurs at the surface again, where it is enhanced by a high roughness, an increased roughness sensitivity due to work hardening, and an unfavorable residual stress state. Therefore, the bending fatigue strength decreases, and there is no improvement by deep rolling at all. In the end, the maximum bending fatigue strength of the notched specimens (remember, evaluated as nominal stress amplitude) is higher than the maximum bending fatigue strength of the smooth specimens. These results show that the gradients of the micro and the macro residual stresses in comparison to the gradient of the loading stresses are of great importance, and this will become even more evident in the next section. High-Strength Steels. The S-N curves of quenched SAE 1045 steel in Fig. 42 prove that there is a detrimental effect of tensile grinding residual stresses on bending fatigue strength and, contrary to the quenched-and-tempered state (see Fig. 34) also on finite fatigue life. This is because there is only a weak relaxation of the initial residual stresses even at rather high stress amplitudes. Similar to quenched-and-tempered specimens, compressive grinding residual stresses with very small penetration depth ( 20 lm, see Fig. 43) have almost no effect on bending fatigue strength and finite fatigue life. Therefore and since in the quenched state the compressive residual stresses are retained to the largest part during fatigue loading in the range of the fatigue limit, one may expect that crack initiation occurs below the surface. Analogous to the quenchedand-tempered state, this could not be proved definitely (Ref 49). Since in the quenched state a grinding-induced work softening occurs close to the surface and an influence of the surface roughness always exists, it is very probable that crack initiation occurs at the surface. Then, one must conclude that compressive residual stresses with a penetration depth of only 20 lm do not retard

or stop the propagation of microcracks existing after crack initiation. The extrapolated bending fatigue strength versus surface residual stresses curves in Fig. 44 cross in the range of tensile residual stresses at 1125 MPa. This means that the fatigue notch factor becomes unity. On the other hand, at negligible or compressive residual stresses, the fatigue notch factor approaches the stress-concentration factor, as shown in Fig. 54. Qualitatively similar to the quenched-and-tempered state, the influence of tensile residual stresses is stronger than that of compressive residual stresses and the residual stress sensitivity of notched specimens is smaller than that of smooth ones. However, this cannot be explained by different residual stress relaxation so far. Careful x-ray analyses prove that in notched specimens loaded with a stress amplitude of 450 MPa and in smooth specimens loaded with 750 MPa (corresponding to the fatigue limit of each) the relaxation of compressive residual stress is small and of equal amount. This is not astonishing, since an elastic estimation of the stress amplitude in the notch root (r* ⳱ kt • r ⳱ 765 MPa) yields almost the same value as the stress amplitude of the smooth specimen. No corresponding measurements for smooth and notched specimens with tensile residual stresses were performed. However, since the fatigue limit is reduced by tensile residual stresses, it is clear that their relaxation is negligible. A comparison of Fig. 45(a) with Fig. 37(a) shows that the shot peening treatments performed increases the bending fatigue strength of smooth specimens in the quenched state less than in the quenched-and-tempered state. In view of the different residual stress states and their different stabilities in both heat treating states, this finding is rather astonishing. In Fig. 55, the depth distribution of residual stresses in shot peened quenched specimens before fatigue loading and after 107 cycles at the fatigue limit is shown. In the range of specimen scatter, the results are identical. Contrary to quenched-andtempered specimen (see Fig. 52), the shot peening residual stresses are much higher and much more stable in quenched specimens. However, in the former, crack initiation occurs at the surface. Hence, the shot-peening-induced changes of the micro and the macro residual stress state have a strong influence on the measured bending fatigue strength. In smooth quenched specimens, cyclic loading at the fatigue limit initiates cracks below the surface. Therefore, the influence of the shot-peening-induced changes of the residual stress state have a rather small influence on the measured bending fatigue strength. This is treated more detailed in the section “Modeling the Influence of Residual Stresses on Fatigue Behavior.” Contrarily, in the range of finite fatigue life, crack initiation in both states occurs at the surface, and there is a strong influence of shot peening regarding quenched specimens and a very small one regarding quenched-and-tempered specimens. This finding is directly correlated with very different residual stress relaxa-



tion. While surface residual stress relaxation is definitely complete in quenched-and-tempered specimens after 50,000 cycles at a stress amplitude of 570 MPa, there is hardly any change of the surface residual stresses in the quenched specimens after the same number of cycles even at 1200 MPa (Ref 49), although there may be some residual stress relaxation below the surface. Regarding notched specimens, a different picture appears (compare Fig. 45b with Fig. 37b). Now, shot peening of quenched specimens pro-

800 Smooth η = 0.4

600

400 Ground Shot peened Milled

200


0 –1500 –1000 –500 0 500 1000 rs Maximum residual stress (σmax ), MPa

Alternating bending fatigue strength of smooth and notched specimens made from quenched plain carbon SAE 1045 steel with different surface conditions versus surface residual stress

Fig. 56

Before loading –500

rs


0

σn,a = 640 MPa

N ≥ 107 –1000

–1500 0


0.5

(a)

after 107 cycles. In this case, a significant relaxation and redistribution of the residual stresses occur.

Modeling the Influence of Residual Stresses on Fatigue Behavior Haigh Diagram Basic Relationships. One obvious way to account for the influence of (macro) residual stresses on the fatigue behavior is to treat them as local mean stresses. In doing so, one has to realize that there are several important differences between (loading) mean stresses and residual stresses, as discussed in the section “Comparison between Loading Stresses and Residual Stresses” in this article. Figure 58 shows a Haigh diagram for smooth and notched specimens made from a medium-strength steel (Ref 1, 62). The Goodman approximation (see Eq 9) is used to account for the influence of residual stresses on the fatigue strength. If the amount of the minimum stress or the maximum stress in smooth specimens does not exceed the critical stress amplitude ra,crit, which is a function of the cyclic yield strength (see the article “Stability of Residual Stresses” in this Handbook), the residual stresses do not relax, and the line AB gives the influence of the residual stress on the fatigue strength. Then, all combinations of residual stress and stress amplitude inside the shaded area result in neither residual stress relaxation nor fatigue failure. However, if the amount of the minimum stress or the maximum stress exceeds the critical stress amplitude, it is assumed that the residual stresses relax to the value given by the points A and B, respectively, and the fatigue strength remains constant at the value given by these points. In the case of notched specimens, the cyclic yield strength and the notch fatigue strength (both in terms of nominal stress amplitudes) are less than the respective values of smooth specimens. However, the ultimate tensile strength of notched specimens is larger than that of smooth ones in such a material state because

Before loading –500

rs


0

duces a strong increase of both fatigue limit and finite fatigue life. Milling, which may generate rather high compressive residual stresses, is less effective. In all cases, crack initiation was observed at the surface. However, as evident from Fig. 46, the surface residual stress state is not an appropriate parameter to assess bending fatigue life in the presence of compressive residual stresses. In Fig. 56, the bending fatigue strength is plotted as a function of the maximum residual stresses. Again, the arrows mark the shift of the residual stresses and bending fatigue strength obtained from shot peening. Now, the data of ground notched specimens with tensile or negligible residual stresses and of notched specimens peened with shot of different hardness are described satisfactorily by one common line covering a residual stress range of 2350 MPa. The data points of ground and those of milled specimens bearing compressive residual stresses fall below this line, which has the slope ⳮ0.214. In Fig. 56, it becomes even more clear than in Fig. 46 that the improvement of the bending fatigue strength of smooth specimens by shot peening is very limited. As a consequence, the notch effect on bending fatigue strength is completely eliminated at high compressive residual stresses. It is interesting to look at the stability of very high compressive residual stresses. As already shown in Fig. 55, fatigue loading of smooth specimens in the range of the fatigue limit does not cause any significant change of the residual stress state. As shown in Fig. 57(a), the same holds for notched specimens peened with shot of relatively low hardness, which have a very similar depth distribution of the residual stresses. Elastic calculation of the minimum stress 70 lm below the notch root (at the maximum of the compressive stresses) yields the value ⳮ2035 MPa. This stress value may occur more than 107 times without effecting any change of the residual stress state. As shown in Fig. 57(b), notched specimens peened with shot of higher hardness bear even higher compressive residual stresses. In this case, elastic calculation of the minimum stress in a depth of 100 lm yields the initial value ⳮ2475 MPa and the value ⳮ2130 MPa

σn,a = 760 MPa

–1000

N ≥ 107 –1500 0


0.5

(b) Residual stress of notched ground and additional shot peened specimens made from quenched plain carbon SAE 1045 steel before loading and after 107 cycles versus distance from surface. (a) Shot peened with shot of a hardness of 46 to 50 HRC. (b) Shot peened with shot of a hardness of 54 to 58 HRC. Source: Ref 46–49

Fig. 57

Fig. 58

Haigh diagram. Bending fatigue strength Rf of smooth and notched specimens made from a medium-strength steel versus residual stress. After Ref 1, 62

44 / Effect of Materials and Processing of the triaxial stress state in the interior of the notched specimens. Now, the Goodman relationship holds between points C and D, and residual stress relaxation occurs outside the lightly shaded area. From these relationships, it is expected that the residual stress sensitivity of notched specimens is less than that of smooth specimens. Application to a High-Strength Steel. Figure 59 shows Haigh diagrams for smooth and notched specimens made from a high-strength steel, which are adopted to Fig. 44, 46, and 56. In Fig. 59(a), the data points give the correlation

(a)

(b) Haigh diagrams. Bending fatigue strength Rf of smooth and notched specimens made from quenched plain carbon SAE 1045 steel with different surface conditions. (a) Versus surface residual stress. (b) Versus maximum residual stress

Fig. 59

between the residual stress and the nominal stress amplitude at the surface. In Fig. 59(b), the data points give the correlation between the maximum residual stress and the nominal stress amplitude at the locus of the maximum residual stress. In the range of tensile residual stresses, this is always the surface. The arrows connecting some data points illustrate the residual stress relaxation that occurs during bending fatigue loading. The ultimate tensile strength Rm ⳱ 1910 MPa of smooth specimens was taken from Ref 49. The ultimate tensile strength Rm,no of notched specimens is unknown, but the value 2000 MPa, which results from an extrapolation of the data given in Fig. 44, is reasonable for this highstrength material state and the stress-concentration factor 1.7 (Ref 63, 64). The cyclic yield stresses of smooth and notched specimens are also unknown. However, using the results shown in Fig. 55 (smooth specimens) and Fig. 57(a) (notched specimens), a border line for residual stress relaxation can be obtained. As obvious from the figures and discussed in the previous section, the cyclic loading indicated there causes no residual stress relaxation. The corresponding data points are given in Fig. 59(b) as open square (smooth specimens) and open circle without arrow (notched specimens). Assuming that residual stress relaxation starts at a limiting amount of the minimum or maximum stress irrespective of the fractions of the mean stress and the stress amplitude, one gets the shaded areas in which the residual stresses are stable. These areas are transferred to Fig. 59(a), too. The two open circles connected with an arrow illustrate the change of the amount of the surface residual stress (Fig. 59a) and of the minimum stress (Fig. 59b) during the cyclic loading of notched specimens indicated in Fig. 57(b). In milled specimens, there is also some residual stress relaxation as indicated by the triangles connected with an arrow. Obviously, the amounts of the minimum stresses are reduced to a value corresponding to the border line, confirming this estimation. Extrapolation of this line to zero residual stress yields the values 1785 MPa (smooth specimens) and 1660 MPa (notched specimens), respectively, which are higher than the corresponding yield strengths (Ref 49). Even though there are some uncertainties in establishing the relationships in Fig. 59, the following conclusions can be drawn for a highstrength steel with tensile residual stresses: ● Residual stress relaxation has no influence re-

Haigh diagram. Bending fatigue strength Rf of smooth and notched specimens made from quenched-and-tempered (600 C/2 h) plain carbon SAE 1045 steel with different surface conditions versus surface residual stress

Fig. 60

garding the effect of tensile residual stresses on the fatigue strength. ● The influence of tensile residual stresses on the bending fatigue strength corresponds satisfactorily to the Goodman approximation. This means that the residual stress sensitivity and the mean stress sensitivity of the bending fatigue strength is almost the same. ● In this formalism, the different residual stress sensitivity of smooth and notched specimens, which causes a reduction of the fatigue notch factor with increasing residual stress (see Fig. 54), is related to the different stress states in

smooth and notched specimens via the different ultimate tensile strengths. In the range of compressive residual stresses, the relationships are much more difficult. The fatigue strength of smooth specimens is much less than expected by the Haigh diagrams, regardless of whether the existing surface or the maximum residual stresses are concerned. In the case of shot peened specimens, this finding is clearly related to subsurface crack initiation. Therefore, neither the stress state at the surface (Fig. 59a) nor the stress state in the depth of the maximum compressive stresses (Fig. 59b) is directly relevant for the fatigue strength. Regarding notched specimens, the fatigue strength of shot peened states is much higher than expected by the Haigh diagram, if it is correlated with the surface residual stresses (Fig. 59a). This simply means that crack initiation must occur at the surface, if the specimens are loaded with amplitudes in the range of the fatigue limit. On the other hand, the stress amplitude in the depth of the maximum of the compressive stresses of shot peened specimens is somewhat lower than expected from the Haigh diagram (Fig. 59b). The same holds for the data points of milled specimens, which have maximum compressive residual stresses at the surface. These findings can only be understood if crack initiation and crack propagation or crack arrest are treated separately. This is done in the sections “Concept of Local Fatigue Strength” and “Propagating and Nonpropagating Cracks.” Application to a Medium-Strength Steel. In medium-strength steels, residual stress relaxation definitively influences the relationships in the Haigh diagram. Since the manufacturing process, which generates the macro residual stresses, almost always changes the micro residual stresses and, hence, the local cyclic yield strength, there are no unique borderlines for the onset of residual stress relaxation as assumed in Fig. 58. Nevertheless, Fig. 60 tries to bring the results shown in Fig. 36 and 38 into a Haigh diagram. Regarding smooth specimens, the ultimate tensile strength was taken from Ref 49. In ground specimens with tensile residual stresses, stress relaxation (marked by an arrow) brings the corresponding data point rather close to the Goodman line. The border lines for the onset of residual stress relaxation are constructed using this data point. However, these border lines are not valid for shot peened specimens, in which the residual stresses relax to a much smaller extent than expected as shown by the lower arrow. Obviously, the resistance to residual stress relaxation is enhanced by shot peening, which results in a stronger work hardening and, hence, stronger increase of micro residual stresses than grinding. Work hardening, however, should also increase the fatigue strength at zero residual stress and, hence, should produce deviations from the solid line established with the aid of the data points of ground specimens. However, as already discussed in the paragraphs on medium-


SWT parameter, MPa

strength steel in the section “Evaluation of Experimental Results,” there is a detrimental effect of a very high surface roughness. The second arrow illustrates the correction, which is based on Fig. 47, for this effect. Compressive residual stresses produced by grinding show some relaxation, although their initial value is inside of the border lines. This finding is consistent with the consideration given so far, since work hardening is almost negligible in this specimen. Moreover, the data point corresponding to the relaxed compressive grinding residual stresses still falls below the Goodman line. This finding was already attributed to the low penetration depth of the grinding residual stresses. The residual stress sensitivity of notched specimens with kt ⳱ 1.7 is significantly smaller than that of smooth specimens, even though the consideration is based on the relaxed residual stresses. Therefore, the different residual stress sensitivity of the fatigue strength of smooth and notched specimens, respectively, is not solely based on different residual stress relaxation, and the third conclusion given previously for a highstrength steel is also valid for a medium-strength steel to some extent. From an extrapolation of the Goodman line plotted, an ultimate tensile strength of 1133 MPa is obtained, which is significantly higher than the ultimate tensile strength of smooth specimens. Again, this finding results from the triaxial stress state in the interior of the notched specimens and is consistent with data measured on other mediumstrength steels (Ref 63, 64). Regarding material states with compressive residual stresses, the data point of milled specimens comes rather close to the Goodman line. No measurements were done concerning the stability of this residual stress state. Since the data point falls inside of the border lines, the residual stress state should be stable. Contrarily, there is some relaxation of the compressive residual stresses in ground specimens even though their initial value falls inside of the border lines, too. Again, this is a consequence of different micro residual stress states. Similar to smooth specimens, the data points fall below the Goodman line as a result of the small penetration depth of the com-

1000 800

SAE 1045

600 400

AISI 304

300 200

100 103

Untreated Shot peened Deep rolled 105 106 104 Number of cycles to failure, Nf

107

Smith-Watson-Topper parameter versus number of cycles to failure for specimens made from normalized SAE 1045 and AISI 304 steel in different surface conditions. After Ref 28

Fig. 61

pressive grinding residual stresses. The same holds for notched specimens with kt ⳱ 2.5, g ⳱ 5. The data points of shot peened specimens fall above the expected relationship as a consequence of pronounced work hardening, which increases both fatigue strength and resistance of the compressive residual stresses against relaxation. From the relationships shown in Fig. 60, the following conclusions can be drawn for a medium-strength steel: ● Residual stress relaxation plays a significant

role for the influence of residual stresses on fatigue behavior. ● Residual stress relaxation depends on the work hardening produced by the various manufacturing processes. Not only the amount, but also the penetration depth of work hardening is important. As a consequence, even for one initial material state there are no unique borderlines for the onset of residual stress relaxation. ● If comparable work-hardening states (or micro residual stress states) are concerned, the influence of relaxed residual stresses on the bending fatigue strength corresponds satisfactorily to the Goodman approximation. This means that the relaxed residual stress sensitivity and the mean stress sensitivity of the bending fatigue strength is almost the same. ● In this formalism, the different initial residual stress sensitivity of smooth and notched specimens, which causes a reduction of the fatigue notch factor with increasing residual stress, is related to both the different residual stress relaxation and the different stress states in smooth and notched specimens via the different ultimate tensile strengths.

Damage Parameters As discussed in the section “Lifetime Behavior,” there are some so-called damage parameters that correlate fatigue life with loading parameters. The well-known Manson-Coffin relationship (Eq 5) is not applicable to material states with residual stresses, because it does not account for mean stresses. On the other hand, the Ostergren parameter (Eq 12) and the Smith-Watson-Topper parameter (Eq 11) include the mean stress via the maximum stress. With the limitations already outlined in the previous section, one could try to use these parameters to assess the effect of residual stresses on fatigue life. However, the application of the Ostergren parameter requires the knowledge of the local plastic strain amplitude, which in turn needs sophisticated modeling of the local cyclic elasticplastic deformation behavior. This seems not to be a useful approach. However, the Smith-Watson-Topper parameter (SWT parameter) is easier to evaluate and was used in Ref 28 to account for surface treated steels (normalized SAE 1045 and AISI 304). Figure 61 shows characteristic plots of the SWT parameter versus the number of cycles of stress-controlled tests on both steels

in shot peened as well as deep-rolled conditions in comparison with the untreated states. For each steel, a unique curve is obtained for the three material conditions. Hence, concerning these steels the quantities that are included in the SWT parameter—the maximum stress and the total strain amplitude (see Eq 11)—form a reliable basis for the assessment of the influence of residual stresses on the fatigue life.

Concept of Local Fatigue Strength Basic Relationships. As shown in the previous section, in the paragraphs on applying the Haigh diagram to high-strength and mediumstrength steels, the use of the Haigh diagram for the assessment of the effect of residual stresses on the fatigue behavior has serious limitations. Regarding, for example, smooth specimens made from a high-strength steel, shot peening produces much less improvement in fatigue strength than expected from the residual stress state. This finding is combined with subsurface crack initiation. Regarding medium-strength steel, difficulties arise because not only the (macro) residual stress state is changed by manufacturing processes, but also the micro residual stress state. The latter influences the fatigue strength at zero mean stress and the resistance of the residual stress state against relaxation. Therefore, it is appropriate to look for the local fatigue strength, which depends on the local micro residual stress state, the local macro residual stress state, and (as far as crack initiation at the surface is concerned) on the topography of the surface of the component. Strictly speaking, the local resistance against fatigue crack initiation is concerned, as shown later. The concept of the locally effective fatigue strength, which has its origin in Ref 38 and 39, enables quantitative predictions of the effect of the depth distributions of residual stresses on the locus of crack initiation as well as on the fatigue strength. The basic assumption of the concept is that a crack can only be initiated at or below the surface if the local loading stress exceeds the local fatigue strength. Especially in the case of relatively hard materials, for example, hardened steels, this concept yields to a good estimation of the corresponding properties. For that purpose, it is necessary to have a good knowledge of the depth distributions of the fatigue strength in the residual-stress-free condition R0f (z) as well as of the macro residual stress rrs(z) and the residual stress sensitivity m(z). The locally effective fatigue strength Rf(z) as a function of the distance x from the surface is calculated by the relationship: Rf(z) ⳱ R0f (z) ⳮ m(z) • rrs(z)

(Eq 18)

where the residual stress sensitivity m(z) approaches the mean stress sensitivity M of the Goodman relationship (e.g., Eq 9) if the residual stresses are stable. Then, the residual stress sensitivity is determined approximately by m(z) ⳱

46 / Effect of Materials and Processing R0f (z)/Rm(z) (Ref 39). However, if residual stress relaxation occurs, the residual stress sensitivity m is smaller than the mean stress sensitivity M, if the initial residual stress distribution is used (Ref 39, 62). However, if the relaxed residual stress distribution is used, the residual stress sen-

sitivity m again approaches the mean stress sensitivity M as shown in the paragraphs applying the Haigh diagram to medium-strength steels in the previous section. The depth distributions of the tensile strength Rm(z) and of R0f (z) can be estimated from appropriate correlations with

Notched Residual stress, σrs

Residual stress, σrs

Smooth 0

(a)

0

(b)



N f = 104

σa and Rf,loc

σa and Rf,loc

N f = 104

Nf =

Local fatigue strength Loading stress 0

Nf = 0


(c)


(d)

Distribution of residual stress (a) and (b) and distribution of loading stress and local fatigue strength for loadings in the range of finite and infinite lifetime (c) and (d) for smooth (a) and (c) and notched (b) and (d) specimens made from a high-strength steel

Fig. 62

Propagating crack Not propagating crack

d = 0.6 mm 1000

Rf 800

Loading stresses

1200

d = 0.3 mm

σa and Rf,loc, MPa

σa and Rf,loc, MPa

1200

1000

Rf 800

600

600 0

0.1 0.2 0.3 Distance from surface, mm

0.4

400

0

0

rs

400 800

1200

0.4

0


0.4

400 800

1200 0

(c)


(b) 400 σl, MPa

rs

σl, MPa

(a)

0


0.4 (d)

Distribution of the local fatigue strength and the loading stress for different stress amplitudes with marking of the locus of crack initiation (a) and (b) and distribution of residual stress (c) and (d) for specimens made from a quenched SAE 1045 steel after shot peening with shot with a mean diameter of 0.6 mm (a) and (c) and 0.3 mm (b) and (d), respectively. After Ref 38, 39

Fig. 63

measured depth distributions of the hardness (see e.g., Ref 65). Application to High-Strength Steels. In a high-strength steel, manufacturing processes may generate very large (macro) residual stresses, as shown by several examples in the paragraphs on high-strength steel in the section “Characteristic Examples.” Contrarily, the changes of the micro residual stress state are rather small. Therefore, the local fatigue strength is almost entirely determined by the initial material state and the depth of the (macro) residual stresses. Figure 62(a) and (b) show depth distributions of compressive residual stresses in smooth and notched bending specimens produced by shot peening. In Fig. 62(c) and (d), the resulting depth distributions of the fatigue strength for infinite life and for one arbitrarily chosen finite life are plotted together with the corresponding depth distributions of the loading stress. It becomes clear from this figure that the improvement of the fatigue strength for infinite life of smooth specimens (low stress gradient) by shot peening is small because crack initiation occurs below the surface in a depth with vanishing residual stresses. Contrarily, with increasing stress amplitude, the crack initiation site is shifted toward the surface, and the shot-peeninginduced stresses influence crack initiation and early fatigue crack growth. Hence, there is a large influence of shot peening on the low-cycle fatigue strength and a small influence on the high-cycle fatigue strength. This is shown in Fig. 45(a). Contrarily, crack initiation in notched specimens (high stress gradient) occurs always at the surface and both low-cycle and high-cycle fatigue strength are improved, as shown in Fig. 45(b). The assumption of the local fatigue concept that fatigue life determining cracks initiate only in places where the loading stress exceeds the local fatigue strength is verified by several experimental results (e.g., Ref 38, 39, 62). Figure 63 presents for two series of specimens of the aforementioned investigations from Ref 38 and 39 on hardened and shot peened SAE 1045 steel graphs of the depth distribution of the local fatigue strength (see Fig. 63a and b). Rf,loc can be calculated from the compressive residual stress distributions (Fig. 63c and d) under the assumption of uniform hardness. The closed circles mark the initiation sites of damage-relevant cracks for each load stress distribution, which could be taken from SEM of the fracture surface (see Fig. 24). As can be seen, the actual crack initiation positions agree with the expectation after the concept of the local fatigue strength. For high stress amplitudes (1150 MPa), the cracks that determine fatigue life can initiate at the surface. For lower stress amplitudes (1150 MPa), the damage behavior is changed. Of course, stress amplitudes between 1000 and 1100 MPa are able to initiate cracks at the surface (open circles in Fig. 58a and b). However, these stress amplitudes are too small to propagate the cracks into greater depth because of the high compres-

Residual Stresses and Fatigue Behavior / 47 sive residual stresses existing there. This aspect is treated in more detail in the paragraphs on high-strength steel in the section “Propagating and Nonpropagating Cracks.” At stress amplitudes below 1000 MPa, cracks are generated only beneath the surface as expected by the plotted straight lines of the loading stress in comparison with the courses of the local fatigue strength (Fig. 62a and b). The fatigue strength Rf is determined by the maximum loading stress amplitude, which in any cross section of the specimen exceeds the local fatigue strength and initiates a crack that is able to propagate. The corresponding distributions are plotted in Fig. 63(a) and (b) as dashed straight lines. Figure 64 applies the concept of local fatigue strength to shot peened smooth and notched specimens according to Fig. 55 to 57. In notched specimens peened with shot of low (Fig. 64a) and high (Fig. 64b) hardness and loaded in the range of the fatigue strength, crack initiation is predicted at the notch root, as actually observed. However, the surface loading stress amplitude is much higher than the surface fatigue strength. The same result is obtained from the Haigh diagram in Fig. 59(a). Therefore, one has to assume that loading stress amplitudes below the fatigue limit can initiate a crack at the surface

and that the fatigue strength is not determined by the maximum loading stress amplitude that does not initiate a crack. This shows the limitations of the concept of the local fatigue strength and is treated in more detail in the paragraphs on high-strength steel in the section “Propagating and Nonpropagating Cracks.” Figure 64(c) shows that crack initiation in smooth specimens is expected below the surface where the local fatigue strength is hardly increased by compressive residual stresses. This is verified by metallographical investigation (Ref 46, 49). This is the reason for the small improvement of the bending fatigue strength by shot peening shown in Fig. 45, 46, 56, and 59. However, from Fig. 45(a) it becomes clear that shot peening significantly improves finite fatigue life. This finding cannot be understood on the basis of the local fatigue strength alone and is treated in the paragraphs on high-strength steel in the section “Propagating and Nonpropagating Cracks.” In the case of notched specimens finished by milling (see Fig. 45b, 46, and 56), the concept of local fatigue strength predicts crack initiation below the surface, because the gradient of the residual stresses is steeper than the gradient of the loading stresses. Hence, the increase of the

σa and Rf,loc, MPa

1500 Local fatigue strength 1000

Propagating and Nonpropagating Cracks

Loading stress

500

0 0

0.2

0.4

0

Distance from surface, mm (a)

0.2

0.4

0


0.2

0.4


(b)

(c)

Distribution of the local fatigue strength and the loading stress with marking of the locus of crack initiation for notched (a) and (b) and smooth (c) specimens made from a quenched SAE 1045 steel after shot peening with a shot of a hardness of 46 to 50 HRC (a) and 54 to 58 HRC (b) and (c), respectively. Source: Ref 49

Fig. 64

σa and Rf,loc, MPa

1500

1000

Local fatigue strength

500 Loading stress 0 0

0.2

0.4

0

Distance from surface, mm (a)

0.2

0.4

Distance from surface, mm (b)

Distribution of the local fatigue strength and the loading stress with marking of the locus of crack initiation for notched (a) and smooth (b) specimens made from a quenched-and-tempered (600 C/2 h) SAE 1045 steel after shot peening with a shot of a hardness of 46 to 50 HRC

Fig. 65

bending fatigue strength is smaller than expected in view of the high surface compressive residual stresses (see the Haigh diagram in Fig. 64a), but larger than in shot peened smooth specimens with subsurface crack initiation. This is a consequence of the higher loading stress gradient in notched specimen compared to smooth specimens. However, crack initiation below the surface of these specimens was not proved (Ref 49). Application to Medium-Strength Steels. The application of the concept of the local fatigue strength to medium-strength steels is somewhat more difficult compared to high-strength steels because residual stress relaxation becomes important. Therefore, a knowledge of the initial depth distribution of the residual stresses and of the residual stress sensitivity m or of the relaxed residual stress distribution is necessary. In Fig. 65, the concept is applied to shot peened smooth and notched specimens made from quenchedand-tempered SAE 1045 steel. The initial and relaxed residual stress distributions are given in Fig. 52 and 53. Again, in notched specimens (Fig. 65a) crack initiation at the surface is predicted as actually observed. Regarding smooth specimens, crack initiation below the surface is expected. Contrarily, crack initiation at the surface is found in metallographical investigation. In both cases, the difference between local loading stress and local fatigue strength is small throughout the depth range under consideration. Therefore, factors such as the high roughness of the smooth specimens may well account for the deviation of the expected locus of crack initiation.

General Remarks. It is well known that in notched specimens or components that are loaded in the range of the fatigue strength, cracks may initiate in the root of sharp notches and may arrest in a certain depth, where the driving force for crack propagation falls below its threshold value because of the steep drop of the loading stress. In most cases, such sharp notches are not relevant for components (Ref 57, 66). However, in the presence of high residual stresses, the interaction of loading stresses and residual stresses may produce strong gradients of the driving force for crack propagation making crack arrest possible even in notches with low stress-concentration factor. On the other hand, in smooth specimens with large compressive residual stresses at and below the surface, crack initiation may occur below the surface because the gradient of loading stresses is small. Then, the question arises whether or not the crack can propagate toward the surface where its propagation is hindered by the residual stress field. Both situations are illustrated by the Haigh diagrams in Fig. 59. In the case of shot peened smooth specimens, the fatigue strength falls below the values expected by the Haigh diagrams, because crack initiation occurs below the surface, where no ben-

48 / Effect of Materials and Processing eficial effect of the compressive residual stresses is effective. Contrarily, the combination of surface loading stress and surface residual stress occurring at the notch root of specimens with kt ⳱ 1.7 (Fig. 59a) falls significantly above the corresponding Goodman line. As already men-

∆Keff, MPa m

8

(Eq 19)

DKeff ⳱ kt • rn,a • 冪p • aY ⳱ Kmax Without residual stresses

4 Range of ∆Kth,eff 0 0

0.05

0.1

0.15

0.2

0.25

0.3

Distance from surface, mm Range of effective stress intensity factor DKeff with and without consideration of the residual stresses versus distance from surface for ground notched specimens made from a quenched SAE 1045 steel at cyclic bending loading (kt ⳱ 1.7, g ⳱ 2)

Fig. 66

(Eq 20)

for smooth (kt ⳱ 1) and notched (kt 1) specimens without residual stresses. rn,a is the nominal stress amplitude. If residual stresses are present, the maximum stress is increased or decreased, depending on the sign and the amount of the residual stresses, leading to: DKeff ⳱ (kt • rn,a Ⳮ rrs) • 冪p • aY ⳱ Kmax

(Eq 21)

if Kmin 0 or: DKeff ⳱ kt • Drn • 冪p • aY

60 Without residual stresses ∆Keff, MPa m

DKeff ⳱ Kmax ⳮ Kop DKth,eff

(see Eq 16). The following concerns alternating bending fatigue (R ⳱ ⳮ1). In a rough approximation, it is assumed that Kop equals zero, resulting in:

With residual stresses

12

tioned, this means that cracks initiate at the notch root, but are arrested below the surface. A crack is arrested when the driving force for its propagation falls below the threshold value:

Initial residual stresses

40

Relaxed residual stresses


0.1

0.2

0.3

0.4

0.5

0.6

Distance from surface, mm Range of effective stress intensity factor DKeff without and with consideration of the initial and the relaxed, respectively, residual stresses versus distance from surface for shot peened (shot of a hardness of 54 to 58 HRC) notched specimens made from a quenched SAE 1045 steel at cyclic bending loading (kt ⳱ 1.7, g ⳱ 2)

Fig. 67

(Eq 22)

if Kmin ⱖ 0. Application to a High-Strength Steel. In a high-strength SAE 1045 steel, literature data for the threshold value Kth,eff fall in the range from 2.2 to 3.2 MPa 冪m (Ref 67). As a first example, ground notched specimens (kt ⳱ 1.7, g ⳱ 2) with tensile residual stresses (see Fig. 43, curve with open circles) are treated. Concerning the half-elliptical cracks that initiate at the notch root, a geometry factor Y ⳱ 1 is assumed. The interaction of this residual stress state with the loading stress amplitude ra ⳱ 230 MPa—which corresponds to the fatigue strength—results in the depth distribution of DKeff shown in Fig. 66. In a depth of 5 lm only, DKeff exceeds the threshold value. Therefore, a crack that initiates at the notch root will always propagate into the interior of the specimen, and the fatigue limit

40

Without residual stresses

30


∆Keff, MPa m

∆Keff, MPa m

15

Initial residual stresses Range of ∆Kth,eff

20 10

Initial residual stresses


10

Range of ∆Kth,eff

5

Crack initiation

0 0

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.2

0.4

0.6

0.8

1.0

1.2


Distance from surface, mm Range of effective stress intensity factor DKeff without and with consideration of the initial and the relaxed, respectively, residual stresses versus distance from surface for shot peened (shot of a hardness of 46–50 HRC) notched specimens made from a quenched SAE 1045 steel at cyclic bending loading (kt ⳱ 1.7, g⳱ 2)

Fig. 68

Range of the effective stress intensity factor DKeff for subsurface crack initiation without and with consideration of the initial and the relaxed, respectively, residual stresses versus distance from surface for ground and additional shot peened smooth specimens made from a quenched SAE 1045 steel at cyclic bending loading (g ⳱ 0.4)

Fig. 69

corresponds to the maximum stress amplitude that does not initiate a crack. This is in full agreement with the Haigh diagram in Fig. 59(a). It is interesting to note that DKeff has a local maximum in a depth of 80 lm. Up to a depth of 150 lm, the residual stress field increases significantly DKeff as compared with the loading of a specimen without residual stresses (dotted line). A completely different situation prevails regarding shot peened notched specimens (kt ⳱ 1.7, g ⳱ 2) with the initial and the relaxed residual stress distributions shown in Fig. 57(b). As shown in paragraphs on high-strength steel in the sections “Haigh Diagram” and “Concept of Local Fatigue Strength,” a crack will initiate at the notch root if a specimen is loaded in the range of the fatigue strength. Hence, if the crack has the length a, the loading stress and the residual stress in the distance a from the surface determines if the crack will continue propagation or not. In Fig. 67, DKeff is plotted versus the distance from the surface. If the initial residual stress distribution is concerned, DKeff becomes zero at a depth of 40 lm, and higher stress amplitudes than the measured bending fatigue strength would be necessary to propagate a crack into the interior of the specimen. However, if the relaxed residual stress distribution is concerned, DKeff approaches the threshold range between 50 and 200 lm below the surface, and cracks may or may not propagate. Hence, the fatigue limit corresponds to the boundary between propagating or nonpropagating cracks that initiate at the notch root. It is interesting to note that at depths greater than 0.3 mm, DKeff becomes much larger than in Fig. 66 as a consequence of the high loading amplitude. This means that the strong increase of finite fatigue life by shot peening is entirely based on very small crack propagation rates at small distances from surface. Regarding shot peened notched specimens with the residual stress distributions shown in Fig. 57(a), almost no residual stress relaxation occurs during loading in the range of the fatigue limit. Therefore, the depth distributions of DKeff corresponding to the initial and the relaxed residual stress distributions shown in Fig. 68 are almost the same. At a depth of 40 lm, DKeff becomes zero and exceeds the threshold value only at a depth of 170 lm. Therefore, one would expect that cracks could still be arrested at stress amplitudes higher than the measured bending fatigue strength. This shows the limitations of the simple estimation given here. Figure 64(c) shows that crack initiation in shot peened smooth specimens with the residual stress distribution plotted in Fig. 55 occurs below the surface at a depth of 500 lm. For the following rough estimation, it is assumed that the crack has a circular shape (see Fig. 24), that it propagates with the same rate toward the surface as well as into the interior of the specimen, and that the residual stresses in depths greater than 500 lm are zero. If the loading stress in the depth of the crack front and a geometry factor Y ⳱ 0.63 (Ref 68) are used for the calculation of DKeff, one finds the relationship shown in Fig.


8 With residual stresses ∆Keff, MPa m

6

4



0.05

0.1

0.15

0.2

0.25

0.3

Distance from surface, mm Range of the effective stress intensity factor DKeff with and without consideration of the residual stresses versus distance from surface for ground notched specimens made from a quenched-and-tempered (600 C/2 h) SAE 1045 steel at cyclic bending loading (kt ⳱ 1.7, g ⳱ 2)

Fig. 70

∆Keff, MPa m

20


15

Initial residual stresses Relaxed residual stresses

10

Range of ∆Kth,eff

5 0 0

0.1

0.2

0.3

0.4

Distance from surface, mm Range of the effective stress intensity factor DKeff without and with consideration of the initial and the relaxed, respectively, residual stresses versus distance from surface for ground and additional shot peened notched specimens made from a quenched-andtempered (600 C/2 h) SAE 1045 steel at cyclic bending loading (kt ⳱ 1.7, g ⳱ 2)

Fig. 71

Relaxed residual stresses Without residual stresses

∆Keff, MPa m

16 12 8

Initial residual stresses 4 Range of ∆Kth,eff

0 0


0.5

of the effective stress intensity factor Fig. 72 Rangewithout and with consideration of the iniDKeff tial and the relaxed, respectively, residual stresses versus distance from surface for ground and additional shot peened smooth specimens made from a quenched-andtempered (600 C/2 h) SAE 1045 steel at cyclic bending loading (g ⳱ 0.4)

between 300 and 200 lm below the surface and finally crack arrest. However, in this stage of crack propagation the crack extension will be large compared to the depth of the compressive residual stresses. Therefore, loading stress redistribution will occur, as will relaxation of the compressive residual stress field in the process zone ahead of the crack front. The crack will continue to propagate toward the surface causing final failure. Then, the fatigue limit is correlated with the maximum stress amplitude that does not cause crack initiation below the surface. Therefore, the improvement of the fatigue strength of smooth specimens by shot peening is limited, as shown in Fig. 45(a). However, Fig. 69 illustrates that the overall value of DKeff and, hence, the driving force for crack propagation is rather small (compare, for example, Fig. 69 with Fig. 66 in view of the very different loading stress amplitudes). Therefore, already in the transition from infinite to finite fatigue life—where crack initiation still occurs below the surface (see Fig. 63)—there is a strong influence of shot peening on fatigue life, as shown also in Fig. 45(a). The influence of shot peening on finite fatigue life increases with increasing stress amplitude, because the crack initiation site is shifted toward the surface, as discussed in the paragraphs on high-strength steel in the section “Concept of Local Fatigue Strength.” Application to a Medium-Strength Steel. In a medium-strength SAE 1045 steel, the threshold value Kth,eff ranges from 2.3 to 3.3 MPa 冪m (Ref 67). In the following, ground notched specimens (kt ⳱ 1.7, g ⳱ 2) with tensile residual stresses (see Fig. 35, curve with open circles), are treated. The interaction of this initial residual stress state with the loading stress amplitude ra ⳱ 143 MPa—which corresponds to the fatigue strength—results in the depth distribution of DKeff shown in Fig. 70. At a depth of 15 lm, DKeff exceeds the range of threshold values. Therefore, a crack that initiates at the notch root will always propagate into the interior of the specimen, and the fatigue limit corresponds to the maximum stress amplitude that does not ini-


69. It becomes obvious that a crack, once initiated, can propagate. Regarding crack propagation toward the surface, the simple model predicts very slow crack growth in the range

1200

R m = 1650 MPa

Final failure 1000

Transition range 1400 MPa No final failure 1150 MPa

800

600 400 0

0.2

0.4

0.6

0.8

1.0

1.2

Length of arrested crack, mm Influence of the nominal bending stress amplitude on the length of arrested cracks in deeprolled notched specimens (kt ⳱ 2) made from SAE 5135 steel with the ultimate tensile strengths indicated. After Ref 66

Fig. 73

tiate a crack. Again, similar to the quenched state (see Fig. 66), DKeff has a local maximum in a depth of 70 lm, and up to a depth of 150 lm the residual stress field increases significantly DKeff as compared with the loading of a specimen without residual stresses (dotted line). The corresponding relationships for shot peened notched specimens with the residual stress distributions shown in Fig. 53 are given in Fig. 71. The loading stress amplitude ra ⳱ 310 MPa which corresponds to the bending fatigue strength, is considered. From Fig. 60 it becomes clear that crack initiation at the notch root occurs under such loading conditions because the corresponding data point (open square) falls significantly above the Goodman relationship. On the basis of the initial residual stress distribution, there is no driving force for the propagation of such a crack up to a distance of 170 lm from the notch root. However, if the distribution of the relaxed residual stresses is considered, DKeff comes close to the threshold in depths ranging from 30 to 200 lm. Therefore, the fatigue limit corresponds to a loading condition where cracks that initiate at the notch root may propagate or not. In the case of smooth shot peened specimens with the residual stress distributions shown in Fig. 52, it is difficult to determine on the basis of the concept of the local fatigue strength whether crack initiation occurs below or at the surface, if the loading approaches the fatigue limit (see paragraph on medium-strength steel in the section “Concept of Local Fatigue Strength” and Fig. 65b). Actually, crack initiation at the surface is observed that is favored by the rather high roughness. Figure 72 gives the depth distribution of DKeff for the loading stress amplitude ra ⳱ 414 MPa, which corresponds to the bending fatigue limit. Regarding the initial residual stress state, the longest nonpropagating crack would have a length of 250 lm. Due to stress relaxation, this value is reduced by 50%. Still, rather long cracks have to be formed during the initiation stage to be able to propagate into the interior of the specimen. The difference between the minimum loading stress amplitude for crack initiation at the root of notched specimen and the maximum loading stress amplitude at which crack arrest is observed may be very large in deep-rolled specimens, which have rather small or even tensile residual stresses at the notch root, but large compressive residual stresses down to a relatively great depth below the surface. Then, the length of an arrested crack will strongly depend not only on the depth distribution of the residual stresses, but also on the loading stress amplitude. This is proved by Fig. 73 concerning notched specimens (kt ⳱ 2) made from differently heat treated SAE 5135 steel with the ultimate tensile strength indicated (Ref 66). The diagram gives the length of arrested cracks as a function of the nominal stress amplitude. The higher the strength of the material state, the less the crack length increases with increasing stress amplitude because the amount and the stability of the com-

50 / Effect of Materials and Processing pressive residual stresses produced by deep rolling increase with increasing hardness. From this figure it becomes clear that the large increase of the notch fatigue strength visible in Fig. 41 is almost entirely based on an increase of the resistance against crack propagation produced by deep rolling. In view of the relationships presented so far, it is interesting to look again at Fig. 39 and 40. The lowest bending fatigue limit was determined with ground specimens having low tensile residual stresses at the surface (curve 1 in both figures). An increase of 324 MPa (curve 6 in Fig. 39) was achieved with specimens that were shot peened according to curve 4 in Fig. 40 and from which a surface layer of 100 lm thickness was

removed electrolytically, resulting in a shift of the maximum compressive residual stresses into the surface. Taking the slope of the straight line for smooth specimens, g ⳱ 0.4, in the range of (initial) tensile residual stresses in Fig. 36 as a rough approximation, one would expect a difference of both specimen series of 316 MPa caused by the different residual stresses. On the other hand, on the basis of the Goodman line in Fig. 60, one would expect a much higher difference of 429 MPa. This shows that stress relaxation occurs in this medium-strength steel state, as expected. Anyway, the bending fatigue limit of both specimen series is determined by crack initiation at the surface. The specimens corresponding to curve 5 in both figures have a lower

30 Without residual stresses σn,a = 640 MPa σn,a = 600 MPa

∆Keff, MPa m

Initial residual stresses 20 Condition 6 σn,a = 640 MPa

Condition 5 σn,a = 600 MPa

Assumed relaxed residual stresses

10

Range of ∆Kth,eff

0 0

0.1


0.5

0.6

Range of the effective stress intensity factor DKeff without and with consideration of the initial and the relaxed, respectively, residual stresses versus distance from surface for (corresponding to Fig. 39) shot peened smooth specimens made from a blank-hardened AISI 5115 steel at cyclic bending loading

Fig. 74

ηrs

ηls Smooth

Fatigue strength, Rf

kt Rh

fatigue limit, but higher finite fatigue lives than the specimens corresponding to curve 6. Applying the same procedure with the aid of Fig. 36 as above to the surface residual stress state, an increase of the bending fatigue limit of 220 MPa compared to ground specimens is expected. Actually, a difference of 279 MPa is determined. This finding means that the bending fatigue limit is not determined by crack initiation at the surface, but by the largest amplitude at which crack arrest below the surface occurs. These relationships become more clear in Fig. 74. There, DKeff for surface cracks developing in conditions 5 and 6 at nominal stress amplitudes corresponding to the bending fatigue strength are plotted as a function of the distance from the surface. Regarding the initial residual stress distribution, cracks smaller than 320 lm (condition 5) or 100 lm (condition 6) would not be able to propagate. Actually, stress relaxation occurs, the extent of which, however, is not given in Ref 54 to 56. If it is assumed that the residual stresses relax by 50%, one gets the curves for the relaxed residual stress state in the figure. Now, one can see that a crack once initiated in condition 6 will continue propagation. Hence, the bending fatigue strength of this condition is determined by the resistance against crack initiation, as stated above. Contrarily, in condition 5 the bending fatigue strength corresponds to the maximum nominal stress amplitude at which crack arrest below the surface occurs. From these considerations, it becomes clear that the depth distribution of relaxed residual stresses must be taken into account to gain a reliable assessment of the influence of residual stresses on the fatigue behavior of mediumstrength steel. Frequently, these data are not known. Then, the use of initial tensile residual stresses for the dimensioning of components is a conservative procedure, because their detrimental effect on the fatigue behavior of a component will be reduced by residual stress relaxation. However, the beneficial effect of compressive residual stresses will be overestimated by using the initial values, and this results in a nonconservative dimensioning. Therefore, it is important to estimate the remaining residual stresses conservatively, for example with the article “Stability of Residual Stresses” in this Handbook.

rs

σmicro

ηrs

ηls

Summary and Recommendations kt Rh

Notched Smooth rs

σmicro

ηls

Notched

Smooth

kt

Rh

Notched

Some important conclusions that can be drawn from this article are illustrated by Fig. 75, in which the fatigue strength Rf is plotted as a function of the macro residual stress. The following parameters are regarded: ● The material strength; a low-strength steel

Residual stress ,σrs Influence of the macro residual stress and some other parameters on the fatigue strength of smooth and notched specimens made from a low-strength steel (lower band), a medium-strength steel (middle band), and a highstrength steel (upper band)

Fig. 75

(for example, a normalized steel, lower band in the figure), a medium-strength steel (for example, a quenched-and-tempered (at a medium temperature) steel, middle band in the figure), and a high-strength steel (a quenched


● ● ● ● ●

or quenched-and-tempered (at a low temperature) steel, upper band in the figure) are concerned The depth distribution of the macro residual stress rrs, characterized by its sign, magnitude, and gradient grs The depth distribution of the micro residual stress rrs micro The notch factor kt (smooth and mildly notched specimens are regarded in the figure) The gradient of the loading stress gls The surface topography, characterized by the roughness height Rh

Low-Strength Steel In a low-strength steel, there will be no or very little influence of the macro residual stress, because it is relaxed more or less completely if the cyclic loading approaches the fatigue strength (see Fig. 32 and 48). A change of the micro residual stress state by work hardening may significantly increase Rf since the resistance against cyclic plastic deformation and hence, crack initiation increases (see Fig. 31). Then, also the resistance against macro residual stress relaxation is raised resulting in a certain sensitivity of the work-hardened zone to macro residual stress. This may be detrimental or beneficial (see Fig. 33b) for Rf depending on the sign and the magnitude of the macro residual stress. The influence of the surface topography is rather small in a low-strength steel (see Fig. 47). The fatigue notch factor kf is significantly smaller than the notch factor kt because cyclic plastic deformation and stress redistribution occur in the notch root (see Fig. 32). With increasing loading stress gradient at a given kt, the fatigue strength increases due to the decrease of the highly stressed volume of the component or specimen (compare kt ⳱ 2.5, g ⳱ 2 with kt ⳱2.5, g ⳱ 5 in Fig. 32).

Medium-Strength Steel In a medium-strength steel, there is a significant influence of the macro residual stress on Rf since only a small part of rrs relaxes during cyclic loading in the range of the fatigue limit (see Fig. 36, 38, 51a, and 52). However, in the lowcycle fatigue range, relaxation becomes more complete with increasing amplitude, and the influence of the macro residual stress vanishes (see Fig. 34, 37, 39, 51b). Tensile residual stresses are always detrimental to Rf. Therefore, in the presence of large tensile residual stresses a medium-strength steel may have equal or even lower fatigue strength than a low-strength steel (compare Fig. 32 with 36). If relaxed tensile residual stresses are concerned, the residual stress sensitivity m of the fatigue strength approaches the mean stress sensitivity M (see Fig. 60). In material states of similar hardness loaded in the range of the fatigue limit, compressive residual stresses relax stronger than tensile ones simply because of the different corresponding stress am-

plitudes. However, the micro residual stress state may be changed significantly by the processes that generate the macro residual stress. Hence, in a medium-strength steel the local resistance to residual stress relaxation may be quite different even if the same initial material state is concerned, and unique borderlines for the onset of residual stress relaxation do not exist (see Fig. 60). A significant benefit from compressive residual stresses is only obtained if their penetration depth is sufficiently high and/or their gradient is sufficiently low as compared to the gradient of the loading stresses. Therefore, compressive residual stresses produced by grinding do hardly influence the fatigue strength of smooth and notched specimens (see Fig. 36). Contrarily, compressive residual stresses generated by deep rolling or shot peening increase the notch fatigue strength (see Fig. 38, 39, and 41). The fatigue strength of smooth specimens is less improved, if subsurface crack initiation occurs. Then, the fatigue strength of notched specimens may even be higher than corresponding values of smooth specimens (see Fig. 41). This means that the fatigue notch factor kf becomes less than unity. At vanishing residual stresses, kf comes rather close to kt if the loading stress gradient is small, but is significantly less at higher gls values. With increasing tensile residual stresses, the fatigue notch factor is reduced again, as expected on basis of the Goodman relationship for smooth and notched specimens (see Fig. 58 and 60). There is a considerable influence of the surface roughness on the fatigue strength, as shown in Fig. 47.

High-Strength Steel In high-strength steels, stress relaxation during cyclic loading in the range of the fatigue strength only occurs in notched specimens bearing very high compressive residual stresses. Then, the resulting fatigue strength is also high, and during corresponding cyclic loading very high magnitudes of the minimum stress occur, which leads to some residual stress relaxation (see Fig. 57b). Contrarily, in the range of high tensile residual stresses and cyclic loadings that lead to infinite life or to technically relevant lifetimes the occurring maximum stresses are much lower and no residual stress relaxation is observed even in the range of low-cycle fatigue. Consequently, the residual stress sensitivity and the mean stress sensitivity of Rf are identical (see Fig. 59), and the fatigue strength is strongly reduced with increasing tensile residual stress. This is also true for the finite fatigue life (see Fig. 42). In the range of compressive residual stresses, complex relationships exist. A strong effect of rrs will only occur if cracks are initiated at the surface. However, in thick smooth specimens or components cyclically loaded in the range of the fatigue strength, the loading stress gradient is usually lower than the gradient of the local fatigue strength, which depends on the depth distribution of the residual stresses. Consequently, cracks are initiated below the surface

(see Fig. 62a and c, 63, and 64c) and the improvement of the fatigue strength even by high compressive residual stresses is limited (see Fig. 45a, 46, and 56). With increasing stress amplitude and hence loading stress gradient, the crack initiation site is shifted to the surface. Therefore, the finite fatigue life is much more improved than the fatigue strength (see Fig. 62a and c, 63, and 45d). In notched specimens, the loading stress gradient is larger than in smooth ones. If high compressive residual stresses with a sufficient depth and/or a small gradient exist, crack initiation will occur in the notch root resulting in a strong improvement of the fatigue strength (see Fig. 64a and b, 45b, 46, and 56). However, if the penetration depth of the compressive residual stresses is low and therefore the gradient of the local fatigue strength high—for example, after grinding—the improvement of the notch fatigue strength will be small (see Fig. 44 and 59). Frequently, after shot peening or deep rolling, maximum compressive residual stresses occur below the notch root. Then, the fatigue strength may not be determined by the maximum cyclic loading, which does not result in crack initiation, but by the maximum cyclic loading at which crack arrest below the surface is possible (see Fig. 67, 68, and 73). As a consequence of all these relationships, the fatigue notch factor may vary strongly in the presence of compressive residual stresses regarding one-notch geometry and may take values ranging from less than unity to the notch factor kt, as sketched in Fig. 75. In fact, regarding smooth and notched specimens, Fig. 44 and 54 prove that kf of ground specimens with compressive residual stresses produced by grinding approaches kt. From Fig. 56 it can be deduced that kf of shot peened specimens approaches unity. At vanishing residual stresses, kf comes close to kt as expected in a high-strength steel. With increasing tensile residual stress, the fatigue notch factor is reduced and finally approaches unity (see Fig. 44 and 54). Again, this finding is in correspondence with the Goodman relationship for smooth and notched specimens (see Fig. 58 and 59). The surface roughness has principally a large influence on the fatigue strength of high-strength steel, as shown in Fig. 47. On the other hand, in practice the roughness height of hard steel is rather low even after mechanical surface treatments such as shot peening.

Recommendations From all of these relationships, some recommendations may be deduced. In medium- and high-strength steels tensile macro residual stresses must strictly be avoided since they always promote crack initiation and crack propagation and are detrimental to the fatigue strength and—at least in higher strength steel—to finite fatigue life. In a low-strength steel, the influence of tensile macro residual stresses is usually small or negligible, and the change of the micro residual stress state by work hardening is much more important. In most cases, work hardening will be

52 / Effect of Materials and Processing beneficial for fatigue strength and—if the micro residual stress state is sufficiently stable—for finite fatigue life. However, processes must be avoided in which strong work hardening is combined with the generation of tensile residual stresses. Then, residual stress relaxation during cyclic loading will be incomplete, and the detrimental influence of tensile residual stresses on the fatigue strength will appear. The beneficial influence of compressive macro residual stresses ranges from almost nil to the full extent expected after the mean stress sensitivity of the material state under consideration and depends on the wholeness of the parameter considered in Fig. 75. In a low-strength steel, it is recommended to use processes in which the generation of compressive residual stresses is combined with strong work hardening. Then, there will be on one hand the beneficial influence of work hardening on the reduction of cyclic plasticity and the increase of the materials resistance against crack initiation. On the other hand, the resistance against residual stress relaxation will also increase, resulting in some beneficial influence of the compressive macro residual stresses on crack initiation and crack propagation. One example is deep rolling (see Fig. 33). Another example would be shot peening. However, shot peening of a low-strength steel will produce a rather rough surface, and this will eventually counterbalance a large part of the beneficial influence on the fatigue behavior. In medium-strength steels it is also recommended to utilize processes that produce both work hardening and compressive macro residual stresses. Again, deep rolling (see Fig. 41) or shot peening (see Fig. 37 and 39) can serve as examples. Now, for a significant effect it is necessary to adjust the penetration depth of the macro residual stresses and the width of the work-hardened zone to the depth distribution of the loading stress. Clearly, this is impossible in push-pull loading of smooth specimens or components (gls ⳱ 0) and very difficult in any cyclic loading of thick smooth specimens or components, where gls is rather small. Then, some improvement of the fatigue behavior will be obtained because crack initiation at the surface is retarded or crack initiation is shifted below the surface (see Fig. 37a and Fig. 41, smooth specimens). However, in notched or rather thin smooth specimens or components with higher gls it is possible and recommended to produce a depth distribution of the macro and micro residual stresses and, hence, of the local fatigue strength that ensures that crack initiation can only occur at the surface. Then, a strong improvement of the fatigue strength and finite fatigue life is possible by one of two mechanisms. On one hand, the resistance of the steel against crack initiation and growth of very short cracks may strongly be increased by a smooth surface, strong work hardening, and maximum compressive residual stresses at the surface. Examples are given in Fig. 37(b) (shot peened notched specimens) and Fig. 39 (condition 6, shot peened smooth specimens). In these cases, the fatigue

strength is determined by the maximum loading stress amplitude that does not initiate a crack at the notch root. On the other hand, by high compressive stresses below the surface, the resistance against propagation of cracks with lengths up to the distance of the residual stress maximum from the surface may strongly be increased. Again, strong work hardening, is essential to prevent the compressive residual stresses as much as possible from relaxation. Examples are given in Fig. 39 and 40 (condition 5, shot peened smooth specimens) and Fig. 41 and 73 (deeprolled notched specimens). In these cases, the fatigue strength is determined by the maximum loading stress amplitude at which crack arrest below the surface is obtained. In high-strength steels, residual stress relaxation is negligible except for extreme conditions that were discussed above (see Fig. 57b). Apart from this item, principally the same relationships as just discussed are valid. Again, it is difficult to achieve a large improvement of Rf in thick smooth specimens or components, since crack initiation will occur below the surface (see Fig. 56, 63, and 64c). However, a significant improvement of finite fatigue life in the low-cycle fatigue range may be obtained, since crack propagation toward the surface is hindered by the high compressive residual stresses (see Fig. 69) and/or the crack initiation site is shifted to the surface as a result of the increasing loading stress gradient (see Fig. 63). In thin smooth or in notched specimens and components it is recommended to produce high compressive residual stresses with a large penetration depth by processes such as shot peening, deep rolling, and others described in this Handbook. Then, crack initiation and early crack growth is forced to occur at the surface, and enormous increases of the fatigue strength are obtained by one of the two mechanisms described previously. However, by application of the aforementioned processes to a high-strength steel, frequently rather small surface compressive residual stresses are obtained and maximum values of |rrs| occur below the surface. Then, the second mechanism (crack arrest below the surface) is solely effective (see Fig. 67 and 68), and the fatigue strength may be much higher than expected by the surface residual stress and loading state plotted in a Haigh diagram (see Fig. 59a). Regarding surface roughness, numerous investigations exist. The interaction of an increased roughness with tensile residual stresses will always be detrimental to the fatigue strength and to finite fatigue life, especially in highstrength steels. In the presence of compressive residual stresses, different influences exist. If the fatigue strength is entirely and the finite fatigue life mainly determined by crack initiation at the surface, there will be decisive influence of the surface roughness. A much smaller influence of surface roughness, however, may exist if the fatigue strength is determined by crack initiation or crack arrest below the surface or if the finite fatigue life is mainly influenced by crack propagation below the surface. If compressive resid-

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52. B. Syren, Dr.-Ing. Thesis, University Karlsruhe (TH), 1975 53. H. Traiser and K.-H. Kloos, Z. Werkstofftechn., Vol 16, 1985, p 135–143 54. R. Schreiber, H. Wohlfahrt, and E. Macherauch, Arch. Eisenhu¨ttenwes., Vol 49, 1978, p 207–210 55. R. Schreiber, H. Wohlfahrt, and E. Macherauch, Arch. Eisenhu¨ttenwes., Vol 48, 1977, p 653–657 56. H. Wohlfahrt, Mechanical Surface Treatments, H. Wohlfahrt and P. Krull, Ed., Wiley-VCH, Weinheim, Germany, 2000, p 55–84, in German 57. K.-H. Kloos, B. Fuchsbauer, and J. Adelmann, J. Fatigue, Vol 9, 1987, p 35–42 58. P. Starker and E. Macherauch, Z. Werkstofftechn., Vol 14, 1983, p 109–115 59. P. Starker, Dr.-Ing. Thesis, University Karlsruhe (TH), 1981 60. A. Navarro and E.R. de los Rios, Philos. Mag. A, Vol 57 (No. 1), 1988, p 15–36 61. K.J. Miller and E.R. de los Rios, The Behavior of Short Fatigue Cracks, Mechanical Engineering Publications Limited, London, UK, 1986 62. B. Scholtes, Structural and Residual Stress Analysis by Nondestructive Methods: Evaluation, Application, Assessment, V. Hauk, Ed., Elsevier Science B.V., Amsterdam, 1997 63. W. Backfisch and E. Macherauch, Arch. Eisenhu¨ttenwes., Vol 50, 1979, p 167–171 64. K. Wellinger and D. Dietmann, Calculation of Strength, A. Kroener Verlag, Stuttgart, 1969, in German 65. B. Winderlich, Mater.wiss. Werkst.tech., Vol 21, 1990, p 378–389 66. K.H. Kloos, Notches and Structural Durability, H. Nowack, Ed., Deutscher Verband fu¨r Materialforschung und-pruefung e.V., 1989, p 7–40, in German 67. J. E. Hoffmann and D. Loehe: to be published 68. T. Fett and D. Munz, Stress Intensity Factors and Weight Functions, Computational Mechanics Publications, 1997



Stability of Residual Stresses D. Lo¨he and O. Vo¨hringer, Institut fu¨r Werkstoffkunde I, Universita¨t Karlsruhe, Germany

RESIDUAL STRESSES are generated in structural components during manufacturing processes such as forging, machining, heat treating, shot peening, and many others. These stresses are always a consequence of inhomogeneously distributed dimensional changes due to inhomogeneous plastic deformations, thermochemical treatments, and/or phase transformations. They can be either beneficial or detrimental to component behavior in service, depending on the materials state as well as the sign, magnitude, and stability of the residual stresses, mechanical loading, and environmental conditions (Ref 1–15). Compressive macro residual stresses in the surface region of materials with medium and high hardnesses increase the fatigue life and the fatigue limit at cyclic loading compared to materials states that are free of residual stresses. This improvement is caused by an increased resistance against crack initiation and, to a certain extent, against crack propagation if the residual stresses are sufficiently stable in the areas of highest loading (in most cases, the component surface areas). Moreover, compressive macro residual stresses can increase the resistance of certain materials against corrosion fatigue and stress corrosion cracking. They can also improve the wear resistance. Therefore, in many cases compressive macro residual stresses are intentionally generated in near-surface regions by controlled heat treatments or by posttreatments such as shot peening or deep rolling. The stability or relaxation behavior of these residual stresses at purely thermal or mechanical loadings as well as superimposed thermal and mechanical loadings is thus of decisive importance for the service behavior of components and hence of great interest from a scientific as well as a practical point of view (Ref 16–18). If residual stresses are relaxed by annealing or mechanical treatment, they naturally have little if any influence on subsequent component failure. Residual stresses can be reduced or completely relaxed by the application of mechanical and/or thermal energy. The elastic residual strains, ee, that are associated with the residual stresses via Hooke’s law can be converted into micro plastic strains, ep, by suitable deformation processes. For example, this transformation can be achieved by dislocation slip, dislocation creep, grain-boundary sliding, and/or diffusion

creep (Ref 16–17). If these processes occur to only a limited extent or not at all, relaxation of residual stresses is also conceivable by crack formation and propagation. Relaxation of residual stresses in the real case occurs by complex interaction of a large number of factors. It depends not only on the residual stress state itself but also on the material state, loading condition, geometry, and environment of the component under consideration. The best known and most important techniques for inducing residual stress relaxation are annealing (tempering), uniaxial deformation (drawing, stretching), and cyclic deformation (Ref 16–18). Relaxation can also be caused by thermal cycling, quenching, neutron bombardment, the effect of alternating magnetic fields (in the use of ferromagnetics), vibration, and partial damage. As discussed in other articles in this Handbook, residual stresses can be differentiated by their technological origins (i.e., whether they were produced during forming, machining, heat treatment, joining, coating, or casting). Before the effect of applied thermal or mechanical energy on the residual stress state can be assessed, the latter must be determined quantitatively. In the case of mechanical methods, the necessarily large number of measurements involve considerable expenditure of both time and money. Most investigations have thus employed x-ray methods—for example, the sin2w method (Ref 19) with CrK␣ radiation on the {211}-interference plane of the ferrite, as well as interference-profile analyses (e.g., Ref 20, 21). In this article, current knowledge about residual stress relaxation of steels is presented in a condensed and, as far as possible, systematic form. The abundance of available experimental data nevertheless necessitates a limited scope. Thus, the findings of residual stress relaxation by annealing, tensile loading, compressive loading, and cyclic loading will be taken as examples to demonstrate universally valid rules. Shot peening residual stresses are particularly suitable for such investigations due to their sign and their relatively large absolute value. Possible formulas that can be used to quantify residual stress relaxation are discussed, and the underlying microstructural as well as micromechanical mechanisms are considered.

Relaxation of Residual Stresses by Annealing If a pure metal is annealed for several hours at a temperature of Ta 0.5 Tm [K]

(Eq 1)

where Tm is the melting or solidus temperature, and then cooled slowly to room temperature, almost total relaxation of the residual stresses arising from forming, machining, heat treatment, or joining operations can be achieved. The necessary annealing time depends essentially on the workpiece dimensions and the material state. Since an annealing temperature of 0.5 Tm corresponds to the recrystallization temperature of ferritic steels, complete relaxation of macro residual stresses can be expected. In the case of pearlitic steels, macro residual stresses are completely eliminated during the pearlite-austenite transformation above the A1 temperature. Micro residual stresses are considerably reduced but not entirely removed, since lattice defects (particularly dislocations) and, in the case of heterogeneous materials, the different expansion coefficients of the various phases are always responsible for some micro residual stresses. Residual stress relaxation by annealing is brought about by so-called thermally activated processes for which the annealing temperature and the annealing time are interchangeable within certain limits. In order to achieve comparable residual stress relaxation at a lower annealing temperature, the annealing time must be increased correspondingly (Ref 16, 17). Thermal residual stress relaxation is fundamentally affected by the residual stress state itself and by the material state. This is convincingly demonstrated by the findings presented in Fig. l and 2 (Ref 16, 17), which show the effect of 1 h anneals on surface macro residual stresses of a variety of origins in a variety of steels investigated using x-ray methods. Figure 1 is a bar chart showing the macro residual stresses present in the original state and after the normal industrial stress relieving for hardened components of 1 h at 200 C (390 F). The materials deformed in tension have undergone negligible residual stress relaxation. The greater the original compressive residual stresses, the greater the residual

Stability of Residual Stresses / 55 stress relaxation produced by annealing of surface-machined specimens: 11% for a plain carbon steel with 0.45 wt% Carbon, SAE 1045 (Fig. 1C); 17% for SAE 1045 (Fig. 1D); and 19% for the rolling bearing steel AISI 52100 (Fig. 1E). The most pronounced relative residual stress relaxation, however, is observed in the hardened materials: 25% for plain carbon steel with 0.22 wt% C, SAE 1023 (Fig. 1F); and 37% for SAE 1045 (Fig. 1G). Figure 2 shows the relative residual stresses rrs(Ta)/rrs(293 K) for the same steels as a function of the homologous annealing temperature, Ta /Tm. It can be seen that a 1 h anneal at 0.5 Tm (about 600 C, or 1110 F) results in complete relaxation of the macro residual stresses in every case. Characteristic, material-specific stresstemperature curves are obtained. Clearly, residual stresses produced by hardening are relaxed at lower temperatures, machining residual stresses at medium temperatures, and deformation residual stresses at higher temperatures. In order to achieve the same degree of residual stress relaxation, (e.g., 50%) in 1 h in hardened and in deformed SAE 1045, a temperature difference of 150 C (270 F) is necessary. Furthermore, according to Fig. 1, larger initial residual stresses result in a shift of the rrs versus T curve to lower annealing temperatures in the case of hardened or machined materials. Micro residual stresses and their relaxation behavior can be determined directly from the halfwidth values (HW) of the x-ray interference lines, which are a measure of the microstructural work-hardening state as well as the dislocation density. The change of the HW values are approximately proportional to the changes of the micro residual stresses (DHW Drrs micro). Again, the micro residual stresses in steels are more effectively relaxed at a higher temperature and, like macro residual stresses (see Fig. 2),

hardening micro residual stresses are relaxed at lower temperatures, such as those produced by machining; likewise, machining micro residual stresses are relaxed at lower temperatures, such as those produced by deformation in tension. In comparable steel states, micro residual stresses are relaxed only after a longer period or at a higher temperature than macro residual stresses (Ref 16, 17). For example, in order to achieve 50% micro residual stress relaxation in tensiledeformed SAE 1045 annealed for 1 h, the annealing temperature must be 100 C (180 F) higher than that needed to achieve the same degree of macro residual stress relaxation. Data pertaining to the thermal relaxation of micro residual stresses for hardened steels are available by analyzing x-ray interference lines of different steels in (Ref 22–24). The mean lattice distortions e21 / 2, which are proportional to the micro residual stresses according to 2 1/2 rrs micro ⳱ E110 • e

(Eq 2)

E110 is the Young’s modulus of iron in the 110 direction, increase with growing carbon content mainly due to the increasing dislocation density and, secondarily, to the increasing number of solute carbon atoms in octahedral sites of the tetragonal martensite lattice. Usually, it can be assumed that with increasing carbon content the temperature for the onset of residual stress relaxation is lowered and the recovery rate increases. However, it must be remembered that with the annealing-induced formation of carbides on dislocations, which leads to their pinning, the relaxation procedure slows. The relaxation behavior of residual stresses depends for a similar surface treatment, as for example by shot peening, as shown in Fig. 3 for the plain carbon steel SAE 1045 with 0.45 wt% C, from the heat treatment before shot peening

400 Ck22 F Ck45 A

Ck22 B

Ck45 C

Ck45 D

Ck45 G

and thus, from the hardness of the material (Ref 25). The macro residual stresses (left-hand side of Fig. 3) and the micro residual stresses (righthand side; characterized by the half-width ratio DHW/DHW0), yield with the hardness increasing from the normalized to the quenched and tempered and to the hardened condition, greater relaxation rates. Figure 3 also illustrates the delay of the relaxation of the micro residual stresses, which was mentioned above in comparison with the macro residual stresses. Further experimental investigations of the macro and micro residual stress relaxation of metallic materials—tempering steel AISI 4140 (Ref 26–28), titanium alloy Ti-6Al-4V (Ref 29), and several CuZn alloys and AlMg alloys (Ref 30, 31)—lead to similar results. Materials with surface residual stresses produced by grinding, milling, deep rolling, or shot peening frequently show different residual stress relaxation behavior when comparing the surface layer with subsurface areas. In most cases, this behavior is connected with work-hardening gradients, where an increasing work hardening due to increasing dislocation densities causes growing mean strains and greater half-width values. Characteristic examples of depth distributions of the macro residual stresses and the half-width values in SAE 1045, which were produced after different heat treatments and electrolytical removal of thin material layers, are shown Fig. 4 and 5 (Ref 25). Normalized SAE 1045 samples in the ground, milled, or shot-peened condition result in typical depth distributions that depend on the heat treatment (Fig. 4). In this case, the relaxation behavior of the macro residual stresses (left-hand side), and of the half-widths (right-hand side), is more pronounced at the surface than in deeper layers. After selected annealing treatments, this behavior holds to completely relaxed shot peening residual stresses in the near-surface layers in contrast to the interior, where remaining residual stresses exist (see Fig. 4, bottom row, left, after annealing 30 min at 550 C, or 1020 F). The relaxation behavior of normalized SAE 1045 in the shot-peened condition is reproduced

100Cr6 E

0

Ta, °C

−400

Normalized +5% deformed in tension Normalized + ground

−800 Untempered −1200

Fig. 1

200 °C/1 h tempered

1.0 σrs(Ta)/σrs(293 K)

σrs, MPa

Hardened

Hardened + shot peened

Macro residual stress (rrs) of different steels before and after annealing for 1 h at 200 C (390 F). Ck 45 ⳱ SAE 1045; Ck 22 ⳱ SAE 1023; 100 Cr 6 ⳱ AISI 52100

0

100

200

300

400

C B

0.6

0.2 0 0.15 0.20

600

ta = 1 h

0.8

0.4

500

A

E F G

D

0.25 0.30 0.35

0.40 0.45 0.50

Ta/Tm, K Macro residual stress ratio versus homologous annealing temperature of different steels (see Fig. 1) after annealing for 1 h

Fig. 2

56 / Effect of Materials and Processing again in Fig. 5 (top row) in comparison with shot-peened conditions of quenched and tempered as well as hardened states of SAE 1045. The shot peening residual stresses in the hardened state (bottom row) are reduced by annealing of 1 h at 300 C (570 F) almost 50% at the surface and in the depth of the maximum of compressive residual stresses. The corresponding HW values in the area close to the surface are smaller than those measured in deeper regions. This finding is well known from relatively hard materials, such as hardened steels (500 HV) with relatively high dislocation densities, where the shot peening process causes decreasing HW values due to work-softening effects (Ref 32). The higher the hardness, the more effective the work softening. In these material states, decreases in HW values are caused by rearrangements of the dislocations with high density in low-energy structures. However, in the quenched and tempered condition, and in the normalized condition, enlarged relaxation effects are observed in the surface layer due to a dislocation-induced higher driving force and the relaxation rate decreases with increasing distance from the surface. These findings must be

taken into account for the valuation of residual stress relaxation of corresponding components.

can be linearized with the help of a Zener-WertAvrami function (Ref 33) to: m rrs/rrs 0 ⳱ exp [ⳮ(Ata) ]

Thermally Activated Relaxation Processes In order to analyze the thermally activated processes responsible for residual stress relaxation, the influence of annealing time, ta, and of annealing temperature, Ta, must be known. If the time and temperature ranges are sufficiently restricted and if rrs(Ta,ta)/rrs(293 K) ⳱ constant (abbreviated in the following to rrs/rrs 0 ), the relationship ta ⳱ t0 exp (DH/kTa)

(Eq 3)

should hold between annealing time and temperature. In Eq 3, t0 is a time constant, k is the Boltzmann constant, and DH is the activation enthalpy for the relaxation process in the ta versus Ta range under consideration. Data in the form of rrs versus 1og ta plots as in Fig. 3 are not suited to a direct evaluation using Eq 3. The effect of time on residual stress relaxation

where m is a numerical term dependent on the dominant relaxation mechanism and A is a function dependent on material and temperature according to A ⳱ B exp (–DH/kTa)

Ta, °C

Ta, °C

200 250 300 350 400 450 500 550

200 250 300

0.5

350 400 450 500 550

0.5

Normalized 0

0

1.0

150 150

1.0

250

250

0.5

350

350 450

0

1.0

Quenched and tempered

0.5

∆HW/∆HW0

σrs, (Ta , t a )/σrs(293 K)

1.0

450

0

1.0

150

150 250

250

0.5

0.5 350

350 450

0 0

10

100

1000

450

Hardened

0 0

10

100

1000

Anealing time, ta, min Macro residual stress ratio versus annealing time, and ratio of the changes of the half-width values DHW/DHW0 versus annealing time, at different annealing temperatures at the surface of shot-peened SAE 1045 samples in normalized, quenched and tempered, and hardened states

Fig. 3

(Eq 5)

where B is a constant. It follows from Eq 4 that rs log ln (rrs 0 /r ) ⳱ m log ta Ⳮ m log A

(Eq 6)

with the result that for a constant annealing temperature Ta, a plot of log ln(r0rs/rrs) versus log ta gives a straight line (see Fig. 6). Corresponding annealing temperatures and times for rrs/r0rs ⳱ constant can be derived from such plots, as schematically illustrated in Fig. 6 in the log ta versus l/kTa plot. The values for rrs/rrs0 ⳱ constant lie on a straight line. Based on Eq 5 and 6, this line results in log ta ⳱ constant Ⳮ

1.0

(Eq 4)

DH ln 10 • kTa

(Eq 7)

which can be rearranged to give Eq 3. The slope of the log ta versus l/kTa plot in Fig. 6 yields to the activation enthalpy for residual stress relaxation. An experimental verification of Eq 6 is presented in Fig. 7, with results for shot-peened turbine blades made from a 12% Cr steel that was annealed for residual stress relaxation in the temperature range from 150 to 600 C (300 to 1110 F) up to 104 h (Ref 34, 35). The measuring data are fitted very well by straight lines with a slope of approximately m ⳱ 0.10. The evaluation of these lines by Eq 7 leads to the activation enthalpy DH 3.5 eV. This finding will be discussed together with the following results. A complete quantitative description of the thermal relaxation of residual stresses is of practical importance. This was achieved by an extensive study on the steel AISI 4140, which was quenched, tempered 2 h at 450 C (840 F), and then shot-peened. The shot peening was carried out with cast steel shot S170 (44 to 48 HRC), at a pressure of 1.6 bar and a coverage of 98% (Ref 26, 27). The absolute values of the macro residual stresses are plotted in Fig. 8(a) versus the logarithm of the annealing time for different annealing temperatures. They decrease with increasing time and temperature. Because the conventional way for determining the Avrami quantities DH, m, and B in Eq 4 and 5 requires strong extrapolations to very high and low annealing times, a new iterative method was used that allows determination of these parameters by a nonlinear minimization of the residual sum of squares (Ref 26, 27). To achieve this, all measurements in the evaluation are taken into account with the same weight. The algorithm

Stability of Residual Stresses / 57 yields DH ⳱ 3.3 eV, m ⳱ 0.122, and B ⳱ 1.22 ⳯ 1021 min – 1 for the surface values of the macro residual stresses. The curves in Fig. 8(a) were calculated using these constants in Eq 4 and 5. They describe the time and temperature dependence of the relaxation process very well. The alterations of surface half-widths by annealing at temperatures between 250 and 450 C (480 and 840 F) for different annealing times are shown in Fig. 8(b) for the same steel. The reductions of the HW values are similar to the relaxation of the macro residual stresses presented in Fig. 8(a). Again, the Avrami approach is used to describe the relaxation of half-widths, applying the new iterative method to the differences between the half-widths after annealing and the value HW ⳱ 1.65 of a normalized specimen related to their starting values instead of the ratio rrs(Ta,ta)/rrs 0 in Eq 4. The curves in Fig. 8(b) were calculated by means of the material properties DH ⳱ 2.48 eV, m ⳱ 0.116, and B ⳱ 1.09 ⳯ 1013 min – 1 and agree well with the measured values. The dependence of the relaxation of mean strains e21 / 2 and micro residual stresses rrs micro, respectively, on the annealing time was measured in the temperature range between 250 and 450 C (480 and 840 F). The data can also be modeled by the Avrami approach using e2(Ta, ta)1/2/e201/2 instead of

rrs(Ta, ta)/rrs0 in Eq 4. The new algorithm was used to determine the material parameters DH ⳱ 2.64 eV, m ⳱ 0.096, and B ⳱ 5.32 ⳯ 1012 minⳮ1, which allow description of the measured values as shown in Fig. 8(c). Comparison of these relaxation data in Ref 26 and 27 shows that the relaxation of macro residual stresses at the surface of the shot-peened state is a bit faster than the relaxation of half-widths and mean strains; this corresponds with the fact that the constant B differs by nearly nine orders of magnitude (see Table 1). The reason for the differences in the relaxation rate is that for the relaxation of macro residual stresses, dislocation movement is sufficient. For a distinct relaxation of micro residual stresses, however, additional dislocation annihilation is necessary. The exponents m show no significant alterations, and the activation enthalpies approach the values of the activation enthalpy of self-diffusion of iron: DHS 2.8 eV. Additional data for the same steel in a normalized and another quenched and tempered state in Table 1 (with exception of the hardened state) confirm this statement (Ref 28). Accordingly, volume diffusion-controlled dislocation creep in the residual stress field that is dominated by climbing of edge dislocations should be the rate-controlling process for the relaxation of the shot peening residual stresses of

3.0 400

Ground 350 °C/22 min 2.5

200 2.0 0 0 2.4

350 °C/22 min −100

2.2

HW, °2θ

σrs, MPa

Milled

2.0

−200

0

0.1

0.2

0

0.1

0.2

0 Shot peened 3.0

400 °C/30 min 500 °C/30 min

−200

550 °C/30 min

2.5

−400

2.0 0

0.1

0.2

0.3

0

0.1

0.2

0.3


Fig. 4

Macro residual stress and half-width of the x-ray interference line versus distance from surface before and after annealing of ground, milled, and shot-peened SAE 1045 samples in a normalized state

AISI 4140 in normalized as well as quenched and tempered states. In order to obtain some information about the relaxation behavior of macro residual stresses in subsurface layers, the values of the residual stresses after the annealing processes of AISI 4140 mentioned above were measured for different distances from the surface (Ref 26, 27). The evaluated parameters of the Avrami approach vary only at the surface itself from those values measured below the surface. There, the evaluated data show no significant tendency and amount to the mean values DH ⳱ 2.99 eV, m ⳱ 0.172, and B ⳱ 6.09 ⳯ 1017 minⳮ1. As shown in Fig. 9, the dependence of the macro residual stresses after different annealing times at 450 C (840 F) on the distance from surface can be described quantitatively using the surface material properties and the mean values for all subsurface layers. The agreement between measured values and modeled curves is very good. During heating to sufficiently high annealing temperatures, a distinct relaxation of macro residual stresses occurs. An attempt was made to model this behavior by extending the Avrami approach to nonisothermal stress relaxation (Ref 27). The transient relaxation of the macro residual stresses was calculated for specimens that were immersed up to 90 s in a salt bath at 450 C (840 F). The temperature at the specimen surfaces developed according to the T(t) curve shown in Fig. 10. For calculation of the relaxation of residual stresses, the real T(t) relationship was partitioned into a staircase curve with small equidistant steps and isothermal sections. Calculation of the relaxation was determined by a numerical integration after the so-called stresstransient method (Ref 27) under the application of the Avrami quantities DH, m, and B (Table 1) which are valid for the surface state. The magnitudes of the macro residual stresses measured after interruption of the heating and cooling down to room temperature are marked with triangles. It becomes evident that the stresstransient method describes the measured values in an excellent manner. Figure 10 also shows the isothermally calculated relationship between heating time and absolute values of residual stresses. While there are distinct differences during the first stage of heating time of approximately 20 s, the curves calculated isothermally and by the stress-transient method closely approach at long annealing times. A similar discussion of thermally activated processes was carried out for other steels (Ref 16, 17, 28, 30, 31) and for AlMg alloys and CuZn alloys (Ref 30, 31) with surface residual stresses originating from a variety of processes. In the case of these steels, the activation enthalpy DH depends on the state of the material and lies in the range of 1.1 to 2.6 eV. DH is lowest for relaxation of residual stresses due to hardening and highest for those due to deformation in soft annealed states. That proves unequivocally that residual stress relaxation in steels can occur by several processes. Characteristic structural changes occur during

58 / Effect of Materials and Processing the deformation, machining, or hardening of steels. Typically, an increase in the dislocation density and a change in the dislocation arrangement are observed. In the case of hardening, the concentration of solute interstitial atoms differs from the equilibrium value, and this, together with the presence of dislocations, has a decisive influence on the residual stress fields. If a single heat treatment is carried out in the temperature range corresponding to recovery (T 0.5 Tm), the dislocations adopt arrangements of lower energy by elementary processes such as glide and cross slip by screw dislocations and glide and climb by edge dislocations. In the case of hardened material, diffusion of carbon atoms dependent on the annealing temperature and accompanied by the formation of characteristic carbides is superimposed on these processes. The rate-determining process, with the exception of the early stages in the annealing of hardened steels (Ref 36), is clearly the thermally activated climb of edge dislocations (Ref 17). If diffusion of matrix atoms occurs along the edge dislocations to the dislocation core, the activation enthalpy should be DH 0.5 DHS, where DHS is the activation enthalpy of self-diffusion. If volume diffusion predominates, the DH value for climb is determined by DHS. In the real case, both processes occur simultaneously but to different degrees. The dislocation density and arrangement are of considerable importance. In the

case of randomly distributed dislocations or tangles of extremely high density, qt —for example, in hardened steels where qt 1012 cmⳮ2 (Ref 23, 24)—residual stress relaxation is expected to involve dislocation-core diffusion-controlled climb by edge dislocations. Predominantly volume diffusion will determine recovery if the dislocation configurations are relatively stable and consist of plane arrangements, cell walls, or subgrain or low-angle grain boundaries. This recovery process probably occurred in the investigated shot-peened quenched and tempered steels and normalized steels as well as nonferrous alloys. In view of the activation energies, the residual stress relaxation in the hardened steels can probably be classified between these two extremes and occurred by two recovery mechanisms in competition with each other. Up to now, discussion has centered on residual stress relaxation at temperatures Ta 0.5 Tm —that is, those temperatures brought about by typical recovery processes. In this case, mechanical parameters such as hardness and yield strength are not significantly altered. During a recrystallization anneal at Ta 0.5 Tm, the dislocation density rapidly takes very small values as a result of the growth of new grains. This leads to complete removal of macro residual stresses and to small micro residual stresses, but is associated with pronounced changes in mechanical properties. If extensive residual stress reduction

is required in a component without significant change in yield strength or tensile strength, the annealing temperature and time must be chosen to correspond with the recovery stage and not with recrystallization.

Resistance to Residual Stress Relaxation Residual stress relaxation by heat treatment is fundamentally impossible if in a predominantly uniaxial residual stress state rrs is smaller than the creep yield strength. This resistance for the onset of plastic creep deformation, designated in the following by Rce, is characterized by the creep strain limit at vanishingly small plastic deformation. As shown schematically in Fig. 11, Rce decreases with increasing temperature and load time. In contrast to relevant times regarding the creep condition of a high-temperature component at service, only very short times are necessary for residual stress relaxation by creep processes (dislocation creep, grain-boundary glide, or diffusion creep). With increasing T and/or t, Rce approaches a localized residual stress peak of magnitude rrs. For T ⳱ Tti, rrs equals Rce associated with the localized onset of creep deformation. Further increases in temperature or time result in an increasing and measurable microplastic creep strain. As illustrated in Fig. 11, residual stress relaxation begins at higher temperatures (Ti) the smaller the load time (ti) or the residual stress (rrs) and the greater the creep resistance (Rce) of the material. Changes in Rce can be achieved by deliberate alterations in the state

0 Shot peened 400 °C/30 min

−400

3

500 °C/30 min 550 °C/30 min

−800

Ta,4

Normalized

2

Ta,3

6 300 °C/60 min

−400

5

Quenched and tempered

4

HW, °2θ

Shot peened σrs, MPa

Ta,2

rs

0

log ln (σ0/σrs)

Normalized

m

Ta,1 < Ta,2 < Ta,3 < Ta,4

−800 Quenched and tempered

Ta,1

log ta

3

0

−400

5 4 Shot peened

−800 Hardened 0

Fig. 5

log ta

6

0.2

Hardened 0.4 0 Distance from surface, mm

300 °C/60 min 0.2

∆Ha/ln10

3 0.4

Macro residual stress and half-width versus distance from surface before and after annealing of shot-peened SAE 1045 samples in normalized, quenched and tempered, and hardened states

1/kTa

Fig. 6

Schematic of conventional determination of Avrami approach parameters

Stability of Residual Stresses / 59

Loading stresses acting in opposition to the residual stresses in a given region of the material delay the onset of microplastic deformation in this region. Since the distribution of residual stresses in a component is always inhomogeneous, there will be other regions in which superposition of rrs and rls in the same sense promotes plastic deformation. Therefore, it depends on the superposition of rls and rrs at any point in the component if a loading stress retards (|rls Ⳮ rrs|max |rrs|max) or enhances (|rls Ⳮ rrs|max |rrs|max) residual stress relaxation. At this stage it is interesting to explain the result shown in Fig. 1 and 2, where residual stress relaxation in a deformed sample of SAE 1045 is delayed in comparison to that in SAE 1023 despite the compressive residual stresses having double the magnitude. Due to its higher carbon content, SAE 1045 contains a greater number of ferrite-cementite phase boundaries than SAE 1023. These phase boundaries represent stable obstacles to dislocation slip. Apparently, the restricted possibilities for recovery-driven movement of dislocations to arrangements of lower en-

1

冪2

冪(rrs1 ⳮ r2rs)2 Ⳮ (r2rs ⳮ r3rs)2 Ⳮ (r3rs ⳮ r1rs)2

(Eq 9)

on the basis of the von Mises hypothesis. The equivalent residual stress is thus dependent on the differences between the principal residual stress components. These in their turn are proportional to the shear stresses acting on dislocations in the slip systems. Residual stress relaxation therefore does not occur for rrs eq Rce

ep ⳱ C(T)rntm

but does occur for

can be established for constant loading stress rls (Ref 16, 17). C is a quantity depending on the temperature and the condition of the material; the exponents have the values n 1 and 0 m 1; and the creep strain increases with applied stress and with time. Residual stress relaxation

600

rrs eq ⱖ Rce

0.4

10

500

250 °C

400

300 °C

300

350 °C

200

400 °C

100

The case rrs eq Rce obtains only briefly, since the immediate onset of creep deformation attempts to restore the condition rrs eq ⳱ Rce.

1

10 102 ta, min

103

104

(a)

Effect of the Magnitude of Residual Stresses on Relaxation Behavior

3.2

Ta = 250 °C

The data in Fig. l and 2 clearly show that the residual stress relaxation in machined or hard-

102

300 °C 2.8 350 °C 400 °C 450 °C 2.4

103

104 600 °C

90

525 °C

0 10−∞

80

410 °C

60

375 °C 340 °C 320 °C

50

250 °C

20

40 30

−0.8

200 °C

10

150 °C

1

102 10 ta, min

103

104

(b) 1.4

200 Ta = 250 °C

< ε2 >1/2 in 10−3

70

rs

−0.4

50 °C Ta = 4

Residual stress relaxation, %

0

log ln (σ0/σrs)

Ta = 450 °C

0 10−∞

Annealing time, h 1

(Eq 10)

1.2

300 °C 350 °C 400 °C

1.0

250

450 °C

200

σrs , MPa micro

(Eq 8)

rrs eq ⳱

ened steels occurs more quickly or at lower temperatures, the greater the magnitude of the residual stresses themselves. This is a consequence of temperature, time, and stress-dependent processes similar to those observed in so-called primary microcreep. Empirical relationships of the form

|σrs|, MPa

|rls Ⳮ rrs| ⳱ Rce

ergy outweigh the increasing driving force of the larger residual stress. The delayed residual stress relaxation in deformed SAE 1045 is thus explained by an increase in the creep resistance Rce. In the case of a multiaxial residual stress state, the residual stress rrs employed in the arguments just given must be replaced by an equivalent residual stress rrs eq. If the principal components are rs rs rrs 1 , r2 , and r3 , it can be formulated to

HW, °2θ

of the material. All thermally stable obstacles that have an additional work-hardening effect (Ref 17) shift the onset of residual stress relaxation and the entire rrs versus T curve to higher temperatures. Residual stress relaxation is also affected by the superposition on a localized residual stress rrs of an applied loading stress rls in the same direction. Increasing rls values shift the onset of residual stress relaxation to shorter times and/or lower temperatures according to the relation

0.8 150 0.6 10−∞

−1.2

1

102

10 ta, min

103

104

(c)

−1.6 −1

Fig. 7

Influence of annealing time and temperature on the (a) absolute values of macro residual stress, (b) half-width, and (c) mean strain and micro residual stress on the surface and their description by the Avrami approach for shot-peened AISI 4140 in a quenched and tempered condition

Fig. 8

0

1

2 log ta

Plot of log ln versus log ta for a shot-peened 12% Cr steel

3

4

5


(Eq 11)

However, macro residual stresses are inhomogeneously distributed over the cross section, and for the residual stress relaxation in a localized area the following relationship holds true: rrs 0 E

e˙ t ⳱ e˙ p Ⳮ e˙ e ⳱ 0

(Eq 13)

Thus, the Norton law and Eq 13

rs

⳱ constant ⳱ ep Ⳮ

r E

e˙ p ⳱ C*(T) • (rrs)n ⳱ ⳮ e˙ e ⳱

rs (rrs 0 ⳮ r ) ep ⳱ E

ⳮr˙ rs E

(Eq 14)

(Eq 12)

Regarding real values of the residua1 stresses, plastic strains of several tenths of a percent maximum are produced by complete residual stress relaxation (rrs ⳱ 0); that is, the deformation is in the microcreep range. Equations 10 and 11 form the basis for quantitative estimates of the residual stress relaxation. Multiaxial and inhomogeneous residual stress states are neglected or excluded. Although Eq 10 cannot be substituted directly in Eq 11 on account of the variable value of the stress (r ⳱ rrs), it can be seen qualitatively from a combi-

give a proportionality between the elastic and plastic strain rates, and between the residual relaxation rate and the actual residual stress to the power of the Norton exponent n, respectively. The experimental data shown in Fig. 12 reveal strain rates that present a strong dependency on temperature and residual stress values (Ref 26). Furthermore, the data reveal strain rates that are typical for creep processes. This finding supports the conclusion drawn above that diffusioncontrolled dislocation creep in the residual stress field should be the rate-controlling process for the relaxation of residual stresses in steels.

650 200

500

T( t )

−200

Ta = 450 °C

σrs, MPa

σrs, MPa

ta = 6000 min 60 min

−400 6 min

−600

Measured Calculated

400

Tsalt = 450 °C

300

Surface data

450

Transient relaxation

350

T, °C

550

0

0

250


0.4

Measured and calculated macro residual stress at Ta ⳱ 450 C (840 F) and different annealing times versus distance from the surface of shot-peened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h)

Fig. 9

σrs+ σls •

t2, ε2

•

0

20

40

60

80

100

Quenched and tempered 650 C (1200 F) 450 C (840 F) Hardened

T1

T2

Temperature, T

Fig. 11

Absolute values of macro residual stress after short-time immersion in a salt bath at 450 C (840 F) versus time. Comparison is made with curves calculated with the stress-transient method using the occurring T(t) dependence and with modeling for isothermal annealing.

Fig. 10

Measuring property

DH, eV

m

B, minⴑ1

Macro residual stress

3.30

0.080

1.40 ⳯ 1018

Macro residual stress Macro residual stress Half-width Mean strain (micro rs) Macro residual stress

t2 >> t1 • ε2 ε1

Creep yield strength versus temperature at different creep times and strain rates

t, s

Table 1 Material properties DH, m, and B of the Avrami approach determined for different heat treatment conditions of the shot-peened steel AISI 4140 Normalized

T ′1

0

100

10−5 10−6 10−7

•

Heat treatment

•

t1, ε1

σrs

200

Isothermal relaxation 0 min

−800

In certain cases in practice, uniaxial deformation is often employed in addition to stressfree annealing to relieve residual stresses. In the case of forming, for example, the residual stresses can be reduced by a second forming stage using a smaller reduction in the crosssectional area. This can be achieved by redrawing, restretching, rerolling, repressing, and straightening (Ref 16, 17). However, these techniques can be used only on simply shaped components with a uniform cross section. In the case of welded seams, a uniaxial load is applied to reduce or redistribute macro residual stresses. When a critica1 value of the applied loading stress is exceeded, directed dislocation movement converts the elastic strain associated with the macro residual stress into micro plastic strain. Several typical examples will serve to illustrate the relaxation of residua1 stresses due to joining and shot peening by uniaxial deformation. In an evaluation of the effect on the strength of macro residual stresses set up during welding, it is important to know the stability of these stresses on loading the weld. Figure 13 illustrates the considerable reduction in macro residual stresses accompanying tensile loading of joints

Creep yield strength, Rce

r E

Residual Stress Relaxation by Uniaxial Deformation

Strain rate εp, s−1

et ⳱ constant ⳱ ep Ⳮ ee ⳱ ep Ⳮ

nation of the two expressions that increasing residual stress values lead to a more effective residual stress relaxation. As a result of the greater driving force, shorter times and/or lower temperatures are necessary. This is in agreement with the experimental results presented. The influence of the magnitude of the residual stresses can also be illustrated by describing the residual stress relaxation with the Norton approach, which is known from high-temperature creep. The total strain rate as the sum of elastic and plastic strain rate must vanish according to

>>

cannot, however, be compared directly to a creep test. It is much more like a stress relaxation experiment. In the latter case, the total strain remains constant while elastic strain is converted into plastic strain. With a homogeneous stress distribution over the cross section of a specimen, the following expression would be valid:

3.38 3.29 2.48 2.64 2.33

0.080 0.122 0.116 0.096 0.110

1.90 ⳯ 1021 1.22 ⳯ 1021 1.09 ⳯ 1013 5.32 ⳯ 1012 1.20 ⳯ 1016

10−8

T = 450 °C

10−9

400 °C 350 °C 300 °C

10−10 10−11 60

100

200

400

250 °C 600

1000

σrs, MPa Plastic strain rate versus mean residual stress of shot-peened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h). Determined from the data of Fig. 8(a)

Fig. 12

Stability of Residual Stresses / 61 produced by electron beam welding and tungsten inert gas (TIG) welding in a maraging steel (Ref 37). In the electron beam welded specimen, it begins at about 70% of the yield strength Re of the unannealed weld. Residual stress relaxation is not complete. In the case of the TIG weld, noticeable residual stress relaxation first occurs above Re. By the time the tensile strength Rm is reached, residual stress relaxation is virtually complete. Shot peening residual stress states under tensile or compressive loading are unstable, and relaxation occurs when critical loading stresses are exceeded. Corresponding results of surface residual stresses of the quenched and tempered steel AISI 4140 are presented in Fig. 14 as a function of loading stress and in Fig. 15(a) as a function of total deformation (Ref 38). At tensile loading, relaxation of the peening-induced compressive residual stresses in the surface of ⳮ540 MPa (ⳮ80 ksi) sets in at 95% of the yield strength of the unpeened material (Re(t) Rp0.01(t) 1180 MPa, or 170 ksi). In compression, relaxation starts at 45% of the yield strength of the unpeened material (Re(c) Rp0.01(c) 1300 MPa, or 190 ksi). In the quenched and tempered condition of this material exists a typical strengthdifferential effect of Re(c) ⳮ Re(t) 120 MPa (20 ksi) (Ref 38). The relaxation rate of macro resid-

200

Re

b

ual stresses directly after the onset of relaxation occurs much more rapidly during tension than during compression. After a total strain et ⳱ ⳮ1% (rls ⳮ1250 MPa, or ⳮ180 ksi), the surface residual stresses rrs are completely removed (see Fig. 15a). If et ⳮ1%, the sign of rrs changes. In the case of tensile loading, the residual stress relaxation, however, is incomplete. Thus, the relaxation behavior is different and anisotropic during tensile and compressive loading. Combined with the relaxation of macro residual stresses, only a relatively small decrease of the half-width values, which are a measure of the micro residual stresses, is observed at the surface. Figure 15(b) illustrates this behavior as a function of total strain. The effect of different strengths on the relaxation behavior of shot peening residual stresses at the surface of AISI 4140 due to uniaxial deformation is illustrated in Fig. 16. Results of Fig. 14 for specimens quenched and tempered at 450 C (840 F) are compared with results for normalized specimens and for specimens quenched and tempered at 650 C (1200 F) (Ref 39). The courses of rrs versus rls are similar. However, the absolute values of the critical loading stresses for the onset of residual stress relaxation in tension |rlscrit(t)|, and in compression, |rlscrit(c)|, increase with increasing yield strength of this steel in different heat treatment conditions. Figure 17 represents the influence of loading stresses rls on the shot peening residual stresses

Rm

rrs at the surface of quenched and tempered AISI 4140 for different testing temperatures (Ref 40). The rrs versus rls course at 25 C (75 F) is the same as in Fig. 14. At higher temperatures (250 and 400 C, or 480 and 750 F), the initial macro residual stresses are reduced by heating and waiting for temperature compensation due to thermal residual stress relaxation. The values of the critical loading stresses for the onset of residual stress relaxation during tension and compression as well as the relaxation rate decrease clearly with increasing temperature. The relaxation of macro residual stresses by uniaxial deformation begins at relatively small loads or plastic strains. It may be complete or partial, both the degree and rate of residual stress relaxation depending on the type and state of the material as well as on the nature of the applied load.

Resistance to Residual Stress Relaxation The deformation behavior and relaxation of macro residual stresses in materials can be roughly approximated in terms of a cylindrical rod with longitudinal residual stresses—namely, constant compressive residual stresses (rrs s ) at the surface and constant tensile residual stresses (rrsc ) in the core (Fig. 18). The surface is characterized by the yield strength Re,s and the core by Re,c. Plastic deformation commences in the core at the critical tensile loading stress: rlscrit(t) ⳱ Re(t),c ⳮ rrs c

(Eq 15)

Plastic deformation under compressive load first occurs in the surface region due to the superposition of loading and residual stresses at the critical compressive loading stress:

200

−200

−400

a

0

400

800

Re Rm

1200

0 σrs, MPa

σrs, MPa

0

σls, MPa Welding residual stress versus tensile loading stress of a maraging steel. (a) Transverse residual stresses in the welding seam center of an electron beam welded joint. (b) Transverse residual stresses 3 mm (0.12 in.) from the welding seam center of a TIG welded joint

Fig. 13

−200

|rlscrit(c)| ⳱ |Re(c),s| ⳮ |rrs s|

−400

Residual stress relaxation does not occur during tensile loading for

−600 −6

rls rlscrit(t) ⳱ Re(t),c ⳮ rrs c −4

−2

εt, %

0

2

and during compressive loading for |rls| |rlscrit(c)| ⳱ |Re(c),s| ⳮ |rrs s|

15

∆HW, min

σrs, MPa

0

0 −200

−600 −1600

−15 −30 −45

−400

−800

0

800

1600

−60 −6

σls, MPa Macro residual stress at the surface versus loading stress under tension and compression, respectively, of shot-peened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h)

Fig. 14

−4

−2

εt, %

0

2

4

Influence of total deformation on (a) the macro residual stress and (b) the half-width change at the surface of shot-peened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h)

Fig. 15

(Eq 17)

4

30

200

(Eq 16)

(Eq 18)

The properties rlscrit(t) and rlscrit(c) thus have the meaning of resistances against residual stress relaxation by uniaxial deformation. The critical compressive loading stress, rlscrit(c), can be determined experimentally from corresponding loading and unloading tests. The yield strength of the surface, Re(c),s, can be estimated from Eq 16 with measurements of the surface residual stresses and the knowledge of the initial surface residual stress by this relationship: ls |Re(c),s| ⳱ |rcrit(c) | Ⳮ |rrs s|

(Eq 19)

In the case of a multiaxial residual stress state, modified yield strengths of the surface occur. Consideration of an isotropic biaxial surface re-


req ⳱ |Re(c),s| 2 ls rs ⳱ 冪(rlscrit(c))2 Ⳮ (rrs s ) Ⳮ rcrit(c) • rs

(Eq 20)

where req is the equivalent loading stress. This relationship leads to somewhat smaller yield strengths, as with a uniaxial estimation (Ref 29, 41). The application of Eq 20 for the shot-peened AISI 4140 in different conditions results in the Re(c),s values summarized in Table 2. The corresponding critical loading stresses for initiation of macro residual stress relaxation rlscrit(c), the yield strengths of the unpeened conditions Re(c), the ratio Re(c),s /Re(c), and the half-widths ratio of surface and core are also indicated. For the normalized condition the relation |Re(c),s| |Re(c)|

is valid. For the quenched and tempered conditions, however, the yield strengths show with |Re(c),s| |Re(c)|

a reverse behavior. The shot peening treatments thus generate in comparison with the core a work-hardened surface state in the normalized condition and a work-softened surface state in the quenched and tempered conditions. The final observations seem to be in contradiction with the work-hardening behavior obtained on the basis of the measurements of the half-width values of surface and core. The last column in Table 2

presents the ratio HWs /HWc with values between 1.05 and 1.58. Therefore, in all cases a peeninginduced microstructural work-hardening effect appears. The smallest effect occurs at the 450 C (840 F) quenched and tempered condition. The other heat-treated states show a considerably larger microstructural work-hardening effect. These apparent contradictions become clear with a more exact consideration of the conditions of the local deformation of the surface layers during shot peening and the subsequent uniaxial compression test. Besides a biaxial plastic stretch-forming of the surface area with maximum flow stresses and work hardening direct at the surface, the peening-induced deformations include additional Hertzian stresses with maximum effects below the surface (Ref 42). Now, at the determination of the surface yield strength Re(c),s under homogeneous compressive loading, the direct surface layer is deformed exactly inverse to the deformation direction during shot peening. In this case, the Bauschinger effect relieves the deformations in the inverse direction and reduces the resistance of the work-hardened surface layers due to back stresses and an anisotropic mobility of dislocations. It is known that the Bauschinger effect appears especially distinctive in quenched and tempered steels (Ref 43). Therefore, it is not surprising that the shot peening treatments of quenched and tempered AISI 4140 lead to values of Re(c),s /Re(c) 1. The surface yield strengths are controlled not only by the peening-induced surface work-hardening, which is characterized by the half-width ratio HWs /HWc, but also by the Bauschinger effect. Obviously, the condition Re(c),s /Re(c) 1 is valid if the peening-induced work-hardening has a stronger effect than the Bauschinger effect. If the

Bauschinger effect dominates, however, the ratio of the yield strengths is Re(c),s /Re(c) 1.

Modeling of the Relaxation Behavior A quantitative description of the relaxation behavior of multiaxial macro residual stresses with known distribution over the specimen cross section under uniaxial deformation is possible with the aid of finite-element modeling (Ref 28, 44). Isoparametric rectangular elements with plane strain behavior were applied for this purpose. The corresponding depth courses of the macro residual stresses as well as the initial parts of the stress-strain curves under tensile and compressive loading must be known and must be input with certain assumptions in a discrete form. Figure 19 shows corresponding results of tests at 25 and 400 C (75 and 750 F) for AISI 4140 in a quenched and tempered condition. There is a good agreement between experimental results and finite-element modeling. An important finding is that besides the pure mechanical and thermal relaxation of macro residual stresses during heating and waiting for temperature compensation, no additional relaxation effects occur under 200 0 σrs, MPa

sidual stress state that is generated due to vertical shot peening results on the basis of the von Mises hypothesis for the onset of residual stress relaxation at compressive loading to:

T = 25 °C T = 250 °C T = 400 °C

−200 −400 −600 −1600

−800

0

800

1600

σls, MPa , 200

, ,

Macro residual stress at the surface versus loading stress under tension and compression, respectively, at different deformation temperatures for shotpeened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h)

Fig. 17

Quenched and tempered 450 °C Quenched and tempered 650 °C Normalized

σrs, MPa

0

Surface

Core σrs σrs

−200

c

Surface Cross section area

0

−400

σsrs −600 −1600

−1200

−800

−400

0

400

800

1200

1600

σls, MPa Macro residual stress at the surface versus loading stress under tension and compression, respectively, of shotpeened AISI 4140 in different heat treatment conditions: normalized; quenched and tempered at 450 C (840 F), for 2 h (qt 450); and quenched and tempered at 650 C (1200 F) for 2 h (qt 650)

Fig. 16

Simplified distribution of longitudinal macro residual stress for residual stress relaxation due to uniaxial loading

Fig. 18


The fatigue strength of steels can be greatly influenced by macro and micro residual stresses. Since in certain cases they can be considered as locally variable mean stresses, they can lead to substantia1 increases in fatigue strength (cf. Ref 16, 17). The interaction of macro residual stresses with the cyclic deformation mechanism during fatigue in the microcrack-free stage is of particular importance. Coupled with this is the stability or the cyclic relaxation of residual stresses. Residual stress relaxation occurs when a critical value of the applied loading stress amplitude is exceeded and a cyclic directed dislocation movement converts the elastic strain associated with the macro residual stress into micro plastic strain. Numerous investigators have shown that the effect of macro residual stresses decreases with increasing stress amplitude and growing number of cycles as a result of residua1 stress relaxation (cf. Ref 16, 17). This is illustrated in Fig. 20 for quenched and tempered AISI 4140 in a shotpeened condition that has undergone a push-pull fatigue test (Ref 28, 46). Figure 20(a) presents cyclic deformation curves with a plot of the plastic strain amplitudes, ea,p, versus the number of cycles, N, during stress-controlled cyclic loading for different stress amplitudes, ra. Initially, the specimens show macroscopically a quasi-elastic cyclic deformation behavior at 400, 500, and 600 MPa (60, 70, and 90 ksi). At loading with ra ⳱ 700 MPa (100 ksi), small plastic strain amplitudes occur from the beginning of the test. After a distinct number of cycles for incubation, which decreases with increasing stress amplitude, cyclic work-softening occurs at all amplitudes. This augmentation of plastic strain amplitude continues until specimen failure. The maximum plastic strain amplitude observed just before failure increases with increasing stress amplitude. The alterations of the shot peening-induced macro residual stresses at the surface rrs with the number of cycles are shown in Fig. 20(b). The residual stress values are strongly reduced in the first cycle. Afterward, a linear dependence of the

Micro residual stresses behave in a complex fashion during the relaxation of macro residual stresses by uniaxial deformation. So far, only isolated experimental data based on x-ray profile analysis are available. When a material is formed or machined, both directed and inhomogeneous micro residual stresses are set up. Those of the first type are the result of back stresses due to dislocation pileups at grain or phase boundaries and elastic strained second phases of heterogeneous materials. If these dislocations move in the reverse direction during localized plastic deformation, the back stresses and hence the directed micro residual stresses are initially reduced. Further deformation causes renewed buildup of back stresses in the opposing direction associated with dislocation multiplication and hardening, which must once again increase the micro residual stresses. Dislocation arrangements in a random distribution or in tangles or cells give rise to inhomogeneous micro residual stresses. Microplastic deformation can lead to the rearrangement of dislocations into arrangements of lower energy and thus bring about micro residual stress relaxation. If new dislocations are produced, a renewed buildup of micro residual stresses is superimposed on the relaxation process. A reduction in the micro residual stresses in hardened steels is observed both on deformation and on machining (Ref 16, 17, 32, 45). Two superimposed effects can operate here. After hardening, a very high density of dislocations is present—either randomly distributed or in tangles. Microplastic deformation brings about a rearrangement of these dislocations into configurations with lower distortion energy and therefore a reduction in the micro residual stresses. On the other hand, solute carbon atoms may be induced to jump into the energetically more favorable octahedral sites in the martensite lattice under the influence of the stress field of the moving dislocations. This causes a reduction in the tetragonality and hence the lattice distortion due to solute carbon atoms (Ref 45).

rrs ⳱ A(ra) ⳮ m(ra) • log N

(Eq 21)

200 T = 25 °C

0 σrs, MPa

Behavior of Micro Residual Stresses

residual stresses on the logarithm of N occurs according to a logarithmic creep law:

−200 −400 −600

Calculated Measured T = 400 °C

200 0 σrs, MPa

Residual Stress Relaxation by Cyclic Deformation

−200 −400

Calculated Measured

−600 −1600

−800

0

800

1600

σls, MPa Measured and calculated macro residual stress at the surface versus loading stress under tension and compression, respectively, at different deformation temperatures for shot-peened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h)

Fig. 19

4

σa = 700 MPa

3

εa,p in 10−3

quasi-static uniaxial loading at elevated temperatures.

2 1

(a)

600 500 400 0 0 700

rlscrit(c)

Temperature

Re(c)

F

MPa

ksi

MPa

ksi

MPa

ksi

Re(c),s /Re(c)

25 250 400

75 480 750

ⳮ275 ⳮ300 ⳮ340

ⳮ40 ⳮ45 ⳮ49

ⳮ345 ⳮ300 ⳮ275

ⳮ50 ⳮ45 ⳮ40

ⳮ480 ⳮ496 ⳮ516

ⳮ70 ⳮ72 ⳮ75

1.39 1.65 1.87

1.58 1.33 1.28

Quenched and tempered 650 C (1200 F) 20 450 C (840 F) 25 250 400

70 75 480 750

ⳮ340 ⳮ600 ⳮ400 ⳮ360

ⳮ49 ⳮ85 ⳮ60 ⳮ52

ⳮ805 ⳮ1300 ⳮ950 ⳮ830

ⳮ115 ⳮ190 ⳮ140 ⳮ120

ⳮ685 ⳮ953 ⳮ758 ⳮ606

ⳮ100 ⳮ138 ⳮ110 ⳮ88

0.85 0.73 0.79 0.73

1.56 1.05 1.05 1.05

Normalized

500 σa = 400 MPa

−400

Re(c),s

C

Heat treatment

−200

l

Table 2 Critical compressive loading stress rlscrit(c), yield strength Re(c) of unpeened conditions, surface yield strength Re(c),s, yield strength ratio Re(c),s /Re(c), and ratio of half-width values HWs /HWc of shot-peened AISI 4140 in different heat treatment conditions

σrs, MPa

600

HWs /HWc

−600 10−∞

(b)

1


106

Plastic strain amplitude and longitudinal macro residual stress versus number of cycles during strain-controlled push-pull tests with different stress amplitudes of shot-peened AISI 4140 in a quenched and tempered condition (600 C, or 1110 F, for 2 h)

Fig. 20

64 / Effect of Materials and Processing tionally peened conditions and warm-peened conditions—the changes in the macro residual stresses, rrs l,s, measured at the side of the specimens primarily loaded in compression as a function of the logarithm of the number of cycles. For both peening variants, the residual stresses at the surface relax more rapidly with increasing stress amplitude during the first cycle as well as during further cycling. The linear correlation between residual stresses and the logarithm of the number of cycles N according to Eq 20 can be recognized for wide intervals of N ⱖ 1. In the conventionally peened samples, however, the

900 800

−200

700 600

−300

l,s

500 400

−400

300 −500

−600

−700

1

10

102


105

106

107

(a) 0 σa,s, MPa −100

1000

Tpeen = 290 °C

900 −200

800 700

σrs , MPa

600 500

−400

400

−500

400

−600

Top longitudinal Bottom longitudinal Top transverse Bottom transverse

200

0 10−∞

1000

−100

l,s

|σrs|, MPa

600

σa,s, MPa

Tpeen = 20 °C

−300 800

macro residual stresses relax faster than in the warm-peened condition. Pronounced differences can be seen—especially in the first cycle, where the residual stresses in the warm-peened samples show a higher stability than those in conventionally peened samples. For N ⱖ 1, the relaxation rate of the variant peened at room temperature is also higher compared to the variant peened at 290 C (555 F). The resulting surface values of the half-widths HWs, related to their initial values HWs,0, are given in Fig. 23 as a function of the logarithm of the number of cycles. The half-widths of the

0

σrs , MPa

due to the so-called cyclic creep, where the properties A and m can be determined for each stress amplitude from the experimental data in the linear sections of the curves in Fig. 20(b). In the case of the stress amplitude ra ⳱ 400 MPa (60 ksi), after the first cycle no further residual stress relaxation is observed with increasing number of cycles N. Obviously, this ra value is smaller than the materials resistance against cyclic residual stress relaxation ra,crit at the surface. For the two highest stress amplitudes, ra ⳱ 600 and 700 MPa (90 and 100 ksi), at the end of fatigue life greater residual stress relaxation rates are observed than predicted by the rrs /log N law. The beginning of this phase can be correlated with the onset of cyclic work softening in the ea,p versus N curves in Fig. 20(a). Hence, increasing plastic strain amplitudes at constant stress amplitude may cause increasing relaxation rates of residual stresses. For shot-peened AISI 4140 in a quenched and tempered state and subjected to alternating bending at the stress amplitude ra,s ⳱ 700 MPa (100 ksi), Fig. 21 presents the course of the absolute values of the macro residual stresses at the surface of flat specimens versus the number of cycles in the longitudinal and transverse directions (Ref 40). While the longitudinal residual stresses at the top side (which was loaded in compressive direction in the first half-cycle) relax from ⳮ600 MPa (ⳮ90 ksi) to about ⳮ480 MPa (ⳮ70 ksi), the longitudinal residual stress at the bottom side shows no considerable relaxation. In the second half-cycle, this trend is reversed and the residual stresses measured become similar. In the course of further cyclic loading up to 105 cycles, the residual stresses decrease linearly with the logarithm of the number of cycles according to Eq 21. After crack initiation at 105 Ni 4 ⳯ 105, further reductions in the magnitudes of the residual stresses are measured. The residual stresses in the transverse direction always relax more slowly than in the longitudinal direction. For initial stress amplitudes at the surface between 300 and 1000 MPa (45 and 145 ksi), Fig. 22 summarizes for the same steel—in conven-

1


−700

106

1

10

102


105

106

107

(b) Absolute values of macro residual stress at the surface versus number of cycles during alternating bending tests of shot-peened AISI 4140 in a quenched and tempered condition (450 C, or 840 F, for 2 h) for a surface stress amplitude of 700 MPa (100 ksi)

Fig. 21

Macro residual stress at the surface in longitudinal direction versus number of cycles during alternating bending tests of quenched and tempered AISI 4140 (450 C, or 840 F, for 2 h) at different surface stress amplitudes. (a) Conventionally shot-peened condition (Tpeen ⳱ 20 C, or 70 F). (b) Warm-peened condition (Tpeen ⳱ 290 C or 555 F)

Fig. 22

Stability of Residual Stresses / 65 conventionally peened samples relax for ra,s ⱖ 700 MPa (100 ksi). With increasing stress amplitude, an increasing relaxation is observed. The reduction of the half-widths and, hence, of the micro residual stresses is much more pronounced for the samples peened at room temperature compared to the other peening variant. For the warm-peened states, the measured values after cycling are often a bit higher than the initial values. Only for ra,s ⱖ 900 MPa (130 ksi) and N ⱖ 104 can a significant decrease be seen. For the same samples peened at 20 or 290 C

(70 or 555 F), the stability of the residual stresses was investigated in detail (Ref 47, 48). The depth distribution of the residual stresses and the half-widths in the region close to the surface was determined at different numbers of cycles at a surface stress amplitude 1000 MPa (145 ksi). The curves for the conventionally peened samples in Fig. 24(a) show that the compressive residual stresses in the region close to the surface are strongly reduced with increasing number of cycles. During the first cycle, the absolute value of the residual stress of the surface decreases from about 600 MPa (90 ksi) to 350

1.0

0.9

σa,s, MPa

HWs/HWs,0

300 400 0.8

500 600 700

0.7

800 900 1000

0.6 1

10

102

103

104

105

106

107

Number of cycles, N

(a)

1.0

MPa (50 ksi). After N ⳱ 1000, the |rrs| value is 150 MPa (20 ksi). The depth where the residual stresses change their sign is not significantly affected. As shown in Fig. 24(a), a shot peening treatment at 290 C (555 F) considerably delays the relaxation of residual stresses. During the first cycle, the initial absolute value of the residual stress at the surface, |ra,s| ⳱ 660 MPa (95 ksi), is reduced only by about 140 MPa (20 ksi). After N ⳱ 1000, |ra,s| ⳱ 380 MPa (55 ksi) is measured. The affiliated depth distributions of the half-widths of the conventionally peened condition in Fig. 25(a) verify that with increasing number of cycles, reductions of the halfwidths and consequently of the micro residual stresses occur due to larger rearrangements of mobile dislocations in the surface layers. In opposition to this finding, under the same loading conditions the warm-peened condition shows practically no relaxation of the micro residual stresses. Obviously, the dislocation arrangements in the warm-peened condition under cyclic loading are considerably more stable than in the conventionally peened condition. This is due to dynamic and static strain aging effects that occur during and after warm peening (Ref 47, 48). Dynamic strain aging results in a more diffuse and stable dislocation structure caused by pinning of dislocations by solute carbon atoms and formation of extremely fine carbides. The effect of stabilized residual stresses on fatigue behavior is illustrated in Fig. 26, with S-N curves at alternating bending of the conventionally peened and two warm-peened conditions in comparison with the ground condition. The S-N curves for a failure probability of P ⳱ 50% were determined in each case from approximately 30 tests after the arcsin 冪P procedure (Ref 49). Shot peening at room temperature increases the fatigue strength Rfb for about 90 MPa (13 ksi) from 440 MPa (65 ksi) to 530 MPa (80 ksi) compared to the ground condition. Compared to that, peening at 200 and 290 C (390 and 555 F) increases the fatigue strength to 590 and 640 MPa (85 and 95 ksi), respectively.

σa,s, MPa 0.9

Resistance to Residual Stress Relaxation

400

The cyclic relaxation of macro residual stresses can be divided into four phases (Ref 16, 17, 50):

HWs/HWs,0

500 600 0.8

700

● Quasi-static relaxation during the first half of

800

the first cycle, which is caused by quasi-static deformation processes ● Quasi-static relaxation during the second half of the first cycle, which is influenced by the load reversal ● Cyclic relaxation at 1 ⱕ N ⱕ Ni (Ni ⳱ number of cycles to crack initiation) due to cyclic deformation processes, which usually leads to a linear reduction of the residual stresses as a function of the logarithm of the number of cycles according to Eq 21 due to cyclic creep ● Cyclic relaxation at Ni ⱕ N ⱕ Nf (Nf ⳱ number of cycles to failure) for sufficiently high stress amplitudes at the surface, which is

900 0.7

1000

0.6 1 (b)

10

102

103

104

105

106

107

Number of cycles, N

Ratio of half-width at the surface versus number of cycles during alternating bending tests of quenched and tempered AISI 4140 (450 C, or 840 F, for 2 h) at different surface stress amplitudes. (a) Conventionally shotpeened condition (Tpeen ⳱ 20 C, or 70 F). (b) Warm-peened condition (Tpeen ⳱ 290 C, or 555 F)

Fig. 23

66 / Effect of Materials and Processing enforced in the plastic zones at the tips of initiated surface cracks. Assuming a predominantly uniaxial macro residual stress state, it is a fundamental principle that relaxation of residual stresses at the surface will commence within the first cycle, if the stress amplitude ra reaches the critical loading stress rs,crit. It should be noted that in the case of pushpull tests the critical loading stress rs,crit is identical with the property |rlscrit(c)| (see the section “Residual Stress Relaxation by Uniaxial Deformation” in this article). If ra rs,crit, the macro residual stresses should remain stable in the first cycle. For N 1, relaxation of macro residual stresses can begin gradually if the critical loading stress amplitude ra,crit is exceeded (Ref 16, 17, 40, 41, 47, 48, 50): ra ra,crit

Thus, the property ra,crit has the meaning of a resistance against relaxation of macro residual stresses. Equation 16 is equally valid for the critical cycling loading stress ra,crit if Re(c),s is replaced by the corresponding cyclic yield strength for surface R cycl e,s . That means for a predominantly uniaxial residual stress state, relax-

200

ation of macro residual stresses starts together with cyclic plastic deformation in the direct surface if this condition is fulfilled: rs ␣a ⳱ ra,crit ⳱ Rcycl e,s ⳮ m • |rs |

(Eq 22)

The property m has the meaning of a residual stress sensitivity factor. In this consideration, it is assumed that m ⳱ 1. The macro residual stresses are stable if the condition is fulfilled: rs ra ra,crit ⳱ Rcycl e,s ⳮ |rs |

(Eq 23)

For cyclic bending tests under the conditions illustrated in Fig. 27, the critical loading stress rs,crit can be found by plotting the residual stress values after the first cycle from Fig. 22 versus the loading stress on the surface. This is given in Fig. 28 for conventionally peened and warmpeened samples. The data points at N ⳱ 1 show that the critical loading stress at which quasistatic residual stress relaxation begins is much higher for the warm-peened condition (rs,crit ⳱ 500 MPa, or 70 ksi) than for the conventionally peened variant (rs,crit ⳱ 310 MPa, or 45 ksi) due to the above-mentioned strain aging effects. The residual stress relaxation during cyclic loading

Tpeen = 20 °C

l

σrs, MPa

0

−200

N=0

−400

N=1 N = 10 N = 102 N = 103

−600

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35 0.40

Distance from surface, mm (a) 200

Tpeen = 290 °C σa,s = 1000 MPa

l

σrs, MPa

0

−200

N=1 N = 10

−400

N = 102 −600

N = 103

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35 0.40

Distance from surface, mm (b) Macro residual stress in longitudinal direction versus distance from surface for quenched and tempered AISI 4140 (450 C, or 840 F, for 2 h) after different numbers of cycles at the surface stress amplitude of 1000 MPa (145 ksi). (a) Tpeen ⳱ 20 C (70 F). (b) Tpeen ⳱ 290 C (555 F)

Fig. 24

Knowledge of the critical loading stress rs,crit and the initial residual stress value rrs s at the surface enables the estimation of the compressive yield strength of the peened surface region Re(c),s with Eq 20 if the property |rlscrit(c)| is substituted by rs,crit according to: (Eq 24)

Applying Eq 24 for the shot-peened variants investigated, clear differences of Re(c),s can be recognized (see Table 3) (Ref 48). For both variants, however, the resulting compressive yield strength at the surface is smaller than that of the core region, which is qualitatively in agreement with the results in Table 2. This is also due to the Bauschinger effect. However, the Bauschinger-induced work softening is much smaller for the warm-peened samples than for the samples peened at room temperature, due to the dynamic and static strain aging effects that occur during and after warm peening. By using the critical loading amplitude ra,crit as well as the residual stresses at the surface rrss,N⳱1 after N ⳱ 1, and the assumption that the residual stress state at the surface is still almost axisymmetric, the cyclic yield strength at the surface Rcycl e,s can be calculated similarly to Eq 24 by: 2 rs 2 rs Rcycl e,s ⳱ 冪(ra,crit) Ⳮ (rs,N⳱1) Ⳮ rs,N⳱1 • ra,crit (Eq 25)

N=0

−800

Evaluation of the Relaxation Behavior

|Re(c),s| 2 rs ⳱ 冪(rs,crit)2 Ⳮ (rrs s ) Ⳮ rs • rs,crit

σa,s = 1000 MPa

−800

due to cyclic creep is characterized by a linear reduction of residual stresses with increasing logarithm of the number of cycles for 1 ⱕ N ⱕ 104 according to Eq 21. Therefore, the residual stress values at the surface after 104 cycles from Fig. 22 can be taken as a measure of the degree of cyclic residual stress relaxation. These values are shown also in Fig. 28 for both shot-peened variants versus the absolute value of the applied loading stress amplitude at the surface ra,s. The linear fit of these points intersects the line fitted through the residual stresses measured at N ⳱ 1 at the critical loading amplitude ra,crit, which is a measure for the onset of cyclic residual stress relaxation. This procedure leads to ra,crit ⳱ 514 MPa (74 ksi) for the conventionally peened condition and ra,crit ⳱ 714 MPa (103 ksi) for the warm-peened condition (see Fig. 28).

These values are listed in Table 4 (Ref 48). It can be seen that Rcycl e,s for the conventionally peened samples is much smaller than for the warm-peened state. Moreover, the ratio of the calculated cyclic yield strength at the surface and that for the core region Rcycl ⳱ 1090 MPa, or e 160 ksi) found in push-pull tests (Ref 28) indicates that the cyclic work softening that is typical for quenched and tempered steels does not apcycl pear in the warm-peened variant Rcycl ⳱ e,s /Re 1.07). The increase of Rcycl at the warm-peened e,s


Behavior of Micro Residual Stresses Residual stress relaxation when N l can be attributed to cyclic plastic deformation. In this case, the dislocation arrangements present in the as-received materials are rearranged to configu-

Summary The stability of the mechanically treated surface state of components during the application of thermal and/or mechanical energy is desirable

800

P = 50% 700

Tpeen = 290 °C Tpeen = 200 °C

600

Tpeen = 20 °C 500 Ground 400 104

105

106 Nf

640 590 530

Rfb, MPa

rations characteristic of the fatigued condition at the given stress amplitude. Especially for steels with high dislocation densities (cold-worked as well as hardened or quenched and tempered conditions), dislocation rearrangements are frequently associated with work-softening processes in the microcrack-free stage of fatigue. Rearrangement of dislocations from configurations typical of the machined or heat-treated condition to that of the fatigued state is fundamental to the relaxation of macro residual stresses. Residual elastic strains associated with the macro residual stresses are once again converted into microplastic strains. If fatigue softening processes are involved, relaxation of micro residual stresses can also be expected. In the case of machined and heat-treated materials, this manifests itself in decreasing hardness and sharper x-ray interference lines (Ref 16, 17). Differences in the residual stress relaxation behavior of cold-worked, machined, and heat-treated materials under cyclic load can be attributed to different dislocation arrangements and densities. The closer the similarity to the dislocation configuration characteristic of fatigue, the less the extent of dislocation rearrangement and hence of residual stress relaxation.

σa,s, MPa

samples is assumed also to be the result of a very strong pinning of dislocations by clouds of carbon atoms and extremely fine carbides that exist due to strain aging effects. This pinning is so strong that even at highest loading amplitudes, ra,s, the pinned dislocations cannot move. Therefore, dislocations that were newly generated during cyclic loading cause the macro residual stress relaxation. The increase of the half-widths for these variants during alternating bending tests (see Fig. 23) is a further hint for this assumption. With these relationships, the effects of the different peening treatments on fatigue strength can be interpreted. Compared to the conventionally peened condition, the significantly higher fatigue strength of the warm-peened variants cannot be explained only by the slightly higher compressive residual stresses. Moreover, their higher stability seems to be the main reason for this behavior.

440

107

108

S-N curves (failure probability, P ⳱ 50%) for quenched and tempered AISI 4140 (450 C, or 840 F, for 2 h). Samples shot-peened at different temperatures are compared with the ground condition.

Fig. 26

Cross section area

Surface

4.0


N=0 N=1 N = 10

3.5

σsrs

HW, °2θ

N = 102

Core

0

N = 103

σrs

σrs c

3.0

2.5 Surface 2.0

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35 0.40


Simplified distribution of longitudinal macro residual stress for residual stress relaxation due

Fig. 27 to bending

(a) 4.0


−100

N = 1 N = 104 Tpeen = 20 °C

N = 102

−200

Tpeen = 290 °C

N = 103

−300

l,s

3.0

σrs , MPa

N=1 N = 10

3.5 HW, °2θ

0

N=0

2.5

−400 −500

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35 0.40

Distance from surface, mm (b) Half-width versus distance from surface of a quenched and tempered AISI 4140 (450 C, or 840 F, for 2 h) after different numbers of cycles at a surface stress amplitude of 1000 MPa (145 ksi). (a) Tpeen ⳱ 20 C (70 F). (b) Tpeen ⳱ 290 C (555 F)

Fig. 25

σs,crit

−600 −700 200

2.0

σa,crit σs,crit

σa,crit 400

600 800 |σs| or σa,s, MPa

1000

Macro residual stress at the surface in longitudinal direction versus absolute value of surface stress or surface stress amplitude of quenched and tempered AISI 4140 (450 C, or 840 F, for 2 h) after alternating bending to N ⳱ 1 and N ⳱ 104 in conventionally shotpeened and warm-peened conditions

Fig. 28

68 / Effect of Materials and Processing Table 3 Quasi-static surface yield strength in compression Re(c),s of quenched and tempered AISI 4140 in conventionally peened and warm-peened conditions Shot peening temperature C

20 290

rrs s

rs,crit

Re(c),s

F

MPa

ksi

MPa

ksi

MPa

ksi

Re(c),s /Re(c)

70 555

310 500

45 75

ⳮ600 ⳮ660

ⳮ90 ⳮ95

801 1008

116 146

0.60 0.78

Table 4 Cyclic surface yield strength Rcycl e,s of quenched and tempered AISI 4140 in conventionally peened and warm-peened conditions Shot peening temperature C

20 290

rs,rs Nⴔ1

ra,crit

cycl Re,s

F

MPa

ksi

MPa

ksi

MPa

ksi

cycl Rcycl e,s /Re

70 555

514 714

74 103

ⳮ520 ⳮ620

ⳮ75 ⳮ90

895 1156

130 168

0.82 1.07

in order to preserve improvements in mechanical properties. In this connection, residual stress relaxation behavior is the most important aspect to be considered. Macro and micro residual stresses can be reduced or completely relaxed either by heat treatment or under unidirectional or cyclic mechanical loading. Elastic residual strains related to macro residual stresses can be converted into microplastic strains by suitable deformation processes—for example, by dislocation slip or creep. The onset of residual stress relaxation is determined by the critical applied loading stress, rcrit, with the meaning of a resistance against relaxation of residual stresses, which is accompanied by the beginning of plastic deformation. In the case of thermal treatment (rcrit ⳱ 0), unidirectional deformation (rcrit ⳱ rlscrit(c) and rs,crit, respectively), as well as cyclic loading (rcrit ⳱ ra,crit), residual stress relaxation occurs when under the assumption of a predominantly uniaxial stress state this relationship is valid: |rls| ⳱ |rcrit| ⳱ |Ri| ⳮ |rrs|

(Eq 26)

The characteristic materials resistances are Ri ⳱ Rce for thermal treatment, Ri ⳱ Re(c),s and Re(t),s, respectively, for unidirectional loading, and Ri ⳱ Rcycl e,s for cyclic loading. Stability of the residual stress state exists, and residual stress relaxation does not occur, if this condition is fulfilled: |rls| |rcrit| ⳱ |Ri| ⳮ |rrs|

sufficient stable obstacles to dislocation movement, which increases rcrit at the loads given. For T 0.4 Tm (Tm ⳱ melting temperature in K) these could, for example, be grain and phase boundaries, finely dispersed incoherent particles, coarse secondary phases, and, as long as no diffusion can occur, solute alloying atoms and certain dislocation arrangements. The onset and extent of residual stress relaxation is influenced in a complex manner by the combined effects of heat treatment, unidirectional and cyclic stress, and multiaxial applied and/or residual stress states. The kinetic of residual stress relaxation is essentially determined by the difference |rls| Ⳮ |rrs| ⳮ |Ri|. The greater the applied loading stress is—that is, the higher the temperature, the longer the time, and the greater the magnitude and amplitude of the applied stress, plastic deformation, or number of cycles—the greater the increase in the rate of residual stress relaxation. The rate often increases as the absolute value of the residual stress increases. The fewer the stable obstacles to dislocation slip, the faster the rate.

(Eq 27)

The applied loading stress r may be zero, have a value that does not vary with time (e.g., thermal residual stress relaxation), have a steadily increasing value (e.g., unidirectional deformation), or have a value varying periodically with time (e.g., cyclic deformation). Since, according to Eq 26, the onset of residual stress relaxation depends on the resistance of the material rcrit as well as on the applied loading stress r, all the parameters characterizing the state of the material as well as temperature and time or frequency are of importance. The onset of residual stress relaxation is delayed by the presence of

REFERENCES 1. E. Macherauch and V. Hauk, Ed., Proc. Int. Conf. Residual Stresses 1, DGM-Informationsgesellschaft, Oberursel,1987 2. B. Beck, S. Denis, and A. Simon, Ed., Proc. Int. Conf. Residual Stresses 2, Elsevier Applied Science, London, 1989 3. H. Fujiwara, T. Abe, and T. Tanaka, Ed., Proc. Int. Conf. Residual Stresses 3, Elsevier Applied Science, London, 1992 4. M. James, Ed., Proc. Int. Conf. Residual Stresses 4, Society for Experimental Mechanics, 1994 5. T. Ericsson, M. Oden, and A. Andersson, Ed., Proc. Int. Conf. Residual Stresses 5, Institute of Technology, Linko¨pings Universitet, 1998 6. A. Niku-Lari, Ed., Proc. Int. Conf. Shot Peening 1, Pergamon Press, Oxford, 1982 7. H.O. Fuchs, Ed., Proc. Int. Conf. Shot Peen-

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28.

29. 30. 31.

32.

33. 34.

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Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking A.I. Kovalev, D.L. Wainstein, V.P. Mishina, Surface Phenomena Researches Group, Moscow V.V. Zabilsky, Physical Technical Institute, Russia

METALLURGISTS AND METALS SCIENTISTS traditionally consider hydrogen an undesirable impurity in metals and alloys, associating its presence with the origination of floccules, porosity, and corrosion. Due to specific behavior of the element in steel, it makes worse technological and exploitation properties of the material. Hydrogen embrittlement (HE), as well as other types of brittle fracture, of metals result from nucleation and development of microcracks caused by internal stresses. Peculiarities of HE are involved with steel physical properties and mechanisms of its interaction with hydrogen. Considerable hydrogen solubility difference depending on external factors, a high diffusion mobility, and the capability to form molecules on interfaces that induces a high internal hydrostatic pressure all promote various types of brittleness.

Hydrogen in Steel Sources of Hydrogen Penetration in Steel. Water-containing raw charge materials and fur-

nace gases involved in the open-hearth (Martin’s) process are the main sources of hydrogen penetration in steel (Ref 1). Industrial cast usually contains H2 of not less than 1.5 to 2.0 cm3 / 100 g. Use of vacuum evaporation in a ladle or at casting is the only way to decrease the content of hydrogen in steel down to a concentration not affecting the mechanical properties, of the steel. Penetration of hydrogen into a carbonic and alloyed steel was observed in a hydrogen atmosphere at a high pressure (Ref 2, 3). Metal welding is one of the most dangerous technological processes inducing penetration of hydrogen in steel. During the process, hydrogen, contained in electrode coatings as organic compounds and water molecule, is dissociating, then being in the atomic state it dissolves in a molten metal and partly diffuses into neighboring zones of the basic material. Various electrochemical processes, etching in acids, and interaction with liquid agents containing hydro-sulfide also promote to steel saturation with hydrogen. Therefore, hydrogen is an inevitable impurity in steel pro-

T, °C

Solubility of hydrogen, cm3/100 g Fe

102

900 800 700

600

500

K ⳱ K0 p1 / 2 exp(D

H / RT)

lg H ⳱ ⳮ1376/T ⳮ 0.665

400

(Eq 1)

where K is constant of solubility, K0 is constant of solubility in standard conditions, R is gas constant, T is temperature, and DH is endothermal heat of solution. Those of hydrogen in pure iron, calculated by W. Geller and T.H. Sun (Ref 4) and then experimentally refined (Ref 5–7), account for 27230 J/ 0.5 mol H2 (6500 cal/0.5 mol H2). Solubility of hydrogen in iron at various temperatures and atmospheric pressures (Ref 5– 8) is shown in Fig. 1. From recent data, solubility of hydrogen in a metal also depends on its purity, microstructure, grain size, and a character of distribution of dislocations (Ref 9–15). The solubility curve equation for ␣-Fe at H pressure of 0.1 MPa (0.015 ksi) is: (Eq 2)

where H is hydrogen concentration, at.%. Temperature dependence of hydrogen solubility in cFe can be evaluated from (Ref 3): lg H ⳱ ⳮ1411/T ⳮ 0.468

(Eq 3)

That in liquid iron at a pressure of approximately 0.1 MPa (0.015 ksi) lg H ⳱ ⳮ1820/T Ⳮ 0.112

1

10–1 0.4

Fig. 1

1700 1400 1100

duced during most modern metallurgical methods. Hydrogen Solubility and Diffusion in Steel. Hydrogen solubility in steel depends on temperature and pressure to suit the following equation:

0.6

0.8

1.0 1.2 1000/T, K–1

1.4

1.6

1.8

Hydrogen solubility in iron in dependence on temperature at atmospheric pressure. Data source: Ref 2–5

(Eq 4)

A large quantity of H2, measurable with tens cm3 per 100 g of metal, can be brought into a steel from a gas phase only at high pressures and temperatures (Ref 16). At standard conditions, hydrogen gradually escapes from steel, its solubility in steel then being negligible. At temperatures higher than 200 C (392 F) a real solid solution

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 71 of hydrogen in iron becomes unstable (Ref 17). Thermodynamic data of H diffusion in iron at high temperatures are well reproducible in various works (Ref 18–20) that cannot be told about the data obtained below 200 C (392 F). Diffusion mobility of hydrogen in iron at low temperatures varies in a wide range and depends on imperfection of the crystal lattice and the content of impurities. For example, Ref 21–24 there were obtained values of the diffusion coefficient at 25 C (77 F) varying from 10ⳮ9 up to 10ⳮ5cm2 /s. When studying diffusion in pure iron by intensity of hydrogen emission out of massive samples, it was found that its diffusion mobility is sharply depressed at lower than 200 C (392 F) (Fig. 2). Above 200 C (392 F) the diffusion coefficient is the following: D ⳱ 1 • 4 • 10ⳮ3 exp (ⳮ3200/ kT) cm2 /s

(Eq 5)

Below 200 C (392 F) that is: D ⳱ 0.12 exp (ⳮ7820/ kT) cm2 /s

(Eq 6)

Just as impurities forming interstitial solid solutions, hydrogen interacts with various crystal defects, creating nonuniform solid solutions. Presence of microdeformation near the crystal imperfections increases hydrogen solubility there. Therefore, the solubility of hydrogen in steel rises with an increase in density of defects. When diffusing inside the crystal, hydrogen atoms are retained by the lattice imperfections, and its effective diffusion coefficient essentially decreases. This results in sharply diminishing diffusion mobility of hydrogen in iron at low temperatures. Defects retaining hydrogen are known as traps. Its concentration controls an excessive hydrogen solubility, compared with the lattice one (i.e., in an ideal lattice). Moreover, the number of places capturing hydrogen is inversely proportional to the value of the effective diffusion coefficient. The role of traps can be played by edge dislocations, boundaries of mosaic blocks or grains, single pores uniformly distributed in crystals, inclusions of a second phase, and atoms of alloy-

ing elements. The energy of hydrogen interaction with different structural components varies in a narrow interval (0.1–0.4 eV per atom). In particular, the one with dislocations in iron was evaluated as about 1.6 • 10ⳮ20 J (0.1 eV per atom) (Ref 25). The Role of Stresses. Hydrogen atoms interact with any anisotropic strain field, similar to its interaction with dislocations. If concentration of hydrogen atoms is insignificant, then distribution of the dissolved ones in a strain field of a crystal lattice can be found using: C ⳱ C0 • exp (ⳮU/kT)

(Eq 7)

where C is a concentration of hydrogen in a certain point of the field, C0 is an average concentration, k is the Boltzmann constant, T is the kelvin temperature, and U is the interaction energy of hydrogen atoms with the strain field in the place of a defined concentration, C. Accounting for only hydrostatic components of the field, the interaction energy, U, makes: U ⳱ p • dV

(Eq 8)

where p is an average hydrostatic pressure, that is, p ⳱ 1⁄3(rxx Ⳮ ryy Ⳮ rzz), and dV is the lattice volume alteration under the influence of hydrogen. From these equations it follows that at a constant temperature the following condition is valid: ln (C/Co) • A ⳱ 1⁄3(rxx Ⳮ ryy Ⳮ rzz)

(Eq 9)

where A ⳱ kT/dV. According to (Eq 9), hydrogen in the crystal lattice is redistributed under stress influence. These deductions were confirmed with experiments (Ref 26, 27). It is settled that the effective diffusion coefficient of hydrogen essentially decreases, and its solubility increases under loading the metal in a macro-elastic interval (below yield strength). Thus, stresses promote nucleation of new reversible hydrogen traps, disappearing after elimination of an external stress. Similar sites arise near the crack tip, in a several

micron size zone of maximal three-axis stresses, where hydrogen dissolved in the metal lattice diffuses and its concentration in steel at equilibrium conditions attains maximal values as: C rmax ⳱ C0 • exp (1.9 • 10ⳮ3 • ry)

Therefore, in steel having the yield strength ry of approximately 1725 MPa (250 ksi) the equilibrium concentration of hydrogen in the zone of maximal tensile stresses exceeds its content in volume by 26 times (Ref 28) (Fig. 3). At absence of a crack or any other concentrator, the stresses are localized in front of a dislocation pile-up, where considerable enrichment with hydrogen also can be observed. Both factors, concentration of tensile stresses and dissolved hydrogen, initiate nucleation of cracks and promote its propagation. Hydrogen Effect on Structure and Phase Transformations in Steel. The basic consequence of hydrogen presence in iron and steels at solidification is the development of porosity, due to a gas-eutectic transformation (Ref 29) similar to the well-investigated eutectic one. Total amount of pores is proportional to those of dissolved hydrogen and is inversely proportional to the pressure of crystallization. Hydrogen in steel stabilizes austenite and decreases the critical point A3, the temperature of martensite transformation, and the critical rate of cooling for quenching (Ref 29). This is the cause of martensite formation even in a carbon-free iron at standard rates of cooling. Unlike a carbonic martensite, at low temperatures of tempering there arises a hydrogen-free martensite and a gaseous hydrogen escaping from a sample or accumulating in micropores, creating high pressure and microcracks like floccules (Ref 29). States of Hydrogen in Steel. Hydrogen absorbed by metal can be present in various states: ● An interstitial solid solution ● A segregating one on imperfections of the

crystalline structure ● Adsorbing one on the surface of micropores

and particles of second phases

T, °C 10−7

800

400

200

100

25

σ1

D, cm2/s

10−7

10−7

10−7 10−7 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 1000/T, K–1

Fig. 2

Diffusions of hydrogen in pure annealing iron. Source: Ref 18–25

1

2

H

H H2

HH

H2 H2

H HH

H

HH

H HH H

H

H H2

H

H2 H2

H

H

H

H

H H

H

Fig. 3

(Eq 10)

Influence of hydrogen on crack propagation. Source Ref 28

H

H H H

72 / Effect of Materials and Processing ● In a molecular form, accumulating in micro-

pores ● Forming hydrides ● Interacting with alloying elements and second phases When hydrogen solutes in transition metals, its s-electrons transfer to a vacant d-shell of a metal with the lower energy level. The free proton of hydrogen is partly screened by electrons, which as electronic gas can be involved in its moving in the metal lattice (Ref 28). Hydrogen reduces a shear modulus of ␣-iron; at 100 K temperature, this is approximately an 8% decrease per 1% of hydrogen atoms (Ref 30). At a room temperature and standard atmosphere pressure the solubility of hydrogen in steel is insignificant; its supersaturated solid solution is unstable and decomposes over time. One part of hydrogen dissolves into the atmosphere and another is caught by crystalline lattice imperfections. It is necessary to distinguish two types of defects active in relation to hydrogen—pores (or collectors) and traps. Collectors represent volumes where hydrogen molization is observed and a considerable hydrostatic pressure develops. Traps represent defects of smaller sizes than collectors, such as vacancies, substitution and interstitial atoms, edge dislocations, its pile-ups and thresholds, high-angle boundaries, and fields of a volume tension (i.e., near the crack tip). There is a principle difference between traps and collectors. Transition of hydrogen from a crystal lattice into traps is reversible, while transition into collectors is accompanied by formation of H2 molecule and is nonreversible. The considered features depend on a steel structure. Ferrite-Pearlite Steels. Nonmetallic inclusions, such as manganese sulfides, are traps of hydrogen in these soft steels. The maximum solubility of hydrogen in such steel depends not only on the content but also on the shape of manganese-sulfide particles. The rolled-out prolonged ones increase hydrogen solubility and decrease its effective diffusion coefficient in

direction perpendicular to the planes enriched by the inclusions. Globularization of the sulfides decreases hydrogen solubility and increases its effective diffusion coefficient. Sulfide-matrix boundaries are the sites of a preferential accumulation of dissolved hydrogen, essentially weakening the cohesive forces and promoting disruption of the interface continuity. Martensitic Steels. High interior residual stresses inducing an elastic bend of the martensite crystals and localizing in places of its junction with boundaries of primary austenitic grains are characteristic for these steels having the structure of an untempered martensite. In addition, martensitic steels feature a high density of crystalline structure defects, which are boundaries of grains and twins, single dislocations. All these elements of structure affect solubility and diffusion of hydrogen in steel. Dispersed cementite particles observed after tempering also act as traps for hydrogen. In maraging steels such a role is executed by intermetallic-matrix interfaces and elastic deformation fields around the inclusions. Types of Hydrogen Embrittlement. In general, hydrogen affects metals in two ways: ● Physical action at low temperatures when

chemical reactions are not observed

● Physical-chemical effect when a chemical in-

teraction of hydrogen with various phases and components of an alloy on the surface and in the bulk is observed. The attempt to enumerate all the phenomena tied with harmful influence of hydrogen in metals was made in 1972 (Ref 31). Reference 28 specifies the following results. ● Hydrogen corrosion: Develops in carbonic

● ●

● ● ●

●

Fig. 4

Microfloccule in ferrite-pearlite steel. Courtesy of A.I. Kovalev

and low-carbon steels at long-term exposure in a high-pressure hydrogen at high temperatures. The cause of this brittleness is hydrogen-carbon interaction accompanied by steel surface decarbonization and methane formation (Ref 32). Primary gas porosity: Develops due to hydrogen precipitation in a molecular form in a smelt or in the front of crystallization (Ref 33) Secondary porosity: Develops at decomposition of a supersaturated solid solution with formation of small submicroscopic pores filled by hydrogen (Ref 33, 34) Decreasing plasticity under tension: Observed at low-rate deformation of steel containing hydrogen (Ref 33, 34) Delayed fracture: Steel cracking under constant loading below the yield limit Floccules or disruption cracks: Defects mainly found in large forged pieces. Floccules are the result of gas hydrogen precipitation in pores and micro flaws during steel crystallization and cooling of the slab or the forged piece (Ref 35, 36). Blisters or bubbles: Develop at electrolysis, metal exposing in a water vapor or in corrosion agents containing H2S (Ref 33, 35)

● Corrosion cracking: For the most part is tied

with precipitation of an atomic hydrogen during corrosion reactions, its adsorption on the surface and dissolution in metal with development of hydrogen embrittlement Main Aspects of the Hydrogen Embrittlement Theory. Definite kinds of HE involve two basic aspects—the mechanism of hydrogen transfer to a fracture place, and 2-H influence on the steel fracture toughness. Usually hydrogen is transported by moving dislocations or diffuses (itself) through the crystal lattice under inhomogeneous fields of elastic stresses (Ref 37–40). Being in steel, hydrogen decreases the fracture work by influencing mechanisms of plastic deformation and reducing the energy of disruption of interatomic bonds near the crack tip. In ferrite-pearlite steels, HE is accompanied by nonreversible structural damages in the form of micropores containing molecular hydrogen under high pressure. Those conditions, however, are not enough for steel fracture that occurs due to hydrogen migration together with moving dislocations into the zone of deformation near the tip of a developing crack. Fracture of soft steels is always accompanied by a considerable plastic deformation essentially affected by hydrogen (Ref 37) facilitating the beginning of plastic deformation of ferrite due to adsorption effects. However, hydrogen increases the hardening coefficient at higher deformation degrees (Ref 41). As a result, it localizes the plastic deformation in the zone of fracture, essentially reducing the plasticity of steel and diminishing the total fracture energy. In steels with martensitic structure, hydrogen migrates through the field of elastic deformations into the zone of three-axial stresses before the front of a crack (Ref 42, 43). When the content of external and dissolved hydrogen reaches a critical value, the crack immediately propagates by the mechanism of disruption of interatomic bonds (Ref 44). In this case, the basic mechanism of HE is tied with breaking weakened bonds in grain boundaries and decreasing the plastic deformation energy in local sites of ductile fracture. Forms of HE of steels are numerous, but only in some cases (floccules, delayed fracture, and stress corrosion) the role of macro and micro stresses influencing hydrogen behavior is clearly defined.

Floccules Floccules are interior cracks (flaws) observed in steel: in the central zone of deformed preforms and, as an exception, in some sites of molded wares. In polished (not etched) cross macro-grinds these defects look like hairline cracks (Fig. 4) opened along a plastic flow direction of forged pieces and rolled products. Only when considerable axial stresses are present in a pre-form, the orientation of floccules al-

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 73 ters and can be perpendicular to the axis. By macroscopic investigation of fracture surfaces of steel affected by floccules, the light brilliant spots of an oval shape are observed. Fractography research of those sites, using an electronic microscope, allows the detection of the micro quasi-chips involving a slightly expressed riverpattern picture, pores, and plastically opened hairline cracks (Ref 44). These defects can be found in all steels, but mostly they are observed in chromic, chrome-nickel, chrome-nickel-tungsten, and chrome-manganese steels. Floccules originate in forged pieces or rolled stock of large section some distance apart on the surface under accelerated cooling at temperatures below 150 to 200 C (302 to 392 F), sometimes at 300 C (572 F), but more often at room temperature. One of the main reasons of floccules formation is a dissolved hydrogen that does not have enough time to escape large forged pieces at temperatures below 200 C (392 F) and diffuses into neighboring pores, creating molecules and considerable gas pressures (Ref 45, 46). However, hydrogen present in metal is a necessary, but not the only, condition for origination of the defects under consideration. Internal tensile stresses developing under plastic deformation, non-uniform cross section cooling of steel wares, and structural transformations stimulate formation of floccules (Ref 47–49). Decrease of rupture resistance in sites enriched by nonmetallic inclusions or in liquation zones promotes this kind of brittleness. The most favorable conditions occur when the flocculation temperatures coincide with an interval of development of martensite transformation. Dissolving in austenite in a higher quantity than in martensite, hydrogen during martensite transformation moves from a solid solution into pores. Resultant high hydrostatic pressures summarize with stresses caused by volume alteration under c → ␣ phase transformation. For this reason, a quenched-in-air chrome-nickel steel is very susceptible to flocculation. This is the result of total action of the molecular hydrogen pressure in pores and the field of tensile stresses existing in the metal (Ref 50). Floccules are developing during the time, and the process quite often does not terminate when cooling finishing and continues for many hours at room temperature. At high contents of hydrogen and temperatures approximately 400 to 600 C (752 to 1112 F), formation of H2 molecules in pores results in intergranular brittle failure of steel, without participation of external (relative to the pores) stresses. For fracture at lower hydrogen concentrations and temperatures below 200 C (392 F), the combined effect of tensile stresses and gas pressure in pores is necessary. In that case, a brittle transgranular failure develops. Processes of formation of floccules are nonreversible. An extremely slow cooling after deforming a preform made of steel susceptible to flocculation prevents its development. The same effect was observed at a prolonged isothermal annealing at heightened or high temperatures. However, heating in an atmosphere containing

even 12 to 15% hydrogen can again make steel susceptible to flocculation. That tendency of steel can develop at welding or cementation when wares are quenched directly after treatment heating. Floccules are not observed in a number of superalloyed steels such as ferritic, semiferritic, and austenitic. High-speed steels are not susceptible to flocculation, in spite of the fact that very high internal stresses at accelerated cooling develop there. Influence of alloying elements on steel susceptibility to flocculation is tied with action on austenite transformation under cooling, anisotropy of properties, and a quantity of generated hard inclusions. At Ac3 temperature decreasing and Ac3-Ar3 hysteresis increasing the diffusion of hydrogen and its escaping off steel pre-forms becomes slower. This explains a high susceptibility to flocculation of a chrome-nickel steel after its alloying with molybdenum or tungsten. Manganese and silicon, promoting anisotropy of mechanical characteristics of a rolled stock, favor its susceptibility to flocculation. Increasing concentration of carbon in a hydrogen-containing steel promotes formation of methane and floccules. Preventing Flocculation in Steel. The main condition of preventing floccules in steel is decreasing its supersaturation with hydrogen and elimination of H2 molecule formation at temperatures below 200 to 300 C. Also, it is necessary to minimize the anisotropy of mechanical properties of deformed pre-forms. Melting and casting of steel in a vacuum is the basic and the most effective way to eliminate of floccules. Transportation to forging and rolling of ingots in a hot state, being in common practice, is undesirable for a steel susceptible to flocculation, because a high quantity of hydrogen remains. Special heat treatment schemes preventing flocculation are available for large pre-forms made of steels of various classes.

Delayed Fracture in Steels Delayed fracture, or the real hydrogen embrittlement, is an evolving-in-time process of cracking (fracture) materials exposed to hydrogen and static stresses. This type of hydrogen embrittlement is the greatest practical problem, especially for high-strength steels, as far as the initiation and the growth of crack with hydrogen present are observed at stresses much less than the yield strength of steel. The crack growth up to the critical value with hydrogen present begins accordingly at the threshold value of the stress intensity coefficient, K1th, which has a much lower value than the fracture toughness in the air or inert medium, K1C. Thus, the danger of the delayed fracture process exists in that the fracture of constructions occurs under loads that are entirely undangerous under normal operating conditions (i.e., in the absence of hydrogen). Another important point is that the process of delayed fracture develops most intensively at temperatures close to room temperature, at which the overwhelming majority of materials and products are used.

The main factors determining the kinetic features of delayed fracture are the chemical composition and the structure of steel, a hydrogen content, the presence of stress concentrators, the test temperature, the amount and the distribution of impurities and nonmetallic inclusions, and the presence of inherent stresses (Ref 29). In this case the delayed fracture can develop both under the effect of external hydrogeneous media and inherent hydrogen having entered the metal as the result of melting, welding, etching, anticorrosive electroplating, and other production operations. An example is in the formation of so-called cold cracks in the heat-affected zone while welding alloyed steels (Ref 51). The increased hydrogen content in the near-weld zone is the result of hydrogen diffusion from the melt where it enters due to dissociation of moisture in electrode coating (welding flux) (Ref 52, 53). The effect of the steel-strength level on the resistance to delayed fracture has been supported by many studies. It has been shown that at the low-strength level (up to 750 MPa, or 110 ksi) the influence of hydrogenation is comparatively moderate. At strength more than 1000 MPa (145 ksi), the resistance to delayed fracture reduces so that the value of the threshold stress, rth, decreases to ⱕ200 MPa (29 ksi) (Ref 53). It has been found also that as to the high-strength steels, especially in the presence of stress concentrators, delayed fracture can develop even with the low-hydrogen content not exceeding approximately 10 – 4 at.% (1.1 cm3 per 100 g of metal) (Ref 1). Numerous examples of delayed fracture of products fabricated from highstrength alloyed steels (shafts made of Fe-0.45C2Ni-Cr-Mo-V steel, axles made of Fe-0.2C-2Cr4Ni steel in the carburized state, etc.) are presented in a monograph (Ref 54). The presence of internal hydrogen in association with high residual stresses with a value reaching 1000 MPa, (145 ksi) is the most commonly occurring cause for delayed fracture in the case under consideration. A great deal of publications in which various methods of hydrogenation are presented are devoted to the study of delayed fracture of steels. A main body of experimental data has been obtained with the use of the cathode polarization method. Therefore, in analysis of the influence of chemical composition and structure, it is necessary to take into consideration that, because of electrolytic hydrogenation of large-size samples, the occurrence of nonuniform distribution of hydrogen over the section can give rise to the largescale effect (Ref 55). Hydrogenation from the gas phase under conditions of elevated temperatures (above 473 K) may cause irreversible damages in the form of bulgings and pores appearing because of high pressure during the formation of inner molecular hydrogen or methane. Additionally, in this case the probable surface decarburization can also have an effect on the initiation and growth kinetics of cracks (Ref 56). From a practical standpoint, on the contrary, these im-

74 / Effect of Materials and Processing portant experiments make it possible to simulate service conditions for the purpose of developing adequate measures to eliminate delayed fracture. Main Criteria of Delayed Fracture of Steels. In general, steel delayed fracture takes

σ1 1 Stress, σ

2

σth

Time for failure, τ Curves of long-term strength of hydrogenated steel (scheme). 1, time before failure s; 2, incubation period si, r1, upper critical stress; rth, lower criticastress. Source: Ref 35, 56, 57

Fig. 5

Stress, σ, MPa

900

4

700

3 4′

500

2′

2

300 1

100 0

3′

1′ 20

10

30 40 50 Time to failure, τ, h

60

100

Dependences of long-term strength of iron (1, 1⬘), steel Fe-0.2C (2, 2⬘), steel Fe-0.45C (3, 3⬘) and steel Fe-0.8C (4, 4⬘). 1–4, unhydrogenated state (testings in the air); 1⬘–4⬘ testings in the process of hydrogenation. Source: Ref 59

Velocity of crack propagation, dl/dt

Fig. 6

IV

III

II

I

K1c

K1t

Stress intensity factor, K1

Fig. 7

Schematic illustration of kinetic diagram of cracking of hydrogenated steel. Source: Ref 57

three stages—crack initiation; its slow growth up to the critical value; and the stage of the unstable, accelerated crack growth. It is common practice to characterize the sensitivity of steels to delayed fracture depending on their chemical composition and structure by so-called long-term strength dependencies (Fig. 5), which usually are represented in coordinates: applied stress r, logarithm s, where s is the time up to fracture. Dependencies mentioned are typical for both smooth samples and samples with the stress concentrator. The preliminary hydrogenation in constructing dependencies, s ⳱ f (r), can be performed by any of the known techniques—cathode polarization, for example. These dependencies take the analogous character on tests performed just in hydrogeneous media (e.g., on tests in gaseous hydrogen medium, hydrogen sulfide medium, or in the process of the electrolytic hydrogenation) (Ref 35, 56, 57). In an analysis of dependencies s ⳱ f (r), the following characteristics are used as the main parameters: ● The upper critical stress, r1, which corre-

sponds to the value of the tensile strength of hydrogenated samples ● The lower critical (threshold) stress, rth (i.e., the stress lower which the delayed fracture process does not develop) ● The time before the crack initiation, si (an incubation period) ● The time up to final failure, s, which characterizes the prolonged strength of steel (Ref 35). Thus, a “dangerous” area of stresses where the delayed fracture process develops is an interval between the upper and lower critical stresses. In this case the value of the lower critical (threshold) stress, rth, represents a crucial important characteristic, namely, the prolonged strength limit of steel under the specific conditions of hydrogen embrittlement. It is apparent that as the hydrogen content in steel increases, all of the parameters mentioned are changed. This especially affects the value of the threshold stress, rth; the duration of the incubation period, si; and the time up to fracture, s. From the data given in (Ref 58), for example, it follows that as the hydrogen content in highstrength steel (1600 MPa, or 232 ksi) increases, the duration of the incubation period successively decreases from several tens of hours to several seconds. The time up to fracture in the limiting case does not exceed 0.1 h. The duration of the incubation period, si, is influenced by the preholding under load including holding under stresses r rth. Reduction of si, observed in this case is due to the formation of sites with the increased hydrogen concentration, which then serve as points of the crack initiation (Ref 35). Curves of the long-term strength of iron, and steels Fe-0.2C, Fe-0.45C, and Fe-0.8C are given in Fig. 6 (Ref 59). Samples have been polished mechanically and annealed in vacuum. Delayed fracture tests have been carried out while holding the samples under load in the conditions of con-

tinuous cathode saturation with hydrogen in the 26% aqueous solution H2SO4 (the current density i ⳱ 10 mA/sm2). Smooth thin plates with the cross section of 0.8 ⳯ 3 mm (0.03 ⳯ 0.12 in.) that ensures the through saturation of samples with hydrogen have been used as samples. From the results obtained it is evident that the higher the hydrogen content in steel is, the more tangible the decrease of the long-term strength, and it does not practically take place in the case of armor-iron and low-carbon steel Fe-0.2C. The value of the threshold stress for steel Fe-0.45C is of 150 to 170 MPa (20 to 25 ksi) that is several times lower than the yield strength of this steel. The lifetime of samples with the stress concentrator under load is mainly determined by the time before the crack initiation (i.e., the duration of the incubation period) (Ref 55). In the study of crack growth it is worthwhile to construct socalled kinetic diagrams of cracking (i.e., dependencies of the crack growth rate, v, on the stress intensity factor, K1. To construct kinetic diagrams of cracking, fatigue precracked samples are used. The character of kinetic diagrams of cracking is shown schematically in Fig. 7. Some characteristic sections can be distinguished in the diagram. At section I, which corresponds to the threshold value of the stress-intensity factor, K1th, the crack does not practically grow or grows very slowly. Therefore, it is assumed that the value of K1th characterizes the condition of crack nonpropagation in metal. In section II, the crack growth rate increases rapidly, whereupon in region III, the crack growth rate over a wide range, K1, is retained practically unchanged. Unlike the stage of accelerated, unstable fracture (section IV), the stage of the slow, stable crack growth can embrace the greatest part of longevity of a product. It is apparent that the delayed fracture development at this stage is controlled by the rate of transferring hydrogen to the region of the crack top. At section IV, the crack growth rate increases rapidly again, and at K1 ⳱ K1C (plane-strain fracture toughness) the final fracture occurs. The characteristic most sensitive to the hydrogen content is the value of the threshold coefficient of stress intensity, K1th. According to data given in Ref 60, an increase of diffusely moving hydrogen content in high-strength steel Fe-15Cr-5Ni-2Cu-Ti from 0.14 • 10ⳮ4 to 2 • 10ⳮ4 at.% causes the value of K1th to reduce by 77%. Besides the main characteristics just discussed, a number of other characteristics also have been suggested for defining the sensitivity to delayed fracture. For example, dependencies of the initial coefficient of stress intensity, K10, the time up to fracture, s, type are suggested to be used (Ref 60). In this case long-term strength curves can be described by the logarithmic relations of the K10 ⳱ ⳮa • ln s Ⳮ b type bounded by the value K1C at the top and the threshold value of the stress intensity coefficient K1th at the bottom. In work (Ref 61) it was suggested to construct the long-term strength curves in coordinates r ⳮ 1/Zs, but not in conventional coordinates r ⳮ lg s. In this case dependencies of

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 75 the long-term strength s ⳱ f (r) are transformed into straight lines convenient for further treatment according to the equation r ⳱ rth Ⳮ c(1/ 冪s), where c is a constant. And finally, the material sensitivity to delayed fracture may be estimated by its sensitivity to the deformation rate, namely, by the degree of their plasticity decrease under static loading at the rate of e˙ ⳱ 10ⳮ4 ⳮ 10ⳮ6 secⳮ1. Such tests, for example, are in common practice among Japanese researchers in making an estimate of the sensitivity to the delayed fracture of high-strength maraging steels (Ref 62–64). Mechanism of Crack Initiation and Its Growth. It is the opinion of the authors who studied a phenomenon of delayed fracture, that in a qualitative sense the mechanism of the crack initiation when the inner hydrogen embrittlement is as follows. For a crack to be initiated, the critical concentration of hydrogen C* must be created in local sites. The hydrogen redistribution in the solid solution is initiated by the stress field produced by outer load. With the uniform distribution of tensile stresses, the value of the chemical potential of hydrogen, l0, is the same in the whole iron-hydrogen system; therefore, the hydrogen redistribution does not take place. With the nonuniform distribution of stresses, for example, because of the presence of a concentrator, the pattern is essentially changed. At the top of the concentrator (in the region of maximum tensile stresses), the hydrogen chemical potential, l1, becomes less than that one in the rest of the regions of the system, l2. The appearance of the chemical potential gradient (l1 l2) brings about the diffusion of hydrogen into the tensile stress region that with time gives rise to the critical concentration of hydrogen C* and the crack initiation. The critical concentration of hydrogen C* is directly proportional to the square root of the time of diffusion (C* ⳮ C0 ⳱ q冪t, where q is the coefficient of proportionality) and must be so much higher than the level of applied stresses is lower (Ref 61). It is apparent that the increase of the hydrogen content causes a decrease of the duration of the incubation period, si, which is necessary for creating the critical concentration of hydrogen. Lowering of the temperature gives the reverse result (i.e., an increase of si caused by a decrease of the hydrogen diffusion rate). Since to create the critical concentration of hydrogen it is essential to localize tensile stresses, the crack initiation depends on the type of samples used. In samples with no concentrator, the crack initiation occurs, as a rule, in the axial part of a sample (i.e.. in the zone of maximum three-axis stresses where the hydrogen concentration is also maximum). In samples with the sharp stress concentrator, the crack initiation takes place adjacent to its top; in the case of the less sharp and deep notches, the failure begins at a certain distance from the notch top (i.e., under the surface) (Ref 35). At the moderate temperatures, hydrogen gathers mainly on phase boundaries, microdiscontinuities, grain boundaries, piling-up dislocations, and other defects. Therefore, sites of or-

igin of fracture can be both the interphase boundaries between ferrite and cementite and nonmetallic inclusions as well—for example, sulfides, which are the most efficient traps for hydrogen (Ref 56). The crack growth kinetics upon the internal hydrogen embrittlement also is controlled by the hydrogen diffusion rate into the region of maximum tensile stresses ahead of the crack top. It is suggested that this region is on the boundary of the plastically deformed zone or at the much less distance equal to the double opening of the crack, d. As soon as the hydrogen concentration becomes critical in the weakest element of a structure, fracture of this element occurs, following which the crack formed merges into the main one (Ref 65). The crack propagation is under progress due to the multiple recurrence of this process. Therefore, the crack growth can be considered as the process consisting of a sequence of incubation periods, followed by the restricted advance of the crack. The process of the crack stepwise growth is displayed evidently under the testing conditions at lowered temperatures when the process of hydrogen diffusion is retarded (Ref 35). The occurrence of the incubation period of the crack start and the stepwise advance of separate sections of the crack front is evident from the results of the registration of the acoustic emission, which have been obtained from testing of low-alloy steel with 0.4% C content (Ref 66). In addition, the registration of the acoustic emission is indicative of the realization of more complicated mechanisms of the crack growth. For example, when performing work (Ref 67) for testing the high-strength maraging steel, a growth of a great quantity of microcracks, 30 to 50 mkm in size, which appeared at 1 to 3 mks intervals, was revealed. Contrary to the internal hydrogen embrittlement, in the external hydrogen embrittlement the crack growth kinetics is controlled mostly by the following surface phenomena: adsorption, dissociation, and chemosorption of hydrogen on the metal surface. The following experimentally observed effects serve as a guide for this statement: ● The crack growth in the gaseous hydrogen

medium begins practically instantaneously after applying an external load with no marked incubation period. ● The activation energy of the process at the stage of the stable crack growth (region III, Fig. 7) differs noticeably from the activation energy of the hydrogen diffusion in a solid solution and is comparable to the activation energy of surface processes. ● When gaseous hydrogen is doped with impurities, which activate (H2S) or suppress (SO2), the process of the surface interaction of metal with hydrogen, the crack growth rate is also increased or reduced, respectively (Ref 57). The location of the failure zone ahead of the growing crack front depends also on the type of hydrogen source. In case of the external hydrogen embrittlement, the failure zone, as a rule, does not reach the point of the

maximum tensile stresses (i.e., it is located much nearer to the crack top than it is at the internal hydrogen embrittlement) (Ref 65). The extent of the embrittlement in the medium of gaseous hydrogen depends both on the pressure and the chemical composition of a medium, in part, of the steam content and oxygen, as well. In the case of high-strength steels a dramatic effect of the hydrogen pressure on the crack growth rate has been revealed at pressures not exceeding 1.3 • 10ⳮ3 MPa (Ref 68). The presence of steams in the hydrogen atmosphere has a quite profound initiating effect on the delayed fracture development. Oxygen has the opposite effect of efficacious retarding of the crack growth up to the critical value. On data given in Ref 69, for example, a mere 0.6% of O2 is sufficient for the complete stop of the crack development in the medium with humidified hydrogen (steel with the yield strength of 1600 MPa, or 232 ksi). The crack stopped by oxygen begins to grow again only after the complete removal of oxygen from the medium of tests. It is suggested that oxygen forms oxides that prevent the hydrogen from penetration into the crack top, and after the removal of oxygen the reverse process occurs (i.e., oxides are restored by hydrogen) (Ref 70). The temperature factor should be set off from other factors that affect the character of delayed fracture. According to the data in hand, the maximal sensitivity of steels to delayed fracture takes place at temperatures close to, room temperature (Ref 29). But in a number of cases this regularity is not obeyed. In Ref 71, the temperature dependence of the delayed fracture of the high-strength steel Fe-15Cr-5Ni-2Cu-Ti containing 5 • 10ⳮ4 at.% of hydrogen was studied. The threshold value of the stress intensity coefficient for this steel is K1th ⳱ 46 MPa m1 / 2. At 20 C (68 F) the crack growth occurs at the rate of 2 • 10ⳮ7 m/s. At 100 C (212 F) the crack growth rate up to the critical value increases by more than 300 times and reaches 6.6 • 10ⳮ5 m/s. In this case the time up to fracture (s) reduces from 500 to 600 min at 20 C (68 F) to s ⳱ 5 to 6 min 100 C (212 F). At the temperature of 180 C (356 F) the development of delayed fracture stops completely. The calculation of the activation energy of the crack growth Q has shown good agreement between the obtained value (64.8 kJ/mol) and the activation energy of the hydrogen embrittlement (60.9 kJ/mol). Chemical Composition and Structure Influence. The resistance of steels to delayed fracture depends on the carbon content, alloying, and impurity elements. From the data given in Fig. 6, it is evident that a buildup of the carbon content is attended by the significant reduction in the resistance to delayed fracture. This effect derives from the fact that with increased carbon content the strength properties of steel are improved, the level of residual internal microstresses is raised, and the amount and volume of the carbide phase are increased. The interphase surface area (i.e., the number of places, or traps, for the accumulation of hydrogen and the crack initiation) is correspondingly increased (Ref 29).

76 / Effect of Materials and Processing The influence of alloying elements is also quite profound. The effect of noncarbide-formative alloying elements (Mn, Al, Si, Co, Ni) is mainly connected with their influence on the properties of matrix—that is, with the change of its resistance to the viscous, brittle, and grainboundary fracture. These elements (but Ni) decrease the long-term strength of steels subjected to quenching followed by high tempering (Table 1). Carbide-formative elements (Cr, Mo, Ti, Nb, V) have an influence mainly through the change of the amount of the carbide and carbide-nitride phase, its distribution, and morphology. The positive influence of molybdenum, niobium, and vanadium, which bring about to an abrupt increase of the time up to fracture, s, is most pronounced (Table 1). In the case of noncarbideformative elements there is, as a rule, a direct relationship between the resistance to the hydrogen embrittlement and standard characteristics of brittle fracture—for example, the critical temperature of brittleness, T50. In the case of carbide-formative elements such an unambiguous relationship usually is not observed (Ref 72). As to impurity elements, phosphor and sulfur have the most negative influence (Table 1). The negative influence of sulfur is connected with the formation of manganese sulfides MnS, which, just as indicated, are the most effective traps for hydrogen. Manganese sulfides assist in initiating cracks at more low critical concentration of hydrogen C* in the region of maximal tensile stresses as evidenced by the results of the reg-

istration of hydrogen in the fracture zone (Ref 73). In this case, a decrease of sulfur to a degree less than 0.005 wt% does not protect against the development of the hydrogen embrittlement. The form of nonmetallic inclusions also has a dramatic influence, especially in steels with the ferrite-pearlite structure. Inclusions of the spherical form are considered to be the safest ones. The negative role of sulfur can be connected in that this element has a retarding effect on the recombination of hydrogen atoms on the steel surface and so brings about an increase of the amount of absorbed hydrogen (Ref 74). Phosphorus and its analogs (Sb, Sn) are the most dangerous on formation of segregation at grain boundaries—that is, in the process of thermal treatment, which results in the development of the temper embrittlement (Ref 75–77). In the absence of segregations the steels fracture in hydrogeneous media connected with the intensive plastic deformation in the crack top. Fracture mainly occurs transgranularly (i.e., along a grain). In this case, in fractograms of the crack growth up to the critical value, either a viscous cup fracture or a quasi-spall takes place. During the formation of segregation another mechanism, the brittle fracture along grain boundaries, is realized with a consequent abrupt decrease of K1th. In this case, an intensive reduction of K1th takes place already at initial stages of the segregation formation when temper embrittlement has hardly shown up. It is considered that one of the reasons

Table 1 Influence of alloying elements and impurities on transition temperature, T50; work of propagation of a ductile crack, A; plasticity loss after hydrogenation, Fw and resistance to hydrogen embrittlement, s (chromium-molybdenum steel, 0.2% C) Element (limits of alloying, mass, %)

Dependence of fracture characteristics on element concentration (per 0.1% of each)

Optimal content of the element, mass, %

T50, C

A, MJ/m2

Fw%

s, h

for such a strong influence of phosphorus, antimony, and tin segregation is a buildup of hydrogen concentration on the grain boundaries as a consequence of the chemical interaction of hydrogen with these impurities (Ref 75). The steel structure has a determining effect on the resistance to delayed fracture. The least resistance is typical for the martensitic structure, especially at low tempering temperatures. An increase of the tempering temperature to 420 C (788 F) causes the value of rth to increase by several times. The decrease of the volume fraction of martensite to 20 to 30% means to that even in the hardened state delayed fracture does not develop (Fig. 8) (Ref 78). In Ref 54 attention is drawn to the increased sensitivity of steel Fe0.4C-Cr-Si with the lower bainite structure to delayed fracture, although this structure is characterized by high-impact toughness and adequate plasticity. Unlike the martensitic structures, whose failure process develops mainly along boundaries of former austenitic grains, the bainite structure fails along the grain body (by mechanism of quasi-spall). On evidence given in Ref 74 the resistance to the hydrogen embrittlement of low-alloyed pipe steels increases in the direction from normalization to the controlled rolling, but the best results are ensured by the thermal improving (quenching Ⳮ high tempering) and quenching from the intercritical temperature interval. A comparison shows that the thermal improving and quenching from the intercritical interval ensure about the sixfold enhancement of the longterm strength as compared with the normalization. Water quenching at 775 C (1425 F) when the structure contains approximately 30% of bainite affords the best combination of properties. The marked enhancement of the resistance to delayed fracture is provided by the high-temperature thermomechanical processing of the

C (0.2 to 0.8)

0.2–0.3

20 to 60

ⳮ0.1 to ⳮ0.2

…

ⳮ32

Solid solution Si (0.2 to 1.8)

0.4–0.7

ⳮ4 to ⳮ6(a) 5 to 8(b) 3(a) 7 to 16(b) ⳮ4 to ⳮ10 1 to 1.5 9

… ⳮ0.12 ⳮ0.05 ⳮ0.05 0 0 ⳮ0.17

… 3 2 2 ⳮ7(a) to 1.3(b) 1.2 4

… ⳮ5 ⳮ15 ⳮ23 6.5 ⳮ5.7 ⳮ7.5

0.04 ⳮ0.01 0

ⳮ2.9 1.5 ⳮ8

80 ⳮ1 260

0 0 0

ⳮ36(a) to 10(b) ⳮ12 ⳮ10

… 250 250

400

0.04 0

… …

35 70

0

ⳮ2.4 ⳮ1.0 ⳮ2.5 ⳮ2.5 0.04

0 80 … …

ⳮ360 ⳮ500 … … 32

ⱕ1.2

Ni (0 to 3.0) Co (0 to 3.0) Al (0.03 to 0.7

0.5–1 0.5 0.25

Carbide-forming Cr (0.5 to 3.0) Mo (0 to 1.0)

0.4 to 0.5

Ti (0 to 0.15) Nb (0 to 0.20) V (0 to 0.4)

0.05 0.02 to 0.06 0.1

ⳮ1(a) 2 to 5(a) ⳮ15 to ⳮ30(a) 3 to 5(b) ⳮ60(a) to 14(b) 0(a) to 40(b) ⳮ20(a) to 15(b)

Modifiers Rare-earth (Ce)(0 to 0.5) AIN, VN, NbN (0 to 0.2)

0.1 to 0.3 0.2

ⳮ10 ⳮ40

Impurities S (0.015 to 0.045) P (0.004 to 0.026) Sb (0.0006 to 0.027) Sn (0.0005 to 0.03) Cu (0 to 1.5)

1–1.5

1400 5

1200 Stress σ, MPa

Mn (0.6 to 2.5)

1600

3

6

1000 800

4

600 2

200 1

0.01 0.015 0.01 0 ⱕ0.5

0 230 180 180 ⳮ1

(a) Alloying for optimal content. (b) Alloying over optimal content. Source: Ref 143

0

1

2 3 Time to failure , h

4

5

Influence of martensite content and tempering temperature on delayed failure of quenched carbon steel from 0.35% C. 1, 100% of martensite, 0.023% of S, without tempering; 2, the same, tempering at 200 C; 3, the same, tempering at 420 C; 4, 70–80% of martensite, 0.025% of S, tempering at 200 C; 5, 70–80% of martensite, 0.005% of S, tempering 200 C; 6, 20–30% of martensite, 0.026% of S, without tempering. Source: Ref 78

Fig. 8

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 77 high-strength steel Fe-0.3C-2Ni-Cr-Mn-Si (Ref 79). Some Specific Cases of Delayed Fracture. In the scientific literature, including the educational one, it was a widespread opinion that delayed fracture of steels can develop involving no hydrogen—that is, under the effect of only structure factors (Ref 28, 54, 80). In particular, the question about the nature of the enhanced sensitivity to delayed fracture of steels in the socalled newly quenched state is long discussed. Cases of quenched products cracking, which are met in practice of thermal processing (Ref 52, 54), have been associated with the development of delayed fracture of untempered martensite. Initiation and growth of crack provoking delayed fracture occurs mostly over the boundaries of primary austenitic grains. The short-term tempering or resting of quenched samples at room temperature enhances resistance to delayed fracture; therefore, its development calls for further hydrogenation. Within the span of more than 50 years of investigations, alternate hypotheses for explaining this phenomenon have been proposed. The “structure” hypothesis based on the prevailing role of residual microstresses inherent in the untempered martensitic structure has received the most acceptance (Ref 79, 80). The role of internal hydrogen, which is always present in steel as an inevitable impurity, has not been discussed practically in the literature. The phenomenon of delayed fracture of quenched steels has been studied in detail in Ref 81–83. Steels Fe-0.3C-Cr-Mn-Si and Fe-0.4CCr-Mn quenched in oil at 860 C (1580 F) have been chosen as objects of investigation. The pro-

cess of initiation and growth of a crack when testing on a delayed fracture in a freshly hardened state is quite the same as that in the grain boundaries. The typical initiating crack found in the stress concentrator top is shown in Fig. 9. The work has been methodically performed in the following way. First, regularities of the initiation and crack growth have been studied thoroughly by methods of mechanical tests in conjunction with the acoustic emission. In particular, the effect of the deformation-rate inhibition of the crack growth has been established, durations of the incubation period, si, under different conditions of loading have been determined and so on. Second, the simulation of the newly quenched state has been performed. For this purpose, after approximately 70 h exposure at room temperature (to eliminate the sensitivity to delayed fracture) quenched samples have been hydrogenated by the special procedure. Subsequent tests have shown that all the characteristics of delayed fracture of quenched steels—the threshold stress, rth, the duration of the incubation period, si, and so on, as well as the mechanism of fracture, are analogous with the case of delayed fracture caused by hydrogen. Therefore, it is beyond the reason to consider that in the case of the untempered martensite structure a certain different type of delayed fracture that is not connected with the presence of hydrogen in steel takes place. The fact that the kinetics of relaxation of interior microstresses in the process of resting at room temperature does not correspond to the kinetics of the change of the threshold stress, rth, bears witness to this also. Judging by the change of the interior fric-

80 3

ψ, %

60 40 1 20 2 0 2500 3′

σB, MPa

2000 1500 2′ 1′ 1000

500 340

380

420

460

500

540

T, °C Nucleating grain boundary crack revealed at the top of the stress concentrator on testings of quenched steel Fe-0.3C-Cr-Mn-Si for delayed failure. 1100⳯. Source: Ref 81

Fig. 9

Influence of testing media on delayed failure of steel Fe-18Ni-9Co-5Mo-Ti. 1,1⬘ testings in the air, u ⳱ 40–45%; 2.2⬘, the same, u ⳱ 65–70%; 3,3⬘, vacuum testings, P ⳱ 1.3 Pa. Source: Ref 86

Fig. 10

tion, the microstress relaxation process completes in a time of no more than 10 to 20 h since quenching. In this state a material still possesses the sensitivity to delayed fracture. In the process of holding samples at room temperature, the evolution (desorption) of hydrogen from them into the atmosphere has been found to occur. The sensitivity to delayed fracture is just concurrently with termination of hydrogen desorption (i.e., about 70 h after quenching has been elapsed). According to the data of the laser spectroscopy, the amount of desorbent hydrogen over the period of holding comes to approximately 2 ⳯ 10ⳮ6 at.% (Ref 84). The source of diffusive-mobile hydrogen in the structure of the quenched steel is inner hydrogen, whose amount at conventional process of melting makes up no less than 2 to 3 ⳯10ⳮ4 at.%. The lattice solubility of hydrogen increases from approximately 10ⳮ7 at 20 C (68 F) to 4.4 ⳯ 10ⳮ4 at.% at 860 C, (i.e., by about 3 orders of magnitude), as a result of heating to the austenization temperature. A reverse decrease of solubility in the process of the fast quenching results in a part of hydrogen being kept for some time in the oversaturated state in the ␣-solid solution and has the increased diffusive mobility and the property of localizing in the region of maximal tensile stresses. High interior microstresses inherent of the quenched steel structure make the process of the crack initiation and the crack growth easier but are not the factors that control kinetic parameters of delayed fracture. Another interesting case is delayed fracture of high-strength maraging steels, which develops over the certain temperature interval of aging— 400–460 C (Ref 85). The development of delayed fracture in these steels requires no special hydrogenation. Therefore, within a long period of time this phenomenon was also connected only with the peculiarities of the structure state forming at indicated aging temperatures. Furthermore, this problem is urgent because aging in the indicated interval provides for obtaining the maximum elastic limit of steel. However, owing to the low resistance to delayed fracture, this mode of aging usually is not practiced. An analysis of data in hand has shown that the key question in explaining the phenomenon of delayed fracture of maraging steels is a question on the role of the testing environment (air, vacuum) as well as the role of titanium (Ref 85). The investigations have been carried out with steels Fe-16Ni-10W-Mo-Ti and Fe-18Ni-9Co5Mo-Ti (Ref 86, 87). The tests have been performed under static loading at the reduced rate of e˙ ⳱ 2.8 • 10ⳮ5 sⳮ1. Dependencies of the mechanical properties of steel Fe-18Ni-9Co-5MoTi on the aging temperature when testing in the air and in vacuum are presented in Fig. 10. A crevasse in curves of the change of mechanical properties on tests in the air (curves 1,1⬘) corresponds to the aging temperature of 420 to 460 C. Plastic properties of steels in this range come practically to the zero level. An effect of delayed fracture for steel Fe-16Ni-Mo-10W-Ti is observed within a more narrow temperature inter-

78 / Effect of Materials and Processing val at 420 C. On testing in vacuum (residual pressure of 1.3 Pa) the indexes of mechanical properties abruptly increase (curves 3,3⬘). An effect of the delayed fracture elimination is due to the change of the crack-initiation mechanism. On testing in the air the brittle grain-boundary fracture occurs, on vacuum testing the viscous inter-granular fracture takes place (Fig. 11). In the study of the titanium influence it has been found that the influence of the testing environment takes place only with a definite content of titanium in steel exceeding 0.5%. When titanium content is ⱕ0.5%, mechanical properties tests in the air and vacuum tests do not practically differ from one another (i.e., delayed fracture does not develop). It has been found also that resistance to delayed fracture depends on moisture of the environmental atmosphere (the laboratory air), namely, on a season in the course of which tests are carried out. The figure shows that an increase of relative humidity (from 40–45% to 65–70%)

Fig. 11

results in the deterioration of plasticity and the reduction of the tensile strength by 30% (curves 1,1⬘, 2,2⬘). Thus, tests have been carried out in the air-dried chamber, for which purpose the special procedure has been devised. On testing in the air-dried atmosphere (u ⳱ 0.04%) plastic and strength properties of steel Fe-18Ni-9Co5Mo-Ti come to such a degree that corresponds tests in vacuum (i.e., the effect of delayed fracture disappears). This means that the structure state formed on aging within the interval of 400 to 460 C possesses the increased sensitivity to the presence of water vapors in the air environment—that is, delayed fracture of high-strength maraging steels is caused by the effect of atmospheric moisture adsorbed on a surface. Investigations of grain boundaries of fractured samples by x-ray electron spectroscopy have shown that on the grain boundaries there are hydrides, first of all, titanium hydrides, TiHx, apart from “apparent” components (segregations of alloying elements, oxides, hydroxides, and inter-

Mechanism of failure of steel Fe-16Ni-10W-Mo-Ti at crack initiation stage (aging at temperature of 420 C). (a) Testings in the air. (b) Vacuum testings (P ⳱ 1.3 Pa). 1050⳯. Courtesy of A.I. Kovalev

H3O

+

102 Å

H2O

10-20 Å

Oxide-hydroxide layer

P Grain 1

~10 Å H3O

+

Ni3Ti

P

0

Hads

P

Grain 2

Grain 1

Oxygenless zone

Grain boundary (a)

Fig. 12

(b)

P

Grain 2

Ti segregation Ni3Ti

H2O

Air

Habs TiHx

Grain boundary

Mechanism of the crack growth on delayed failure of maraging steel. (a) Stage before crack initiation. (b) Stage of crack growth. Source: Ref 87

metallics). Since the process of hydride linking of the Ti-H type in the air is practically excluded (titanium, by virtue of its enhanced activity, in its interaction with oxygen and moisture in the air forms first of all the hardly permeable oxide phase TiO2), the conclusion has been drawn that titanium hydrides are formed on inner interfaces (grain boundaries). In other words, the TiHx formation occurs in the zone of tensile stresses ahead of the crack top as diffusive-mobile hydrogen enters there. According to the mechanism suggested (Ref 86), the process of grain boundary embrittlement includes the following successive stages: adsorption of atmospheric moisture at the metal surface, oxidation of the most electronegative steel components (iron atoms), transport of H3OⳭ ions in the film of adsorbed water toward the top (mouth) of the growing crack, formation of atomic hydrogen H0ads on the freshly formed surface by cathodic reduction of H3OⳭ ions on nickel atoms, transition of atomic hydrogen H0ads into the absorbed state and subsequent diffusion of hydrogen to the tension-stressed zone ahead of the crack top, and embrittlement of grain boundaries due to both the formation of titanium hydrides and segregations of hydrogen solutes ahead of the crack top. Thus, the final stage of the process is the formation of diffusivemobile hydrogen, which causes embrittlement owing to both the formation of titanium hydrides, TiHx, and the direct action (decohesion). This is the main difference of the studied type of brittleness from the delayed failure of the quenched steel, which is caused by internal diffusive-mobile hydrogen formed in the process of steel heat treatment. The mechanism of the crack growth, which illustrates the sequence of stages under consideration is represented schematically in Fig. 12 (Ref 87). The formation of titanium hydrides in the crystal lattice is attended with the considerable volume effect, which is about 3 times higher than for the martensite transformation in steel. Besides, hydrides favor the crack growth owing to the reduced strength of the hydride-matrix interface (Ref 28). Atomic hydrogen H0ads formed in the crystal lattice is ionized producing ions HⳭ and Hⳮ, which quantitative ratio, on data given in Ref 88, makes up 1:9, approximately. The rate of diffusion of ionized hydrogen is 1 to 2 orders of magnitude higher than that of atomic hydrogen. According to data obtained by the method of the secondary ion mass-spectrometry (Ref 88, 89) more mobile ions Hⳮ, which serve as main carriers of diffusive-mobile hydrogen in metal, are responsible for the formation of the hydride phase and the process of embrittlement of the grain boundaries. Ion HⳭ possesses the lesser mobility in the crystal lattice, and its contribution to the embrittlement is not so considerable essential. In Ref 90 and 91, delayed failure of high-alloy steel Fe-24Cr-7Ni-3Mo-Al-Ti containing no martensitic structure has been studied. This steel displays the enhanced sensitivity to delayed failure in the so-called “newly-smelted” state (i.e.,

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 79 under the effect of metallurgical hydrogen determining the role of which in the development of delayed failure is of great practical importance). The studied steel structure is embrittled d-ferrite with austenite c-phase interlayers uniformly distributed in it. Unlike the cases discussed previously, the initiation and the crack growth in the structure under study occur in accordance with a transgranular mechanism, with defects of the cast structure (pores) of 20 mkm in size being the source of fracture. As evident from the registration of the acoustic emission, the crack grows according to the mechanism of the discrete (stepwise) growth of separate sites of the crack front followed by the stop at viscous sites (austenitic inter-layers). According to observations, the resistance to delayed fracture depends on the period of the natural recreation after smelting. Within the span of 4 years the metallurgical hydrogen content drops from approximately 18 ⳯ 10ⳮ4 to 6 ⳯ 10ⳮ4 at.%, and it is a limiting one at which the development of delayed fracture is still possible. The object under study is of interest as far as it allows the different mechanisms of the embrittlement of grain boundaries or their volume to be realized. The thermal treatment has been carried out under operating conditions including the high-temperature preheating to 1250 C (2282 F) for obtaining the one-phase structure of d-ferrite and postaging (annealing) at different temperatures. The hydrogen content in thermally treated samples does not exceed 1.4 ⳯ 10ⳮ4 at.%. Annealing at 680 C (1256 F) makes it possible to obtain the brittle fracture along the grain boundaries, which, on data of the auger spectroscopy, arises from the segregation of sulfur and phosphor impurities. After the 850 C (1562 F) annealing on the grain boundaries of ferrite, the abundant precipitation of embrittling r-phase responsible for the quasi-brittle grain boundary fracture takes place. Aging at 440 C (824 F) makes it possible to obtain the brittle intergranular fracture in accordance with the transgranular mechanism. The tests performed on embrittled samples have once again favored the view that structure factors bringing about the embrittlement of the grain boundaries or their volume cannot in themselves result in the development of delayed fracture. As is obvious from this data obtained from steels with the different structures, the development of delayed fracture is only possible with the participation of diffusive-mobile hydrogen independently of the source of its origination, namely on quenching, smelting, from atmospheric moisture, and so on.

Stress-Corrosion Cracking of LowAlloy Steels Stress-corrosion cracking (SCC) is a specific type of delayed fracture that develops under the concurrent action of tensile stresses and the corrosion medium. The given type of fracture occurs in chemical, gas-oil producing, metallurgic,

shipbuilding, and other branches of industry, and accounts for approximately 30% of material damage caused by corrosion. The most dangerous media that can cause SCC under the certain conditions have been established for most steel classes used. The greatest body of information accumulated to date refers to high-alloy steels, in part, to corrosion-resistant steels with austenitic structure. Stress-corrosion cracking of lowalloy steels has been studied least, although such steels, especially in the high-strength state, have an enhanced tendency to corrosion-mechanical fracture. Low-alloy steel cracking can occur under the action of various actuating media including solutions of acids, nitrates, alkali, and sulphur-hydrogeneous media as well. The low resistance of high-strength steels to SCC makes itself evident even in such, at first sight, undangerous media as pure water, moist air, and water vapors (Ref 92, 93). One of the characteristic peculiarities of SCC is a pronounced selectivity of a material relative to a corrosion medium. Therefore, the results of one “metal-medium” system investigation cannot be extended to another system. Besides, the noncorrodive media, in common conception of this term, may appear to be the most aggressive ones, because the corrosion cracking process is actively developing in them under the effect of tensile stresses. Another interesting peculiarity lies in a usual insensitivity of high-pure metals, including iron, to SCC in any environment. The susceptibility of iron to cracking under the effect of stresses appears only in the presence of introduction impurities, namely, carbon and nitrogen. The response to the cold plastic deformation is also intriguing. Unlike austenitic corrosion-resistant steels, the cold plastic deformation of carbon steels makes them relatively insensitive to SCC. Annealing of the cold-deformed 0.15% Ccontaining steel at 600 C (1112 F) restores this sensitivity to the level of nondeformed steel (Ref 70). Peculiarities of Crack Initiation and Growth Mechanism under SCC. The mechanism of initiation and growth of cracks under SCC depends on the steel structure, the value of applied stresses, and the testing medium. Fracture along the primary austenitic grain boundaries is the most dangerous from the standpoint of loss in corrosion-mechanical strength. Carbon steels, as well as many of the low-alloy steels, fail in alkaline, nitrate, phosphate, carbonate solutions, and also in aqueous acid solutions by such a mechanism (Ref 75). Depending which reaction controls the cracking process—electrochemical, anodic, or cathodic—two main SCC mechanisms are differentiated: the active-part corrosion (APC) or the hydrogen-induced corrosion cracking (HISCC). Kinetics of the anodetype cracking is determined largely by the conditions of passivation (i.e., by the peculiarities of the protection corrosion films formation and by their properties). This is reflected in the fact that the region of danger of the given type of SCC corresponds to the so-called active-passive region of potentials in the polarization curves. The

region of cracking by the HISCC mechanism has no clearly defined boundaries and extends from the potential of free corrosion to the potential of cathodic protection (Ref 94). The mechanism of part cracking presupposes the accelerated metal dissolution, which is considered to be connected with the local disruption of passivity at the crack top i.e., with the protective film breakdown and occurrence of the newly formed (juvenile) surface. The mechanism of HISCC involves the following main reactions: discharge of hydrogen H3OⳭ ions from water solution onto the steel surface, the transport of hydrogen to the region of the elevated stress concentration ahead of the crack top, and the crack propagation caused by the local hydrogen embrittlement. The concrete mechanism of the hydrogen embrittlement depends on the structure and properties of steel, the loading conditions and the ability of a medium to hydrogenation (Ref 94). Whatever the mechanism of corrosive-mechanical fracture is, the three stages of the process are distinguished: incipient defects (microcracks) formation, microcracks growth, and fast fracture as soon as the main crack reaches the critical size. Both metallurgical defects of the surface and defects of corrosion origin may present as incipient defects (Ref 93). In the SCC theory, particular attention is given to the processes proceeding in the crack top, which are much different from the processes proceeding on the surface. In particular, an important role is given to the newly formed (juvenile) surface, which appears either under the effect of the external loading or in the process of APC. All the particular SCC reactions, namely, APC, cathode precipitation of hydrogen, its absorption, and so on, are sharply speeded up on such a surface. The newly formed surface possesses a more negative potential compared with both the previous surface and the passivated surface of crack edges. It is suggested that in the corrosion crack there is a local galvanopair of the newly formed surface-crack edges surface type that contributes to the accelerated selective crack propagation (Ref 95). Criteria and Methods of Estimating Sensitivity to SCC. A great body of different criteria, namely, mechanical, electrochemical, physical, and so on, has been suggested to estimate the sensitivity of steels to SCC (Ref 92). All the known methods of corrosion-mechanical testings can be divided into three main groups: ● Testings under constant external load (P ⳱ constant) ● Testings under constant strain (e ⳱ constant) ● Testings at the constant load rate (˙e, v ⳱ constant). Samples without a notch, with a notch, and with the precreated fatigue crack can be used in each of these above-stated methods. The service conditions are best reproduced by corrosion-mechanical testings under constant external load. In this case, as the crack initiates and grows, the stress rises in the rest part of a sample that contributes to the development of fracture.

80 / Effect of Materials and Processing By analogy with delayed fracture (see the section “Delayed Fracture in Steels”), the sensitivity to SCC is characterized by the time till a crack initiation, si, durability till complete failure, s, and the value of the threshold stress, rth. Unlike delayed fracture, it often occurs that dependencies, s ⳱ f (r), are not brought out onto the plateau, when testings for corrosion cracking are performed (i.e., there is no threshold stress). The conventional threshold stress, rth, which should be determined in this case, is determined at the specified (base) duration of testings. The duration of the incubation period si during which the crack initiation occurs takes usually 80 to 90% of the whole time prior to fracture (s) (Ref 96). Testings under constant (fixed) strain are usually carried out according to the scheme of threeor four-point bending of samples fixed in the rigid attachment. On such testings the external load is reduced gradually because of the crack formation and the residual bending strain accumulation. Testing under constant strain render well the cracking processes in the material structure that develop under the action of residual stresses. Tests at constant load rate are mainly performed by the slow strain rate testing procedure (SSRT). In this case the resistance of a material to cracking is characterized by the value of tensile strength in the corrosion medium, characteristics of plasticity, W, d, the critical fracture stress, r*, and the area below the strain curve, r ⳮ e, characterizing the fracture work. With the plasticity characteristics taken into accounts, the relative (as compared to the air) sensitivity of a material to corrosion cracking is determined. Used as criteria in this case are the so-called coefficients of medium effect of the (W0 ⳮ W1)/ W0 type, where W0 and W1 are the relative narrowing on testings in the air and in the corrosion medium, respectively. The strain rate e˙ with the use of the SSRT method is usually selected within the range of 10ⳮ4 to 10ⳮ6 secⳮ1. When using samples with a crack, a load, the load line displacement, the crack length, and the crack opening displacement (COD) are registered as per the SSRT method. For analyzing the test results, the criteria of fracture mechanics are used. The threshold (critical) stress-intensity factor, KISCC, which makes it possible to estimate quantitatively the steel resistance to cracking in the corrosion medium is taken as the main criterion. The value of KISCC corresponds to the beginning of the crack growth before the critical value (Ref 97). It is apparent that if K1 KISCC or r rth, the fracture of the construction element inevitably takes place. When the criterion KISCC is used, the sensitivity of material to the action of the corrosion medium is characterized by the ratio KISCC /KIC, where KIC is the stressintensity factor when testing in the air (planestrain fracture toughness) (Ref 98–100). In all the schemes of testings the maximum length of a crack resulting in fracture, the crack growth rate, the number of cracks per unit surface, etc., can be used as characteristics of a material (Ref 101, 102).

The most reliable values of KISCC are obtained on the basis of standard kinetic cracking resistance diagrams analogous to that represented in Fig. 3. The plateau-figurative regions in kinetic diagrams are connected with the branching and blunting of a crack. If relative resistance of materials to the action of corrosion media is to be determined quickly, the SSRT method has an advantage over the constant load testing method for determining KISCC, although it is considered the basic one. The fact of the SSRT method high efficiency is evidenced by the data of many scientists. The console samples made of Fe-0.3C2Ni-Cr-Mn-Si steel, for example, have been tested in the NaCl 3.5% solution (Ref 103). The values of KISCC obtained at a constant rate of load and on standard testing (under constant load) have turned out practically to be equal to 11.69 and 1196 MPa m1 / 2, respectively. To choose the proper load rate is of great importance in this case. At the high load rate the corrosion process has no time to produce changes at the crack top; at low rate, on the contrary, the passivation process develops at the crack top, thus preventing from corrosion cracking propagation (Ref 96). The linear mechanics of fracture are unsuited for high-ductility steels. In this case, resistance to crack growth is characterized by the value of the J-integral, in particular, its threshold value, JISCC. A tendency to corrosion-mechanical cracking is estimated also by electrochemical parameters, namely, by the critical value of the hydrogen index of the medium pH, the electrode potential, E and the density of anodic current at which the cracking process begins. When testing the carbon steel in the 3% solution of NaCl, strong jumps of the electrode potential (300 mV) and the anodic current at the moment of a crack propagation have been detected (Ref 104). This effect is connected with revealing the juvenile surface, which has an enhanced electrochemical activity and it can also be taken as one of criteria for the sensitivity of steels to corrosion-mechanical fracture. The important information on kinetics of SCC, especially at initial stages of the process, can be obtained from acoustic emission measurements (Ref 105–107). Effect of Alloying Elements on Resistance to SCC. The effect of most alloying elements on steel resistance to SCC depends on their concentration, the presence of other alloying elements, impurities, the corrosion medium content, the value of electrode potential, and other factors (Ref 108). For high-alloy austenitic steels there is a certain relationship between the effect of an element and its position in the periodic system. The analogous relationship is not observed for low-alloy steels (Ref 109). The theory of alloying that makes it possible to predict the resistance of low-alloy steels to SCC in different media also has not been developed. Hypotheses suggested provide, as a rule, an explanation for the role of alloying elements by only one of some factors, namely, effect on strength of interatomic bonds, the rate of forming protective films, the effect on the carbon distribution in steel, and so on (Ref 108).

Information on the effect of alloying elements on mechanisms of the crack growth in different corrosion media is necessary to develop successfully new grades of steels with an enhanced resistance to corrosion cracking. For lack of this information, the empirical data are usually used which are often contradictory. The findings on the individual and combined effects of 27 alloying elements and impurities on the resistance to SCC of iron and low-alloy steels, including highstrength steels, have been generalized in Ref 108. The effect of elements depending on the medium (aqueous solutions of chlorides, nitrates, carbonates, alkali, hydrogen sulfide, etc.), the temperature, the electrode potential, and the pH value have been considered. The following elements have been analyzed: N, Al, B, V, H, Ge, Ca, O, Co, Si, La, Mn, Cu, Mo, As, Ni, Nb, Sn, Pb, S, Sb, Ti, C, P, Cr, Ce, Zn. It has been shown that the majority of these elements, especially in the case of combined alloying, ambiguously affects resistance to SCC. The same element can have both a positive and negative effect depending on the corrosion medium. Silicon, for example, enhances steel resistance to cracking in nitrate solutions but reduces it in alkali ones. However, the previously listed elements can be divided arbitrarily into four main groups: those that enhance the resistance to SCC (Ti, Nb, Mo, Al, Co, Cu, Pb, B, Ce, Ca, La), those that reduce it (N, O, H, S, P, V, Sb, Cr, Mn, Ge), elements of the alternating effect (C, Si, Ni), and neutral ones (Sn, As, Zn). The characteristic properties of distribution of elements and impurities in the steel structure are of great importance. Segregations of sulphur and phosphor impurities, for example, change the electrochemical characteristics of the grain boundaries and initiate fracture by the local parth corrosion mechanism (Ref 108). Steels produced by vacuum melting possess the enhanced resistance to SCC in so far as they contain 2 to 3 times as few detrimental impurities as standard steels do (Ref 110). It has been noted that the effect of alloying elements can be judged by the mechanism of fracture. Elements with a positive effect assist in realizing the transgranular mechanism of the crack growth. Those that have a negative effect cause cracking along the grain boundaries. The effect of the chemical composition may manifest itself indirectly, namely, through the change of the structure and mechanical properties of the steel. Therefore, the thermal processing can drastically change degree and even the direction of some alloying elements effect. Role of Structure and Thermal Processing in the SCC Process. The basic parameters of the SCC, namely, the threshold stress, rth, corrosion crack-toughness, KISCC, the crack growth rate, and so on, depend to a great extent on the following structure factors: phase composition, austenite grain size, state of grain boundaries, and nature and amount of nonmetallic impurities (Ref 111). Figure 13 shows that the crack-tough-

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 81 ness reaches its peak values KISCC in hightempered steels. In the region of high-strength states realized at low tempering, the parameter KISCC takes quite low values not exceeding 20 MPa m1 / 2. As for steels of mean and low strength, the structures of fine-grain ferrite, martensite, and bainite possess the best properties. The spheroidized structure with uniformly distributed finegrain carbides possesses somewhat worse properties, and the lamellated pearlite structure possesses the worst ones (Ref 112). There is also evidence that compound structures, for example, consisting of fine-grain ferrite and bainite wherein the intergranular ductile mechanism of failure is realized (Ref 113, 114) show the highest resistance to SCC. For the steel Fe-0.3C-MnSi-Ni with the compound structure of martensite Ⳮ lower bainite, the value KISCC in the NaCl 3.5% solutions is 21 MPa m1 / 2. In the case of the martensitic structure this index is reduced by half (i.e., steel with this structure possesses the much lower resistance to SCC) (Ref 115). The positive role of residual austenite is observed frequently. In the scope of the SCC model by the hydrogen embrittlement mechanism this derives from the fact that the saturability of austenite with hydrogen is essentially higher, and the hydrogen diffusion factor is three to four orders of magnitude lower than that in the martensite structure. Cracks propagating in martensitic slow down in the region bordering hydrogen-resistant austenite. However, with the insufficient stability of residual austenite its negative effect is a possibility. In this case, as residual austenite is turned to martensite under deformation at the crack top, the resistance to SCC reduces (Ref 116). The use of high-temperature thermo-mechanical processing which raises both the parameters

100 1 2 3 4 5 6 7

KISCC, MPa • m1/2

80

60

40

20

0

1000

1400 σB, MPa

1800

Strength level effect of steels Fe-0.3C-2Ni-CrMn-Si (1,2,3), Fe-0.4C-Cr-Ni-Mn (4,5), and Fe0.3C-Cr-Mn-Si (6,7) on value of threshold stress-intensity factor KISCC in corrosion medium. 1,4,6,8, tests in water; 2,5,7, tests in H2S solution; 3, tests in gaseous H2S. Source: Ref 93

Fig. 13

KISCC and KIC in the case of high-strength combined-alloy steels (when testing in the NaCl 3.5% solution), holds promise (Ref 117). Quenching from the intercritical temperature interval can also be profitable. The formation of the ferritic-martensitic structure as the result of quenching from the intercritical temperature interval (740 C, or 1364 F) makes it possible to enhance vastly the resistance of steel Fe-0.5CCr-Mo to the hydrogen SCC in salt water (Ref 118). The two-stage austenitization (high-temperature Ⳮ conventional one) forms a toothed structure of grain boundaries, which also inhibits the grain boundary failure by enhancing the resistance to SCC. The effect of grain size on the resistance of steels to SCC is then ambiguous. In many works it was pointed out that the finer the austenitic grain, the higher resistance to SCC is observed. For example, on the data given in Ref 119 and 120 the time before failure in the NaCl 3.5% solution increases by 2 to 3 orders of magnitude with decreasing the austenite grain in the steel Fe-0.4C-Cr-Ni-Mo from 172 to 12 mkm in size. However, there is other evidence. For example, overheating in the process of the austenitization of the high-strength steel Fe-0.45C-2Ni-Cr-MoV favors a great increase of KISCC when testing in distilled water (Ref 121). The high-temperature austenitization is most profitable for cast steels in so far as they are less prone to the grain growth as compared to hot-strained steels (Ref 122). Unlike quenching, the overheating in normalizing, as a rule, has a negative effect, especially in the case of low-alloy steels containing manganese and vanadium (Ref 123). The problem on the effect of initial structure is of great importance. It is found that, compared with hot-strained steels, cast steels have higher values of the corrosion cracking resistance, although standard mechanical properties of cast steels are much lower (Ref 122). Studied in Ref 124 is the effect of different methods of melting (an electric furnace, an arc-vacuum furnace, a vacuum induction furnace, electroslag remelt) and their combinations on the corrosion mechanical properties of maraging steel. It has been shown that combined methods of melting make it possible to increase considerably (by 25%) KISCC when testing in the NaCl 3% solution. The analogous data have been obtained in work (Ref 110). Commercial Fe-0.4C-2Ni-Cr-Mo and Fe0.4C-2Ni-Cr-Mo-Si steels that have been melted in the air and vacuum were tested in the chloride medium at K ⳱ 0.9KI. Vacuum-melted steels possessed the enhanced SCC resistance, whereas in air-melted steels, cracks developed practically at once. In corrosion-mechanical steel failure one of the key problems is the problem of nonmetallic impurities. In this case, both morphological characteristics of impurities (the quantity, form, sizes, and distribution) and their chemical activity in the given corrosion medium are of importance. The impurities of sulphides, silicates, and oxides as well, which play the main role in the process of the crack initiation, are the most ac-

tive (Ref 111). The local electrochemical corrosion processes developing in the corrosive medium around the impurities, resulting in inevitable formation of aggressive medium-filled microcavities. The role of MnS impurities in the course of corrosion-mechanical failure of the Fe0.2C-Cr-Ni-Mo type reactor steel intended for the production of high-pressure containers was studied in (Ref 125). The suggested mechanism of initiation and growth of cracks includes, as the first stage, the appearance of a slot between an impurity and a matrix owing to dissolving MnS in the electrolyte. Atomic hydrogen is adsorbed at crack lateral surfaces, following which it diffuses into the metal toward the crack top and causes local cracking. In acid media sulfide impurities dissolve and yield H2S that greatly reduces the resistance to SCC (Ref 126). Dissolution products of some impurities enhance the adjacent metal corrosion that also promotes the cracking process. The enhancement of cracking in dissolving nonmetallic impurities is supported by the data given in Ref 127 devoted to the study of SCC of the Fe-0.2CMn-Ni-Mo steel in the medium intended for cooling atomic reactors. As the medium has been contaminated by dissolution products, the MnS samples have broken down due to the development of the corrosion cracking process, whereas in the medium free of the corrosion products, this process has not occurred. At the same time, as shown in Ref 128, with cathode deposits present, the SCC process of pipe steels of Fe-0.1C-2MnSi-V-Nb and Fe-0.1C-2Mn-Si-V, and so on type, which have been chosen from zones of main pipeline failure cannot be explained in the context of the suggested model of the sulphide impurity dissolution (Ref 128). On authors’ data, the negative effect of sulphides is connected mainly with their role as concentrators of internal stresses (Ref 129). Nonetheless, in spite of distinctions between interpretations, it is believed that the enhancement of the corrosion-mechanical steel strength can be attained by reducing the nonmetallic impurity content that is achieved in part by rational deoxidizing and by modifying the steels by the addition of rare-earth and alkaline-earth elements. Stress Corrosion Cracking of Steels for Main Gas-Pipe Lines. In many countries, namely, the United States, Canada, Australia, and Russia, there are recorded emergency failures of subterranean buried gas-pipe lines because of pipe steels SCC (Ref 130, 131). The summary data displaying the time of trouble-free operation of main gas-pipe lines used by three major Russian companies are given in Fig. 14. Pipes of different diameter (1020, 1220, 1420 mm) and different chemical composition have been analyzed. It has been found out that pipes put into service from 1967 to 1980 have the resistance to SCC much higher than those which have been laid recently in a period from 1981 to 1989. The time of safe service of the former is from 9 to 23 years, that of the latter is only from 2 to 14 years. It is significant that all the shortlived pipes have been fabricated from steels of

82 / Effect of Materials and Processing the Fe-0.1C-2Mn-Si-V-Nb and Fe-0.1C-2MnSi-V type produced in France, Italy, Germany, and Japan. Also, it has been found that in the most cases (more than 60% of emergencies) the failure happens in places with the increased ground humidity. Cracks are revealed most often in the lower part of pipes. The mean rate of crack growth is about 1.15 mm/year (0.05 in./year). The critical length of cracks that cause failure is in the range of 140 to 150 mm (5.5–5.9 in.) (Ref 129). According to current concepts, main gas-pipe line steels are susceptible to two types of SCC: APC and HISCC. The first (classical) type of SCC is developed at medium acidity of pH 9.5 (high pH SCC); the second one is developed at pH 6.5 (low pH SCC). In both cases crack groups (colonies) orientated along the axis of the pipe arise (Ref 94). More high density of cracks in the colony is inherent in cracking by the APC mechanism. Furthermore, it has been found that in the overwhelming majority of cases, SCC at a high pH is observed within the limits of regions in extent of 20 km (12.4 miles) from the compressor station—that is, where the temperature and the pressure of gas have their top values (Ref 132–134). As to cracking by the HISCC mechanism, the analogous regularity is not fulfilled, but in this case, the well-defined connection with the weld location becomes evident. A major part of failures at low pH begins in centers located at a distance of 200 to 250 mm (8–10 in.) from the weld that is connected with the increased level of processing residual stresses. The failure at high pH develops mainly in the intercrystalline manner (i.e., along the grain boundaries), at low pH, it develops in the transcrystalline manner (Ref 94).

Period of safe service, years

30 25 20 15

C T Y

C

T

C

T 10 T

C

5 0 1966

1971

1976

1981

1986

1991

Year of putting into operation Period of gas main pipes service till first emergency failure depending on year of puttingthem into operation and manufacturing country. Closedcircle data points, steels Fe-0.1C-2Mn-Si-V-Nb and Fe-0.1C-2Mn-Si-V made in Germany, Italy, France, and Japan; open circle data points, steels Fe-0.17C-Mn-Si, Fe0.15C-2Mn-Si made in Russia; rhomb, steels Fe-0.14C2Mn-Si-N-V, Fe-0.17C-2Mn-Si-N-V made in Russia. Size of small circle corresponds to 1020 mm pipe diameter; middle one, to 1220 mm pipe diameter; and large one, to 1420 mm pipe diameter. Y, T, and C denote companies Ultransgas (Y), Tyumentransgas (T), and Severgasprom (C), respectively. Source: Ref 129

Fig. 14

The composition of the corrosion medium forming under the peeled-off insulation is the main factor on which the realization of the given SCC mechanism depends. High pH media are concentrated carbonate-bicarbonate earth solutions with temperatures up to 75 C (135 F). These solutions are formed under conditions of the cathode protection that initiates an increase of pH (acidifying) of the corrosion medium on the pipe surface. The crack grows as a result of the rapid electrochemical metal corrosion at its top where the main processes stimulating the crack growth, namely, the stress localization, the plastic strain, emerging of slip strips on the newly formed surface, are grouped. Low pH SCC develops in deleted earth electrolyte media containing dissolved CO2. It is suggested (Ref 130, 133–137) that hydrogen arises in microregions filled with the electrolyte (i.e., in slots, pittings, etc.). As a result of corrosion product hydrolysis, the electrolyte in these microregions is acidified to a level sufficient to discharging ions of hydrogen, which then diffuses into the region of tensile stresses ahead of the crack top. As in the classic model (high-pH SCC), the plastic strain at the crack top, which benefits the metal hydrogenation, is required as the obligatory condition (Ref 135, 138). In this case, as seen from the direct measurements (Ref 94), the zone of the increased hydrogen concentration extends for approximately 10 mm (0.4 in.) beneath the crack surface. Pipe surface metallurgical defects arising from rolling may present as nucleous cracks. These defects, for example, arise from surface microcracks generating at the stage of continuous steel casting. Cracks initiate on the continuously casted ingots over definite temperature intervals, mainly over the interval from 700 to 1000 C (1292–1832 F) (webbed and cross cracks), and at temperatures close to the solidus one (spider-shaped cracks). In the given temperature intervals, low-alloy steels are subject to the strong embrittlement connected with the change of the grain boundary chemical composition. The present state of the problem concerning high-temperature steel brittleness and the mechanism of the surface crack initiation in continuous casting has been analyzed thoroughly (Ref 139, 140). Practically all the steels applied in the presentday gas-pipe lines, whatever their chemical composition, structure, and strength level, are prone to SCC to some extent. That is why the prediction of a steel’s resistance to SCC takes on great significance. The results of testing a number of pipe steels for SCC have been correlated with their mechanical properties determined in the air (Ref 141). In addition to the standard mechanical properties, the mechanical properties of samples under bending with the preliminary-created fatigue crack have been determined. Any correlation between the resistance to SCC and the standard mechanical characteristics has not been detected. At the same time, according to the analysis made, a distinct relation is observed between the threshold stress, rth, in the corrosion

medium and characteristics of the mechanical properties of samples with a crack while performing bending tests in the air. The resistance to SCC in the studied aggressive media enhances with an increasing of such characteristics as failure work, yield strength, and ultimate strength. On this basis, the conclusion has been drawn regarding the necessity of introducing an additional testing of pipe steels in manufacturing plants, namely, tests of samples with a crack to predict the resistance of different types of steels to SCC.

Effect of Alloying and Impurity Elements on Hydrogen Embrittlement Resistance of Steel Hydrogen-resistant engineering steels should have a number of the following basic characteristics: ● High resistance to a brittle fracture for pre-

vention of development of an origin crack

● Low content of nonmetallic inclusions and

phases suitable as hydrogen traps

● Low level of internal stresses for elimination

of an opportunity of crack nucleation

● Presence of surface protecting films prevent-

ing penetration of hydrogen in bulk To ensure the first requirement, the structure and alloying of steel should provide: ● Hardenability of steel to gain a homogeneous

structure of martensite or its mixture with lower bainite ● Decreasing the ductile-brittle transition temperature, T50, and growth of an energy for a ductile crack propagation, ac ● Low-grain-boundaries concentration of harmful impurities Influence of alloying elements and impurities on these basic characteristics has been set (Ref 51). The corresponding data, also involving the optimal content of the basic and impurity elements providing a high hydrogen resistance of steel, are shown in Table 1. In this case, tendency of steel to hydrogen embrittlement was estimated from the relative reduction of its plasticity under tension: FW ⳱

W0 ⳮWH • 100% W0

before (W0) and after (WH) hydrogenation of plain samples during 5 h, and also from reduction of the average time for failure, st, of the ringnotched ones (h ⳱ 1 mm, r ⳱ 0.25 mm) under approximately 0.6 ry loading. Carbide-forming elements affect the quantity, distribution, and morphology of carbonitrides. The carbides are spheroidized in such a manner that interfaces of the particles with a matrix are not collectors for hydrogen. These elements in a solid solution depress the hydrogen thermodynamic activity; as a result, the occluding ability of steel is essentially diminished (Ref 142).

Effect of Residual Stress on Hydrogen Embrittlement and Stress Corrosion Cracking / 83 Those additions in steel have dissimilar influence on the resistance to different kinds of fracture. If its content does not exceed an optimal value (Table 1), resistance to all kinds of brittleness increases (Ref 143). At higher contents, the resistance of steel to hydrogen is increased, but it is reduced to other kinds of brittle fracture. Carbide-non-forming elements affect steel resistance to a ductile, brittle, and intergranular fracture. Addition of 0.1 % Si, Mn, Co or Al in a solid solution of an improved engineering steel reduces its fracture resistance; the transition temperature, T50 rising by 5; and the impact strength at decreasing by 0.07MJ/m2. Nickel is an exception; 0.1% of it makes T50 lower by 4 to 10. Similarly, these elements influence hydrogen resistance of steel. Thus, manganese, aluminum, silicon, and cobalt decrease the time for failure, st, and increase the loss of plasticity, Fw, under hydrogenation. Nickel increases steel resistance to hydrogen. Thus, when these elements are added in a solid solution, the direct dependence between the hydrogen and brittleness resistance characteristics, T50, ac, is observed. Impurities such as sulfur, phosphorus, antimony, tin, and other elements have great influence on the resistance of engineering steels to hydrogen embrittlement. Their action is manifested via weakening of grain-boundary binding (temper-embrittlement processes) and via nonmetallic inclusions formation. According to existing opinions (Ref 144), loaded grain junctions can be zones for the origination of three-axial stress state. These grain junctions are energetically preferable for the accumulation of hydrogen atoms having a low chemical potential value. It is assumed that hydrogen decreases the cohesive forces between iron atoms at grain boundaries (Ref 145). Segregation of impurities (phosphorus, antimony, tin, etc.) at boundaries of original austenite grains results in recurring temper embrittlement, which further weakens intergranular cohesive forces. These considerations have been proved by direct experiments (Ref 146). The results indicate that hydrogen does not interact with impurities or segregations at grain boundaries (i.e., the grain-boundary embrittlement actions of impurities and of hydrogen mutually supplement each other). Published data indicate that steel improving with impurities and gases cleanliness enables it to boost its fracture resistance (Ref 147). The use of metallurgical refining and remelting processes greatly increases hydrogen-embrittlement resistance due to the removal of nonmetallic inclusions from the steel, especially sulfides and stringer oxide inclusions (Ref 148). Improving the quality of heat-hardenable engineering steels (unalloyed with molybdenum and tungsten) enables them to boost by 2 to 3 times their resistance to brittle and ductile fracture. Sulfur is present in steel mainly in the form of manganese sulfides. Nonmetallic inclusions of this type are very ductile and, hence, during rolling are rolled out in the form of elongated

streaks. Sulfide streaks have S:Fe:Mn ratio of 2:1:1, which comply with the formula (FeMn)S; their thickness is 10 to 15 nm, and they are mainly located at the boundaries of original austenite grains (Ref 149). The sulfide-matrix interfaces are sites for the accumulation of diffusionmobile hydrogen atoms, which at subsequent stages cause hydrogen blistering in low-alloy ferritic-pearlitic steels due to hydrogen molecules formation from its ions and greater (than the yield strength) planar pressure. Under loading conditions the hydrogen also will accumulate at the sulfide-matrix boundaries and other sites where there is a high stress level and will cause sulfide stress cracking, which is characteristic both to mild and alloy high-strength steels (Ref 150, 151). Shape modification of sulfide inclusions from plate-like to globular lowers the sensitivity of steels to hydrogen cracking, since the globules are less favorable to hydrogen accumulation than plates are. Calcium and rare-earth metals are suitable for shape modification of inclusions (Ref 152). Thus, the nonmetallic inclusions, especially sulfides, enhance accumulation of hydrogen in steels and increase the susceptibility of steels to hydrogen embrittlement. Therefore, in order to lower the sensitivity of steels to hydrogen embrittlement, it is necessary to decrease the sulfur content in them and to modify the shape and type of sulfide inclusions. Sulfur, therefore, is a harmful impurity in steels, lowering their resistance to fracture and hydrogen embrittlement. In mild steels with ferritic-pearlitic structure, the sulfur, forming manganese sulfides of plate-like shape (stringers), enhances hydrogen blistering, which is manifested even at 0.001% S. Sulfide (hydrogen) stress cracking of such steels is sharply reduced with the decrease of sulfur content below 0.007%. An effective way for prevention of blistering and hydrogen stress cracking is modification of engineering steels with rare-earth elements (0.1–0.3%), especially with cerium spheroidizing sulfide inclusions. Phosphorus, Antimony, and Tin. The adverse effect of these elements on steel properties is well studied. Impurities enriching grain boundaries during tempering cause reversible temper brittleness. This phenomenon has a considerable effect on the level of steel resistance to fracture. Phosphorus in engineering steels greatly lowers brittle and ductile fracture. Phosphorus facilitates steel hydrogen embrittlement by enhancing temper brittleness development and establishing chemical and structural heterogeneity. Quantitative relationships have been found for the embrittling effect of phosphorus, tin, and antimony on steel: Each 0.01% of the impurities increases brittle fracture temperature, T50, by 20 to 23 C; (36–41 F), decreases crack-development energy, Ap, by 10 J/cm2; and increases plasticity loss value during hydrogenation by 8%. Reference 153 describes a study on the influence of phosphorus content on the resistance of

heat-hardenable steel (0.4% C, 1.0% Cr, 0.37% Mo, Fe-bal) to hydrogen-sulfide cracking, and it has been shown that increasing its content from 0.009 to 0.06% lowers the threshold stress from 518 MPa (75 ksi) to 140 MPa (20 ksi). Such an effect of phosphorus is attributed, first, to the fact that it activates the hydrogen absorption process and, second, that it changes the shape and distribution of carbides. Phosphorus or manganese segregation can be formed at a pearlite band in low-alloy steels (Ref 154). Such formation causes structural changes, an increase of steel occlusive capacity by 2 times, and a decrease of the time for failure under load in a hydrogenating medium by 2 times. The adverse effect of phosphorus on steel resistance to brittle fracture is comparable with the favorable effect of nickel and molybdenum: Each 0.01% lowering of phosphorus content in steel is equivalent, in its influence on the T50 level, to steel alloying with 1% nickel or 0.1% of molybdenum. Antimony and Tin. The resistance of engineering steels to brittle fracture depends, to a large extent, on its cleanliness with regard to antimony and tin impurities. These impurities are brought into steel in considerable quantities (0.01–0.03%) during melting when using scrap. Both elements increase the cold-shortness threshold and lower the impact strength level (Ref 155). The degree of its influence may vary with the steel alloying system to a great extent. In low-alloy steels with ferritic-pearlitic structure, the addition of antimony, which is a more electro-positive noble element than iron, improves the corrosion resistance in hydrochloric and sulfuric acids, assumed to be due to a film containing antimony forming on the steel surface. The surface layer inhibits penetration of hydrogen into steel (Ref 156). To a greater extent, antimony and tin lower the steel resistance to brittle fracture: Each additional 0.01% Sb or Sn raises the T50 by an average of 18 C (32 F). Their adverse effect in this respect is comparable with the favorable influence of nickel and molybdenum. It is possible to assume that at an antimony content above 0.3%, the effect of lowering steel resistance to brittle and ductile fracture will prevail over the effect of lowering the quantity of absorbed hydrogen. Hence, additional alloying with approximately 0.20 to 0.30% antimony is advantageous for low-alloy steels to be used in hydrogen-sulfide media. The associated reduction in the level of toughness properties is insignificant as compared with the improvement in the resistance to hydrogen embrittlement by 2 times. With respect to these considerations the following conclusions can be drawn: ● Antimony and tin impurities lower the resistance of structural steels to brittle and ductile fracture: Each 0.01% increase in antimony or tin raises T50 of heat-hardenable steels by 18 C (32 F), and each 0.01% increase in antimony raises T50 of low-alloy steels by 1 to 5 C (1.8–9 F).

84 / Effect of Materials and Processing ● The embrittling effect of antimony and tin is

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Deflection Methods to Estimate Residual Stress H.W. Walton, Consultant

NOT EVERYONE has sophisticated instrumentation such as x-ray or neutron diffraction readily available for the determination of residual stresses. Nor do they have the time or inclination to use these procedures for checking production parts. Mathematical derivations such as the one for plate by the Treuting and Read method are also very time consuming (the method is described at the end of this article). To determine if residual stresses from prior processing are the cause of uncontrollable distortions during processing of thin section parts, it is a simple matter to slit an as-received piece and note the amount of deflection resulting from relaxation of residual stresses, for example, the net opening of the saw cut. If no deflection occurs, then it can be safely assumed that the problem lies with the processing parameters and not with the material (e.g., high feeds and speeds or high chucking pressures during machining, or surface overheating during grinding resulting from insufficient wheel dressing). These simple techniques, sometimes known as dissection, are old but still very useful. However, because slitting a component is a destructive method, there are limitations, particularly if the component in question is large. This article provides a low-cost, easy method of determining if residual stresses are the cause of component distortion during manufacture.

Residual Stress To understand the type of stress that is being measured, a distinction first needs to be made between microstresses and macrostresses extending over large volumes. Microstresses resulting from changes occurring at the atomic level are equilibrated over very small volumes and cannot be measured by use of deflection methods. Macrostresses, on the other hand, are primarily the result of forming operations or thermal imbalances during casting, welding, heat treating, and so on. If the stress induced by nonuniform cooling exceeds the yield strength of the material, plastic deformation occurs. On cooling to a uniform am-

bient temperature, the deformed volume being restrained by the surrounding material is now placed under significant elastic stress. This would be considered macrostress and is the stress most likely to cause deformation during subsequent processing. Consider the simple example of bending a bar to form a permanent set. The surface material at the elbow or concave surface undergoes permanent plastic deformation while the inside diameter is undergoing compressive plastic deformation. When the applied force is removed, the underlying elastically stretched material (at the elbow) is now prevented from relaxing completely. The result is that the plastically deformed surface layers of the elbow are placed under elastic compression by the underlying elastically stretched material. The opposite is true for the inside diameter. It follows that if the bar is placed in service in this condition, corrosion and development of cracks are more likely to occur at the surface of the inside diameter. In general terms, if a surface undergoes permanent plastic deformation by cold rolling, shot peening, machining, thermal processing, and so on, which in turn results in the underlying material being elastically stretched or compressed, the material plastically deformed by tensile forces is left in elastic compression. Material plastically deformed by compressive forces is in elastic tension. The influence of nonuniform residual stress is sometimes dramatically illustrated by “fishtailing” of large hot-rolled steel plate. As the plate cools after rolling, transformational stresses are developed and, if an extensive central lamination is present due to inadequate discard or casting problems, these stresses can cause the plate to separate into two halves (Fig. 1). The stress distributions present before and after the occurrence of a fishtail are shown in the sketch. In the as-rolled plate, tensile stresses (Ⳮtv stress) on the surface are trying to contract the surface while compressive stresses (–tv stress) are trying to expand the plate core. How this stress distribution develops is illustrated in Fig. 2. After fishtailing, the two halves of the plate attain a new equilibrium stress distribution.

While air cooling after hot rolling, the plate surface will be cooling faster than the core material, and thermal stresses developed at this stage will be relaxed by the plastic deformation of the low strength austenite. At lower temperatures, transformation to ferrite and pearlite begins at the surface (Fig. 3), causing complex interactions and a variety of stress conditions. Because of the relatively low yield strength of the various phases and the role of transformation induced plasticity, the final stresses are low. However, over a large surface area even low residual stresses can have a profound effect, particularly in the presence of large defects such as a lamination. If not fixtured in a vertical position, severe distortion of quenched flat steel sections may occur. This is due to differences in the cooling rate and transformation behavior between the top and bottom surface. In a carburized product, because of the compositional changes causing transformation to progress from the inside out and the considerably higher-strength case, the final residual stress profile is reversed and a beneficial high-compressive surface stress is developed (Ref 1). Figure 4 shows the development of these residual stresses during the heat treatment of a carburized component. It is very important to avoid heating small, isolated areas on the surface of hardened steel.

Fig. 1 stress

Schematic representation of fishtailing in plate steels. Ⳮtv, tensile stress; ⳮtv, compressive

90 / Measurement and Prediction of Residual Stress and Distortion Examples of where this may occur are: ● Components ground with inadequate cooling

fluid or faulty equipment (vibrating wheel heads) ● Using a gas flame to enlarge a hardened component for assembly on a shaft ● Electrical arcing from inadequately earthed drive motors ● Accidental arcing during magnetization for magnetic particle inspection The thermally damaged area is restrained from expanding by the surrounding material and becomes plastically deformed under compression. Consequently, on cooling to ambient temperature, the surface is left in a tensile condition, and cracking ensues either immediately or after the component is placed in service (more worrying). Heating at temperature above the original tempering temperature may also lead to a contraction. Shot peening appears to be an anomaly. At first sight, the impact of the shot particles seems to cause plastic deformation in compression. It should follow that the surface is in tension following the peening treatment. However, the ad-

ditive influence of the multiple small areas of plastic extension of the surface must be considered. The overall surface undergoes a plastic extension, thus putting the underlying layers in tension. Consequently, on completion of the shot-peening operation, the surface is restrained in a beneficial compressive state. The maximum level of residual stress that can be generated is approximately equal to the elastic limit or yield strength of the material measured under the same stress condition and for the same cross section. The existence of triaxial stresses in heavy section components has a major influence on the ease of plastic flow (plane-strain conditions). If surrounding material inhibits plastic flow by significantly limiting shear stresses, the levels of residual tensile stress may become high. Catastrophic fracture occurs when the tensile stress level exceeds the cohesive strength of the steel.

Manufacturing Implications of Residual Stresses There are many examples that show how relaxation or redistribution of residual stresses

contributes to high processing costs. One example is the need to use multiple grinding passes to avoid distortion in thin section components. A frequent problem often wrongly attributed to the heat treatment department is heat treatment distortion from prior residual stresses in the raw material. Premature failure due to harmful residual surface tensile stress in the manufactured product is to be avoided at all costs. On the other hand, the presence of residual stresses may be advantageous, as in the example of compressive stresses from case hardening and shot peening. Using residual stresses to intentionally deform a component can be illustrated by the use of shot peening to shape the aircraft fuselage, by using a peen hammer to straighten a long shaft, or by simply hot spotting to bend a simple bar of steel. For example, a small area on one side of a steel bar is heated rapidly to a temperature, T, of approximately 600 C (1100 F) (Ref 2). If free to expand, the heated disc-shaped region increases in length, l, by: l⳱ ␣⳯ T ⳱ 14 ⳯ 600

Cooler outside surface

⳱ 8.4 ⳯ 10ⳮ3 lm/mm

Hotter core

Transformation Consider a slice through half the thickness of a plate. At the onset of the cooling, both the surface and the core are austenitic and stress free.

Transformed

Not transformed The surface will transform first, acccompanied by an expansion. Restraint by the underlying material will place the transformed element in compression "C". Although the adjoining austenitic element "stretches" and plastically yields, it will be in tension "T".

CT

where ␣ is the coefficient of thermal expansion in lm/mm • K. However, the surrounding cooler material restrains expansion. Because of the relatively low yield strength at 600 C (YS600) of approximately 30 MPa (4.5 ksi), the heated steel deforms plastically under compression, increasing the thickness of the heated disc. On cooling, the disc contracts the same amount and, assuming no stress relaxation occurred, a tensile stress, r, is now developed in the disc: r ⳱ (E ⳯ l) ⳮ YS600 ⳱ (200 ⳯ 103 ⳯ 8.4 ⳯ 10ⳮ3) ⳮ 30 ⳱ 1650 MPa (240 ksi)

Schematic representation of transformational expansion in the absence of any restraining effect by the surrounding material

The already extended underlying element then undergoes transformation and expands further. This induces tensile stresses in the material on either side, but due to the restraining influence of surrounding material, compressive stresses are induced in the newly transformed steel.

TCT

Fig. 2

T

T

TCT

T

T

T

The transformation front proceeds deeper into the section, leaving behind a surface that is in tensile. The magnitude of stress is determined by the relative yield strength of the phases. Because of the TRIP effect (transformation induced plasticity), the plasticity of the transforming steel is considerably higher.

C

C

C

The development of residual stresses during cooling of steels

where E is the modulus of elasticity (MPa). The stress in the disc cannot be greater than the yield strength of about 500 MPa (73 ksi). Therefore, either the disc stretches plastically, or the bar bends elastically to balance the stresses (or both). The manufacture of seamless high-carbonbearing steel tube involves hot rolling, sizing, straightening, and spheroidize annealing. Each stage of manufacture introduces various degrees of residual stress. If residual stress levels are higher than normal, difficulties may be experienced during subsequent machining and heat treatment of the rings. As seen from the previous calculation, the higher the yield strength of the material, the greater the potential for high levels of residual stress. As thermal and mechanical treatment of steel increases the strength of a material, potential problems with residual stress also increase. For example, a small area of thermal damage on the surface of a hardened high-

Deflection Methods to Estimate Residual Stress / 91 carbon steel (e.g., electric arc discharge) may result in a level of triaxial residual stress close to the cohesive strength of the material, possibly leading to immediate or delayed cracking. Although the stress may be multidirectional, hoop stress that arises at several stages of manufacture is the primary cause of many of the problems. When a length of tube is parted off and slit in a longitudinal direction, any hoop stress present tends to open the slit (Fig. 5). Opening of the slit indicates compressive stress in the inside diameter (ID) of the tube and tensile stress on the outside diameter (OD). On rare occasions, the slit may close, indicating the reverse condition. The stress is not always uniform along the length of the tube. Stress measurements have, on occasions, indicated a cyclic variation corresponding to differences in cooling of areas in contact with the cooling bed cross ties. Shot peening intensity is monitored by using a method developed by J.O. Almen of General Motors Company. In this method, 75 mm long by 18.75 mm wide (3.00 by 0.75 in.) strips of 1070 spring steel are quenched and tempered to a deep-blue oxide finish (“blue tempered”) for a hardness of 45 to 50 Rc and exposed on one side to the same shot intensity as the component undergoing treatment (Ref 3). Three different thicknesses are used: “N,” 0.79 mm (0.031 in.); “A,” 1.30 mm (0.051in.); and “C,” 2.38 mm (0.0938 in.) to allow for differences in degree and shot peening required and materials being treated. For example, peen forming of an aluminum alloy requires considerably less peen intensity than a carburized gear tooth. During treatment, the Almen strip assumes a concave shape. The lift height is proportional to the level of compressive stress developed in the upper sur-

face during peening. Peening is continued until the material has reached saturation; that is, when the lift height increases by no significant amount and the compressive stress in the surface layers corresponds closely to the elastic limit of the steel strip (Fig. 6). Consider the residual stress distribution through the Almen strip. Deflection of the strip occurs in order to relieve some of the high surface compressive stress. The peened surface area endeavors to expand by bowing in order to nullify the compressive stress. The magnitude of bowing is limited by the restraint of the remainder of the material, and equilibrium is reached when the remaining compressive stress is in balance with the elastic compressive stress developed in the lower surface. The depth and intensity of the compressive layer is proportional to the lift height at saturation. The Almen strips are primarily used to ensure that the process is in control (shot condition, uniformity in application, impeller operation, etc.). A photograph of three typical strips is shown in Fig. 7. Metal Improvement Company, Inc., in collaboration with ENSAM, a French advanced engineering school, has developed a software program called PeenStress (Metal Improvement Co., Inc., Paramus, NJ) that is used to assist in shot peening callouts (Ref 4). The user selects a material from a library of about 80 materials, then selects a shot size and shot intensity and inputs some basic geometry considerations. Figure 8 is a curve generated on a chromium-silicon spring wire shot peened with a hardened, 0.023 in. ⭋ shot to a 10 A intensity. A 10 A intensity equates to a 0.25 mm (0.010 in.) arc height on the A-strip. One of the older standard tests for evaluating

Ar3 Ar1 Austenite

quench distortion is the Navy C-ring test (Ref 5– 7). The amount of distortion (deflection) of a quenched test piece is measured by the change in the gap width (Fig. 9).

Methods for Measuring Residual Stresses from Deflection Data Sectioning to allow relaxation of residual stress in actual components where stresses are thought to be present can be performed by several methods, from simple saw cutting to the more sophisticated compliance method (Ref 8– 10). In the latter method, the residual stress profile is calculated from the strains caused by introducing a cut of progressively increasing depth into the component. The strains are measured by using suitably positioned strain gages cemented to the surface adjacent to the cut. The cutting is performed by using various techniques, however, electrical discharge machining is the preferred method. Usually, two computer-based approaches are used to analyze the data. These are the forward and inverse solution. The forward solution derives the measurable strains (compliance functions) that develop from introducing a successively deeper slot into a part containing an arbitrary known stress distribution. The inverse solution develops the original residual stress distribution that best matches the actually measured strains. Similar methods based on drilling small holes in the stressed material have been around for some years. Strain relaxation is measured using strain gages or photoelastic coatings. Strain gages have been used to measure strain relaxation in bevel gears following successive removal of layers by electrochemical machining (Ref 11). Saw cutting or slitting is an easy quality control test that gives a global overview of the state of residual bulk hoop stress in rings. Interestingly, such a technique was used recently to validate the measurements of residual stress levels in railway wheels using electromagneticacoustic transducers (Ref 12).

Ferrite Pearlite Temperature

Core Bainite Surface

Martensite

Time, T Schematic representation of the relative transformation at the surface and in the core of the mild steel plate. At time, T, the core is still austenitic while the surface has already transformed to a ferrite-pearlite structure. Ar3 and Ar1, upper and lower transformation temperatures, respectively, on heating (refroidissant) a hypoeutectoid steel

Fig. 3

Mathematical Derivations for Simple Cases Based on the Saw-Cut Methods Definitions of the symbols used in the following derivations are given in Table 1. To develop the mathematical algorithms for interpreting deflection measurements after slitting a simple shape (plate, round bar, or tube), simple beam theory is used (Fig. 10). The basic formula for the state of affairs at any point (x) along a beam is (Ref 13): M r E ⳱ ⳱ I c R

(Eq 1)

where M is the bending moment to which the beam is subjected at x. Bending moment M is

92 / Measurement and Prediction of Residual Stress and Distortion

%C

Carbon profile through case. As the carbon level decreases, the transformation temperature during quenching increases (Ms). Although the cooling rate is less below the surface, transformation occurs from the inside out.

Consider a section through the carburized case. At the onset of quench, both the surface and the core are austenitic and stress free.

Start of transformation Even though the cooling rate is lower than at the surface, the low carbon core will begin to transform, starting first below the case and progressing inward. The adjoining austenitic case element will plastically expand outward to accommodate the resulting tensile stress.

C

equal to load multiplied by distance (lbf • in., or kgf • m). If M is not obvious from the first principles for a given case, it may be obtained from the data given subsequently. I is the moment of inertia of the section of the beam at x, usually in inches. Moments of inertia are treated in textbooks of elementary mechanics. The moment of inertia in question is that about the neutral axis which, in most beam problems, will be a line through the center of gravity of the section. If the I of the section is not already known, it is usually easily calculated by applying one of the following formulae. For a rectangle:

bt3 12

Schematic representation of transformational expansion in the absence of any restraining effect by the surrounding material

C

C CC T T

+tv

T

Following the progressive transformation of the core, the innermost element of the case transforms. The resulting expansion of the already extended case element creates tensile stresses in both remaining austenitic case and adjoining core.

Sections made of rectangles, such as rectangular tubes, H-beams, and channels, can be calculated by subtracting the I of the empty areas. For a circular cross section:

The continued transformation of the progressively higher carbon case and the resulting expansion of the already plastically stretched elements result in high compressive stresses. Consequently, the underlying transformed core is pulled into tension.

I⳱

Stress profile through case. Compressive stress near the surface of the case can reach levels of 300/500 N/mm2 and is one of the primary reasons for carburizing.

−tv

Fig. 4

(Eq 2)

The development of compressive stress in the case of a quenched carburized steel. Source: Ref 1

pr 4 4

(Eq 3)

The moment of inertia for hollow tubes can be calculated by subtraction, where: r is stress in the material. c is distance from the neutral axis. In symmetrical sections this is the distance from the midpoint or center of gravity of the section. E is Young’s modulus. (In thick cross sections and/or high-strength steels, this should be corrected for Poisson contraction where m is Poisson’s ratio [0.3 for steel].) E⳱

E 1 ⳮ m2

(Eq 4)

R is the radius of curvature of the beam when it bends under load. To calculate the stress in a simple beam: r⳱

Mc I

(Eq 5)

For a rectangular beam at the surface where the stress is greatest:

Fig. 5

Schematic of the residual stress distribution in rings manufactured from tube before and after slitting. ID, inside diam; OD, outside diam

I⳱

bt3 12

(Eq 6)

c ⳱

t 2

(Eq 7)

so

Deflection Methods to Estimate Residual Stress / 93

rmax ⳱ 6

M bt2

(Eq 8)

EI R

Symbols used in the derivations and formulas Units

This explains why a beam that is twice as thick is four times as strong. The distribution of residual stress in actual components is unlikely to be linear. However, for the subsequent approximate analysis, the beam stress is assumed to vary linearly through the section. In sheet and bar, as the sheet fishtails or is cut in a central planar direction, the bending moment created by the residual stress is released (Fig. 11). The bending moment may be expressed as: M⳱

Table 1

(Eq 9)

Symbol

Description

M I

Bending moment Moment of inertia

r c

Stress in material Distance from neutral axis

E R L r t d c

Young’s modulus Radius of curvature of beam or displaced section Length of curved beam Radius of round bar cross section Thickness of beam/plate/tube wall Measured deflection Poisson’s ratio

SI

English

Notes

N•M m4

lbf • in. in.4

Pa m

psi in.

Pa m m m m m Dimensionless

psi in. in. in. in. in. ...

... I ⳱ bt3/12 for rectangle (where b and t are the dimensions of the cross section) I ⳱ pr 4/4 for circle ... In a symmetrical section this is the distance from the midpoint or center of gravity ... ... ... ... ... ... 0.3 for steel

given that: c ⳱

t 4

(Eq 10) 30 ± 0.015 in.

where t is plate thickness, and assuming the distribution of the residual stress that resulted in the fishtail varies linearly over the half-thickness of the sheet, the maximum longitudinal stress at the surface is given by: r⳱

Mc I

(Eq 11)

0.0310.001 in. Measuring dial

0.0510.001 in.

N strip

Peening nozzle

A strip C strip

Almen strips

0.09380.001 in. 0.7450.750 in.

Shot stream 4-6 in.

Almen test strips

Substituting Eq 9 and 10 in Eq 11 gives: r⳱

Et 4R

Hardened ball supports

10/32 screws

(Eq 12)

Arc height 3.0 in.

If the deflection, d, is small compared to the radius of curvature, R, R may be expressed in terms of the deflection, d, and the length of the curved surface, L, by: R⳱

L2 2d

3.0 in. Holding fixture

0.75 in. Strip removed. Residual stresses induced arching

Fig. 6

Use of Almen strips to monitor the degree of shot peening. Source: Ref 3

Fig. 7

Almen strips used to monitor different levels of shot peening intensity

(Eq 13)

This is derived as in Fig. 12. Referring to Fig. 12, the two radii O1 and O2 are drawn as shown, and the tangents 1,3 and 2,4 are drawn to these radii. A chord is drawn between the points of tangency 1 and 2 and the line 2,3 is drawn perpendicular to the chord at 2. The two isosceles triangles RLk and mdn are similar and therefore: R m ⳱ L d

(Eq 14)

or R⳱

Lm d

(Eq 15)

For small angles, L is the arc 1,2 and m is 1⁄2 the arc 1, 2, or

Arc height Strip mounted for height measurement


m⳱

1 L 2

(Eq 16)

therefore (as in Eq 13): R⳱

L2 2d

(Eq 17)

where d is the deflection of the strip (Fig. 11a). According to Eq 12: Et r⳱ 4R

(Eq 18)

it follows: r⳱

A simpler technique to measure the circumferential hoop stress in a thin-walled tube is to slit the tube longitudinally with a carborundum cutoff wheel (using plenty of coolant to avoid heating of the surfaces) and measuring the change in diameter of the tube (Fig. 13b):

Etd 2L2

r ⳱ Et

1 0

ⳮ

冣

1 D1

● Using a carborundum wheel, a ring, either

parted from the tube or machined, is cut axially through the section. ● If unknown, the saw curf width (width of saw

(Eq 22) 0.600 0

where D0 is initial diameter and D1 is diameter after slitting. Alternatively, the net opening displacement at the saw cut is measured by subtracting the width of the saw blade, and the residual hoop stress is measured using the formula:

(Eq 19)

A similar derivation can be obtained for round bar (Fig. 11b):

冢D

following method is often used to identify the possible cause:

冢

1 1 r ⳱ Et ⳮ x D0 Ⳮ D0 p

冢

1.000

2.900 B

A

冣

C

1.900

(Eq 23)

冣

E 5.000 (a)

r⳱

1.65 Erd L2

(Eq 20)

For thin-walled tubing (Fig. 13), the longitudinal stress is given by: r⳱

Etd L2

(Eq 21)

Equation 21 is the same as Eq 19 except that t/2 is used in the former case because only half the sheet thickness deflects. The method of sectioning a tube to obtain the previously mentioned approximate measurement is shown in Fig. 13(a).

where x is the net opening displacement. A summary of the derivations is given in Table 2. A Practical Example. The formulas in Table 2 are used extensively for measuring residual hoop stresses in seamless tube and machined bearing rings. These stresses may arise from tube straightening without a stress-relief anneal or nonuniform rapid cooling following the spheroidized anneal. In the past, contact with the support bars on cooling beds has been recognized as being a potential cause of cyclic nonuniform stress along the length of a tube. Where 52100 bearing steel rings are being machined on multispindle machines and the operator is having difficulty in maintaining size, the

0.25 in.

0.50 in.

A

2.50 in. 0.5 in.

1.45 in.

(b) 2 in. 1/4 in.

1 1/4 in.

Residual stress , ksi

4

3/4 in.

2000:5:9 Peen stress ENSAM−MIC

Residual stress distribution 8 Depth, mils

5/8 in.

d = 5.198 mils h = 0.294 mils 10 A S 230 shot V = 124 ft/s HS/4320 • CB/SP

−100

(c) Examples of C-ring test specimens used for quench distortion studies. (a) Source: Ref 5. (b) Source: Ref 6. (c) Source: Ref 7

Fig. 9

Dir. Z

x ∑s (ksi)

−102

∑m (ksi)

−203

P∑m (in.)

0.001

P∑0 (in.)

0.008

B d

A l

−200

W M = Wx Max. M = Wl at B

Fig. 8

Calculated residual stress distribution in a shot peened chromium-silicon spring wire. d, depth; h, height. Source: Peen Stress, Metal Improvement Company, Inc.

Fig. 10

Simple beam theory—definition of bending moment. W, weight in lbs or kg

Deflection Methods to Estimate Residual Stress / 95 cut) is determined by measuring a shallow cut adjacent to the final cut. ● The gap width is measured using internal calipers. The net opening (x) equals the gap width minus the saw curf (width). On occasions the gap may decrease, indicating a compressive hoop stress. In extreme situations, the blade may become nipped and may even disintegrate. Ensure proper protection when using this method. For greater accuracy in large cross sections, the value for E can be corrected for Poisson’s ratio by: E⳱

E ⳱ 28.57 ⳯ 106 psi 1 ⳮ m2

these may lead to quenched-in nonuniform stress. During subsequent grinding operations, the stress distribution undergoes a redistribution and may, in extreme cases, lead to the rings distorting. Although heat treating receives the blame, many similar problems may, in fact, be attributed to the incoming raw material.

Validation of Net Opening Calculation Considerable work has been accomplished in recent years in the area of heat treatment modeling and, in particular, of software capable of

Elastic constants for several materials are given in Table 3 (Ref 16). (These must only be used as a guide. For more rigorous treatment of elastic and plastic distortion, actual values should be obtained for each material and condition under consideration.) From experience in dealing with distortion problems in manufacturing that are attributable to residual stress in tube stock, it was determined that the following criteria could be used as a guide to the acceptability of the calculated stress levels. Residual stress

Acceptability

5000 psi 5000–10,000 psi 10,000 psi

Acceptable Borderline Unacceptable

The criteria used to determine what residual stress is acceptable must also be based on the cross section of the ring: the more rigid the design, the higher the stress level tolerated. However, this only applies to holding tolerance during machining. During subsequent heat treatment, the magnitude of residual stress may still be sufficient to cause distortion during heating. As the temperature increases, the yield strength of the steel decreases, allowing relaxation by plastic deformation. This is manifested in the parts being out-of-round exiting the furnace. In very thin sections, some of the stress may be from the machining operation (e.g., feeds and speeds too high). In order to lessen the effects of residual stresses during heat treatment, pre-heating at a subcritical temperature has been found to be useful. A portion of the stress is allowed to relax without causing a gross shape change. Examples of extreme levels of residual stress in tube material are usually seen when it was impossible to machine an acceptable part. Stress relieving one particular batch of tubes (new supplier) resulted in them moving so far out-ofround that they no longer fit in the multispindle machine collets. In an attempt to avoid out-of-round rings, die quenching techniques are often used. However,

predicting distortion in heat-treated products. An example is DANTE (Deformation Control Technology, Inc., Cleveland, OH), developed by a collaborative team comprising Ford Motor Company, General Motors Company, The Torrington Company, Eaton Corporation, IITRI, Colorado School of Mines, The Department of Energy National Labs, Deformation Control Technology, Inc., and under the auspices of the National Center for Manufacturing Science. In order to accurately predict the thermal and allotropic stressinduced size changes and distortion in heat-treated products (including carburized), it is necessary to incorporate many factors into the finite element-based model, including the transformational characteristics of the steel, the ele-

2d

L

t

Residual stress distribution

(a)

L

2d + 2 r

r

(b)

Fig. 11

Determination of longitudinal residual stress by the deflection method. (a) Rolled sheet. (b) Drawn bar. Source: Ref 14

t d L

(a)

D1

D0

x (b) Determination of residual stresses in thinwalled tube by deflection methods. (a) Longitudinal stress. (b) Circumferential stress. t, thickness; d, deflection; D0, initial diam; D1, diam after slitting; x, net opening displacement. Source: Ref 14

Fig. 13

Fig. 12

Diagrammatic representation of the deflection formula derivation. Source: Ref 15

96 / Measurement and Prediction of Residual Stress and Distortion Using DANTE, it has been possible to subject the net opening deflection method to a more rigorous analysis. An example of the simulation of the opening of a slit ring in the presence of an imposed hoop stress is shown in Fig. 14 and 15. Two-dimensional modeling was used, and plane-strain conditions were assumed. The rings were assumed to be 152 mm (6 in.) OD and man-

vated temperature properties and behavior of the individual and mixed phases, geometry of the part, quenching factors, heat-transfer coefficients, and so on. Several papers have been published on the development and application of the model (Ref 17–21). Commercialization of the software package is being handled by Deformation Control Technology, Inc., Cleveland, Ohio.

Table 2 List of formulas used for calculating approximate levels of residual stress in simple geometries by deflection methods Method

Formulas

Longitudinal stress in plate (Fig. 11a)

Etd r⳱ 2 2L

Longitudinal stress in solid bar (Fig. 11b) where r is the radius of the bar

r⳱

1.65 Erd L2

Longitudinal stress in thin-walled tube (Fig. 13a)

r⳱

Etd L2

Circumferential (hoop) stress in tube from change in diameter where D0 and D1 are the initial and final diameters, respectively (Fig. 13b)

r ⳱ Et

Circumferential stress in tube from net opening displacement x

r ⳱ Et

Table 3

冢D

1 0

冢

ⳮ

1 D1

冣

1 1 ⳮ x D0 Ⳮ D0 p

冢

冣

冣

Example: Determining Biaxial Residual-Stress State

Elastic constants for some of the common metals Modulus elasticity

Shear modulus

Materials

GPa

106 psi

GPa

106 psi

Poisson’s ratio

Aluminum alloys Copper Steel (plain carbon and low alloy) Stainless steel Titanium Tungsten

72 110 200 193 117 400

10.5 16.0 29.0 28.0 17.0 58.0

28 41 76 66 45 157

4.0 6.0 11.0 9.5 6.5 22.8

0.31 0.33 0.33 0.28 0.31 0.27

Source: Ref 16

Fig. 14

ufactured from annealed 52100 bearing steel with two different cross sections. A residual stress profile was superimposed on the rings by creating a 93 C (200 F) linear temperature gradient across the cross section from ID to OD. For the ring in Fig. 14, simulating axial slitting of the ring resulted in a net opening of 2.9 mm (0.114 in.) with an accompanying redistribution of the residual stress. Using Eq 23, the average hoop stress in the ring prior to slitting was calculated to be 172 MPa (25 ksi). In thinner cross section rings, the net opening will be larger for the same level of residual stress, as shown in Fig. 15. For a cross section of 9.5 mm (0.375 in.) and a similar residual stress condition, the net opening is calculated to be 6.3 mm (0.247 in.). Equation 23 gives a calculated hoop stress of 179 MPa (26 ksi). These calculations used a Young’s modulus value of 29 ⳯ 106 psi and Poisson’s ratio of 0.33. It is interesting to note that one of the many techniques used to exercise DANTE was based on the carburizing of a modified Almen strip (Ref 22, 23). Excellent agreement between the predicted and measured transverse deflections were obtained.

Simulation of the effects of residual stress on the net opening displacement of a cut 0.75 in. thick ring

Treuting and Read developed a method for determining the biaxial residual-stress state on the surface of a thin sheet (Ref 24). The method assumes the metal behaves in an elastically homogeneous manner and that the stress varies, not in the plane of the sheet, but only through the thickness. To apply the method, the sheet specimen is cemented into a flat parallel surface, and

Deflection Methods to Estimate Residual Stress / 97

Fig. 15

Simulation of the effects of residual stress on the net opening displacement of a cut 0.75 in. thick ring

the thickness is reduced a certain amount by careful polishing and etching. The sheet specimen is then released from the surface and measurements are made of the longitudinal radius of curvature Rx., the transverse radius of curvature Ry, and the thickness, t. Figure 16 illustrates the orientation of the principle stresses and the curvature of the sheet. The measure values of radius of curvature are expressed in terms of two parameters, Px and Py. Px ⳱

1 m Ⳮ Rx Ry

Py ⳱

1 m Ⳮ Ry Rx

rx ⳱ ⳮ

冤(t

0

Ⳮ t)2

ry ⳱ ⳮ

冤(t

0

E 6(1 ⳮ m2) dPx Ⳮ 4(t0 Ⳮ t)Px Ⳮ 2 dt

t

冮

t0

冥

Px dt

E 6(1 ⳮ m2)

Ⳮ t)2

dPy Ⳮ 4(t0 Ⳮ t)Py Ⳮ 2 dt

t

冮

t0

冥

Py dt

Values of dP/dt are obtained from the slope of the curves of P versus t, and the integrals are evaluated by determining the area under the P versus t curve over the appropriate limits. REFERENCES

Measurements of Rx and Ry are made for different amounts of metal removal, and Px and Py are plotted against the sheet thickness, t. The residual stresses in the x and y directions of the sheet are determined for any value of t by the following equations.

1. G. Parrish and G.S. Harper, Production Gas Carburizing, Pergamon Press, 1985 2. F.W. Jones, JISI, May 1969, p 556–562 3. “Shot Peening Applications,” 7th Ed., Metal Improvement Company, Inc., 1995

z z y σy

y

σx

x x

t

t0

(a)

Fig. 16

Rx

Ry

(b) (a) Coordinate system for measuring biaxial stress in thin sheet. (b) Curvature produced by removing material from top surface

4. D. Breuer, Metal Improvement Company, private communication, 1999 5. Heat Treating, Cleaning and Finishing, Vol 2, Metals Handbook, 8th ed., ASM International, 1964, p 41 6. “Tenaxal, Ucon Quench A—The Fast Safe Way to Quench Steel Alloys,” Product Information Bulletin, Tenaxal, Inc., Milwaukee, WI, revised 1972 7. H.J. French, The Quenching of Steels, American Society for Steel Treating, 1930, p 133 8. B. Prime, “Residual Stress Measurement by Successive Extension of a Slot: The Crack Compliance Method,” Los Alamos National Laboratory, Publication LA-UR- 98–3857, 1998 9. W. Gremaud, I. Cheng, M. Finnie, and B. Prime, The Compliance Method for Measurement of Near Surface Residual Stresses—Analytical Background, J. Eng. Mater. Technol., Vol 116, p 550–555 10. I. Cheng, M. Finnie, M. Gremaud, and B. Prime, Measurement of Near Surface Residual Stresses Using Electric Wire Machining, J. Eng. Mater. Technol., Vol 116, p 1–7 11. Kovac, Residual Stress Measurements in Bevel Gear after Different Production Phases, J. Mater. Eng. Perform., Vol 3 (No. 1), Feb 1994, p 61–64 12. E. Shramm, J. Szelazek, and A.V. Clark, “Dynamometer—Induced Residual Stress in Railroad Wheels: Ultrasonic and Saw Cut Measurements,” National Institute of Standards and Technology Publication NISTIR 5043, Report Number 30, March 1995 13. J.E. Gordon, The New Science of Strong Materials, Penguin Books, 1968, p 258– 261 14. G.E. Dieter, Mechanical Metallurgy, 1st ed., McGraw-Hill Book Company, New York, 1961 15. R.L. Anderson and E.G. Fahlman, A

98 / Measurement and Prediction of Residual Stress and Distortion Method for Measuring Internal Stress in Brass Tubes, J. Inst. Met., Vol 32, 1924, p 367–383 16. G.E. Totten and M.H. Howes, Steel Heat Treatment Handbook, Marcel Dekker Inc., New York, 1997, p 256–261 17. D. Shick et al., Development of a Carburizing and Quenching Simulation Tool: Determination of Heat Transfer Boundary Conditions in Salt, Second International Conf. on Quenching and Control of Distortion Proc., ASM International, 1996 18. D. Brammann et al., Development of a Carburizing and Quenching Simulation Tool: A Material Model for Low Carbon Steels Undergoing Phase Transformations, Second

International Conference on Quenching and Control of Distortion Proceedings, ASM International, 1996 19. C. Anderson et al., Development of a Carburizing and Quenching Simulation Tool: Numerical Simulation of Rings and Gears, Second International Conference on Quenching and Control of Distortion Proceedings, ASM International, 1996 20. B.L. Ferguson, A.M. Freborg, and G.J. Petrus, A Software Tool to Simulate Quenching of Alloy Steels, Heat Treating Progress, to be published 21. M.T. Lusk, Y.K. Lee, H.J. Jou, W.E. Elliott, and G.M. Ludtka, An Internal State Variable Model for the Low Temperature Tempering

of Low Alloy Steels, First International Conference on Thermal Process Modeling and Computer Simulation, Jiatong University, Shanghai, March 2000 22. V.C. Prantil, M.L. Callabresi, G.S. Ramaswamy, and J.F. Lathrop, Simulating Distortion and Residual Stresses in Carburized Thin Strips, ASME J. Eng. Mater. Technol., to be published 23. M. Henriksen, D.B. Larson, and C.J. Van Tyne, On the Analysis of Distortion and Residual Stress in Carburized Steels, ASME J. Eng. Mater. Technol., Vol 114, 1992, p 362–367 24. R.G. Treuting and W.T. Read, J. Appl. Phys., Vol 22, 1951, p 130–134



Measurement of Residual Stresses C. Ruud, Pennsylvania State University

THIS ARTICLE PROVIDES an insight into the principles, practices, and limitations of residual-stress measurement procedures for steel. It is not meant to provide sufficient detail for the performance of the various methods described, but references are cited where such procedural details may be found (e.g., Ref 1–5 or for general inquiries, www.residualstress.com on the Internet). There have been many methods and techniques proposed for the measurement of residual stress, but only a few may be applied in practice on components ranging from small to very large, such as bridges and aircraft. These few include x-ray diffraction (XRD) and blind hole drilling with electrical resistance strain gages. For some of the methods described, the component in which residual stresses are to be measured must be brought to the measuring instrument, but for others the measurement devices are portable and may be brought to the component (Fig. 1). However, in some cases it may be feasible to remove a section from the component and bring that section to the residual-stress measuring device. Great caution must be observed in this sectioning because it will change the stress field by relieving and/or inducing stresses.

have resulted in disagreement between residualstress measurements made by the mechanical stress relaxation type methods discussed in the section “Introduction to Destructive Procedures” and the XRD methods discussed in the section “Nondestructive Techniques” in this article. The disagreement is nearly always because the volume of the component in which the stress is measured is not the same in the two methods, and thus a different portion of the stress gradient is measured by each. Ruud et al. (Ref 6) showed that the hole-drilling method resulted in measured stresses approaching that of the stresses measured at the surface by XRD when the holedrilling results were extrapolated to the surface. Furthermore, because of the steep gradients, unless the stress field caused by the process is well understood, stress measurements must be performed at many locations in the manufactured solid in order to establish the magnitude and distribution of the stress field of interest. Many researchers in residual-stress techniques have fo-

Any manufacturing process that changes the shape of a solid, or where severe temperature gradients exist during the process, causes residual stress. By their very nature, processes that change the shape of a solid cause nonuniform plastic deformation in the solid, which leads to residual stress. These processes include forging, rolling, drawing, machining, and so forth. Also, processes that produce high thermal gradients in a solid often lead to residual stress. These processes include quenching, casting, welding, and so forth. Furthermore, processes that induce localized phase changes produce residual stress. These processes include martensitic hardening. The residual stresses caused by manufacturing processes usually show very steep residual stress to distance gradients as shown in Fig. 2. Many of the other articles in this Handbook discuss and describe in detail the causes and mechanisms of residual-stresses development in manufacturing processes. The steep gradients typical of residual stresses induced by manufacturing processes

) dxdσ > 200mmMPa ) σy 650

y

σy

MPa

Welding dσ y ~ 200 dx

0

x

3 mm

σy

x

650

y

MPa

Machining dσ y ~ 3000 dx

y 0

0.1 mm

x

x

σy 650

Measurement of residual stresses on oil-drilling platform component weldments using a portable x-ray diffraction instrument

y

MPa

Drawing dσ y ~ 600 dx

Drawn cup 0

Fig. 1

Fig. 2

3 mm

x x

Residual-stress magnitudes and distributions typical of a 650 MPa yield strength steel

100 / Measurement and Prediction of Residual Stress and Distortion cused on enhancing the accuracy of residual-stress measurement and have ignored the fact that from a practical standpoint, tens to hundreds of stress measurements are needed to define the stress field of interest. Thus, many of the residual-stress measurement techniques require too much time to perform and are thus impractical. This includes some of the techniques developed for XRD, strain gaging, and other methods. Measurement times on the order of a second are available with XRD and some other methods, and automated stress mapping has been performed with such techniques (Ref 7). Another concern in the measurement of residual stresses in manufactured components is that the area or volume over which the stresses are resolved must often be on the order of 1 mm (0.04 in.) or less. This is because the residual-stress gradients are usually quite steep, and measurement resolution larger than this tends to average the stresses to such an extent that high stresses are not detected. Some characteristics of steel that can cause error in residual-stress measurement by the various methods described in this article include phase composition, plastic strain, grain size, crystallographic texture, and others. For example, in a mixed ferrite/austenitic structure the residual stresses in the ferrite are invariably different than those in the austenite (see Table 1). Also, Wimpory et al. (Ref 8) described the influence of varying amounts of cementite in a ferrite matrix. The possibility of one or more of these microstructural characteristics causing error in the residual-stress measurements performed by the methods described in this article should be assessed by an expert in the method selected, and details of the errors and their causes are not discussed in detail in this article. The subsequent sections of this article discuss and describe: ● The need for measurement—what problem is

the engineer or metallurgist trying to solve by obtaining information about the residualstress field? ● The nature of the residual-stress fields in steels—examples of the magnitudes and distributions. ● The strain basics for residual-stress measurements—elastic strain measured, not stresses. Table 1 Sample of residual-stress readings from a 316 stainless steel pipe weldment Distance from the weld fusion line

Stress (a) in austenite

Stress (a) in ferrite

in.

mm

ksi

MPa

ksi

MPa

0.04 0.07 0.11 0.15

1 1.8 2.8 3.8

ⳮ21 ⳮ19 ⳮ16 ⳮ17

ⳮ145 ⳮ131 ⳮ110 ⳮ17

ⳮ46 ⳮ67 ⳮ62 ⳮ65

ⳮ317 ⳮ462 ⳮ427 ⳮ448

Note: The ferrite places tensile stresses on the lattice of the austenite, while the austenite tends to compress the ferrite; therefore, the more compressive the stress in the ferrite, the less compressive the stress in the austenite. (a) The precision of these measurements was Ⳳ3.0 ksi (Ⳳ21 MPa).

● The destructive procedures of residual-stress

measurement—these procedures are all based on sectioning or removal of material to cause a redistribution of the residual stress, which is measured as a strain change. ● The semidestructive methods of residualstress measurement—these methods are based on the same principle as the destructive methods or on the perturbation of the residual-stress field by other means. ● The nondestructive methods of residual-stress measurement—these methods do not permanently disturb the residual-stress field, but directly measure the atomic lattice strain caused by the stress or measure some physical property perturbed by the lattice strain.

Need for Residual-Stress Measurements Before the engineer or metallurgist commits to measuring residual stresses in some component or workpiece, he or she must be sure that the reason for the measurement is clearly understood. The major reasons that residual stresses are of concern are: ● Failures that are suspected as being caused by

fatigue, stress corrosion, corrosion fatigue, or hydrogen embrittlement ● Assessment for the continued serviceability of a component, for example, life assessment; this is usually focused on a concern for inservice failure ● Distortion occurring during processing of a component ● Distortion of components during storage or in service It is extremely important that the investigator understand the mechanism for the inducement of the residual-stress field of concern. As implied by the other articles in this Handbook, most cases of suspected harmful residual-stress fields are induced by manufacturing processing or repair procedures, although sometimes abusive service conditions or an accident may have caused them (Ref 9). When manufacturing processes or sometimes repair procedures are judged the most likely source of the residual stresses, it is often possible to predict the magnitude and distribution of the residual stresses. Such information can be obtained through consulting the literature or the application of computer modeling (Ref 10–18 or the Internet at www.residualstress.com). A preconceived model of the residual-stress field will aid the investigation in determining the best method to measure residual stress and the location and number of measurements that need to be made. Nevertheless, sometimes the cause of the residual-stress field is not evident, and the investigator is compelled to perform measurements as a means to determine the cause. In such cases, measurement methods and location must be selected without the aid of a priori knowledge of the stress field, and it is prudent to consult the

literature and experts in the field of residualstress measurement and manufacturing processes.

Nature of Residual Stresses Residual stresses are the inevitable consequence of thermomechanical processing of steel. The resulting stress fields usually are nonuniform and show high stress gradients. For example, Fig. 2 illustrates the residual-stress magnitudes and distributions typical of a steel with a 650 MPa yield strength. Because of the high stress gradients, tens to hundreds of residualstress measurements with resolution on the order of 1 mm may be required to identify precisely the maximum stress and its location. The characteristically nonuniform, high stress gradient nature of residual stresses require that either the induced stress field is well understood and predictable, or many residual-stress measurements must be performed on one or more components in order to reveal the nature of the stress fields. Often, scientists attempt to gain an understanding of a residual-stress field by making a few measurements on one or two components, and from this often arise erroneous conclusions regarding the nature of the stress field. A few measurements may be useful if the scientist or engineer knows the distribution of the stresses a priori. However, this is seldom the case, and tens to hundreds of measurements are required on a single component or many samples to really understand the residual stresses induced by a given manufacturing process. This means that the measurement method must be as rapid and labor-efficient as possible. Some of the new semidestructive hole-drilling procedures and XRD and ultrasonic (for special cases) instrumentation meet this criteria. Stress mapping is offered with some XRD instruments to map stresses over the surface of a component (Ref 19). Also, because the stress gradients are often very high, the measurement method must be able to resolve the stresses in dimensions on the order of 1 mm or less. Here, some of the hole-drilling procedures and recently developed XRD instruments can offer the best resolution. Finally, the component in which residual stresses are to be determined is often too large to be brought to a laboratory, and removing sections is not a rational solution. Note that sectioning often disturbs the existing stress field to the extent that it is not possible to reconstruct the original stress field from the residual stress measured in pieces removed from the original whole. Hole-drilling, XRD, and ultrasonic instrumentation are available as portable devices that may be brought to the component in the field (Ref 7, 9, 20, 21).

Stress Measurement A number of procedures and methods have been applied to determine the residual stresses

Measurement of Residual Stresses / 101 extant in a metallic component, usually as a result of manufacturing processing. However, stress is never the quantity measured because stress is a quantity that is applied to a metal and can only be measured in the process of its application. What is invariably measured to determine residual stress is elastic strain—either the elastic strain resulting directly from the existing residual stress in the metal or the elastic strain change resulting from relief of some portion, or all, of the existing residual stress. The stress that is causing, or has caused, the strain is then calculated using the applicable elastic constants for the metal. The methods described in the section “Nondestructive Procedures” in this article measure, directly or indirectly, the strain response of the metal to the residual stress in situ, while the methods described in the sections “Destructive Measurement Procedures” and “Semidestructive Procedures” measure the strain change caused in relieving some or all of the residual stress in the metal.

Destructive Measurement Procedures The first concern in selecting a destructive residual-stress measurement procedure is whether it is reasonable to destroy one or more components or samples in order to determine the residual stresses. Usually this implies that one or a few of the components are a small portion of the total number produced. Also coupled to this decision is whether the one or more components in which the residual stresses are to be measured are representative of all the others. In other words, how great is the expected variation of the residual-stress field from part to part? As mentioned at the beginning of this article, the need for the residual-stress information about a component must be clearly understood. This includes whether the triaxial stress field must be established or if the uniaxial or biaxial condition of the stress field along specific directions is sufficient. Examples of these three situations are discussed in this section. However, in any case, the fact that residual stresses are usually not uniform in any direction and show high stress gradients must be kept in mind when stress-measurement criteria are selected. Destructive methods of residual-stress measurement are fundamentally stress-relaxation procedures; that is, the information is obtained by relaxing the residual stress in some finite-volume element of the component and measuring the resulting strain change. The strain change is then used, along with applicable assumptions about the nature of the stress field, to reconstruct the original stress field. Assumptions about the nature of the stress field include the magnitudes and gradients in the stress field and whether it is sufficient to assume that the gradients are one-, two-, or three-dimensional. In particular, the gradients that exist will dictate the size of the element that is to be isolated and made stress-free;

that is, the higher the stress gradient is, the smaller the finite element must be in the direction of that gradient. It must be emphasized that the larger the element and the higher the stress gradient, the less quantitative and more qualitative are the measurement results. Electrical-resistance strain-gage technologies are emphasized as the dominant method of strain measurement due to their economic, procedural, and precision advantages over other methods. However, modern XRD equipment when available has all of these advantages as well and can be used to measure the stresses existing before and after sectioning. A generic destructive stress-relief procedure is described first, along with the issues generally involved in each procedural step. This section on destructive methods concludes with some discussion of qualitative chemical methods of residual-stress measurement.

Generic Destructive Procedure Once the decision is made to measure the residual stresses destructively, the following steps are usually applied in a typical stress-relief technique for residual-stress measurement. Stress-Field Conditions. The engineering problem for which the residual-stress information is needed must be analyzed. This need is often generated by failures of the component in service or by anticipated failures due to problems with similar components. Distortion of a product in storage or during manufacturing can also be a concern. The shape of the component—that is, cylinder, disk, plate, and so forth, or some irregular shape—must be considered. This consideration, along with the process or processes by which residual stresses were introduced, must be analyzed. The justification for assumptions regarding the condition of the residual-stress field can be established from these considerations. This may lead to simplifying assumptions about the stress-field condition such as axial symmetry for a cylinder in which the dominant residualstress field is caused by quenching during heat treat processing or about stress uniformity in the surface plane of a plate where stress gradient with depth is the major concern. These assumptions and considerations lead to the methodology, that is, equations, to be used for computational reconstruction of the stress fields from the measured strains. Strain-Measurement Technique. With the stress-reconstruction approach established, the method of strain measurement and consequently the number and/or spatial frequency of measurements can be determined. The strain-measurement technique selected will greatly affect the resolution of the stress measurement because of the spatial precision inherent in the technique. There are a number of techniques that have been used to measure the strain induced by the relief of stresses due to sectioning or material removal in destructive residual-stress measurement. These include mechanical gages, often dial gages, employed with specially made jigs and

fixtures, reflected light schemes, photoelastic coatings, and electrical-resistance strain gages. However, since the 1960s, the use of the latter has become dominant due to the variety, availability, and precision of these gages. They are available as uniaxial, biaxial, and rosette gages of many sizes. The section “Strain-Measurement Methods” in this article provides some detail regarding these methods. Also, since the late 1970s, extensive use of XRD has been applied to provide rapid and numerous stress measurements on sectioned components to gain information regarding the internal stress field (Ref 2, 22–25). Preparation for Strain Measurement. With the strain-measurement technique selected, the measurement location must be established and the component and/or element prepared for the measurement by, for example, attaching strain gages. A prestress-relief reading must now be made before stress relaxation and isolation of the element is initiated. Isolation of Gaged Element. With the measurement technique in place, material removal to isolate the gaged volume must be performed. The technique for material removal, or sectioning, must be carefully considered because mechanical chip-removal processes such as lathe turning, milling, sawing, grinding, and so forth introduce surface residual stresses that can be as great as the yield strength of the strain-hardened material and several thousandths of an inch (tens of micrometers) in depth. The section “Sectioning and Material-Removal Methods” in this article discusses methods to isolate the gaged element. Post-Stress Relaxation Measurement. After the residual stresses have been relaxed and thus the elements isolated, strain measurements are repeated, the final reading is subtracted from the initial to obtain the strain change resultant from the residual-stress relaxation. The resultant quantities are then used in the residual-stress reconstruction equations to obtain the original stress state of the component. The stress-reconstruction equations were selected as a result of the assumptions made about the stress-field conditions described previously and in more detail in the following sections.

Stress-Field Condition Assumptions Engineers and research scientists have approached the measurement of residual stresses using destructive methods with the aid of assumptions about the stress-field conditions, including that the stresses in only one axis are of interest in order to simplify the measurement and reconstruction of the stress field (Table 2). These have included certain uniaxial, biaxial, and triaxial stress-field assumptions. Uniaxial Conditions. A procedure applicable only to the measurement of residual stresses in rods, cylinders, and tubes—that is, components with axial symmetry—was reported by Heyn (Ref 26). In this work, it was assumed that the stresses were axially symmetric and that only the

102 / Measurement and Prediction of Residual Stress and Distortion longitudinal stresses were of interest. Thus, the change in length of the components (cylinders, rods, and tubes) was measured after removal of an axially symmetric layer from the outside radius, or it was bored out of an inside radius. The length of the component was measured after each layer-removal process and entered into various equations described in their paper. This procedure is called the Bauer-Heyn method (Ref 26) and is applicable only to measuring longitudinal stresses in axially symmetric components. It does not measure radial or circumferential stresses. A second procedure assuming a uniaxial stress field, or that only the stresses in one axis are of interest, was proposed by Stablein (Ref 27). Here the component was a bar with a rectangular cross section, and the residual stresses acting along its length and varying through its thickness (smallest dimension) were measured. The material from one face of the bar, one of the two faces with the largest area, was removed by milling. Equations used to reconstruct the original stress field are described in Ref 27. The depth of the removed layer must be significantly greater than the depth of plastic deformation caused by milling (see the section “Sectioning and MaterialRemoval Methods”) and sufficient to cause a measurable bend in the material. The length of the opposite face of the bar from where the material was removed is measured before and after layer removal to determine the effect of the removal of the stressed layer. Presently, this is usually done using electrical-resistance strain gages (see “Strain-Measurement Methods”), but was performed in the past by sensitive mechanicalgaging techniques. This measurement can also be accomplished by measuring the bend in the bar with suitable mechanical gages and fixtures, for example, a cantilever-beam approach. This procedure is applicable only to components of rectangular cross section where the stresses parallel to the length are to be measured as they vary through the thickness. Biaxial Conditions. A procedure applicable to axially symmetric components is the Mesnager-Sachs boring-out technique (Ref 28, 29). The

Table 2

technique is applicable to cylindrical components with an axially symmetric distribution of stresses. Here the change in length and diameter of the component are measured as material is removed by axially boring-out material from the inside to produce a hollow cylinder. Presently, biaxial electrical-resistance strain gages (see the section “Strain-Measurement Methods”) are usually attached to the outside of the component to measure the dimensional changes in the axial and tangential directions. The strain change results are entered into equations described in Ref 28 and 29. A procedure applicable to measuring biaxial residual stresses homogeneous over the planar surface of a flat metal plate or sheet was proposed by Trenting and Read (Ref 30). It was based on removing uniformly thin layers of the metal on one side of the sheet or plate and measuring the changes in curvature as the layers were removed. It was assumed that the stresses were constant over the plane of the sheet or plate and varied only through the thickness. Electricalresistance strain gages (see “Strain-Measurement Methods”) or mechanical gaging may be used to measure the change in curvature. Another procedure for measuring biaxial stresses homogeneous over the planar surface of a metal plate was developed by Gunnert (Ref 31). This procedure assumes that a biaxial stress condition was uniform throughout the depth of a circular groove that was milled around an elemental volume of material to render it stress free. Thus, the strain change on only one surface was measured. The mechanical-gaging technique involved measuring the distance between each of four sets of shallow holes drilled in the element before the groove was milled into the surface using a core drill. The distance between each set of holes was measured before and after the groove was produced and provided the information necessary to calculate original, assumed biaxial residual-stress condition parallel to the surface of the plate. Theoretically, only three sets of holes are required to measure the biaxial stresses, but Gunnert used a fourth set to improve the accuracy. A mechanical gage,

termed an extensometer, was used to measure the distance between each set of holes. It should be noted that this technique could be used to measure the gradient in the biaxial stress condition by pausing in the milling operation at selected depths and measuring the distance between the holes at each groove depth. Also, as with many of the older techniques that originally applied mechanical strain-gage apparatus, electrical-resistance strain gages or modern XRD techniques could be used. A procedure involving the drilling of a blind hole and electrical-resistance strain gage is somewhat similar to Gunnert’s original technique and is described in the section on semidestructive methods. A more accurate procedure was later used to measure residual stresses in pipe weldments. Here the component (pipe) was divided into a network (grid) of squares, and biaxial electrical strain gages were placed in the center of each grid square on the outside diameter of the pipe. The pipe was then sectioned as shown in Fig. 3 into elements assumed to be stress free, and the strain induced by the stress relief was read from the gages. In placing the gages only on the outside diameter, the biaxial stress field was assumed to be uniform with depth; however, had gages been placed on the inside and outside diameter a more complete measurement of the stress field could have been obtained, albeit assuming a linear variation in the residual stress from the outside to the inside surface. A variation on the Gunnert procedure described previously was later published (Ref 1, 32). This variation was also used for application to plates and implied that the triaxial stress field could be measured by the technique. It assumed that there was a homogeneous residual biaxial stress field that varied with depth through the plate thickness. Four holes were drilled in a square pattern through the plate thickness. The distances between all of the holes was then measured at selected hole depths. Next, a circular groove was milled in steps of, for example, 2 mm around the drilled holes using a core drill as in Gunnert’s original procedure (Ref 31). The distance between the holes at the various depths

Summary of destructive residual-stress measurement procedures

Component shape

Rods, cylinders, tubes Rectangular cross-section bar Plate, sheet

Cylinder, plate Plate, weldment

Stress-field-condition assumptions

Stress direction measured

Method

Uniaxial stresses, axial symmetry Biaxial stresses, axial symmetry Uniaxial stresses varying through thickness Homogeneous planar, biaxial stresses varying through thickness Homogeneous planar, biaxial stresses uniform through thickness Homogeneous planar, biaxial stresses varying through thickness Planar biaxial stresses varying through thickness Planar biaxial stresses varying through thickness Triaxial

Longitudinal Longitudinal, radial Longitudinal Biaxial in the plane of the component Biaxial in the plane of the component Biaxial in the plane of the component Biaxial in the plane of the component Biaxial in the plane of the component All

Bauer-Heyn Mesnager-Sachs Stablein Treuting and Read

Various Triaxial

All All

Moore and Evans Johanssen

Gunnert Gunnert Rosenthal and Norton Moore and Evans Chen

Section and reference

“Triaxial Conditions” (Ref 26) “Biaxial Conditions” (Ref 28, 29) “Triaxial Conditions” (Ref 27) “Strain-Measurement Techniques” (Ref 30) “Strain-Measurement Techniques” (Ref 31) “Strain-Measurement Techniques” (Ref 1, 32) “Strain-Measurement Techniques” (Ref 33) “Strain-Measurement Techniques” (Ref 2) “Preparation for Strain Measurements” (Ref 34) “Strain-Measurement Techniques” (Ref 2) “Strain-Measurement Techniques” (Ref 25)

Measurement of Residual Stresses / 103 was then measured at each core depth until the core was milled completely through the plate. The cored plug was then assumed to be completely free of residual stress. The measured distances were then used to reconstruct the original biaxial stress condition of the plug at each cored depth. The mechanical measuring gage used in this technique was similar to that used in Gunnert’s first technique (Ref 31). Another approach to measuring residual stresses that has a broader application with respect to the shape of the component and the stress-field distribution was proposed by Rosenthal and Norton (Ref 33). It is applicable to plates and plate-shaped weldments. The procedure involved cutting two narrow blocks having the full thickness of the plate, each with its long axis parallel to one of the assumed biaxial principal, residual-stress directions in the surface of the plate (see the near side of Fig. 4). Thus, the long axes of the blocks are perpendicular to each other and parallel to the face, the largest area surface of the plate. The smallest dimension of the block should be several times smaller than the plate thickness and its largest dimension at least twice the thickness. The block then can be further sectioned in order to determine the biaxial stress variation through the thickness of the component. This proceeds by first cutting the block at the location representing the midthickness of the component plate, then

removing thin slices parallel to the original surface and from the bisected block as shown in the upper part of Fig. 4. The change in strain of the blocks is measured using shallow holes or dimples in the original surfaces of the component. These gage points are located along the long axis of the block on the original faces of the plate (see Fig. 4). The distance between these gage marks is measured before and after removal of the blocks from the plate and after each sectioning of the block (Ref 33). This procedure assumes a constant biaxial stress field over the length of the blocks, which is not the case in welded plates in the direction transverse to the weld. The far side of the block in Fig. 4 shows a sectioning procedure that would reveal the stresses parallel to the weld along a gradient transverse to the weld. The far side of the block in Fig. 4 shows a sectioning procedure that would reveal the stresses parallel to the weld along a gradient transverse to the weld. Also, electrical-resistance strain gages could be used instead of measuring the distance between shallow holes or dimples. Another approach to a constant biaxial stress field in a flat plate, varying only through thickness, was described by Moore and Evans (Ref 2). They relied on XRD for the measurement of the strains from which the stress was calculated, and the procedure consisted of removing layers

0° 40

10 20 20 20

50

from the surface of the plate and measuring the strains existing at each layer. The process assumed that the stress perpendicular to the surface was zero. It should be noted that in order for this procedure to be valid, the areas measured by XRD would have to be free of plastic deformation caused by layer removal (see “Sectioning and Material-Removal Methods”). Triaxial Conditions. In reality, in most components in which residual stresses have been induced, usually due to manufacturing processes, the stress field is triaxial and varies from point to point (element to element) in all three directions. Thus, a number of destructive procedures and stress-field condition assumptions have been applied in order to measure the three-dimensional residual-stress-field condition existing in most components of practical engineering interest. Two of these are described in this section. Chen (Ref 34) revised Rosenthal and Norton’s approach to deriving the triaxial residual-stress condition (Ref 33) as follows. The typical method of residual-stress measurement is by mechanically removing part of a body and measuring the change of stress in the rest of the body. The method of Rosenthal and Norton instead deals only with a small element that has been cut free from a plate. The sectioning procedure consists of removal of a narrow block from a plate with gages attached, followed by splitting the block in half with gages attached on the top and bottom surface of the block, and then successive slicing of both halves from the midsection to the outer surface, as shown in Fig. 4. When the half-block is sliced to a thickness of 0.1 in., gages are removed and stresses are measured (at least two points) on the surface by XRD. The basic assumptions are: ● Partial stress relief occurs in the direction of

90° Initial sectioning 270°

Weld

the long axis of the block and a total stress relief occurs in the direction transverse to the long axis. ● The small amount of stress relaxed in the remainder of the block follows a linear law through the thickness when a thin slice of metal is removed. ● Variation of transverse stress along the axis of the weld is small in the middle portion of the plate weldment.

45° 10

Saw cut 180° Fine cutter (i.e., green abrasive saw 0.5 mm thick)

10

5

Further sectioning

5 10

Final sectioning

Gage

Weld 10

10 10

Rosette gage

Residual-stress measurement of a girth-welded pipe by strain gaging and sectioning. Note that strain gages shown in the final sectioning should be placed on the pipe prior to initial sectioning; and for a more complete analysis several of the layer sections detailed in the final sectioning step should be strain gaged and sectioned. Dimensions given in mm

Fig. 3

Welded steel plate, the near side of which shows the two narrow blocks suggested in Rosenthal and Norton’s procedure (Ref 33). The far side shows several blocks sectioned to reveal the stresses parallel to the weld with a gradient transverse to the weld.

Fig. 4

104 / Measurement and Prediction of Residual Stress and Distortion The determination of residual stresses may be divided into the following steps: 1. Determination of e⬘1 and e⬘, t which represent the amount of strain relaxed in longitudinal and transverse directions by cutting one longitudinal and one transverse block free from the plate. This was done by determining the strain relief between two indentations on the top and bottom surface of each block using a mechanical gage (see Fig. 4) and subtracting the strain-gage readings on the blocks from the initial reading from the plate. Note that this measurement can be performed using electrical-resistance strain gages or XRD (Ref 7, 22, 23). 2. Determination of strain relaxed on the top and bottom surfaces by splitting each block in half and then successively slicing the blocks. 3. Determination of the strain relieved (using at least two points) on the top and bottom surface using sensitive mechanical gages to measure the distance between indentations and using XRD after the thickness of the top and bottom halves of the blocks had been reduced to 0.1 in. Note that this restriction was necessary because they are using conventional scanning x-ray instrumentation. With modern x-ray instruments, measurements can be made on any size of specimen (Ref 7, 19, 20, 22–24). 4. An enhancement of the Rosenthal and Norton procedure (Ref 33) was suggested by Chen (Ref 34) where the determination of the residual stress remaining in the top and bottom slices was measured using XRD. Here the lattice strain was measured in the remaining slices in at least two places near the gage points using XRD, and the absolute residual stress, S*t and S*1 remaining was calculated as described in the section “Stress Measurement” in this article. These XRD-determined stresses measured for each block were averaged and designated S* t or S* 1 for that face. The original stress S⬙ present before slicing was determined by: S⬙t ⳱ S*t Ⳮ Ee⬙t

(Eq 1)

S⬙1 ⳱ S* Ⳮ Ee⬙1

The total strain e⬙ may be obtained by dividing S⬙t or S⬙1 by the modulus of elasticity, E. 5. Computation of stress relieved by cutting the blocks from the plate was accomplished using the values of e⬘ and e⬙ obtained in steps 1 and 3, the amount of longitudinal and transverse stress (S⬘t and S⬘) 1 relaxed by cutting the blocks from the plate: S⬘1 ⳱

E mE (e⬘1 Ⳮ me⬘) (e⬙t Ⳮ me⬙) t Ⳮ 1 1 ⳮ m2 1 ⳮ m2

S⬘t ⳱

E mE (e⬘t Ⳮ me⬘) (e⬙1 Ⳮ me⬙) 1 Ⳮ t 1 ⳮ m2 1 ⳮ m2 (Eq 2)

where m is Poisson’s ratio. Equation 2 is valid for the case where the length of the block is at least twice the thickness of the block. In case of shorter blocks:

S⬘1 ⳱

E E (e⬘1 Ⳮ me⬘) t Ⳮ 1 ⳮ m2 1 ⳮ m2

冢me⬙ Ⳮ t

m 2 ⳮ b2 e⬙1 1 ⳮ b

冣

E E S⬘t ⳱ (e⬘t Ⳮ me⬘) 1 Ⳮ 1 ⳮ m2 1 ⳮ m2

冢

me⬙1 Ⳮ

m 2 ⳮ b2 e⬙t 1 ⳮ b

冣

(Eq 3)

where b is the correction factor for a shorter block. When plotted for the top and bottom faces of the block and joined by a straight line, these values give the stress S⬘ relaxed by cutting the block from the plate. 6. Computation of stress (S⬙) relieved by splitting and slicing the blocks was done using:

冦2 d␣ (1 ⳮ ␣) ⳮ 2(e⬙ ⳮ e⬙ )

(S⬙) a t⳱E

1 de⬙t

0

t

e⬙t ⳮ e⬙t 2 dl 0.5 (1 ⳮ l) 0

a

Ⳮ 3(1 ⳮ ␣)

t

冮

冧

Ⳮ (5␣ ⳮ 4)e⬙t Ⳮ (1 ⳮ ␣)e⬙b0 0

(Eq 4)

冦

e⬙b ⳮ e⬙b0 2 dl 0.5 (1 ⳮ l) a

冮

冧

Ⳮ (5␣ ⳮ 4)e⬙b0 Ⳮ (1 ⳮ ␣)e⬙t 0

(Eq 5)

where l is the thickness of the block; ␣ is the fraction of the total thickness removed; e⬙, t e⬙ b are the relaxed strain measured on top and bottom surface for position ␣; and e⬙t 0, e⬙b0 are the relaxed strain on top and bottom surface when splitting the block in half. 7. The total stresses relaxed across the thickness of the block in the longitudinal and transverse directions were obtained by: S1 ⳱ S⬘1 Ⳮ S⬙1

(Eq 6)

St ⳱ S⬘t Ⳮ S⬙t

8. Determination of shearing stresses in the longitudinal and transverse directions were determined by: sxy ⳱ syx ⳱

Sw ⳮ S v 2

(Eq 8)

Sy sxy syz Ⳮ Ⳮ ⳭY⳱ 0 y x z

(Eq 9)

Sz sxz syz Ⳮ Ⳮ ⳭZ⳱ 0 z x y

(Eq 10)

Differentiation of Eq 8, 9, and 10 with respect to x, y, z, respectively, yields: 2Sx 2sxy 2sxz Ⳮ Ⳮ ⳱0 x2 xy xz

(Eq 11)

2Sy 2sxy 2syz Ⳮ Ⳮ ⳱0 y2 xy yz

(Eq 12)

2Sz 2sxz 2syz Ⳮ Ⳮ ⳱ 0 z2 xz yz

(Eq 13)

Subtracting the summation of Eq 11 and 12 from Eq 13, results in: 2Sz 2Sx 2Sy 2sxy 2 ⳱ 2 Ⳮ 2 Ⳮ 2 z x y xy

1 de⬙b (S⬙) (1 ⳮ ␣) ⳮ 2(e⬙b ⳮ e⬙b0) a b⳱E 2 d␣ Ⳮ 3(1 ⳮ ␣)

Sx sxy sxz Ⳮ Ⳮ ⳭX⳱ 0 x y z

(Eq 7)

where s is the shear stress and Sw and Sv are the stresses measured in the direction w and v making angles Ⳮ45 and ⳮ45, with the longitudinal axis. However, if the biaxial stress condition is assumed, only the strain relief in one 45 direction need be determined since they would be equal. This requires that either a block at a 45 angle to the longitudinal block be removed, or that electric residual-strain-gage rosettes be used, or XRD measuring at the 45 angle. 9. Determination of stress in the thickness direction was determined by the equilibrium equations:

(Eq 14)

Variation of Sx along the x-axis is small in the middle portion of the plate; therefore, the first term in Eq 14 can be neglected, and Eq 14 can be approximated using: 2Sz 2 2 Ⳮ (Sy1 ⳮ Sy0) Ⳮ sx2y2 z2 Dy21 Dx2Dy2

(Eq 15)

where Sy0 is the value of Sy at the axis, Sy1 is the value of Sy1 at a distance Dy1 on either side of the x axis, and sx2y2 is the value of sxy at a distance Dx2 and Dy2 from the y axis and x axis, respectively. Therefore, the stress in the thickness direction Sz can be obtained through double integration with the boundary condition that Sz vanishes at both the top and bottom surfaces. In this way, the entire triaxial residual-stress state was determined. Note that this procedure assumes that the residual stresses are uniform along the length of each block. A variation on Rosenthal and Norton’s method (Ref 33) using electrical-resistance strain gages or a nondestructive technique such as XRD is as follows. The largest face of the blocks described by the thickness of the component (plate) and the longest dimension of the blocks is divided into a two-dimensional grid of elements. An electrical-resistant strain gage is placed on each element, or a nondestructive measurement such as XRD is performed, and the block is sectioned along the grid lines to produce elements that are assumed to be stress free. Note that if a nondestructive technique such as XRD is used, the plastically deformed surface created by removing the block from the original component must be removed. This is best done using electropolishing (see the section “Sectioning and

Measurement of Residual Stresses / 105 Material-Removal Methods”). If electropolishing of these cut faces is done to remove the plastic deformation and resultant residual stress induced by a mechanical cutting procedure, and XRD is applied, then the blocks need not be sectioned. The measured XRD stress will provide the absolute residual-stress-field condition in the block, and—coupled with the strain relieved by the original removal of the block from the plate—the entire triaxial residual-stress condition of the plate can be obtained. This variation of Rosenthal and Norton’s method (Ref 33) provides the information necessary to derive the biaxial stress condition of each block, which can in turn be used to derive the triaxial condition of the original plate. The stresses on each of the measured faces of the blocks must be measured in three directions to provide the information necessary to obtain the principal stresses in the block faces in each element. Note that the strain change caused by the sectioning of the blocks must be added to the strains measured in each element. This procedure can be applied to a weldment with a single weld through its center as described by Rosenthal and Norton (Ref 33), or to a more elaborate stress field, for example, where two orthogonal welds existed in the component (plate). With a single weld, only the block intersecting weld needs to be sectioned into elements because the residual-stress field in the block parallel to the weld is likely to be constant along the direction parallel to the weld. Moore and Evans (Ref 2) proposed mathematical procedures for the reconstruction of the original three-dimensional residual-stress fields in cylindrical and flat plate components, and Constantinescu and Ballard (Ref 3) proposed a modification of Moore and Evan’s work. They proposed using XRD as the measurement technique and presented stress-reconstruction equations for the following conditions: ● Solid cylinder bar, rotationally symmetric

are then used to calculate the original stresses rh(r) and rz(r), as well as the radial stress rr(r). The theory of elasticity provides nine partial differential equations: the three equations of equilibrium and the six equations of compatibility. Unique solutions are possible, depending on boundary conditions, and for the case considered they give the following working formulas: rr(r1) ⳱

R

冮

r1

rhm(r) dr r

rz(r1) ⳱ rzm (r1) ⳮ 2

metric stresses ● Hollow cylinder bar, rotationally symmetric stresses ● Flat plate, biaxial stresses The Moore and Evans procedures were summarized in the Society of Automotive Engineers Handbook (Ref 4) as described in the following paragraphs. Solid Cylinder Bar, Rotationally Symmetric Stresses. It is presumed that the residual-stress distribution has both rotational and longitudinal symmetry, except near the ends where measurements are avoided. Stresses are therefore functions of the radius, r, and do not depend on the angle, h, measured around the cylinder, nor on the distance z taken parallel to the axis. By repeatedly removing thin concentric shells, the stresses on the exposed surface in depth can be obtained. The circumferential and longitudinal measured stresses rhm(r) and rzm(r), respectively,

R

rzm(r) dr r

冮

r1

rh(r1) ⳱ rhm(r1) Ⳮ rr(r1)

rr(r1, h) ⳱ ⳮ

(Eq 17)

r1

冤

冥

g0(r) 2r1 Ⳮ 2 g1(r)cos h dr r r

rh(r1, h) ⳱ rhm(r1, h) ⳱ ⳮ

R

冧

g0(r) 2r1 Ⳮ 2 Re[g1(r)eih] dr r r

rh(r1, h) ⳱ rhm(r1, h) ⳱ ⳮ

冦

(Eq 19)

R

冮

r1

冧

g0(r) 6r1 Ⳮ 2 ⳯ Re[g1(r)eih] dr r r

(Eq 20)

R

冮

冥

(Eq 25)

2h0(r) 8r1h1 Ⳮ 2 ⳯ cos h dr r r

冥

(Eq 26)

2r1 g1(r) sin hdr r2

(Eq 27)

冧

srh(r1, h) ⳱ ⳮ

冮

r1

2r1 Im [g1(r)eih]dr r2

(Eq 21)

(Eq 22)

where Re and Im indicate real and imaginary, respectively, of whatever follows. The measured stresses rhm (r1, h) and rhz (r1, h) are related to the g and h functions by a Fourier series relation:

rhm (r1, h) ⳱

兺 gn(r)enih ⳮ

rzm (r1, h) ⳱

兺 hn(r)enih ⳮ

R

冮

r1

冤

srh (r1, h) ⳱ ⳮ

R

冮

r1

If stresses are measured at four points around the cylinder 90 apart, and, regardless of symmetry, the g and/or h functions from Eq 23 become: h ⳱ 0

rm0 (r) ⳱ g0(r) Ⳮ g1(r) Ⳮ gⳮ1(r)

h ⳱ 90

rm1 (r) ⳱ g0(r) Ⳮ ig(r) Ⳮ igⳮ1(r)

h ⳱ 270 rm3 (r) ⳱ g0(r) ⳮ ig1(r) Ⳮ igⳮ1(r) (Eq 28)

in which the summation was expanded using values of n ⳱ ⳮ1, 0, and Ⳮ1. This is a reasonable approximation, providing the stresses do not “drastically” vary with h. Adding the equations cancels the g1 and gⳮ1 terms, giving: g0(r) ⳱ 1⁄4[rhm (r) Ⳮ rhm (r)

r1

2h0(r) 8r1 Ⳮ 2 ⳯ Re[h1(r)eih] dr r r R

r1

g0(r) 6r1 Ⳮ 2 ⳯ g1(r) cos h dr r r

0

冦

R

冮

h ⳱ 180 rm2 (r) ⳱ g0(r) ⳮ g1(r) ⳮ gⳮ1(r)

r1

冦

(Eq 24)

冤

(Eq 18)

冮

rz(r1, h) ⳱ rzm(r1, h) ⳮ

R

冮

rz(r1, h) ⳱ rzm(r1, h) ⳮ

where r is the original radius and r1 is the radius at depth of interest. Solid Cylinder Bar, without Rotationally Symmetric Stresses. Stresses are again assumed to be independent of z but allowed to vary in the circumferential h direction. Complex variable methods give the following general solutions:

stresses

● Solid cylinder bar, without rotationally sym-

(Eq 16)

rr(r1, h) ⳱ ⳮ

1

Ⳮ rhm (r) Ⳮ rhm (r)] 2

(Eq 29)

3

Subtracting the equations in pairs and then adding the results cancels the g0 and gⳮ1 terms, giving: g1(r) ⳱ 1⁄4{[rhm (r) ⳮ rhm (r)] 0

2

ⳮ i[rhm (r) ⳮ rhm (r)] 1

3

(Eq 30)

Equations 29 and 30 can be used in the general solutions, Eq 19 to 22. However, if the stresses are symmetric with respect to a plane through the axis, then rhm (r) ⳱ rhm (r) and Eq 30 becomes: 1

3

(Eq 23)

If the stresses are symmetric with respect to a plane through the axis of the cylinder, the general solutions simplify because the g1(r) and h1(r) functions will be real. This is a reasonable approximation when the residual stresses are induced by heat treatment or straightening and the equations become:

g1(r) ⳱ 1⁄4[(rhm (r) ⳮ rhm (r))] 0

2

(Eq 31)

Equations 29 and 31 are then used in Eq 24 to 27, along with similar formulas for the h function, determined from Eq 23 in the same way. It is again interesting to note that Eq 16 to 18 are included in the general solution of Eq 19 to 21, when the stresses are rotationally symmetric. The shear stress of Eq 22 or 27 exists only as a result of asymmetry of the h stresses. When sym-

106 / Measurement and Prediction of Residual Stress and Distortion metry is obtained, the g1(r) terms are zero, as is srh(r1, h). Hollow Cylinder Bar, Rotationally Symmetric Stresses. If R1 is the inside radius of the cylinder, similar analysis generalizes the previous equations to the following final formulas:

冢1 ⳮ r 冮冢r R21

R

2 1

r1

冣

r2 rhm(r) dr ⳮ R12 r

2

rz(r1) ⳱ rzm(r1) ⳮ 2

2

(Eq 32)

冮

(Eq 33)

r21 Ⳮ R21 2 2 rr(r1) 1 Ⳮ R1

冢r

冣

(Eq 34)

The above equations include those of the solid cylinder when R1 is zero. Flat Plate, Biaxial Stresses. It is assumed that the residual stresses in a flat plate of uniform thickness depend only on the distance from one of the flat surfaces of the plate, except, of course, near the edges. It is also assumed that the principal stresses are rx and ry, lying in the plane of the flat surfaces, and that the stress normal to the flat surfaces, rz, is zero at all points sufficiently distant from the edges. From the authors’ assumptions and conditions of equilibrium, the true stresses rx(z1) at depth z1 can be expressed in terms of the measured stress rxm (z1) by the relation:

ⳮ 6z1

H

冮

z1

H

冮

z1

rxm(z) dz z

rxm(z) dz z2

(Eq 35)

where H is the original thickness of the plate and z1 is the distance from lower surface to uncovered depth of interest. A similar expression holds for the y direction. Equation 35 holds, even if rx and ry are not prin-

in. σI

σII

σIII σI 4 ft 2 ft

1 in.

A 2 by 2 by 4 ft (0.6 by 0.6 by 1.2 m) weldment showing the layers proposed by Johanssen (Ref 25) where the thickness (T) of the layers are 0.5 in. (12.5 mm) and rI ⳱ ry, rII ⳱ rx, and rIII ⳱ rz.

Fig. 5

z1

z1

sxym(z) z

sxym(z) dz z2

(Eq 36)

sxym (z) is determined from:

sin2 ␣ Ⳮ 2sxym(z1) sin ␣ cos ␣

r1

冣

rx(z1) ⳱ rxm(z1) Ⳮ 2

H

冮

H

冮

ram (z1) ⳱ rxm (z1) cos2␣ Ⳮ rym(z1)

R

r2 rzm(r) dr ⳮ R12 r

rh(r1) ⳱ rhm(r1) Ⳮ

1/ 2

sxy(z1) ⳱ sxym(z1) Ⳮ 2 dz ⳮ 6z1

rr(r1) ⳱ ⳮ

冢r

cipal stresses, but in this case a shear stress also exists, expressed by:

(Eq 37)

where ␣ is the acute angle that the measured stress ram (z1) makes with the x axis. When measurements are taken 45 apart, sxym (z1) becomes:

rx

2␾ y2

ry ⳱

sxym(z1) ⳱ r45(z1) ⳮ 1⁄2[rxm(z1) Ⳮ rym(z1)]

Johanssen showed that the change in stresses resulting from the removal of material can be determined by Dr(x) and m(x). These were to be measured at a number of positions xi, i ⳱ 1,…, N, on the lower side of the plate. Drx(x) and m(x) are the difference between the stress and deformation measured prior to and following the removal of material. Changes in the internal stress conditions are thus calculated directly and need not be calculated as accumulated stress changes resulting from several layers of material being removed. By introducing Airey’s stress function u(x, y) that is defined as:

(Eq 38)

meaning that three x-ray stress measurements are required after each layer removed. Johanssen proposed a procedure (Ref 25) for the determination of the three-dimensional residual-stress field in thick plate (plate weldments) components using XRD techniques to measure the strains on the surfaces of the plate and plate sections, and upon removal of layers of surfaces. The procedure includes the measurement of the biaxial stress field existing on the top surface of the component (see Fig. 5), assuming that the stress perpendicular to the surface is zero. Material is removed from this surface by, for example, milling and electropolishing, or electropolishing alone (see “Sectioning and Material-Removal Methods”) and the biaxial stresses remeasured at the new depth. Each time material is removed, the forces that the removed layer exerted on the remaining component must be accounted for, and the subsequent measurements corrected for this change in the stress field. Johanssen based his method on the following assumptions: ● When a layer of material is removed, the re-

sulting changes in the stress condition will be linear elastic; that is, Hooke’s law is applicable. ● The residual-stress distribution is constant in the z-direction, except at the surface, and rz is a principal stress in the z-direction (see Fig. 5). ● Upon material removal, it is assumed that the strain ez remains unchanged. Together with the previous assumption, this implies that the change in stresses can be treated as a plane problem. ● It is assumed that the stresses are symmetrical with respect to the y-z plane. This assumption is, however, not necessary. The procedure can be developed to include asymmetrical stress states. Johanssen’s justification for his procedure to measure the three-dimensional stress field in the weldment shown in Fig. 5 is as follows (Ref 25).

2␾ 2␾ and sxy ⳱ ⳮ x2 xy

(Eq 39)

Equilibrium and compatibility are automatically satisfied if ␾ is a solution to the biharmonic differential equation: 2 2u ⳱ 0

(Eq 40)

The homogeneous boundary conditions are: ry(x, 0) ⳱ 0

(Eq 41)

y ⳱ 0 sxy(x, 0) ⳱ 0

(Eq 42)

sxy(Ⳮa, y) ⳱ 0

(Eq 43)

x ⳱ Ⳳa rx(Ⳳa, y) ⳱ 0

(Eq 44)

and at y ⳱ 0 there should be agreement with experimental measurements; that is: rx(x, 0) ⳱ Drx(x)

(Eq 45)

Pickel (Ref 35) described a method for analytical solution of problems with this type of boundary condition, using infinite, related series; however, in this instance an approximate method is used with trial solutions that are both more convenient and numerically more stable. r The force T is divided into Tx(x) and Ty(x) (see Fig. 6) and as a solution to Eq 45 to 47, u is taken as u ⳱ ux Ⳮ uy where ux is the solution for the loading case where only Tx(x) differs from zero (and therefore the boundary condition ry(x, b) ⳱ 0 must be applied), and uy is similarly the loading case where only Ty(x) is not equal to zero. This ensures that the trial solutions will be sufficiently general and not involve any limitar tions on T (x). The solutions for ux and uy are then adjusted so that they satisfy Eq 43 and as many of the boundary conditions as possible. By direct substitution, it is easily verified that the trial solutions in the following satisfy all the boundary conditions except rx(Ⳳa, y) ⳱ 0; however, this

Measurement of Residual Stresses / 107 condition can be filled and the measurement can be fit using an approximate method, such as the least-squares method. If this can be performed sufficiently accurately, these trial solutions are close to the exact solution, since it has been shown that the solution is uniquely determined by the stated boundary conditions. For the loading case Tx(x): y3 y2 Cnx Ⳮ C0x Ⳮ 2 6 2 n⳱1 ␣n

兺

(1 ⳮ ␣nb coth ␣nb)␣ny sinh ␣ny]cos ␣n

(Eq 46)

is valid where ␣n ⳱ np/a and 2a and 2b are the width and thickness of the plate after removing material. Equation 39 gives:

exy ⳱

Cnx[(␣nb sinh ␣ny ⳮ ␣ny cosh ␣ny) ⳮ (1 ⳮ ␣nb coth ␣nb)␣ny sinh ␣ny]cos ␣nx sxxy ⳱ ⳮ

2␾x ⳱ⳮ xy

N

兺 Cnx[(␣nb(coth n⳱1

␣bb ⳮ 1)(2 cosh ␣ny Ⳮ ␣ny sinh ␣ny) ⳮ ␣nb (sin h␣ny Ⳮ ␣ny cosh ␣ny)]cosh␣nx (Eq 47)

vx y

(Eq 52)

one obtains: (Eq 48)

v(1 Ⳮ v) y2 Cx Ⳮ C0xy E 2

冢

vx(x, y) ⳱ ⳮ

N

兺 Cnx n⳱1

N

1ⳮv E

2

Ⳮ (Eq 49)

兺

冤

Cnx ␣nby sinh ␣ny ⳮ 2b

n⳱1

cosh ␣ny Ⳮ

冣

v ␣nby sinh ␣ny 1ⳮv

Since plane strain has been assumed ␣xz can be calculated from:

Ⳮ (1 ⳮ ␣nb coth ␣n y cosh ␣ny

␣xz ⳱ m(rx Ⳮ ry)

1 v ⳮ sinh ␣ny Ⳮ ␣n 1ⳮv

(Eq 50)

where m is the Poisson’s ratio. Further, the strain exy can be obtained from: exy ⳱

2␾x ⳱ Cxy Ⳮ C0x Ⳮ y2

兺

⳯ (sinh ␣ny Ⳮ ␣ny cosh ␣ny)]sinh ␣nx

[␣nb(sinh ␣ny ⳮ ␣ny cosh ␣ny) ⳮ

rxx ⳱

2␾x ⳱ⳮ x2 n⳱1

[␣2nby sinh ␣ny Ⳮ (1 Ⳮ ␣nb coth ␣nb)

N

␾x(x, y) ⳱ Cx

N

rxy ⳱

1 ⳮ m2 m ry ⳮ rx E 1 ⳮ m

冢

冣

(Eq 51)

where E is the elastic modulus. Since the condition for compatibility is satisfied, the displacement in the y-direction is uniquely determined, excepting rigid body displacements, from the relationship:

冢

冢␣

1

冣冣冥cos ␣ x

sinh ␣ny Ⳮ y cosh ␣ny

n

n

(Eq 53)

A similar treatment is used for the loading case r T (x). In that case, the solution is given by: y3 y2 Ⳮ C0y Ⳮ 6 2

␾y(x, y) ⳱ Cy

N

Cny ␣n2

兺 n⳱1

[(1 Ⳮ ␣nb coth ␣nb)(sinh ␣ny ⳮ ␣ny cosh ␣ny) Ⳮ ␣2n by sinh ␣ny]cos ␣nx

(Eq 54)

from which are obtained: ␣yx ⳱

y

2␾y ⳱ Cy Ⳮ C0y Ⳮ y2

N

兺 n⳱1

Cny[2␣nb cosh ␣ny Ⳮ ␣2n by sinh ␣ny ⳮ (1 Ⳮ ␣nb coth ␣nb) • (sinh ␣ny

Removed layer

Ⳮ ␣ny cosh ␣ny)]cos ␣nx

x σx(x)

Ty (x)

␣yy ⳱

2␾y ⳱ⳮ x2

(Eq 55)

N

兺

Cny

n⳱1

[(1 Ⳮ ␣nb coth ␣nb)(sinh ␣ny ⳮ ␣ny

T (x )

y

cosh ␣ny) Ⳮ ␣2nby sinh ␣ny]cos ␣nx Internal forces

␾ ⳱ ⳮ xy 2

Tx(x)

syxy ⳱ ⳮ

(Eq 56)

N

y

兺

n⳱1

Cny[␣nb sinh ␣ny Ⳮ ␣n2by cosh ␣ny) x

σx(x)

ⳮ (1 Ⳮ ␣nb coth ␣nb) • ␣ny sinh ␣ny]sin ␣nx

(Eq 57)

Finally, the displacement is given by: –αx(x)corr

v(1 Ⳮ v) y2 Ey Ⳮ C0yy E 2

冢

vy(x, y) ⳱ ⳮ

y

1 ⳮ v E

2

Ⳮ

N

兺

冤

Cny b sinh ␣ny

n⳱1

ⳮ ␣nby cosh ␣ny ⳮ (x)

σx(x)

x

冣

v 1 ⳮ v

(b sinh ␣ny Ⳮ ␣nby cosh ␣ny)

冢

Ⳮ (1 Ⳮ coth ␣nb) • y sinh ␣ny –∆αx(x) Residual-stress distributions, forces, and distortion of a plate before and after layer removal. Top: residual-stress distribution in the x-direction in the center of the plate in the x-z plane; center: same as top after removal of a layer with the forces Ti(j) caused by the residual stresses tending to distort the plate; bottom: same as center with the distortion displacement shown (Ref 25)

Fig. 6

2 v ⳮ cosh ␣ny Ⳮ ␣n 1 ⳮ v

冣冥

y sinh ␣ny cos ␣nx

(Eq 58)

108 / Measurement and Prediction of Residual Stress and Distortion By letting the stresses and displacements be equal to the measured values, the following relations are obtained: rxx(xi, 0) Ⳮ ryx(x2, 0) ⳱ Drx(xi) i ⳱ 1, 2, …

(Eq 59)

y

i ⳱ 1, 2, …

(Eq 60)

and satisfying the boundary condition stated in Eq 44 at a suitable number of positions: rxx(a, yi) Ⳮ rxy(a, yi) ⳱ 0

H

冮

r(z1) ⳱ rm(z1) Ⳮ 2

m (xi, 0) Ⳮ m (xi, 0) ⳱ m(xi) x

using the exact equations of the previous sections. The method is summarized for two of the previous cases as follows. Flat Plate (see Flat Plate, Biaxial Stress). A generalized solution is written:

i ⳱ 1, 2, …

(Eq 61)

Equations 53 to 61 form an overdetermined system, from which the unknown coefficients Cnx and Cny can be determined using, for example, the method of least squares. The desired correction of the stresses measured at the surface after removing material can finally be expressed as: rxcorr ⳱ ⳮrxx(x, b) Ⳮ rxy(x, b)

(Eq 62)

z1

H

冮

dz ⳮ 6z1

z1

rm(z) z

rm(z) dz z2

(Eq 64)

The subscripts x, y, or xy have been dropped, because the form of Eq 35 and that of Eq 36 are exactly the same. r(z1) represents the true stress in any direction at depth z1 before a layer was removed, and rm(z1) represents the measured value at that depth. The correction in stress c(z1) at z1 is the difference between the true and measured value, given by: H

冮

c(z1) ⳱ r(z1) ⳮ rm(z1) ⳱ 2

and

dz ⳮ 6z1

H

z1

冮

z1

ⳮm[rxcorr Ⳮ

b) Ⳮ

ryy(x,

b)]

(Eq 63)

Sikarskie (Ref 36) proposed a stress-reconstruction procedure (series method) when thin layers were removed from the surface of a component. He described procedures applicable to flat plates and solid cylinders. The procedure works well for shallow depths (a few percent of specimen diameter or thickness), or in instances where the stress gradient over the total depth removed does not change too rapidly and is of essentially one sign. The practicality of this method depends on the fit of the measured stresses in depth by a Taylor’s series referred to the surface values of stress and successive derivatives at the surface. When the method is applicable, very convenient relations are obtained, which describe the stress correction in terms of the influencing factors, for example, layer depth, stress magnitude, stress gradient, and specimen size. Judgment is necessary, however, in using the series approximation that does not arise when

(Eq 65)

y

σy

x

σx

z

z1

σx

x

Fig. 7

Stresses in flat plate after layer removal

冢

Ⳮ

冣

H ⳮ z1 H

H ⳮ z1 H

冢

r1

2

冣

where, again, the subscripts r, h, and z have been dropped because the form is the same. When rr(r1) is desired: r(r1) ⳱ rr(r1)

rm(r) ⳱ rhm(r)

(Eq 71)

When rz(r1) is desired, r(r1) ⳱ rz(r1) rm(r1) ⳱ rzm(r1)

c(r1) ⳱ r(r1) ⳮ rm(r1)

3

冣

(Eq 72)

Ⳮ …

(Eq 66)

(Eq 67)

where Dz1 ⳱ H ⳮ z1. This correction is seen to be approximately proportional to the magnitude of the surface stress and thickness of the removed layer (Fig. 7). It is inversely proportional to the specimen thickness. By solving for Dz1, the question of proper slice is given by: 1 Hc(z1) 4 rm(H)

(Eq 68)

Thus, for example, if the measured stress is to be in error by less than 5%, ⳮc(z1)/rm(H) ⳱ 0.05 and the appropriate slice depth is:

(Eq 73)

Again, expanding the integrand of Eq 70 in a Taylor’s series and integrating term by term, a final form for the correction is obtained:

冦

R ⳮ r1 1 Ⳮ R 2

冢

c(r1) ⳱ ⳮ k rm(R)

冣

R ⳮ r1 R

冢

[rm(R) ⳮ Rr⬘m(R)] Dz1 H

(Eq 70)

rh(r1) is calculated from rhm(r1) using Eq 18. The correction term in stress, c(r1), is written as before:

where rm(H), r⬘m(H), are true surface stress and successive derivatives with respect to z at the surface. For shallow depths, only the first terms of the series can be used and: c(z1) ⳱ ⳮ 4rm(H)

rm(r) dr r

k ⳱ 2

1 [2rm(H) Ⳮ Hr⬘m(H) 3

ⳮ 2H 2r⬙m(H)] ⳯

R

冮

r(r1) ⳱ rm(r1) ⳮ k

rm(r) ⳱ rzm(r)

冢

Ⳮ [rm(H) Ⳮ 2Hr⬘m(H)]

Dz1 ⳱ ⳮ

Removed layer

H

The integrands are then expanded in a Taylor’s series referred to the surface values, after which the integration is performed term by term. The final form for the correction is: H ⳮ z1 c(z1) ⳱ ⳮ 4rm(H) H

For a plate 0.4 in. (10 mm) thick, for example, the slice depth is 0.005 in. (0.13 mm). If the stress gradient is high, then the next term in the correction series should be included and a quadratic in Dz1 solved. This requires an estimate of r⬘m(H) based on experience. Solid Cylinder (see Solid Cylinder Bar, Rotationally Symmetric Stresses). A generalized solution from Eq 16 and 17 is written:

k ⳱ 1

rzcorr ⳱ ryx(x,

(Eq 69)

rm(r1) ⳱ 0

rm(z) z

rm(z) dz z2

1 (0.05)H 4

Dz1 ⳱

2

冣

Ⳮ

1 6

[2rm(R) ⳮ 2Rr⬘m(R) Ⳮ R2r⬙m(R)] ⳯

R ⳮ r1 Ⳮ… R

冢

冣

(Eq 74)

where rm(R), r⬘m(R), and so forth, are the surface stress and successive derivatives with respect to z at the surface. Insight into the factors that influence the correction holds exactly as previously discussed, as do the limitations of the method. Ruud et al. (Ref 22–24) applied a modification of Johanssen method to measure the triaxial stress condition of thick plate 21⁄4Cr-1Mo plate weldments. Ruud et al. actually measured the strains in all directions and calculated the stresses, but did not correct for layer removal due

Measurement of Residual Stresses / 109 to the complex nature of the stress field. Ruud et al. also measured the residual-stress condition of expanded tubing including 304 stainless steel tubing (Ref 37) but focusing on the residual stresses on the inside surface of the heat-exchanger tube components.

Residual stresses parallel to the milling direction, ksi

0

–10

–20

–30 0

0

4

2

6

8

Distance from the workpiece surface, mils Residual stresses at the surface and near the surface due to milling a medium-carbon steel work-

Fig. 8 piece

–40 –20

Residual stresses, ksi

0 20 40 60 80 100 120

0

4

2

6

8

10

12

14

Distance from the workpiece surface, mils

Sectioning and Material-Removal Methods As discussed in the previous sections in this article, many procedures require that the component (sample or part) be sectioned and/or some material be removed from it to measure the residual stresses. This is especially true for the measurement of internal residual-stress fields where the component nearly always has to be sectioned to reveal the internal stress field. The two exceptions to the necessity of sectioning and material removal, neutron diffraction and ultrasonic methods, are described in the section “Nondestructive Procedures” in this article. Sectioning or material removal is required by a particular residual-stress measurement procedure (see the section “Stress-Field Condition Assumptions”) or method (see the section “StrainMeasurement Methods”). Mechanical chipremoval processes are usually applied because of their economy and speed. All chip-removal processes, including lathe turning, drilling, milling, sawing, grinding, and so forth, introduce surface residual stresses that can be as high as the yield strength of the strain-hardened metal and several thousandths of an inch (tens of microns) in depth (Ref 38–43). Figures 8 to 10 show the residual stresses in steels caused by various machining processes. Furthermore, some steels are especially prone to strain hardening— for example, austenitic stainless steels—and extra care must be used with these materials when selecting a material-removal technique. Figure 11 shows plots of the residual stresses in 304 austenitic stainless steel caused by various grinding methods. Note that these plots are only a sample and may not be typical. If the size of the element in which the strain change is measured is smaller, or thinner in the case of surface-depth gradients, than about 0.1 in. (2–3 mm), then a chemical or electrochemical material-removal technique must be used to remove the surface residual stresses caused by mechanical chip re-

Residual stresses in a 440 C (825 F) stainless steel workpiece induced by facing

Fig. 9

100 80

–20 Residual stresses, ksi

Residual stresses, ksi

0 20 40 60 80

Strain-Measurement Methods

Abusively machine ground

Handheld grinder 60

As discussed in the section “Stress Measurement,” all residual-stress-determination methods measure elastic strain, not stress, and the residual stress is calculated from the strain values. Several methods for the measurement of strain have been applied in residual-stress studies and have been mentioned previously. These methods include:

40 Handheld flapper wheel

20 0

100 120

–20 140

0

2

4

6

0

8

2

4

6

8

10

12

14



Fig. 10

Residual stresses in an alloy steel workpiece induced by turning

Samplings of residual-stress distributions induced in 304 stainless steel workpieces by common grinding procedures

Fig. 11

moval. These techniques may be used solely or in conjunction with, and after, the chip-removal method. It should be noted that material-removal techniques such as electrodischarge milling (EDM) induce residual stresses (Ref 44) as do chip-removal methods. Other methods, such as laser, flame, or plasma cutting that cause heating of the element, must be applied with caution because they may reduce the stress field by annealing before it can be measured. Thus, the only methods for material removal from a component surface that do not induce residual stresses are electrolytic or chemical polishing. Electropolishing is described in some detail in Ref 45, and guidelines are provided for application to various ferrous alloys. In electropolishing, the electrolyte and operating conditions depend on the alloy being polished, as shown in Ref 4 and 45. Electropolishing combined with XRD is used extensively to reveal residual-stress gradients on machined, ground, and hardened surfaces. However, application of these techniques requires that the subsurface stresses be corrected for the removal of prior surface layers (Ref 4). Another concern when reducing components to a more convenient smaller size to place them on or in a measurement device is that the stresses of interest are not changed by the sectioning. Generally, plates should be cut to a length and width of at least three times the thickness to avoid end effects. Cylinders, both thin-walled and solid, should be a minimum of three diameters in length. Where the manufacturing process affects the entire thickness of a component, such as heat treatment or forging, it might not be advisable to section without means of measuring the stress change extensively over the entire component before sectioning. In other words, selection of the stress-measurement procedure and methods should avoid sectioning unless techniques to measure the effects of sectioning are applied before sectioning is initiated. On the other hand, when the processes that have induced the residual stress produce only shallow stress fields, then the three-times rule suggested previously is applicable.

● ● ● ● ● ● ●

Mechanical gages Electrical-resistance gages Optical gages Birefringent methods Diffraction methods (x-ray and neutron) Ultrasonic methods Magnetic methods

110 / Measurement and Prediction of Residual Stress and Distortion Diffraction, ultrasonic, and magnetic methods are discussed in the section “Nondestructive Procedures” in this article. Mechanical Gages. The application of mechanical gages such as those described by Heyn (Ref 26), Stablein (Ref 27), Gunnert (Ref 31), and others generally preceded the availability of electrical-resistance strain gages and are not discussed due to their general lack of precision, poor spatial resolution, and inefficiency. Electrical-Resistance Strain Gages. Most bonded electrical-resistance strain gages are made from either metallic wire or foil materials. There are also the recently developed semiconductor gages. A variety of sizes, shapes, and configurations are available including single-element gages and rosettes with two, three, or four elements. Electrical-resistance strain gages are available in sizes as small as about 1 mm and thus provide a resolution of strain measurement on that order. Information on electrical strain gages is available in numerous sources including Ref 46 and in reviews by Crites (Ref 47) and Masubuchi (Ref 14) as well as suppliers (e.g., Measurements Group Inc., Raleigh, NC). Changes in temperature tend to cause an apparent strain; therefore, some type of temperature compensation is needed. Frequently, a “dummy gage,” which is not subjected to the strain, is exposed to the same temperature as the actual gage to provide a basis for comparison. A temperature-compensated gage can also be used. Gages must be bonded securely to the specimen. Various types of cements have been developed. Sometimes gages must be protected from metal chips produced during machining as well as from the oil or water. A number of systems have been devised for protecting gages under various conditions. Brittle coatings are a simple inexpensive strain gage that will only provide qualitative indications of residual stress. A brittle lacquer is applied to the area where the stresses are to be measured by material removal. After the lacquer has cured (dried), a change in the stress field is induced, and if the change is sufficient strain will be produced in the lacquer, causing it to crack. If the material removal is in the form of a hole drilled in the lacquer, radial cracks indicate a tensile residual stress in the plane of the component surface and circular cracks indicate compressive stress. Optical Gages. Light reflective methods can be used to magnify the movement of a reflective surface in a well-fixtured component that is held securely in place during material removal to change the stress field and therefore induce strain change. This method can also be used if the component can be removed and replaced precisely in a fixture and the position of the reflected light measured before and after removal and replacement during which a change in the residualstress field was induced. Laser Methods. Other techniques applying laser light have been proposed as well. These have included shearography (Ref 48), interferometry (Ref 49), speckle-correlation interferometry (Ref

50), and others. Vikram and others (Ref 50) suggested that a small volume of the material could be stress relieved by heating via a laser to induce a change in the stress field and the strain change measured by an optical technique to reveal the residual stresses existing in the volume before heating. However, it must be recognized that heating a volume of steel sufficiently to change the residual-stress field will result in tensile residual stresses in the heated volume (Ref 51), and this would likely be detrimental to the component in which stresses were being measured. Birefringent Methods. Under the action of stresses, transparent materials become doubly refracting (birefringent), and if a beam of polarized light is passed through a model (under stress) made of such a material, a colored picture is obtained from which the stress distribution can be determined. This technique is called the photoelastic technique (Ref 46). The actual component in which the stresses are to be measured is coated with a photoelastic polymer. When residualstress changes are induced in the component, strain changes are caused and transmitted to the polymer coating, which then becomes birefringent. This can be observed and measured using a reflection polariscope (Ref 14). Instructions for analyzing fringe patterns in this application (nearly the same as those obtained in ordinary photoelasticity) are provided by the manufacturer. The photoelastic coating may be applied by brushing a liquid polymer on the surface of the specimen and polymerizing it by applying heat. Alternatively, a prefabricated flat or contoured sheet of polymer may be bonded to the part at room temperature (Ref 52). The maximum strain that can be measured ranges between 3 and 50%, depending on the type of polymer used; the strain sensitivity usually decreases with the increase in the maximum measurable strain.

Chemical Methods A number of qualitative methods to detect residual stresses that may lead to stress-corrosion hydrogen-induced cracking in steel have been applied to specimens representing components to be manufactured. Magnesium chloride solutions have been applied extensively to the study of stress corrosion in austenitic stainless steels, including some recent work by Bouzina et al. (Ref 53). Masabuchi and Martin (Ref 54) studied the susceptibility of SAE 4340 steel weldments to hydrogen-induced stress cracking. The test procedure was to immerse the weldment specimens in a 4% H2SO4 aqueous solution charged with H2 and to which two drops of a 5% P solution of CS2 was dissolved. A direct current (dc) was applied between a specimen and a lead anode to provide a current density of 0.35 to 0.8 A/in.2 The crack patterns that developed were related to the surface tensile residual-stress distribution in each specimen. Stress-corrosion cracking induced by residual stresses in carbon and low-alloy high-strength

steels has been investigated by several researchers (Ref 54–56). One procedure consisted of immersing the specimens in a boiling aqueous solution of 60% Ca(NO3)2 and 4% NH4NO3 for 31 h. The crack patterns that developed were related to the surface tensile residual-stress distributions in the specimen. A number of standard practices for testing the susceptibility of metals to stress-corrosion cracking have been published by ASTM, including: ● ASTM G 38 “Standard Recommended Prac● ● ● ●

tice for Making and Using C-Ray Stress Corrosion Test Specimens,” 1979 ASTM G 58 “Standard Practice for the Preparation of Stress Corrosion Test Specimens for Weldments,” 1978 ASTM G 39 “Standard Practice for Preparation and Use of Bent-Beam Stress Corrosion Test Specimens,” 1979 ASTM G 30 “Standard Recommended Practice for Making and Using U-Bend Stress Corrosion Test Specimens,” 1979 ASTM STP 425 “Stress Corrosion Testing,” 1967

However, these tests for the most part do not reveal the residual stress, but rather the susceptibility of the metal to cracking under known stresses in the specified corrosion medium.

Semidestructive Procedures Nondestructive methods of residual-stress measurement are characterized as methods that in no way affect the serviceability or reduce the mechanical strength or other properties of the component in which stresses are measured. Between the nondestructive and destructive methods, which have a severe effect on the serviceability, strength, and properties, are the semidestructive methods. These are methods that have a small to negligible effect on the components in which stresses are measured, or methods in which the component may be repaired after the measurement. The methods that are considered semidestructive are those that require small holes to be drilled or rings to be trepanned in the component or indentations to be made in the surface. The first two methods provide quantitative data and the third only qualitative data.

Blind Hole Drilling and Ring Coring The hole-drilling method was proposed in the 1930s (Ref 57) and is based on measurement of the change in surface strain caused by stresses relieved by machining a shallow hole in the testpiece. The principle is that removal of stressed material results in the surrounding material readjusting its stress state to attain equilibrium. The method has been standardized in ASTM E 837 (Ref 58). The ring-core method (Ref 59) is also based on the strain caused by disturbing the stress field, but in this case a relatively stressfree island of material is isolated by making a

Measurement of Residual Stresses / 111 shallow ring around a strain gage. This method is also called trepanning. These two methods are the least destructive mechanical stress-relief techniques and are relatively simple and economical. They, as do nearly all stress-relief techniques, rely on electrical-resistance strain gages to measure the strain change due to metal removal. Rosettes of strain gages are available especially for hole drilling. The size of the rosettes has been progressively reduced over the last few decades and are now available in sizes less than about 10 mm from a number of manufacturers. As with most residual-stress techniques, hole drilling and ring coring have been applied mostly to steels. Most applications have been done on flat plate or cylindrically round parts (Ref 5, 60, 61). Stresses can be determined at various depths into the surface of the material, down to a depth equal to the diameter of the hole or core (Ref 62, 63). Kelsey (Ref 64), however, observed that stresses with depth cannot be measured accurately to greater than half the hole diameter. The thickness of the layers in which measurements are resolved is about 10 to 20% of the hole or core diameter. The equipment necessary to perform the measurement is reasonably inexpensive, portable, and can be used in a manufacturing shop environment. However, experienced technologists are needed to take the readings—from selecting the area in which stresses are to be measured to preparing the surface, applying the strain gages, and reading and interpreting the data. Due to the possibility of residual stresses being induced by the hole-drilling or coring technique, prior calibration of the application is recommended in all cases, with the possible exception of certain applications where holes are produced by abrasive jet machining (AJM) (Ref 65). Rendler and Vigness (Ref 66) developed calibration constants for cold-rolled steel that they proposed as generally applicable to all metals provided that the elastic constants were known. However, they seem to have overlooked variations in the strain-hardening coefficients and the accompanying residual stress, which exist between alloys and even between tempers of the same alloy. Dini et al. (Ref 67) showed that direct experimental determination of the necessary constants for any isotropic material with known elastic constants can be eliminated by using data available for cold-rolled steel and calculating these constants using a formula presented. Despite the success that some researchers have claimed in circumventing the development of calibration constants, experimental calibration is strongly recommended. This is best done by applying strain gages and drilling the holes in testpieces prior to stressing them known amounts (Ref 65, 66). The AJM technique should be applied to any material with high propensity to work-hardening during machining, for example, austenitic stainless steel (Ref 68). The following are general limitations and/or concerns of hole drilling and ring coring: ● Areas of high stress gradients should be avoided because the stress gradient must be

●

● ●

● ● ● ●

assumed to be constant across the hole or ring diameter. Areas where stresses are greater than onethird the yield strength of the material are likely to produce erroneous results due to local plastic yielding during metal removal. The thickness of the part or specimen must be at least four times the hole or core diameter. Strain hardening of the steel in the vicinity of the hole may result during metal removal, which can cause tens of ksi (10 ksi ⳱ 69 MPa) error. Heating may result during the metal removal. Holes or cores must be spaced at least eight times their diameter apart. The area in which stresses are to be measured must be accessible to a rather bulky drilling or coring alignment device. Preparation of the surface for strain-gage adherence may induce residual stresses that introduce substantial error to the subsequent measurement (Ref 69).

In conclusion, the drilling and ring-coring methods are nearly nondestructive variations of the destructive mechanical stress-relief techniques and require only rather simple equipment and instrumentation. The state-of-the-art is relatively well developed compared to many nondestructive methods, some of which require considerable research and development work before they will ever be suitable to general application in terms of alloys and stress-field conditions. Technological advancements in hole drilling and ring coring have largely been due to advancements in the more general area of mechanical stress-relief methods and research in new metalremoval techniques for metal fabrication.

Indentation Methods Engineers and scientists have proposed the use of indentors, such as those used to perform hardness measurements, as a means to measure or detect surface-residual stresses since the 1930s. Kokubo in 1932 reported that stresses applied under bending load changed the apparent Vickers hardness values in carbon-steel rolled sheets, both as-rolled and annealed (Ref 70). He showed that tensile stresses tended to decrease the apparent hardness and compressive stresses tended to increase the hardness. The stresses applied in tension and compression were sufficient to cause 0.3% strain. In the 1950s, Sines and Carlson (Ref 71) proposed a method that required various amounts of external loads to be applied to the component in which residual stresses were to be measured while hardness measurements were made. The loads were made to cause both tensile and compressive applied stresses. The quality, that is, whether the residual stress was compressive or tensile, was then revealed by comparing the effect of the applied stress, and whether it was tensile or compressive, on the hardness measurement. At about the same time Pomey et al. (Ref

72) proposed that residual stresses could be measured by pressing a ball-shaped penetrator into the component in which residual stresses were to be measured and establish the relationship between the pressing load while it was progressively increased, and the electrical resistance at the interface between the penetration and the component. He maintained that a smaller decrease in electrical resistance indicated that portions of material under the ball were plastically yielding and that the corresponding load on the ball could be related to the existing residual stress. Later, Chiang et al. (Ref 73) provided a critique of several existing indentation analyses and proposed an interpretation of indentations exhibiting hemispherical plasticity. Nevertheless, the applications illustrated in this paper focused on brittle materials and not metals. There have been numerous papers published proposing various approaches to interpreting the indentation loads and shapes so as to estimate the residual-stress field on the surface and nearsurface regions of materials. However, indentation methods have not earned the degree of confidence of XRD or hole-drilling methods for general applications and thus are rarely applied.

Spot Annealing Another method that has been proposed to measure residual stresses in metal surfaces is to reduce the residual stresses in a small volume by annealing the metal in the volume. It has been proposed that this annealing be performed by intense laser light (Ref 50). This technique was envisioned to be similar to residual-stress relief by removal of the material as accomplished in the hole-drilling techniques. However, as Cullity discussed in Ref 51, such localized heating would induce high surface residual tensile stresses in the heat-affected region.

Nondestructive Procedures The methods described in the section “StrainMeasurement Methods” all measure the change in some dimension (strain) of the component produced by the removal of a finite volume of stressed metal from that component. Thus, they measure the strain induced by removing material so as to perturb the residual-stress field. On the other hand, nondestructive procedures measure a dimension in the crystal lattice of the metal or some physical parameter affected by the crystal lattice dimension. Whenever a mechanical force, resulting in stress that is less than the yield strength, is placed on a solid metal component, that component distorts and strains elastically. That elastic strain results in a change in the atomic lattice dimension, and this dimension, or change, is measured by the nondestructive stress-measurement procedures. For example, the diffraction methods—x-ray and neutron— measure an actual crystal dimension, and this

112 / Measurement and Prediction of Residual Stress and Distortion dimension can be related to the magnitude and direction of the stress that the metal is subject to, whether that stress is residual or applied. Subsequently, in this section the following methods of stress measurement are described: ● ● ● ●

X-ray diffraction Neutron diffraction Ultrasonic velocity Magnetic Barkhausen noise

X-Ray Diffraction X-ray diffraction techniques exploit the fact that when a metal is under stress, applied or residual, the resulting elastic strains cause the atomic planes in the metallic crystal structure to change their spacings. X-ray diffraction can directly measure this interplanar atomic spacing;

Ns β ψ2

X-ray source

ψ1

S1 Film

Np1 Np2

η

S2

Specimen surface

R

O 2

η

1

One-angle arrangement for the single-exposure technique. N, specimen normal; b, angle that the incident beam makes with Ns, Np1, and Np2 the normals to the diffracting planes 1 and 2, respectively; w1 and w2, angles between Ns, Np1, and Np2, respectively; g, the angles between the incident beam and the diffracting plane normals; Ro, camera radius; O, point of incidence of the x-ray beam of the specimen; 1 and 2, diffracting planes at various attitudes to the specimen surface; S1 and S2, measured parameters representing the distance from a reference point of known distance from the incident beam and the diffracted x-ray beam position. S1 and S2, directly related to the Bragg angles, h1 and h2.

Fig. 12

Miniature x-ray diffractometer for the one-angle technique arrangement of XRD stress measurement. This device incorporates a Ruud-Barrett Position-Sensitive Scintillation Detector and is capable of being inserted in a 4 in. (100 mm) inside diameter and measuring residual stress (Ref 22).

Fig. 13

from this quantity, the total stress on the metal can then be obtained. Since metals are composed of atoms arranged in a regular three-dimensional array to form a crystal, most metal components of practical concern consist of many tiny crystallites (grains), randomly oriented with respect to their crystalline arrangement and fused together to make a bulk solid. When such a polycrystalline metal is placed under stress, elastic strains are produced in the crystal lattice of the individual crystallites. In other words, an externally applied stress or one residual within the material, when below the yield strength of the material, is taken up by interatomic strain. X-ray diffraction techniques can actually measure the interatomic spacings that are indicative of the elastic strain in the specimen. Stress values are obtained from these elastic strains in the crystals by knowing the elastic constants of the material and assuming that stress is proportional to strain, a reasonable assumption for most metals and alloys of practical concern. Reference 74 describes XRD and instrumentation in detail. There are three basic techniques for measuring stresses, based on XRD. They are the doubleexposure or two-angle technique (DET), the single-exposure or one-angle technique (SET), and the sin-square-psi or multiangle technique. The angle of exposure referred to is that between the incident x-ray beam and the specimen surface normal. It should be noted that in any XRD stress-measurement technique, x-ray peaks in the far back-reflection range, that is, peaks with Bragg angles (h) of near 90, are much preferred because they show the greatest effect with a given amount of applied or residual stress. This is illustrated by: r␾ ⳱ (2h1 ⳮ 2h2)

冤

冥

冤冥

cot h1 E 1 p 2 1 Ⳮ m sin2w 180 (Eq 75)

where h1 is the Bragg angle of the planes diffracting at w1 and h2 is the Bragg angle of the planes diffracting at w2. As h1 increases, its cotangent decreases; therefore, a larger difference (2h1 ⳮ 2hw) would result from a given ru to maintain an equality. For a residual-stress measurement, the diffracting angle, h, of interatomic planes of at least two different psi (w) angles with respect to the surface normal must be measured (Fig. 12). These planes are crystallographically equivalent (same Miller indices, hkl ) and in the unstressed state of the metal would have the same interatomic (d) spacing for the planes labeled 1 and 2 in Fig. 12 (Ref 51, 75, 76). In a stressed material, however, the two or more orientations of diffracting planes are selected so that they are at different angles to the surface; thus their normals are at different psi (w) angles to the surface normal. Then, depending on the angle of these planes to the stress vector, their interplanar atomic spacing is increased or decreased by varying amounts.

The most common sources of errors and misapplications in stress measurements by x-rays are related to stress constant selection, focusing geometry, diffracted peak location, cold-working crystallography, texture, grain size, microstructure, and surface condition. The source, significance, and correction techniques for these errors will not be elaborated upon here; details may be found in Ref 77. A point of interest in the error sources concerns cold working and microstresses. As stated previously, microstresses are usually considered to be those manifested by strain variation across single metallic grains. This strain variation is detected in XRD as broadening of the x-ray peak— a distinctly different phenomenon from the peak shift caused by residual stresses. However, microstrain variation can be measured simultaneously with stress. This microstrain phenomenon has been proposed as a means of judging cold work, dislocation density, and fatigue damage (Ref 78). Despite the facts that x-rays provide stress readings only to a depth of less than 0.001 in. (0.025 mm) and that the error sources listed previously must be considered, the noncontact XRD method is presently the only time-proven, generally applicable, truly nondestructive method for measuring residual stresses. Its reliability has been proved and documented by thousands of engineers and scientists since the 1960s, beginning with Bolstad et al.’s classic work at Boeing using x-ray film cameras (Ref 79). This documentation includes measurement of stresses in the Brooklyn Bridge (Ref 20) and tempering evaluation of carburized steels. The Society of Automotive Engineers considers the method of sufficient practical importance to have printed three handbook supplements on the subject (Ref 4), and another is under revision. Even so, this nondestructive technology has been largely restricted to the laboratory because of the general lack of knowledge regarding the state-of-the-art instruments and the limitations of the more widely known and available conventional scanning XRD equipment. Instrumentation for bringing this technology into the field and manufacturing area has advanced rapidly since the 1980s, especially toward increased portability, compactness, and speed of operation. As shown in Fig. 13 and 14, instrumentation has been developed and is commercially available for stress measurement in situ on the inside diameter of 10 mm (4 in.) diam pipe, and soon for 5 mm (2 in.) diam steel tube (Ref 22, 23). Position sensitive x-ray detectors have been largely responsible for these improvements to both laboratory-based and field-deployable residual-stress-measuring instruments (Ref 9, 19, 21–23, 80–82). Also, with the speed of data collection being less than 0.1 s with conventional x-ray tube sources, XRD stress measurement can be performed on moving components (Ref 11). Nevertheless, many engineers have been frustrated in applying XRD to residual-stress measurement. This has been largely due to crystallographers inexperienced in residual-stress

Measurement of Residual Stresses / 113 measurement, attempting to apply conventional scanning x-ray diffractometers and techniques to residual-stress measurement. For example, in conventional XRD analysis and crystallography, sharp resolution of the diffracted spectra is very beneficial. However, in XRD stress measurement the need to measure psi (w) angles that are not zero defocuses the beam, and attempts to refocus leads to significant error in the stresses read (Ref 83). In XRD stress measurement, the ability to repeatedly measure the position of a defocused diffracted x-ray peak is more important than sharp resolution (Ref 84). Thus, it is recommended in most cases that XRD residualstress measurement be performed by trained technologists using x-ray instrumentation specifically designed and built for stress measurement, not conventional scanning diffractometers. Software packages specifically for residualstress measurement used with conventional scanning diffractometers do not in most cases eliminate the mechanical and focusing problems of applying these instruments to residual-stress measurement. It is necessary to mount the component (or specimen) in which stresses are to be measured on the conventional scanning diffractometer, which usually requires sectioning of the component and which complicates and adds error to the measurement procedure.

Neutron Diffraction Neutron diffraction (ND) is capable of measuring the elastic strains induced by residual stresses throughout the volume of relatively thick steel components with a spatial resolution as small as 1 mm3. Such capabilities provide for residual-stress measurement inside components without sectioning or layer removal. Principal ND methods, as with XRD methods, measure the spacing between crystallographic planes in a component, and this spacing is affected by residual and applied stress. The spacing between a selected set of crystallographic planes (u) is related to the angle of incidence and diffraction of

21/ 4 in. (5.7 cm)

the neutron radiation (h), which are equal, and the wavelength of the monochromatic radiation (k) by Bragg’s Law: k ⳱ 2d sin h

(Eq 76)

The elastic strain (e) induced by the residual stress perpendicular to the diffracting crystallographic plane then is related to d by: e ⳱

d ⳮ do sin h0 ⳱ do sin h ⳮ sin h0

(Eq 77)

where do is the distance between the unstressed crystallographic planes. If the orientation of principal stresses are known in the component, the stress in any principal direction may be calculated by: rA ⳱

E (1 Ⳮ m)

冤e

AⳭ

冥

m (eA Ⳮ eB Ⳮ eC) (1 ⳮ 2m)

(Eq 78)

where rA, rB, and rC are the principal stresses, eA, eB, and eC are the strains measured in the corresponding principal directions, and E and m are the Young’s modulus and Poisson’s ratio, respectively. If the principal stress directions are unknown, strains in at least six directions must be measured to determine the residual stresses acting on the volume of material in which strains are being measured. Limitations and Applications. For residualstress measurements in most alloys, especially steels and cast irons, the unstressed spacing (do) between crystallographic planes at the exact point of strain measurement is not known and not easily measured. This means that do or ho in Eq 77 cannot be precisely established, and this leads to various degrees of error in the accuracy and precision of ND residual-stress measurements. This condition is aggravated by the fact that the elemental composition, and thus do, vary considerably within a component and markedly

51/ 16 in. (12.9 cm) 41/ 8 in. (10.5 cm)

within the phase (e.g., martensite, austenite, ferrite) of the alloy at various locations. Additional limitations are that the component must be brought to a nuclear reactor, each strain measurement requires over an hour, a single stress determination in one small volume of the component requires at least three strain measurements, and the measurements are very costly. Nevertheless, the ND methods have been applied to residual-stress measurements in steel weldments (Ref 85), cylindrical steel forgings, plastically deformed steel plate (Ref 86), steel rocket case forgings (Ref 87), and many other types of components.

Ultrasonic Velocity The principle underlying the measurement of stress and thus elastic strain by ultrasonic (acoustic) techniques is the phenomenon of an approximately linear change in ultrasound velocity with applied stress. In addition, it has been shown that under certain narrow conditions residual stress can be measured by exploiting this phenomenon. Stress is measured by inducing a sound wave in the frequency of several megahertz into the metal specimen and measuring the time of flight or some other velocity-related parameter. Since many other characteristics of metals besides stress-induced elastic strain affect velocity, these must be sorted out; however, neither the technology nor the fundamental knowledge for such sorting is usually available. The great interest in ultrasonic techniques for residual-stress measurement stems from their promise for three-dimensional nondestructive measurements within the material. Principle. A number of velocity-related phenomena have been used in various methods to measure stress effects by ultrasound. All utilize the deviation of the reaction of the metal from the linearity of Hooke’s law of elasticity, r ⳱ Me, where r is stress, e is strain, and M is elastic modulus. This has been referred to as the anharmonic property of the solid and may be represented by a power series r ⳱ Me Ⳮ Ce2 Ⳮ De3 Ⳮ…, where C is the third-order anharmonic constant, D is the fourth, and so on. Most research done for stress measurement has used expressions in which terms past the third-order constant, C, are dropped. Of the several anharmonic property effects that may be used to measure stress, the following are probably the most exploited: ● Velocity dependence on the elastic modulus ● Dispersion of frequency amplitudes in sur-

face waves

11/ 4 in. (3.3 cm)

● Birefringence of orthogonally polarized shear

waves

● Harmonic generation in surface waves 1.6 in. (12.9 cm)

Fig. 14

Engineering drawing of the miniature XRD stress measurement head showing major dimensions

A very simplified form of the anharmonic stress strain law has been written as r ⳱ Me Ⳮ Ce2 and rewritten as r ⳱ e(M Ⳮ Ce). The term in parentheses is approximately related to the velocity of sound as qV 2 艑 M Ⳮ Ce, where q is the density of the medium and V is the velocity

114 / Measurement and Prediction of Residual Stress and Distortion of sound. This may be approximately rewritten in terms of velocity dependence on strain as: V⳱

冪 q 冤1 Ⳮ 2M e冥 M

c

(Eq 79)

Then, to solve for strain, e ⳱ 2(V 冪Mq ⳮ 2M)/C (Ref 88). A simple view of the dependency of ultrasonic velocity on the elastic modulus and density may be shown by rewriting the equation pV 2 ⳱ M Ⳮ Ce in terms of V, differentiating, and dividing by V to yield an expression for DV/V. The result will readily show that a fractional change in elastic modulus or density would affect the velocity. The density of metal, for which the Poisson ratio is near 0.3, obviously changes as a compressive or tensile stress is placed on the specimen, and it is reasonable that the speed of sound would then change. Limitations and Applications. Ultrasonic technology offers a number of types of wave modes in which to probe metals; these include bulk waves, such as longitudinal and shear, and surface waves usually confined to Rayleigh type. Each mode offers many unique parameters for extracting information. As has been discussed, the primary effect of stress-induced strain on ultrasonic propagation in metals is on velocity. This may be detected in a number of ways, including measurements of wave velocity, shear wave birefringence, and dispersion. However, there are other characteristics of metals that affect the ultrasonic velocity to the same degree as stress. These include crystallographic texture, microstresses, multiple phases, coherent precipitates, composition gradients, and dislocation density and distribution. Crecraft (Ref 89) discussed velocity effects, manifested as texture-induced birefringence, and the marked change seen with ultrasonic frequency. He also reported birefringence due to cold-work in nickel-steel specimens, but did not attempt to separate the cold-work effects in terms of texture, dislocation density, and so forth. In the early 1950s, Bradfield and Pursey (Ref 90) and Pursey and Cox (Ref 91) reported showing the influence of small degrees of texture on ultrasonically measured elasticity in polycrystalline bars. They showed how the true isotropic elastic constants can be determined using measurements of both longitudinal and shear wave speeds along several directions. They presented stereographic charts that illustrated the relationship between elastic behavior of cubic crystals and results of x-ray texture determinations. McGonagle and Yun (Ref 92) noted the coldwork effects in a paper comparing XRD results with Rayleigh wave velocity measurements. Boland et al. (Ref 93) also recognized that other material properties can affect ultrasonic velocity and recommended that methods be developed to distinguish stress-induced velocity changes from those from other sources. James and Buck (Ref 94) pointed out that since the third-order elastic constants for most

structural materials are not readily available from the literature, ultrasonic stress measurement must be calibrated relative to the particular material being investigated. In the same paper they discounted the possible effect of mobile dislocations on the sound velocity in structural engineering metals with high yield strengths due to the short dislocation loop lengths prevalent. However, they did mention that crystallographic preferred orientation (texture) during deformation or fatigue is capable of severely modifying the elastic constants on which the sound velocity depends. Papadakis (Ref 95) noted marked velocity changes for ultrasonic waves in various steel microstructures, and Moro et al. (Ref 96) measured the effect of microstructural changes caused by tempering on the ultrasonic velocity in low-alloy steel. Tittman and Thompson (Ref 97) evaluated the near-surface hardness of case-hardened steel with Rayleigh waves; because hardness in this case is a combination of composition, microstress, and macrostress, the velocity change was due to a combined effect. The temperature sensitivity of ultrasonic stress measurements has also been cited as an important source of error. Salama et al. (Ref 98, 99) proposed that this dependence be used as a means to measure stress, but also noted the marked effect of dislocations and did not address a methodology of separating the stress from the dislocation effect. Much of the work cited above is concerned with attempts to measure the effects of a variety of material properties on the changes in ultrasonic velocity. However, there apparently is no comprehensive study that demonstrates the capability of quantitatively separating stress effects on ultrasonic propagation from other variables found in structural metals, such as dislocation density or crystallographic texture. Furthermore, most of the studies cited observed velocity changes in bulk waves. Velocity measurements on these waves must be measured through the thickness of a component, and, as most metallurgists recognize, obtaining uniform properties through thicknesses greater than a few millimeters, especially in steels, is difficult. The subtle property variations to which ultrasound velocity is sensitive and the inherent lack of homogeneity in engineering metals present additional serious problems for through-thickness stress measurements. In spite of the microstructural variations in manufactured steel products, success in the application of ultrasonic methods to residual-stress measurement has been achieved in specific cases. One is in the measurement of hoop stresses in railroad wheels (Ref 100). Here changes or variations of the residual stress in the hoop direction is of concern while that in the radial or axial direction can often be assumed to be constant or negligible. Some techniques then for the measurement of the residual hoop stresses has relied on normalizing the hoop velocity against the axial (Ref 101). Also, European railroads have monitored ultrasonic velocity along

the wheel rims during use and attributed changes to residual-stress changes (Ref 102). Schramm in his paper mentioned a number of approaches for the application of ultrasound to the measurement of residual stresses in railroad wheels, and these examples may find application in the measurement of residual stress in other axially symmetric shapes (Ref 100). Ultrasonic residualstress measurements have also been applied to rails as reported by Egle and Bray (Ref 103) and Bray and Leon-Salamanca (Ref 104).

Barkhausen Noise Analysis The Barkhausen noise analysis technique (BNA) is concerned with measuring the number and magnitude of abrupt magnetic reorientations made by expansion and contraction of the magnetic domains in a ferromagnetic metal. These reorientations are observed as pulses somewhat random in amplitude, duration, and temporal separation and therefore are roughly described as noise. Applications. A few applications of BNA to ferromagnetic metallic components have been made, Gardner (Ref 105) mentions a number of applications that include helicopter rotor blade spans, autofrettaged gun tubes, gas turbine engine components, and rolling-element antifriction bearing components. In these examples, the change in residual stresses caused by known service histories was measured. Chait (Ref 106) qualitatively measured the residual-stress condition of a high-hardness laminar composite steel weldment and compared some of the BNA data with XRD stress readings. Sundstrom and Torronen (Ref 107) applied their BNA method to a number of microstructural measurements, including evaluation of grainsize measurement for low-carbon ferritic and ferritic-pearlitic steels, evaluation of anisotropy in deep drawing and textured steels for electrical applications, measurement of the degree of aging in rimmed carbon steels, and pearlite morphology in steel wires. They have also measured iron loss in magnetic material used for transformers and have proposed using BNA for residual-stress measurements, pointing out that quantitative results can be obtained if the material and its fabrication history are known and calibration is possible. Most studies and applications of BNA to stress measurement have focused on the uniaxial stress state. However, Sundstrom and Torronen (Ref 107) implied that the instrumentation they used could simultaneously measure stress in two directions to give biaxial stress conditions for magnetic inspection of roller-bearing components, including BNA for monitoring residualstress change. Summary. The BNA method certainly has been demonstrated to be sensitive to the stress condition in ferromagnetic materials (Ref 108). Nevertheless, its possibilities for application are limited by the condition that the material must be ferromagnetic, the narrow total range of stress sensitivity (i.e., Ⳳ40 ksi, or 5.6 MPa), and the

Measurement of Residual Stresses / 115 shallow depth of measurement. The latter condition might be relieved by using magnetomechanical mechanical acoustic emission (MAE) (Ref 109), an ultrasound analog to BNA. However, the sensitivity of either of these techniques to other characteristics of metallic components and the consequent need for calibration with a nearly identical specimen severely restrict the general applicability of BNA and MAE. Many misapplications have been made that have severely damaged the reputation of the BNA methods (Ref 107, 110). Such restrictions can be removed only if the basic phenomena responsible for the effect of microstructural properties on BNA and MAE are understood and quantified in terms of the signal. Barkhausen noise analysis is not recommended where variations in elemental composition, phase composition, grain size, strain hardening, crystallographic texture grain shape, grain orientation, carbide size and distribution, and other microstructural characteristics accompany variations in residual stress. A recent evaluation of BNA by Allison and Hendricks (Ref 111) confirms the uncertainty of BNA residual-stress measurements.

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Summary and Recommendations Only the destructive stress-relief, semidestructive hole-drilling, or nondestructive XRD methods of residual-stress measurement are generally reliable over a broad range of steel alloys displaying residual-stress fields induced by the various manufacturing processes. Measurement of residual stresses can be very expensive and time consuming, and it is often worthwhile to consult experts in the field before deciding on a measurement method. Before an engineer or scientist who is inexperienced in residual-stress measurement selects a method and attempts to measure stresses he/she should consult someone experienced in residual-stress measurement and analysis.

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98.

99.

XRD Residual Stress Measurement, Adv. X-Ray Anal., Vol 30, 1987, p 511–522 J.H. Root, C.E. Coleman, J.W. Bowden, and M. Hayashi, Residual Stresses in Steel and Zirconium Weldments, J. Press. Vessel Technol., Vol 119, 1997, p 137–141 M. Hayaski, S. Ohkido, N. Minakawa, and Y. Murii, Residual Stress Distribution Measurement in Plastically Bent Carbon Steel by Neutron Diffraction, Fifth Int. Conf. Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 762–769 J.H. Root, R.R. Hosbaus, and T.M. Holden, Neutron Diffraction Measurements of Residual Stresses Near a Pin Hole in a Solid-Fuel Booster Rocket Casing, Practical Applications of Residual Stress Technology, C.O. Ruud, Ed., ASM International, 1991, p 83–93 G.A. Alers, Ultrasonic Methods—Overview, Proc. of a Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76–2, 1975, p 155–161 D.I. Crecraft, Ultrasonic Measurement of Stresses, Ultrasonics, 1968, p 117–121 G. Bradfield and H. Pursey, Philos. Mag., Vol 44, 1953, p 295 H. Pursey and H.L. Cox, Philos. Mag., Vol 45, 1954, p 295 W.J. McGonagle and S.S. Yun, Measurement of Surface-Residual Stress by Nondestructive Methods, Proc. Fifth Int. Conf. Nondestructive Testing (Montreal, Canada), May 21–25 1967, p 159–164 A.J. Boland et al., “Development of Ultrasonic Tonography for Residual Stress Mapping,” EPRI RP 504–2, Final Report, Electric Power Research Institute, 1980 M.R. James and O. Buck, Quantitative Nondestructive Measurement of Residual Stresses, Crit. Rev. Solid State Mater. Sci., Aug 1980, p 61–105 E.P. Papadakis, Ultrasonic Attenuation and Velocity in Three Transformation Products of Steel, J. Appl. Phys., Vol 35 (No. 5), 1964, p 1474–1482 A. Moro, C. Farina, and F. Rossi, Measurement of Ultrasonic Wave Velocity of Steel for Various Structures and Degrees of Cold-Working, NDT Int., Aug 1980, p 169–175 B.R. Tittman and R.B. Thompson, Measurement of Physical Property Gradients with Elastic Surface Wave Dispersion, Proc. Ninth Symp. on NDE, Southwest Research Institute, 1980, p 20–28 K. Salama and C.K. Ling, The Effect of Stress on The Temperature Dependence of Ultrasound Velocity, J. Appl. Phys., Vol 51 (No. 3), March 1980, p 1505–1509 K. Salama and G.A. Alers, Third-Order Elastic Constants of Copper at Low Temperature, Phys. Rev., Vol 161 (No. 3), Sept 1967, p 673–680

100. R.E. Schramm, J. Szelazek, and A. Van Clark, Jr., Ultrasonic Measurement of Residual Stress in the Rims of Inductively Heated Railroad Wheels, Mater. Eval., Aug 1996, p 929–933 101. H. Fukuaka, H. Tada, K. Hirakawa, H. Sakawoto, and Y. Toyo, Acoustoelastic Measurements of Residual Stresses in the Rim of Railroad Wheels, Wave Propagation in Inhomogenous Media and Ultrasonic Nondestructive Evaluation, Vol 6, G.C. Johnson, Ed., ASME, 1984, p 185– 193 102. E.R. Schneider, R. Harzer, D. Bruche, and H. Frotscher, Reliability Assurance of Railroad Wheels by Ultrasonic Stress Analysis, Proc. Third European Conf. on Residual Stress Analysis (Frankfurt, Germany), 4–6 Nov 1992 103. D.M. Egle and D.E. Bray, Ultrasonic Measurement of Longitudinal Rail Stresses, Mater. Eval., Vol 378 (No. 4), March 1979, p 41–46 104. D.E. Bray and T. Leon-Salamanca, ZeroForce Travel-Time Parameters of Ultrasonic Head-Waves in Railroad Rail, Mater. Eval., Vol 43 (No. 7), June 1985, p 854–858 105. C.G. Gardner, Barkhausen Noise Analysis, Proc. Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76–2, Nondestructive Testing Information Analysis Center, 1975, p 211–217 106. R. Chait, Residual Stress Pattern in a High Hardness Laminar Composite Steel Weldment, Proc. Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76– 2, Nondestructive Testing Information Analysis Center, 1975, p 237–245 107. O. Sundstrom and K. Torronen, The Use of Barkhausen Noise Analysis in Nondestructive Testing, Mater. Eval., Feb 1979, p 51–56 108. J.R. Barton, F.N. Kusenberger, R.E. Beissner, and G.A. Matskanin, Advanced Quantitative Magnetic Nondestructive Evaluation Methods, Theory and Experiment, Nondestructive Evaluation of Materials, J.J. Burke and V. Weiss, Ed., Plenum Press, 1979, p 461–463 109. K. Ono, M. Shibata, and M.M. Kwan, Determination of Residual Stress by Magnetomechanical Acoustic Emission, UCLA Department of Materials, ONR Tech. Rep. No. 80–01, Conference on Residual Stress for Designers and Engineers, ASM International, April 1980 110. R.R. King and V.D. Smith, “Residual Stress Measurements in Structural Steels,” Final Report SWRI Project 15–4600, Contract DOT-FH-11–9133, Federal Highway Administration, April 1981 111. H.D. Allison and R.W. Hendricks, Correlation of Barkhausen Noise Signal and XRay Residual Stress Determinations in Grinding-Burned 52100 Steel, Fifth Int. Conf. Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 640–645



Stress Determination in Coatings* COATINGS AND THIN FILMS can be produced by a large variety of deposition techniques. Typical processes are physical vapor deposition (PVD), chemical vapor deposition (CVD), electroplating, electroless deposition, anodizing, thermal growth, and thermal spraying. Since the early 1980s, considerable progress has been made in improving deposition processes for a wide range of high-technology applications. Consequently, many new ceramic coatings and films have been introduced in various industries. Typical examples are metal-oxide semiconductors for microelectronics; titanium nitride, titanium carbide, aluminum oxide, and silicon nitride for machining tools; and thermal sprayed tungsten carbide/cobalt, M-chromiumaluminum-yttrium (where M stands for iron, cobalt, or nickel), and yttrium oxide/partially stabilized zirconia coatings for aerospace applications. Residual stresses, which are internal and therefore locked in, are contained in materials that are produced by nearly every mechanical, chemical, and thermal process, either alone or in combination. As a result, most coatings are in a state of internal stress, including metallics and ceramics. The stress can be either compressive or tensile. It is generally recognized that compressive stresses in coatings are more favorable than tensile stresses because they increase resistance to fatigue failure. However, extremely high compressive stresses may cause either coating separation from the base metal or intracoating spallation. Generally, if a tensile stress causes strain that exceeds the elastic limit of the coating, then it will cause cracking in the coating perpendicular to the direction of the stress. Therefore, understanding the formation of residual stress in the coating is important to prevent the coating from peeling or cracking during service. Furthermore, residual stresses have significant influences on the mechanical and physical properties of the coatings, particularly electrical resistivity, optical reflectance, fatigue, and corrosion. There are three types of residual stresses: ● Macrostresses, which are nearly homoge-

neous over macroscopic areas of the material ● Microstresses, which are nearly homogeneous over microscopic areas, such as one grain or subgrain

● Inhomogeneous microstresses, which are in-

homogeneous even on a microscopic level Residual macrostresses are the ones of most interest in engineering practice because they can substantially affect component service performance. Both residual and inhomogeneous microstresses are of more interest in materials science. This article intends to provide a useful guide for measuring residual macrostress on a coating. The most commonly used measurement methods are mechanical deflection, x-ray diffraction, and hole-drilling strain gage. After a discussion on the origins of residual stress, the fundamental principles, as well as examples of practical measurements, are described for each method.

Origins of Residual Stress Residual macrostress in a coating combines the intrinsic stress and the thermal stress acting in the coating plane parallel to the coating/substrate interface: rt ⳱ ri Ⳮ rth

(Eq 1)

where rt is the total macrostress, and ri and rth are intrinsic stress and thermal stress, respectively. Intrinsic stress results from the growth processes, depending primarily on deposition parameters, whereas thermal stress arises from a mismatch in coefficients of thermal expansion between the coating and the substrate. Many phenomenological models have been proposed to explain the occurrence of intrinsic stresses by correlating them with a variety of coating microstructure and process features. To varying degrees, the intrinsic stress of a coating is associated with these deposition conditions and coating features: ● Incorporation of residual gas atoms in the

coating

● Grain size, microvoid, and dislocation density

in the coating

● Combined effect of surface tension and

growth process at grain boundaries

● Deposition temperature relative to the melt-

ing temperature of the coating material

● Annealing and shrinkage of disordered ma-

terial buried behind the advancing surface of a growing coating Although many studies have described the intrinsic stresses, information on the corresponding structural details is limited. It seems unlikely that one can formulate a generalized model of intrinsic stress for various coating materials and deposition processes. Any coating that is prepared at elevated temperatures (T2) and then cooled to room temperature (stress measurement temperature, T1) will be thermally stressed because of the difference in the coefficients of thermal expansion between the coating and the substrate. Assuming no deformation of the substrate, the magnitude of the thermal stress in the coating is: rth ⳱ (␣c ⳮ ␣s)(T2 ⳮ T1)Ec /(1 ⳮ mc)

(Eq 2)

where ␣c and ␣s are the thermal expansion coefficients for the coating and the substrate, respectively, and Ec and mc are the Young’s modulus and Poisson’s ratio of the coating, respectively. A coating deposited at an elevated temperature exhibits compressive stress if ␣s ␣c, but tensile stress if ␣s ␣c. In the case of ␣s ␣c, the substrate shrinks more than the coating does during cooling from the deposition temperature and compresses the coating to maintain dimensional compatibility. In some cases, thermal stress is the primary residual stress of the coating. For example, a titanium nitride coating can be deposited on a cemented carbide substrate (tungsten carbide-1 wt% Ta-10 wt% Co) via a CVD process at 1000 C (1830 F). With the values of ␣s ⳱ 5 ⳯ 10ⳮ6 /K, ␣c ⳱ 9.54 ⳯ 10ⳮ6 /K, ETiN ⳱ 411 GPa (60 ⳯ 106 psi), and mTiN ⳱ 0.24, the stress in the coating, as calculated from Eq 2, is 2.39 GPa (0.35 ⳯ 106 psi) in tension at 25 C (77 F).

● Energetic particle bombardment during coat-

Deflection Method

ing growth ● Lattice misfit between the substrate and the growing coating

The deflection method is the most widely used technique for determining the residual stress in

*This article is adapted from “Stress Determination for Coatings” by J. Albert Sue and Gary S. Schajer in Surface Engineering, Volume 5, ASM Handbook, ASM International, 1994, p 647– 653.

Stress Determination in Coatings / 119 a coating. In terms of basic principles, it involves measuring the amount of bending in a strip that is due to the deposition of the coating. A formula for calculating the residual stress in an electrodeposited coating was derived first by Stoney (Ref 1) in 1909. Subsequent researchers have derived more complex formulas to improve the accuracy of the stress evaluation. Comparative studies on those stress-evaluation formulas are reviewed and discussed elsewhere (Ref 2–4). Nearly all formulas are variants of Stoney’s formula. Consider a coating deposited on one side of a strip substrate. Both coating and substrate are assumed to be homogeneous. A mismatched force at the coating/substrate interface results in residual stress in the coating, which bends the strip either upward (concave) or downward (convex), depending on whether the stress is tensile or compressive. For overall force and moment equilibrium of the coating/substrate composite, it can be shown that the residual stress in the coating is (Ref 5): rc ⳱ (Es d 2s )/[6(1 ⳮ ms)Rdc](ds dc)

rc ⳱ {Es d s2/[6(1 ⳮ ms)Rdc]} {(1 Ⳮ CH3)/(1 Ⳮ H)}

(Eq 4)

where C ⳱ [Ec(1 ⳮ ms)]/[Es(1 ⳮ mc)] H ⳱ ds /dc R L2 /8f L2 /2d

(Eq 5)

where E is Young’s modulus; m is Poisson’s ratio; d is thickness, with the subscript c denoting coating and s denoting substrate; R is the radius of curvature of the bent strip, L is the length of the strip, f is the deflection from the free end of the strip, and d is the deflection at the center of the strip (Fig. 1).

(Eq 3)

or, in general:

Although Eq 3 is used most often in practice and represents a generalized Stoney’s formula for a planar state of stress, it tends to overestimate the value of measured stress. However, it does not require knowledge of the elastic properties of the coating. Equation 4 provides a much better approximation than Eq 3, but it does require knowledge of elastic properties. Equation 4 differs from Eq 3 in terms of a correction factor [(1 Ⳮ CH3)/(1 Ⳮ H)]. Table 1 compares stresses as a function of ds /dc, calculated from both Eq 3 and 4. In the calculation, it was assumed that Ec ⳱ 400 GPa (60 ⳯ 106 psi), Es ⳱ 200 GPa (30 ⳯ 106 psi), and mc ⳱ ms. It is clear that both equations are in good agreement when ds /dc 50. By choosing a large value of ds /dc, the error can be minimized if Eq 3 is used. Cantilever Beams. To measure the deflection of cantilever beams, various techniques have been developed (Ref 7), including optical, capacitance, mechanical, electromechanical, interferometric, and electromechanical or magnetic restoration. Figure 1(a) shows the setup for the deflection measurement when an optical system is used. In this example, a titanium nitride coating was deposited on a quartz beam via a PVD process, and the average residual stress in the coating was determined by measuring the amount of deflection at the free end, f, of the bent beam, according to the relation: rc ⳱ [4Es d s2 f ]/[3(1 ⳮ rs)L2 dc]

(Eq 6)

With the values of Es ⳱ 71.7 GPa (10.4 ⳯ 106 psi), ms ⳱ 0.16, ds ⳱ 3 mm (0.12 in.), dc ⳱ 3 ⳯ 10ⳮ6 m (1.2 ⳯ 10ⳮ4 in.), L ⳱ 50 mm (2 in.), and f ⳱ 2 ⳯ 10ⳮ6 m (8.0 ⳯ 10ⳮ5 in.), the stress in the coating is determined to be 273 MPa (40 ksi) in compression. Disks. The average stress in the coating on a disk substrate can be determined from the amount of deflection, d, at the center of the disk caused by the deposition of a coating on one side. This value can be measured optically by interferometry or microstylus profilometry. Figure 1(b) shows a typical interferometry apparatus setup. Either technique measures deflection at the same position, across a diameter of the disk, both before and after coating deposition. The stress in the coating is then calculated: rc ⳱ {Es d s2[(Ddx Ⳮ Ddy)/2]}/[3(1 ⳮ ms)r2dc]

Fig. 1

Stress measurement techniques. (a) Bending of cantilever beam. (b) Disk deflection. Source:

(Eq 7)

Ref 6

Table 1 Comparison of average residual stress calculated using Eq 3 and 4 Calculated stress Eq 3

Eq 4

ds /dc

MPa

ksi

MPa

ksi

200 100 50 20 10

ⳮ1143 ⳮ571 ⳮ286 ⳮ114 ⳮ57

ⳮ165.7 ⳮ82.8 ⳮ41.5 ⳮ16.5 ⳮ8.3

ⳮ1137 ⳮ565 ⳮ280 ⳮ109 ⳮ52

ⳮ164.9 ⳮ81.9 ⳮ40.6 ⳮ15.8 ⳮ7.5

Typical patterns of interference fringes. (a) rx ⳱ ry. (b) rx ⬆ ry, where both components are in compression or tension. (c) rx ⬆ ry, where one component is in compression and the other is in tension. Source: Ref 8

Fig. 2

where Ddx and Ddy are deflection changes measured before and after coating deposition, and r is the radius of the disk. Whether the stress is tensile or compressive, it is determined by the curvature of the disk before and after coating deposition, as determined by a depth microscope. When the change in curvature is upward (concave), viewed from the coating side, the stress in the coating is tensile. The opposite change in curvature indicates a compressive stress in the coating. Typical interference fringe patterns are shown in Fig. 2. Figures 2(a) and (b) correspond to

120 / Measurement and Prediction of Residual Stress and Distortion equal and unequal principal stresses of the same sign, whereas Fig. 2(c) corresponds to a biaxial stress state with principal stresses of opposite signs. Using Fig. 2(a) as an example, the measured deflection, d, is equal to the wavelength of monochromatic light multiplied by the number of light fringes (d ⳱ 632.8 nm ⳯ 17). Figure 3 shows typical microstylus traces on the titanium nitride coated surface of an AISI 304 stainless steel disk, both before and after coating deposition. The curvature of the coated surface was downward (convex), viewed from the coated side. With the values of Es ⳱ 193 GPa (28 ⳯ 106 psi), ms ⳱ 0.28, ds ⳱ 4.74 mm (0.186 in.), r ⳱ 11.94 mm (0.4700 in.), dc ⳱ 20 lm (800 lin.), and the deflection Dd ⳱ 6.3 ⳯ 10ⳮ6 m (2.5 ⳯ 10ⳮ4 in.), the stress in the titanium nitride coating is 4.44 GPa (0.644 ⳯ 106 psi) in compression. The measurement errors from both the optical and the microstylus trace setups are within one-half light band and Ⳳ0.1 lm (Ⳳ4 lin.), respectively. Practical Considerations. First, either strip or disk-shape substrate specimens should be parallel within 0.02 mm (0.001 in.) over their length or diameter. Specimen edges should be free from visible flaws and chips. In addition, the surfaces on which the deflection measurements (interferometer or profilometer) will be performed should be ground and lapped to a finish better than 0.08 lm (3 lin.) Ra. Second, the dimensions of a strip of length L, width w, and substrate thickness ds should obey L 10w 10 ds. The substrate thickness of a strip or disk depends on the coating thickness to be deposited. The thickness ratio of the substrate to the coating, ds /dc, should be greater than 50 to ensure the accuracy of the stress calculation from Eq 3. Third, substrate specimens should be stress relieved before coating deposition. They should be placed between two stainless steel surface plates under at least an 8.8 kPa (1.3 psi) normal load, at an annealing temperature, in a vacuum furnace

for at least 1 h. The annealing temperature is dependent on the substrate material. Fourth, for coatings with an inherently smooth surface, such as those produced by PVD and CVD, the deflection can be determined either by interference fringe or microstylus profilometer measurements on the coated surface. For a coating with a relatively rough surface, such as those produced by thermal spraying and electroplating, the measurements can be made on the surface that is opposite the coated surface. Significance and Use. The deflection measurement method is recommended for determining the average stress in the cross section of a coating with a thickness ranging from several hundred angstroms to several hundred micrometers. Typically, the elastic constants of a thin coating are much different from those of a bulk material. Equation 3 provides a means for stress measurement on a thin coating without any knowledge of its elastic constants. The measurement normally applies only to a test sample. The disk deflection method is particularly useful for the direct inspection of silicon wafers used in solar cells or integrated circuits.

X-Ray Diffraction Method Basic Principles. Stress measurement, using the x-ray diffraction method, is based on the change in the interplanar spacing (strain) close to the surface of the specimen material. The details of the theory and interpretation of residual stress measurements are well described in the article “X-Ray Diffraction Residual Stress Techniques” in Volume 10 of the ASM Handbook, as well as in Ref 9 to 11. Consider an isotropic material with a lattice parameter d hkl for un0 stressed material in the sample plane normal. The strain in a direction inclined by an angle y to the surface normal of the coating and the stress acting in the surface plane of the coating at an angle u with the principal axis of the specimen are related by: hkl hkl hkl ehkl uw ⳱ (d uw ⳮ d 0 )/d 0

⳱ [(1 Ⳮ m hkl)/E hkl] • (rx cos2 u Ⳮ sxy sin2 u Ⳮ ry sin2 u ⳮ rz) • sin2 w Ⳮ [(1 Ⳮ m hkl)/E hkl]rz ⳮ (m hkl/E hkl) • (rx Ⳮ ry Ⳮ rz) Ⳮ [(1 Ⳮ m hkl)/E hkl] • (sxz cos u Ⳮ syz sin u) sin w) 2

Typical microstylus trace on titanium nitridecoated AISI 304 stainless steel disk before and after coating deposition

Fig. 3

coating in various stress states can be determined using Eq 8. Biaxial Stress. At a free plane, the out-ofplane stress components rz, sxz, and syz are all zero, at a free surface. Because the penetration depth of x-rays is very small, the resulting measurements refer specifically to near-surface material. Plane stress conditions, therefore, often apply to x-ray measurements, and Eq 8 is simplified to: hkl hkl hkl hkl hkl ehkl uw ⳱ (d uw ⳮ d 0 /d 0 ⳱ [(1 Ⳮ m )/E ]

ru sin2 w Ⳮ (m hkl/E hkl)(rx Ⳮ ry) (Eq 9)

where ru ⳱ rx cos2 u Ⳮ ry sin2 u is the macrostress in the coating parallel to its surface at an angle u with the principal axis of the sample. For a biaxial stress state, rx ⳱ ry ⳱ ru, and at w ⳱ 0: hkl hkl hkl hkl (d hkl u,w⳱0 ⳮ d 0 )/d 0 ⳱ 2m ru/E

(Eq 10)

From Eq 9 and 10: hkl hkl hkl hkl 2 d hkl uw ⳱ d u,w⳱0 Ⳮ rud 0 [(1 Ⳮ m )/E ] sin w (Eq 11)

In practice, high-angle diffraction peaks of an (hkl) reflection are obtained from ⳮw to Ⳮw at a given angle u. Lorentz polarization, absorption, and background corrections are applied to the diffraction peak profile. The peak positions are determined by profile fitting or other methods and are subsequently converted to interplanar spacing d hkl uw for stress analysis. 2 In the linear plot of d hkl uw versus sin w, the intercept is I ⳱ d hkl , and the slope is M ⳱ u,w⳱0 hkl hkl rud hkl ]. The stress of the coating 0 [(1 Ⳮ m )/E can then be determined by: ru ⳱ M/{d 0hkl[(1 Ⳮ m hkl)/E hkl]}

(Eq 12)

Triaxial Stress State without Shear Stress. For a material in a three-dimensional (triaxial) stress state without shear stress, but with the stress component rz having a finite value within the xray penetration volume, Eq 8 becomes (Ref 9, 11, 12): hkl hkl hkl ehkl uw ⳱ (d uw ⳮ d 0 )/d 0

⳱ [(1 Ⳮ m hkl)/E hkl](rx cos2 u Ⳮ ry sin2 u ⳮ rz) • sin2 w Ⳮ [(1 Ⳮ m hkl)/E hkl]rz ⳮ (m hkl/E hkl)

(Eq 8)

where h, k, and l are the indices of the Bragg hkl reflection; ehkl uw and d uw are the strain and interplanar spacing of (hkl) in the direction of (u, w), respectively; m hkl and Ehkl are Poisson’s ratio and Young’s modulus in (hkl) in the coating; rx, ry, and rz are normal stresses; sxy, syz, and sxz are shear stresses; rx is the normal stress acting in the x direction on a plane perpendicular to the x axis; and syz is the shear stress on a plane normal to the y axis (the first subscript) in the z direction (the second subscript). Residual stresses of the

• (rx Ⳮ ry Ⳮ rz)

(Eq 13)

Two data sets, u ⳱ 0 and u ⳱ 90, are needed to obtain rx, ry, and rz. The slopes and intercepts 2 of a linear function of d hkl uw versus sin w at u ⳱ 0 and u ⳱ 90 are given by: hkl hkl Mu⳱0 ⳱ d hkl 0 [(1 Ⳮ m )/E ](rx ⳮ rz)

Mu⳱90 ⳱ d 0hkl[(1 Ⳮ m hkl)/E hkl](ry ⳮ rz) hkl hkl hkl hkl I ⳱ d hkl 0 {[(1 Ⳮ m )/E ]rz ⳮ (m /E )

• (rx Ⳮ ry Ⳮ rz)}

(Eq 14)

Stress Determination in Coatings / 121 Stresses rx, ry, and rz can be determined from the sum of the slopes and the intercept in Eq 14. Triaxial Stress State with Shear Stress. A coating with a three-dimensional (triaxial) stress state, including shear stresses, is fully described by Eq 8. The shear stresses, sxz and syz, have a 2 sin2 w dependence. The d hkl uw versus sin w distribution is no longer linear and has two branches of an ellipse for w 0 and w 0. This effect is termed “w splitting,” which is an indication of the presence of shear stress. To obtain these stress-tensor components, three data sets (u ⳱ 0, u ⳱ 45, and u ⳱ 90) are obtained for both ⳮw and Ⳮw. The average strain a1 and the deviation a2 from the strains of “w splitting” are determined to be (Ref 9, 11, 12): hkl a1 ⳱ (euwⳭ Ⳮ ehkl uwⳮ)/2 hkl hkl ⳱ [(d uwⳭ Ⳮ d uwⳮ )/2d 0hkl] ⳮ 1

⳱ [(1 Ⳮ m hkl)/E hkl] • (rx cos2 u Ⳮ sxy sin2 u Ⳮ ry sin2 u ⳮ rz) • sin2 w Ⳮ [(1 Ⳮ m hkl)/E hkl]rz ⳮ (m hkl/E hkl) • (rx Ⳮ ry Ⳮ rz)

(Eq 15)

hkl a2 ⳱ (euwⳭ ⳮ ehkl uwⳮ)/2 hkl hkl ⳱ (d uwⳭ ⳮ d uwⳮ )/2d 0hkl

⳱ [(1 Ⳮ m )/E ](sxz cosu Ⳮ syz sinu) sin w (Eq 16) hkl

hkl

2

The stress-tensor components can be calculated from the slopes of linear plots of a1 versus sin2 w and a2 versus sin2 w. For a1 versus sin2 w, (rx ⳮ rz) is obtained at u ⳱ 0, (ry ⳮ rz) at u ⳱ 90, and sxy at u ⳱ 45, whereas rz is evaluated from the intercept if d hkl 0 is known. Similarly, sxz and syz are obtained when u ⳱ 0 and u ⳱ 90, respectively, from the slope of a2 versus sin2 w.

Stress Measurement. Modern diffractometers are fully automated and equipped with computer software for performing numerically intensive analyses. Diffractometers are capable of measuring residual stresses efficiently and economically. Typically, the measurement can be completed in several hours. The following examples illustrate some stress measurements using Cu K␣ radiation on cathodic arc PVD titanium nitride coatings on a substrate with various stress states. Biaxial. An approximately 10 lm (400 lin.) thick coating of highly (111) oriented titanium nitride was deposited on AISI 304 stainless steel at 500 C (930 F). The x-ray diffraction sin2 w technique was applied to determine the residual stress in the (333)/(511) reflection of the coating. Figure 4 shows the linear distribution of d hkl uw versus sin2 w, indicating typical biaxial stress in the coating. As shown, the slope M ⳱ ⳮ1.1933 ⳯ 10ⳮ3 nm (4.698 ⳯ 10ⳮ11 in.) and the intercept I ⳱ d hkl uw⳱0 ⳱ 0.082123 nm (0.003233 lin.). Young’s modulus and Poisson’s ratio for titanium nitride in (333)/(511) are 364 GPa (52.8 ⳯ 106 psi) and 0.245, respectively (Ref 13). The calculated residual stress for titanium coating is ⳮ4248 MPa (ⳮ615 ksi) in compression. For highly (111) oriented titanium nitride film, (511) contribution is negligible. This is addressed in Ref 13. The (422) reflection has 2h 130, which is not desirable. Triaxial without Shear Stress. To exemplify a triaxial stress distribution, without shear stresses, triaxial stress analysis was applied to a titanium nitride coating deposited on Inconel 718 sub2 strate at 550 C (1020 F). The d hkl uw versus sin w distributions were obtained from (333)/(511) for u ⳱ 0 and u ⳱ 90 (Fig. 5). The slopes Mu⳱0 and Mu⳱90 are ⳮ0.96782 and ⳮ1.01415 ⳯ 10ⳮ3 nm (ⳮ3.8103 and ⳮ3.9927 ⳯ 10ⳮ11 in.), respectively, and the intercept I is 0.082083 nm (0.003231 lin.). The strain-free interplanar spacing for (333)/(511) is 0.08160 nm

(0.003213 lin.). Based on Eq 14, the stress tensor (rij) from this analysis, in units of MPa, is:

冤冤

冥

rx sxy sxz rij ⳱ syx ry syz szx szy rz ⳱

ⳮ2653 Ⳳ 151 0 0 0 ⳮ2819 Ⳳ 150 0 0 0 815 Ⳳ 140

冥

The result shows that the planar stresses are equal biaxial within experimental error and that the stress perpendicular to the coating surface is in tension. Triaxial with Shear Stress. A triaxial stress distribution, including shear stresses sxy, syz, and sxz, was studied in a cathodic arc PVD titanium nitride coating on AM-355 stainless steel. The 2 d hkl uw versus sin w distributions were obtained from (333)/(511) at u ⳱ 0, u ⳱ 45, and u ⳱ 90 using Cu K␣ radiation. Figure 6 shows the 2 typical ellipse distribution of d hkl uw versus sin w at u ⳱ 0. Based on analysis discussed at the beginning of this section, the stress tensor in the titanium nitride coating, in units of MPa, is: rij ⳱

冤

冥

ⳮ2699 Ⳳ 148 1 Ⳳ 181 110 Ⳳ 32 1 Ⳳ 181 ⳮ2776 Ⳳ 148 ⳮ34 Ⳳ 34 110 Ⳳ 32 ⳮ34 Ⳳ 34 833 Ⳳ 148

Practical Considerations. First, a W-diffractometer is preferable for conducting stress measurements. The X- and W-diffractometers are defined on the basis of the sample axis for w tilt perpendicular or parallel to the plane of the incident and detected x-ray beam, respectively. A W-diffractometer gives symmetric irradiated areas in ⳮw and Ⳮw tilted angles at a given (hkl) reflection line and a greater range of sin2 w (from 0 to 0.95 for a W-diffractometer and 0 to 0.5 for an X-diffractometer). Second, the diffractometer should be mechanically aligned and calibrated using a stress-free standard sample (NIST SRM 660 lanthanum hexaboride powder or SRM 640 silicon powder) to obtain the peak position of the (hkl) reflection line within Ⳳ0.01 at Bragg angles 2h in the range of w 0 and w 0. Third, an appropriate x-ray wavelength should be selected to achieve the desired sampling volume (penetration depth) for a particular set of (hkl) planes. The penetration depth, which is defined as the distance from the surface to the depth with 63% or 1/e of the intensity of the reflection line, is calculated for X- and W-diffractometers, respectively: sX ⳱ (sin2 h ⳮ sin2 w)/[2l(sinh cosw)] sW ⳱ (sinh cosw)/2l

Fig. 4 flection

hkl Linear distribution of d uw as a function of sin2 w of titanium nitride coating from (333)/(511) re-

hkl Linear distribution of d uw as a function of sin2 w of titanium nitride coating from (333)/(511) reflection at u ⳱ 0 and u ⳱ 90

Fig. 5

where l is the linear absorption coefficient, which can be obtained from Ref 14 for various materials and radiations. Fourth, to achieve high accuracy in residual stress, the measurement should only be carried out on an (hkl) reflection line with Bragg angles 2h 130 and with sufficient intensity for peakposition determination.

122 / Measurement and Prediction of Residual Stress and Distortion Fifth, an appropriately sized collimator should be selected. It should have an irradiated area large enough to ensure that a statistically relevant number of grains or subgrains in the coating are included in the measurement. The angular resolution is essential in stress measurement. If the spot mode of x-ray beam cannot sample a sufficient number of grains, one should use another method. Sixth, appropriate methods (Ref 9, 10, 15– 17), such as modified Lorentzian, Gaussian, Cauchy, Pearson VII, parabola, center of gravity, gravity line, and cross correlation should be applied to determine the peak positions of the reflection line (hkl). Seventh, a sufficient number of measurements in the ⳮw and Ⳮw directions should be conducted to obtain an accurately linear distribution 2 or w-splitting of d hkl uw versus sin w. The significance of this distribution should be verified by repeating measurements at different u angles. If a nonlinear relation other than w-splitting is ob2 tained in the d hkl uw versus sin w distribution, then the coating being measured is inhomogeneous and, therefore, the x-ray diffraction sin2 w method is no longer applicable. Eighth, the x-ray elastic constants of the coathkl hkl ing for an (hkl) plane, S hkl and 1 ⳱ ⳮm /E hkl hkl S hkl /2 ⳱ (1 Ⳮ l )/E , can be calculated from 2 single-crystal compliance, according to an appropriate model (Ref 11, 12), or measured experimentally in uniaxial tension or bending tests with a series of loads (Ref 13, 18, 19). X-ray elastic constants and applied loads (ra) obey these equations:

practice. For biaxial stress analysis, the lattice spacing measured at w ⳱ 0, d hkl uw⳱0, can be substituted for d hkl 0 . In this case, the contribution to the total error is less than 0.1%. For a triaxial

stress analysis, the difference between d hkl uw⳱0 and d hkl 0 is included in the calculation. Consequently, a small error in d hkl 0 can lead to a relatively large error in the measured stress. To obtain acceptable stress results, d hkl 0 must be within 0.01% of its true value. The stress-free interplanar spacing d hkl 0 in the strain-free direction w* is given by (Ref 20): hkl sin2 w* ⳱ [ⳮS hkl 1 /(S 2 /2)]

• {1 Ⳮ [(ry ⳮ rz)/(rx ⳮ rz)] hkl Ⳮ [3 Ⳮ (S hkl 2 /2S 1 )rz]/(rx ⳮ rz)}; u ⳱ 0

sin2 w* ⳱ [ⳮS 1hkl/(S 2hkl/2)] • {1 Ⳮ [(ry ⳮ rz)/(rx ⳮ rz)]} when |rx Ⳮ ry ⳮ 2rz| 2|rz| d hkl 0

hkl ⳱ d uw⳱0 /[1 Ⳮ S hkl 1 (rx Ⳮ ry Ⳮ rz)

Ⳮ (S hkl 2 /2)rz]

Significance and Use. The advantage of the x-ray diffraction method is its capability for measuring residual stress directly and nondestructively on a product component. Portable diffractometers are commercially available and can be used for on-site measurement. The method can apply to a coating with a thickness ranging from 0.5 to 350 lm (2 ⳯ 10ⳮ5 to 1.4 ⳯ 10ⳮ2 in.). However, it is difficult to measure residual stresses in extremely thin coatings and, in some cases, highly textured coatings. Furthermore, xray diffraction is inapplicable to amorphous coatings, and a large scatter in stress measurement is often encountered in coatings with large grain size.

hkl hkl S hkl 2 /2 ⳱ (1 Ⳮ m )/E hkl 2 ⳱ (1/d hkl 0 )[/ra(d uw/sin w)]

Hole-Drilling Method

S 1hkl ⳱ ⳮm hkl/E hkl ⳱ [1/(2d 0hkl)](d hkl uw⳱0/2ra) (a) Typical three-element strain-gage rosette. (b) In-plane strain components caused by release of residual stress through introduction of a hole. Source: Ref 21

Fig. 7

Ninth, a stress-free interplanar spacing, d hkl 0 , for a coating may not be readily available in

Fig. 6

Basic Principles. The hole-drilling method for measuring residual stresses involves drilling a shallow hole in the test specimen to a depth approximately equal to the hole diameter. Typ-

hkl Typical ellipse distribution of d uw as a function of sin2 w of titanium nitride coating from (333)/(511) reflection at varying angles. (a) u ⳱ 0. (b) u ⳱ 45. (c) u ⳱ 90

Stress Determination in Coatings / 123 ical hole diameters range from 0.8 to 5.0 mm (0.030–0.200 in.). The creation of the hole redistributes the stresses in the material surrounding the hole. A specially designed three-element strain-gage rosette, such as that shown in Fig. 7(a), measures the associated partial strain relief. The in-plane residual stresses that originally existed at the hole location can then be calculated from the measured strain reliefs using the method described in ASTM E 837–92 (Ref 21). The ASTM standard also gives details of practical drilling procedures. The partial strain relief measured by one of the three strain gages in the rosette in Fig. 7(b) is related to the principal in-plane residual stresses by: er ⳱ (rmax Ⳮ rmin)A Ⳮ (rmax ⳮ rmin)B cos ␣ 2

(Eq 17)

where rmax and rmin are maximum and minimum principal residual stresses, and ␣ is the angle from the gage axis to the maximum principal stress direction. A and B are calibration constants, the values of which depend on the specimen material properties, the rosette geometry, the hole diameter, and the hole depth. ASTM E 837-92 tabulates the calibration constants for the standard rosette pattern shown in Fig. 7. Equation 17 can be inverted to determine the principal residual stresses from the measured strain reliefs. The result is: rmax, rmin ⳱ [(e3 ⳮ e1)/4A] Ⳳ {[(e3 ⳮ e1)2 Ⳮ (e3 Ⳮ e1 ⳮ 2e2)2]1 / 2 /4B} b ⳱ 1⁄2 arctan [(e3 Ⳮ e1 ⳮ 2e2)/(e3 ⳮ e1)] (Eq 18)

Table 2 Numerical values of dimensionless calibration coefficients a¯ and b¯

D0 /D

0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50

Through-thethickness hole(a) a¯ b¯

0.089 0.095 0.101 0.108 0.114 0.121 0.128 0.135 0.143 0.150 0.158 0.166 0.174 0.183 0.191 0.200 0.209 0.218 0.228 0.237 0.247

0.278 0.295 0.312 0.329 0.347 0.364 0.382 0.400 0.418 0.436 0.454 0.472 0.490 0.508 0.526 0.544 0.562 0.579 0.596 0.613 0.629

Blind hole(b), depth ⴔ 0.4D a¯

b¯

0.111 0.118 0.126 0.134 0.142 0.150 0.158 0.166 0.174 0.182 0.190 0.199 0.208 0.217 0.226 0.236 0.246 0.255 0.265 0.275 0.285

0.288 0.305 0.322 0.340 0.358 0.376 0.394 0.412 0.430 0.448 0.466 0.484 0.503 0.521 0.540 0.558 0.576 0.594 0.612 0.630 0.648

(a) In a thin sheet. (b) In a thick material. Source: ASTM E 837–92

where b is the angle measured clockwise from the location of gage 1 to the direction of rmax. The above equations are valid for a homogeneous isotropic material that is wide, when compared with the hole diameter, and thick, when compared with the hole depth. The equations also apply to a through-the-thickness hole in a material in the form of a thin sheet, provided that the sheet thickness is uniform near the hole. The associated calibration constants have slightly different values than those of the thick-material case. Table 2 (from ASTM E 837-92) lists the dimensionless calibration coefficients for both the thin-sheet and thick-material cases. A and B can be determined from the dimensionless coefficients using: A ⳱ ⳮ(1 Ⳮ m)a¯/2E ¯ B ⳱ ⳮb/2E

(Eq 19)

Residual stress measurements in coated materials create an additional complication because the combination of coating and substrate is no longer a homogeneous material. The calibration coefficients provided in ASTM E 837-92 no longer accurately apply. However, the above two equations are still valid for coated materials, if the coating has a uniform thickness. If the substrate is less than several times greater than the hole depth, then it is also necessary for the substrate thickness to be uniform. The calibration coefficients A and B for hole drilling in a coated material differ from the standard values given in ASTM E 837-92. The actual values depend on the elastic properties of the coating and the substrate, the coating thickness, and the hole diameter and depth. These coefficients can be determined by either experimental calibrations (Ref 22) using known externally applied stresses or finite-element calculations (Ref 23). Approximate values of A and B for thick coatings can be estimated from the values given in ASTM E 837-92. For this purpose, a “thick” coating is one that is at least 0.25 times the mean radius of the strain-gage rosette. For the smallest commercially available hole-drilling rosette, the mean radius is about 1.25 mm (0.050 in.). Therefore, the minimum acceptable coating thickness is about 0.3 mm (0.012 in.). An approximate estimation of A and B for a coated material is based on the observation that the hole-drilling method is most sensitive to the stresses closest to the specimen surface. Almost all of the measured strain relief is due to the stresses in the material within a depth of about 0.25 times the mean radius of the hole-drilling rosette. Thus, a specimen coated to at least this depth is likely to behave similarly to a homogeneous thick specimen consisting only of coating material. Thus, the A and B calibration coefficients for a “thick” coating are approximately equal to the ASTM tabulated values for a homogeneous material with the elastic properties of the coating. The A and B coefficients for coatings that are thinner than 0.25 times the mean radius of the

hole-drilling rosette will deviate significantly from the ASTM tabulated values. The coefficients must be determined on an individual basis, either by experimental or computational means. The use of the hole-drilling method with such “thin” coatings is not generally recommended because the sensitivity of the resulting strain measurements is rather low. As a result, small absolute errors in the strain measurements can cause large relative errors in the computed residual stresses. Stress Measurement. The following example illustrates a hole-drilling measurement on a detonation-gun type of tungsten carbide-cobalt (WC-Co) coating deposited on an AISI 1018 steel substrate. The coating was approximately 0.75 mm (0.03 in.) thick and had a macroscopically homogeneous structure. The elastic properties of the coating were Ec ⳱ 172 GPa (25 ⳯ 106 psi) and mc ⳱ 0.3. A 062-RE hole-drilling strain-gage rosette (5.13 mm, or 0.202 in., strain-gage mean diameter) was attached to the coated specimen. A 2.44 mm (0.096 in.) diam hole was cut in the WC-Co coating by abrasive-jet drilling using 27 lm (1080 lin.) alumina particles. Drilling proceeded in four approximately equal depth increments, up to a final depth of 0.356 mm (0.014 in.). The strain measurements listed in Table 3 were made after each hole-depth increment. Using the A and B calibration coefficients from ASTM E 837-92, adjusted for the elastic properties of the coating material, the principal residual stresses in the coating were found to be ⳮ260 MPa (ⳮ38 ksi) and ⳮ286 MPa (ⳮ41 ksi), respectively. As might be anticipated, the residual stresses in the coating are approximately isotropic. Practical considerations for the use of the hole-drilling method are: ● A high-speed drilling technique using carbide

●

●

●

●

●

drills is recommended for producing a hole in a ductile coating. Abrasive-jet drilling is recommended for a brittle, hard coating (Ref 24). The use of specially made hole-drilling strain-gage rosettes is essential. The application of the strain-gage should follow the procedure recommended by the manufacturer. A smooth coating surface less than 0.41 lm Ra (16 lin. Ra) is desirable for secure straingage adhesion. An abrading or grinding process that does not induce significant residual surface stress should be used for surface preparation. The selection of an appropriately sized strain gage should be based on coating thickness, as well as on the depth and diameter of the hole to be drilled. The diameter of the drilled hole, D0, should be related to the diameter of the gage circle, D, where 0.3 (D/D0) 0.5. A depth microscope with a resolution better than 12.7 lm (0.0005 in.) should be used to measure the depth of the drilled hole at each depth increment. The center of the drilled hole should coincide with the center of the strain-gage circle within

124 / Measurement and Prediction of Residual Stress and Distortion Table 3

Hole-drilling residual stress measurements on a detonation gun WC-Co coating Average stress Strain, le

Depth

rx

ry

sxy

rmax

rmin

smzx

mm

in.

e1

e2

e3

MPa

ksi

MPa

ksi

MPa

ksi

MPa

ksi

MPa

ksi

MPa

ksi

␣

0.00 0.10 0.20 0.28 0.36

0.000 0.004 0.008 0.011 0.014

0 56 116 163 210

0 52 107 155 200

0 52 109 168 218

ⳮ271 … … … …

ⳮ39.3 … … … …

ⳮ275 … … … …

ⳮ39.9 … … … …

ⳮ13 … … … …

ⳮ1.9 … … … …

ⳮ260 … … … …

ⳮ37.7 … … … …

ⳮ286 … … … …

ⳮ41.5 … … … …

13 … … … …

1.9 … … … …

41 … … … …

Note: Rosette type, EA-XX-062RE; Young’s modulus, 172.0 GPa (25 ⳯ 106 psi); Poisson’s ratio, 0.3; hole diameter, 2.440 mm (0.0961 in.); and rosette mean diameter, 5.13 mm (0.202 in.)

Ⳳ0.015 D0. A measurement microscope should be used to align the drill holder or abrasive-jet nozzle with the center of the rosette. ● Precautions should be taken to ensure that the walls of the drilled hole are square to the coating surface on which the rosette is cemented. It is important to protect the strain gage from abrasive-particle erosion or mechanical damage during the drilling operation. ● Values for the Young’s modulus and Poisson’s ratio of the coating should be independently measured in order to determine the residual stress from strain relaxations. Significance and Use. The hole-drilling strain-gage method is a semidestructive technique for measuring residual stress on a coating with a thickness of at least 0.1 mm (0.004 in.). The method, which is quite versatile, can apply to test samples as well as to actual components with complex geometries. Furthermore, it can be used for on-site measurements.

Method Comparison The mechanical-deflection method is capable of measuring the average stress throughout the coating thickness, but requires the stress to be uniform over large distances in the in-plane directions. In contrast, the x-ray diffraction and hole-drilling methods can make a much more localized measurement in-plane, but they have a significantly more limited depth capability. A good agreement in stress measurements between the deflection and x-ray diffraction methods has been demonstrated (Ref 13). With the extrapo-

lation of blind-hole measurements to the near surface, the stress measurement is in good agreement with that measured by x-ray diffraction (Ref 25). A user can select the most suitable method based on economics, environment, coating microstructures, and the geometry of the component to be measured. REFERENCES 1. G.G. Stoney, Proc. R. Soc. (London) A, Vol 82, 1909, p 172 2. C.N. Kouyumdjev, Surf. Technol., Vol 26, 1985, p 35 3. C.N. Kouyumdjev, Surf. Technol., Vol 26, 1985, p 45 4. G. Sotirova and S. Armyanov, Surf. Coat. Technol., Vol 28, 1986, p 33 5. M. Ohring, in The Materials Science of Thin Films, Academic Press, 1991, p 461 6. R.W. Hoffman, in Physics of Thin Films, Vol 3, 1966, p 211 7. D.S. Campbell, Handbook of Thin Film Technology, L.I. Maissel and R. Glang, Ed., McGraw-Hill, 1970, p 12–21 8. R.E. Cuthrell, D.M. Mattox, C.R. Peeples, P.L. Dreike, and K.P. Lamppa, J. Vac. Sci. Technol., Vol 6A (No. 5), 1988, p 2914 9. V.M. Hauk, Adv. X-Ray Anal., Vol 27, 1984, p 81 10. Residual Stress Measurement by X-Ray Diffraction, J784a, 2nd ed., SAE Handbook, Society of Automotive Engineers, 1971 11. I.C. Noyan and J.B. Cohen, Residual Stress Measurement by Diffraction and Interpretation, B. Ilschner and N.J. Grant, Ed., Springer, 1987

12. H. Dolle, J. Appl. Crystallogr., Vol 12, 1979, p 489 13. J.A. Sue, Surf. Coat. Technol., Vol 54/55, 1992, p 154 14. C.H. Macgillavry and G.D. Rieck, Ed., International Tables for X-Ray Crystallography, The Kynoch Press, Birmingham, 1962 15. W. Parrish, T.C. Huang, and G.L. Ayers, Trans. Am. Cryst. Assoc., Vol 12, 1976, p 55 16. A. Brown and J.W. Edmonde, Adv. X-Ray Anal., Vol 23, 1980, p 361 17. A. Brown and S. Linde, Adv. X-Ray Anal., Vol 30, 1987, p 343 18. V. Hauk, International Conference on Residual Stresses, ICRS2, G. Beck, S. Denis, and A. Simon, Ed., Elsevier, London, 1989, p 292 19. H. Behnken and V. Hauk, International Conference on Residual Stresses, ICRS2, G. Beck, S. Denis, and A. Simon, Ed., Elsevier, London, 1989, p 341 20. V.M. Hauk, Adv. X-Ray Anal., Vol 27, 1984, p 101 21. “Determining Residual Stresses by the Hole-Drilling Strain-Gage Method,” E 83792, Annual Book of ASTM Standards, ASTM 22. “Measurements of Residual Stresses by Hole-Drilling Strain Gage Method,” TN503-4, Measurements Group, Wendell, NC, 1993 23. G.S. Schajer, J. Eng. Mater. Technol. (Trans. ASME), Vol 103 (No. 2), 1981, p 157 24. M.T. Flaman and J.A. Herring, Exp. Tech., Vol 9 (No. 8), 1985, p 30 25. C.O. Ruud, P.S. DiMascio and J.J. Yavelak, Exp. Mech., Vol 25 (No. 4), 1985, p 338



Methods for Determination of Inhomogeneous Residual Stress Fields I.A. Razumovsky, M.V. Medvedev, and A.V. Fomin, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow

AMONG NUMEROUS PROBLEMS encountered by mechanics of nonrigid solids, analysis of residual stress presents one of the most challenging tasks because it involves the analysis of physical-mechanical processes and structural changes in the material under various mechanical and heat impacts. Although methods of analyzing residual stress have been under development since the 1930s, this field still presents quite a number of problems to be solved. Development of experimental techniques providing for large amounts of strain field data suitable for later mathematical processing gave impetus both to the beginning of new and the development of already available approaches to residual stress analysis, this fact significantly expanding the range of solvable applied problems. The objective of this chapter is to present results from new developments in methodology and applied techniques for solving problems in the field of residual stress analysis. Residual stresses can be subdivided provisionally into two classes: macrostresses (stresses of the first type) and microstresses (stresses of the second type). Microstresses are stresses that actually exist directly in the crystalline grain and experience changes within the crystalline aggregate (grain) due to crystal inhomogeneity, different alignment of crystallographic planes, and some other factors. Macrostresses can be regarded as averaged microstresses on some finite base. It must be noted that to determine macrostresses by microstress averaging is possible only if microstress distributions comply with consistent patterns of statistics. Most methods for determining residual stress aim at obtaining values of macrostresses. This is because the majority of modern approaches to stress-state evaluation are based on continual models of material whose deformation and destruction are described on the basis of continua mechanics. It might be well also to point out considerable difficulties in experimentally determining the microstress due to minuteness of crystal grains characterized by arbitrary irregular form and generally being inhomogeneous. At the same time, for example, the x-ray study of residual macrostress (the so-called sin2 w

method) is based on measuring changes in distances between atomic planes of metal grain lattice (i.e., microstrains). With regard to problems considered in domains of strength evaluation, reliability, and optimal structure design, different methods and respective experimental techniques have been developed to solve typical problems of residual stress analysis for most practical cases. Efficiency of one or another method is determined by the studied object geometry, type of stress state, nature of residual stress distribution, and materials properties. Methodology of research, including distinctive features of experimental techniques and facilities are given in Ref 8. Classical methods of residual stress research used nowadays, both destructive and nondestructive, provide no opportunity to reliably determine residual stresses in terms of their high gradients when a pronounced change of stress occurs on the gage length in the order of 1 mm (0.04 in.). At the same time, determining residual stress on this gage length is necessary when analyzing strength, integrity, and durability of structures with welded joints, welded deposits, and other inhomogeneities. Special methods that provide for analysis of high-gradient (up to breakage) fields of residual stress in parts made of homogeneous and bimetallic materials have been developed to analyze such problems. This chapter is dedicated to methodology developments that accompany experimental determination of significantly inhomogeneous fields of residual stress. It presents a systematic outline of modern methods for determining residual stress fields characterized by significant inhomogeneity, including theoretical foundations of respective methods as well as aspects of their application. These methods are based on mathematical processing of extensive experimental data obtained when notches of various types are made in the part under investigation. Here, the procedure for obtaining stresses from experimental data is based on the fact that residual stress determination is posed as an inverse problem from the mechanics of nonrigid solids.

Also presented are problems encountered in obtaining experimental data necessary for determining residual stress, including requirements to the nature and scope of acquisition procedures as well as descriptions of special equipment used in solving practical tasks. Examples of applying these techniques to the study of high-gradient residual stress fields are given.

Study of Residual Stress as Inverse Problem of Experimental Mechanics The source of residual stress appearance lies in the initial strain, e 0ij, that fails to meet the equations of strain compatibility. This strain is connected by the Hooke’s law to the elastic strain, eij ⳮ e 0ij, emerging in the body (where eij are full strains corresponding to the general solution of the problem with external loads missing). Residual stress is adjusted for equilibrium inside the body after eliminating the impacts that caused it. In the theoretical study of residual stress, either the initial incompatible strain, e 0ij, or the sequence of changes in force and temperature conditions of loading that leads to initial strains, e 0ij, are assumed to be known. The approaches to the study of residual stress presented in this chapter belong to destructive methods. Yet, in contrast to the known investigation techniques that involve notching, these methods do not assume any a priori correlation between distribution of residual stress to be found, on the one hand, and the stress-strain state of the investigated part after notching, on the other, the latter being determined experimentally. Following are experimental design methods of determining the continuous distribution of residual stress in flat parts of arbitrary shape by measured parameters of stress-strain state close to notches made. Such parameters can be represented by stress-strain tensor components or those of displacement vector, as well as by some of their functionals (e.g., the first invariant of stress tensor) that retain the attribute of linear dependence on residual stress to be found.

126 / Measurement and Prediction of Residual Stress and Distortion The problem of determining residual stress from measured parameters of stress state in the vicinity of a created notch belongs, by the manner of posing, to the class of inverse problems. The observed picture of the stressed state is a response of the residual stress that is relieved along the notch line and must be restituted by this response. Inverse problems are distinguished by being ill defined in most natural (with regard to practice) spaces (C and L2), which incorporate initial data and target distributions of residual stress (Ref 1). These problems are ill defined because close distributions of observed stressed-state parameters (close within measurement error limits) can be matched against significantly different distributions of residual stress along the notch line. Consistent procedures for determining residual stress can be based on regulating algorithms for various integral-solving equations. Consider two variants of obtaining consistent derivation procedures with differently posed problems. In the first variant, the notch is gradually expanded and measurements are made for a certain parameter of stress state at some specific locus that follows the shift of a notch tip. Thus, the distribution of the observed parameter is determined along the notch line as the part geometry changes. The corresponding inverse problem is reduced to the Volterra integral equation. In the second variant, the created notch corresponds to its final length, and the respective overall effect along some line in the vicinity of the notch is measured. The corresponding inverse problem is reduced to the Fredholm integral equation. Method of Volterra Integral Equations. As the notch is expanded, residual stress on its edges is relieved, this stress playing the role of edge load for a new section of part boundary (Fig. 1a). Due to the superposition principle, the relationship between the required residual stress, ry (n), and the measured parameter of stress state along the notching line, l(x), (Fig. 1b) may be represented as the Volterra integral equation of the first type: x

冮 B(x,n)r (n)dn ⳱ l(x) 0

y

0ⱕnⱕxⱕ L

(Eq 1)

where L is the maximum length of the notch. The operator kernel, B(x,n), corresponds to values l(x) at point x from d-impact at point n, while the domain of its definition is a triangle (i.e., at n x, B(x,n) ⳱ 0 is obtained. Apart from considering Eq 1, it is possible to suggest its transformation on the basis of an additional condition—smoothness of the changed function l(x). Then, by way of differentiating, Eq 1 is reduced to the Volterra equation of the second type: B(x,x)ry(x) Ⳮ

x

冮

0

B⬘(x,n)r x y(n)dn ⳱ l⬘(x)

(Eq 2)

When applying the method of the Volterra integral equation, the following important fact

should be considered. While preparing the experiment, account is taken of its conditions and measuring tool sensitivity in choosing the value of a step in expanding the notch and taking measurements. In this case, the discrete character of obtained information is in no way connected to the nature of measured distributions. From this factor develops the task of subjecting the initial data to preliminary processing and that of creating some continuous and differentiable analogues from discrete data and within error limits comparable to experiment errors. Particular patterns for processing initial data can be designed in various ways, including regularization methods. Method of Fredholm Integral Equation of the First Type. A line running close to the notch tip is selected (Fig. 2). Due to the linearity of the problem under consideration, the relationship between the required residual stress ry(n) along the notch with length L and the values of the measured parameter l(n) on this line is: L

冮

0

H(s,n)ry(n)dn ⳱ l(s) s 僆 S,n 僆 L

tional experiment to select measurement lines and points with high information resolution. As for Eq 2, its solution is a correctly solvable problem, and the operator of this equation is a regularizing operator for Eq 1. When using Eq 2, the accent in solving is on finding an efficient algorithm for numerical differentiation of discrete experimental data. Values l(x) and l(s) are known from the experiment in the presence of additive random disturbance whose value is dependent both on the experimental method used and the specific conditions of measurements. The accuracy of measurements cannot be increased as far as it is provided by the numerical methods used to determine kernels of integral operators. They are constructed by multiple solving of boundary problems for the notched part studied. As a rule, errors of initial data are always significantly

σy(ξ)

(Eq 3)

The kernel of integral operator H(s,n) is determined in the region S ⳯ L and corresponds to measured parameters l(n) on line S from d impacts at points n 僆 L. From the point of methodology, reducing the problem to solving the Fredholm equation of the first type is very important. First, conducting an experiment is relatively simple compared with the approach that uses the Volterra equation because in this case, all experimental data are obtained from the single length notch. Second, when solving Eq 3 numerically, creating a matrix analogue of an integral equation would require (under equal discrete values) significantly fewer boundary problems to be solved in comparison with the first approach, which allows for the changing boundary of the notch tip area. Solutions of equations of the first type (Eq 1, 3) are unstable toward variations of initial data (right side) and call for regularizing methods. The indicated distinctions in experiment arrangement determine specific features in the mathematical structure of these equations. Thus, the Volterra equation (Eq 1), all other factors being the same, is conditioned with regard to ry to a greater degree (i.e., has wider information possibilities than Eq 3). According to the regularization principle (Ref 1), information possibilities of considered computational/experimental procedures can be evaluated by the maximally admissible degree of smoothness in solving respective integral equations. Information capacities are largely determined by smoothness of integral equation kernel. The higher the kernel smoothness, the higher is the smoothing (averaging) effect of the integral operator, and consequently, the less distribution ry manifests itself in peculiarities of measured distributions l(s). Accordingly, the considered approaches provide for a preliminary computa-

x, ξ

(a)

x µ(x)

x l (b) Design diagram of Volterra integral equation method. (a) Residual stress relieved at notching. (b) Measured parameters of stress state at the notchfollowing point

Fig. 1

S

y

(S) σy(x) +

x

S

–

L

Fig. 2

Design diagram for method of Fredholm integral equation

Methods for Determination of Inhomogeneous Residual Stress Fields / 127 higher than those of the problem operator, and in the event of considered problems, we regard the operator to be specific with precision. Following the principle of regularization, it is necessary to introduce a priori information about functional properties of residual stress distribution when solving integral equations of the first type (Eq 1, 3). Usually, there is no quantitative information about distributions searched for, yet, from the physical viewpoint, it is natural to regard these distributions as sufficiently smooth functions. Regularization methods based on qualitative data about smoothness of searched distributions allow suppression of oscillating components, whatever their nature. Various regularizing algorithms and principles of their construction are given in Ref 1 to 3. One of the most universal methods in solving ill-conditioned problems based on variation principle is the method of smoothing functional (Tikhonov’s method). This functional has the following form (arguments are left out): T a[ry] ⳱ q2L 2(Hry,l) Ⳮ ␣X2[ry], where q2L 2 is a residual in L2; H is the integral operator in Eq 3 (B is for Eq 1); ␣ 0, regularization parameter; and X is the stabilizing functional whose value is a measure of function smoothness. In the considered problem that searches for smooth distributions, when selecting X, it is expedient to apply restriction both to the norm of function ry itself and to that of its first derivative. According to the variation principle, the regularizing solution is represented by function r ay , supplying the minimum to the functional and determined from Euler’s equation for this functional: (H *H Ⳮ

␣L)r ay

⳱ H *l

where H is an H-dependent operator, while the operator L depends on the selected functional X. Accordingly, the functional takes the form: X2[ry] ⳱ q㛳ry㛳l22 Ⳮ p

2

冩 dn 冩 dry

l2

where q and p are nonnegative continuous weight functions. Then: Lry ⳱ qry ⳮ

冢

d dry p dn dn

冣

Regularization parameter ␣ can be selected from the conditions: qL 2(Hry,l) ⱕ d

where d is the specified error of initial data. The constraint for the norm of derivative in the functional X is an important thing when searching for required distributions. In this case, uniform convergence of regularized solutions, ray (n), to the actual one, ry(n), is ensured at decreasing d—that is, max|ray (n) ⳮ ry(n) → 0| at d → 0 and corresponding decrease of ␣ (␣ can tend to zero not faster than d) (Ref 1). It should be noted

that solving Eq 1 and 3 by reducing them to Euler’s equation provides for transition to a respective self-conjugate operator (H *H or B*B), this resulting in the loss of Volterra property. There are ways of regularization to retain this property (Ref 4), but they are more complex and effort consuming. To construct matrix analogues for operators of Eq 1 to 3, grid quantizing is selected for the area, including a created notch where the grid becomes dense. Kernels of integral operators B(x,n), B⬘x(x,n), and H(s,n) are calculated by solving a set of boundary value problems, with d impacts being reproduced by applying a uniform load ry(n*) ⳱ const in the region of notch edge formed by one or several grid steps, where n* is the center of such region. Elements of kernels B(x,n) and H(x,n) are parameters of the stress-strain state analogous to measured parameters l(x) and l(s), respectively. The kernel B⬘x(x,n) is constructed by B(x,n) values with the aid of respective difference formulae. Solutions of boundary-value problems for two-dimensional elasticity theory can be obtained easily on the basis of software complexes ANSYS, NACTRAN, and the like, which provide high accuracy of results for complex geometric parts with high-stress gradients. Calculation of residual stress on the basis of solved integral Eq 1 and 3 is implemented with the smoothing functional method grounded on programs developed by the authors. Evaluation of Method Accuracy. As an example of residual stress restitution in flat parts, consider results of the numerical experiment based on reducing the problem to the Fredholm integral equation of the first type (Eq 3). Such an experiment aims at demonstrating efficiency of proposed approaches because Eq 3, all other conditions being the same, is less conditioned compared with the Volterra equation of the first type (Eq 1). A square plate with the side 2l0 (Fig. 3), where a thin notch with the length l0 was cut along the axis n, was chosen. Residual stress distribution was specified on edges of this notch, and distribution of the stress state parameter l(s) on the line s parallel to the axis y was found by solving a boundary value problem of elasticity theory (direct problem). Values of tangential stress sny(s) were calculated as l(s) with a bearing on photoelastic coatings. These values were used as exact initial data into which random disturbances were introduced with a normal law of distribution, the level of disturbances comprising about 5% from the maximum values sny(s) over the notch length. The disturbance data were used in residual stress restitution (inverse problem). Solution of direct and inverse problems as well as construction of the matrix analogue for the integral operator of Eq 3 was made on the grid crowded in the vicinity of 0.2l0 notch tip. Figures 3 and 4 present restitution results for two variants in distribution of residual stress with different stress gradients. Solution of direct and inverse problems as well as construction of the matrix analogue for

µ

y s

1.0

l0

∆

x

α 0

0.2

0.6

s/l0

(a) σy 12 8 4

δ 0.6

0.2

x/l0

(b) Problem 1. Determining residual stress by Fredholm integral equation (computation experiment). (a) Initial data. (b) Stress along the notch line: full lines, exact values; dotted line, restituted stress for two variants of random disturbance in initial data

Fig. 3

µ

1.0

α 0

0.2

0.6

s/l0

(a) σy 12 δ

8 4

0.2

0.6

x/l0

(b) Problem 2. Determining residual stress by Fredholm integral equation (computation experiment). (a) Initial data. (b) Stress along the notch line: full lines, exact values; dotted line, restituted stress for two variants of random disturbance in initial data

Fig. 4

128 / Measurement and Prediction of Residual Stress and Distortion the integral operator of Eq 3 was made on the grid crowded in the vicinity of 0.2l0 notch tip. The value of error introduced into initial data corresponds to the most real level of random oscillating irregular component in distribution of sny(s) parameter. The fact is that the distribution sny(s) over the line s, every point of which belongs to the regular zone of the considered region, is an analytical function and determined by solving a problem of elasticity theory. Thus, when processing the experimental data preliminarily, it is necessary to use them for constructing the smoothest analogue of this distribution. All coarse oscillating errors of initial data of the order of 10 to 20% will be eliminated when constructing such analogue. The level of oscillating error in initial data of the order of 3 to 5% is difficult to control, thus making the main disturbance value responsible for the “looseness” of the searched solution. As to the systematic error in the form of smooth component of initial data shift, its influence on the accuracy in solving the inverse problem is less than that of the oscillating component. The presented results illustrate the effectiveness of the regularizing algorithm (2.4) when interpreting the distribution sny(s) containing random disturbance. The maximum deviation of restituted values from exact values does not surpass 10 to 12% relative to maximum values over the notch length, this being quite a satisfactory result at 5% error level of experiment, a figure that corresponds to the actual accuracy of the photoelastic coating method. Numerical analysis demonstrated that the regularization parameter in the scheme (2.4) can be chosen out of the condition min㛳␣dray /d␣㛳 (i.e., it is possible to confine oneself to choosing a quasi-optimal value while solving the problem). Attempts to solve Eq 3 without regularization methods are totally invalid. The disturbance level of obtained solution conditioned by irregular random components in initial data is so high that the obtained solution has nothing in common with the actual one. The considered approaches to solving the problem of residual stress continuous distributions demonstrate that recurring to methods for solving ill-conditioned problems, together with numerical ones for solving boundary-value problems, allows for efficient computational/experimental schemes of investigation, which are free from simplifying assumptions about the nature of searched distributions. An important peculiarity of such approaches lies in the combined use of numerical and experimental methods as the unified system for investigation where the main role is played by the computational experiment. The results presented can be extended to problems of determining spatial distributions of residual stress, difficulty in solving such tasks being caused by a large body of information to be processed, and by two-dimensional integral equations. Some Peculiarities in Applying the Method. Practical application of the approach developed for studies of residual stress includes three principle methodological aspects:

● The process of creating notches—indicators

of residual stress—in the part under investigation ● Methods for obtaining the initial information l(x) or l(s) for subsequent calculation of residual stress ● Selection of procedure to solve equations that link the residual stresses to be found with those experimentally discovered—l(x) and l(s) Processes and methods used in indicator-crack studies of residual stress and presented in the section “Evaluation of Method Accuracy” can be applied as techniques of workpiece notching and methods of obtaining source information for subsequent residual stress calculation. Calculation of residual stress on the basis of solved integral Eq 1 and 3 is implemented with the smoothing functional method grounded on programs developed by the authors of this work.

other, can be established after analytically solving the problem of SIFs in the inner crack (Fig. 5), whose edges experience arbitrarily distributed loads ry ⳱ ⳮry(x) and sxy(x) (Ref 6, 7): x

冮 [ r (n)冪n/冪(x ⳮ n)]dn K (x) ⳱ 2/冪(px) 冮 [ s (n)冪n/冪(x ⳮ n)]dn KI(x) ⳱ 2/冪(px)

y

0

x

II

xy

0

It should be observed that the equations in Eq 4 are Volterra integral equations of the first type with the Abel kernel, this providing for the possibility of their analytical conversion. After applying the Abel operator d dx

x

冮

0

n

冪x ⳮ n 2

[…]dn

to both the right and left sides of the equation, the following is obtained:

Indicator Crack Method

冦冮 d/dx冦冮

ry(x) ⳱ 2(px)ⳮ1/2d/dx

Method of crack as indicator of residual stress can be interpreted as a particular case of the general approach considered in the article “Measurement of Residual Stresses” in this Handbook, which regards the determining of residual stress as an inverse problem of experimental mechanics. In this case, the notch, whose edges feature relieved residual stress, is represented by a mathematical cut (crack), while the parameters of stress state l(x) are represented by distribution of stress-intensity factors for normal breakoff and transverse shear, KI(x) and KII(x). Such statement for some boundary-value problems reduces the main equation of the problem to the Volterra integral equation of the first type, with Abel’s kernel, this providing for their closed analytical solution. As a result, the consistent calculation procedure for computing residual stress from experimental data becomes quite simple. At the same time, the experimental investigation procedure is more effort consuming since, in order to obtain the function of stress-state parameter, values KI and KII must be determined at each step of experimental study. Study of Residual Stress in Inner Regions of Plates. This method is intended for determining locally inhomogeneous fields of residual stress in flat parts. The general outline of the method proposed in Ref 5 that makes it possible to investigate residual stress in inner regions of plates can be summarized as follows. A crack is built up stepwise along the line n 僆 [0,x], which must be determined for residual stress (Fig. 5). At each step in the vicinity of the crack tip, the stress field must be determined, which, in turn, is used to calculate values of stress-intensity factors (SIF) for standard breakoff and transverse shear KI and KII. Connection between residual stresses rx(x) and sxy(x) on the one hand, and relationships KI(x) and KII(x) obtained experimentally on continuously increasing the crack length, on the

(Eq 4)

sxy(x) ⳱ 2(px)ⳮ1/2

x

0

冧 [K (n)冪n/冪(x ⳮ n)]dn冧

[KI(n)冪n/冪(x ⳮ n)]dn

x

II

0

(Eq 5)

These expressions are main-calculated relationships for the built-up crack procedure used to determine residual stresses in the inner regions of homogeneous plates. From Eq 5 follows the correctly set task of calculating residual stress on the basis of experimental data, this fact, in turn, ensuring consistency of obtained results against measurement errors. On the other hand, applying this method requires more effort-consuming experiments as compared with the general method considered in the article “Measurement of Residual Stresses” in this Handbook. It should be noted that in contrast to the methods of successive grinding, the method of builtup crack is applicable for the study of two-dimensional fields of residual stress. Moreover, since the indicator crack is a more intense “stress concentrator” in comparison with the circular hole (let alone the methods that require the part to be cut completely), this provides for its higher susceptibility.

0

y – (x ) σ y

ξ

x –τ (x) xy

x, ξ

Fig. 5

Internal crack in infinity plate

Methods for Determination of Inhomogeneous Residual Stress Fields / 129 Steps at crack buildup can be quite small, thus ensuring the possibility of determining residual stresses in regions of higher gradients. For example, in the investigation described in the section “Residual Stress Investigation Examples,” steps for crack buildup amounted to the value of about 1.0 mm (0.04 in.). If applied, the method of hole drilling would call for 0.1 mm (0.04 in.) bores to determine stress for 1.0 mm (0.04 in.) row pitch, this being practically unfeasible (Ref 8). At the same time, the possibility of applying the correlation in Eq 5 to calculate residual stresses from experimentally found dependencies KI(x) and KII(x) is restricted to determining stress in the inner regions of flat parts. Study of Residual Stress Close to Edges of Piecewise-Homogeneous Plates. The method just described, which is based on Eq 5, is applied only to determine residual stress in the inner regions of homogeneous parts. Yet a number of important practical tasks is connected with the necessity to investigate residual stress in the vicinity of borders. In the first place, here belongs the study of residual stress in bimetallic materials used in power installation shells with corrosion-proof surfacing. During the heating process, the difference in thermal-physical and mechanical properties of base and cladding layers of a bimetal causes plastic compressive strains, which, when parts are cooled down to room temperature, lead to residual stresses. These stresses cannot be relieved by subsequent heat treatment. Another important practical task is the analysis of residual stress in members of structures made of heteromodulus materials. Along with the process manufacturing of a structure member or a two-layer material, another important factor re-

+

0

σy(x, 0) = σ(x, y)

y

E1,v1

h

E1,v2

H

σ–y(x, 0)

sponsible for emergency of residual stress is represented by the difference in elasticity moduli of materials with two-layer composition. In this connection, the research (Ref 9) obtained analytical relationships of Eq 5 type in the event of edge crack in a bimetallic band (Fig. 6). These relationships made it possible to determine stress on crack edges ry(x) and sxy(x) (residual stress) on the basis of known relations KI(x) and KII(x), which correspond to behavior on crack edges x 僆 [0,a] (E1, E2 and l1, l2 represent Young’s moduli and Poisson’s ratios for materials of the first and second layers, respectively). When deriving respective relationships, the solution involving calculation of SIFs for an edge crack in the band whose edges experience arbitrary loads ry ⳱ ⳮry(x) and sxy ⳱ ⳮsxy(x), obtained in Ref 10, was used. If the tip of the indicator crack is in the first layer, the expressions for calculating residual stress are of the following form (Ref 9): KI ⳱ 冪paW1(a) KII ⳱ 冪paW2(a)

a

[W1(u)m1(x,u)]du

0

sxy(x) ⳱ (d/dx)

x

0

[sW2(s)/冪(x 2 ⳮ s 2)]ds

[W2(u)m2(x,u)]du

0

(Eq 8)

Expressions for calculating m1(x,s) and m2(x,s) can be found in the subsection “Calculation formulae for determining residual stress.” For an essentially important case, E1 ⳱ E2, l1 ⳱ l2, and h/H → 0 (edge crack in the homogeneous plate), the following expressions are deduced from Eq 7 and 8:

m(x,u) ⳱

Border crack in bimetallic strip under arbitrary loading on the crack bands

x

冮

x 僆 [0,a] (Eq 7)

a

冮

Ⳮ

x

冮

ry(x) ⳱ (d/dx)

τ+xy(x, 0)

[sW1(s)/冪(x 2 ⳮ s 2)]ds

0

冮

ⳮ

0

[sW1(s)/冪(x 2 ⳮ s 2)]ds

a

冮

ⳮ

Fig. 6

x

冮

ry(x) ⳱ (d/dx)

(Eq 6)

[W1(u)m(x,u)]du

0

冮

0

␣u(1 ⳮ ax)e ⳮaxn(au)d␣ p/2

n(au) ⳱ 2/p

冮

0

(1 ⳮ au sin u)e ⳮau sin udu (Eq 9)

0

+ – σy(x) = σ

y

a/2 a

–3σ 2σ –+(x) = – 25 σ y

Fig. 7 cessing

x

+ –σ–(x) = – σy(x) y

Schematic of the test problem for estimation of procedure accuracy for experimental data pro-

The study described in Ref 9 also obtained relationships for determining residual stress in the case that h a H. Being cumbersome, they are not cited here. At the same time, there is no practical need to apply the solution for cases when the crack tip is in the second layer of bielastic band. Preferable is the investigation procedure based on the processing of two experiments during which the indicator crack is, at first, built up in one layer, then at some distance from the first crack in the second layer (or in analogous specimen).

Evaluation of Method Accuracy. Based on experimentally obtained relationships KI(x) and KII(x), the correctly formulated task for residual stress calculation provides consistency of respective procedures. Various approaches can be used to solve the problem. A simple and reliable way to process experimentally obtained relationships KI(x) and KII(x) on the basis of Eq 5 and 7 to 10 is represented by the following procedure: 1. Experiment results obtained as KIi(xi) and KIIi(xi) values (where xi is the length of the indicator crack corresponding to i-step) were smoothed on the basis of spline approximation. 2. Integrals are computed by the trapezium method—for example, on the basis of the Romberg algorithm. 3. Obtained relations are differentiated—for example, using the modified method of Ridder. When solving problems for residual stress analysis in cases described by Eq 5 and 10, it is possible to realize this procedure of experimental data processing by applying standard program complexes. Following is an example of solving the test task for a piecewise-linear stress field of residual stress close to the border of a homogeneous half plane, the example being considered in the context of evaluating the accuracy in the mentioned procedure of data processing (Fig. 7). In this case, the problem of determining the KI(x) function can be represented as a sum from the solution of three boundary problems: Problem A ry(x) Problem B ry(x) Problem C ry(x) ry(x)

⳱ ⳱ ⳱ ⳱

r 2rx/a 0 ⳮ5r

(0 ⱕ x (0 ⱕ x (0 ⱕ x (a/2 ⱕ

ⱕ a) ⱕ a) ⱕ a/2) x ⱕ a)

KI(x) relationships were plotted on the basis of available analytical solutions for problems A, B, and C (Ref 11, 12). To simulate experiment errors with the aid of a random-number generator, random values K I*(xi) ⳱ KI(xi) Ⳮ DKI(xi) were introduced in i-points uniformly distributed in the range [0,a]. Two cases of uniformly partitioned section [0,a] were considered in doing so: I ⳱ 20 and I ⳱ 40. Range of scatter in values of SIF DKI(xi) comprised 10% of the maximum value KI, this being in agreement with experimental error while determining the factor on the basis of modern techniques (the section “Experimental Methods and Equipment” provides details). Residual stress was calculated in accordance with this procedure. The results are shown in Fig. 8. These data reveal high accuracy of calculation for residual stress ry(x) and consistency of results. Even in the vicinity of point x ⳱ a/2— that is, the zone featuring an abrupt change of stress (an unlikely event in practical tasks)—the difference between exact values and those computed by Eq 9 does not exceed 10%. Outside this zone, the value of the mentioned error does not

130 / Measurement and Prediction of Residual Stress and Distortion exceed 5% of the maximal stress (and 3% from the value of stress leap at point x ⳱ a/2) in both considered cases of the partitioned section 0 ⱕ x ⱕ a. Some Peculiarities in Applying the Method. Practical application of the developed approach to investigation of residual stress comprises three principal methodological aspects: ● Technique for creating the indicator crack,

which would preclude extra stresses in the workpiece and coating ● Methods for determining SIFs at combined loading on the basis of results processed for stress fields, strains, or displacements in the zone of crack tip ● Selection of procedure for solving equations that connect residual stresses to be found with experimentally discovered relationships KI(x) and KII(x). A rectangular cutout made by a 0.2 to 0.5 mm (0.008–0.02 in.) milling cutter can be used as an indicator crack. If the cutout length is much greater than its width, h (h/a ⱕ 0.03), then, on the basis of methods described in the section “Experimental Methods and Equipment,” it is possible to determine quite accurately those SIFs that could develop should a corresponding crack be created. In this case, the source information about the stress-strain state is obtained in the region that excludes the vicinity of cut-out extremity r 3h (r, distance to the cut out “tip”). It might be practical to use a narrow rectangular cutout instead of an indicator crack also because at high levels of residual stress, local secondary plastic strains can develop due to high-stress concentration in the vicinity of the crack tip. If narrow indicator-cutouts are used, the likelihood of developing secondary plastic strains is reduced. It is worth noting that the use of SIFdetermination methods presented in the section “Experimental Methods and Equipment” rules out the impact of local plastic strains in the in-

dicator-crack tip zone on the determining accuracy. On the other hand, presence of local plastic strain to some extent influences the stress-strain state of the object surfaces relieved on object cutting. It is determined experimentally (on the basis of strain field results) whether local plastic strains are present or absent. Each specific case calls for assessment of their impact on residual stress to be found with due consideration to their actual level and peculiarities of the problem solved. Still, it should be pointed out that development of secondary plastic strains is not limited to the method of built-up crack. This phenomenon may well attend any destructive method— for example, in the widely used method of circular hole drilling when, due to stress concentration in the contour zone, there may develop stresses that exceed the yield point of the material under investigation. The problem of determining SIF from processed results of polarization-optical measurements at combined loads is that there is a pronounced experimental error (Ref 8, 14, 15, et al.) in the crack tip zone (Fig. 9), where the stressed state is assumed, from the standpoint of fracture mechanics, to be described by Vestergard’s asymptotic relationships: rij(x,y) ⳱

1

冪2pr

3

兺

KN FN (h)

k⳱1

(i.j ⳱ x,y; N ⳱ I, II, III)

(Eq 10)

This calls for applying data obtained at some distance from the crack tip while determining SIF, and this fact, in turn, requires that not only asymptotic elements be considered, but also regular ones of the full solution for the respective problem of elasticity theory. For the reliable determination of the SIFs KI and KII under combined loading, it is necessary to use the methodology, based on mathematical treatment of a substantial volume of the experi-

mental information (Ref 16–18 et al.). Therefore, for the measurement of strains and displacements fields in the area of the crack indicator, the optical-geometrical methods should be used in the first place, as well as the methods of holographic interferometry and electronic digital speckle interferometry, and also the method of photoelastic coatings (Ref 8). In considering the holographic methods, the scheme of the receiving of real-time hologram (Ref 19) can be used for the receiving of the interferencion pictures. The modern methods for SIF determination under combined loading require only the determination of the function coefficients. This function describes the field of stresses in the crack zone on the basis of the experimental information. The function of stresses in the form of the series can be used for the analytical representation of the field of stresses in the crack zone. The terms of the series are the own functions (William’s functions) of the solution of elastic theory problem for the regions with the wedge cutouts:

U(r,h) ⳱

兺 r n/2Ⳮ1f (h) n⳱1

(Eq 11)

where r,h are the polar coordinates, f (h) ⳱ an{sin[(s ⳮ 1)h] Ⳮ (s ⳮ 1)/(s Ⳮ 1) sin [(s Ⳮ 1)h] Ⳮ bn{cos[(s ⳮ 1)h] ⳮ cos [(s Ⳮ 1)h]}; s ⳱ n/2; and an,bn are the coefficients for the symmetric and antisymmetric components of the function U(r,h) expansion. Notice that KI ⳱ a1冪2p, KII ⳱ ⳮb1冪2p. The finding coefficients an, bn, (n ⳱ 1,2,3 … N) are defined on the basis of the mathematical treatment of the measurement data of the band order smax (the method of photoelastic coatings is using) or the normal displacements, w (the holography method) in i points (i N ). Using the method of photoelastic coatings: the expressions for the stresses have the form: 2smax ⳱ r1 ⳮ r2 ⳱ 冪(rh ⳮ rr)2 Ⳮ 4s r2h

rr ⳮ rh ⳱ 2

sr h ⳱

n

兺 r n/2ⳮ1(an F1n Ⳮ bn F2n) n⳱1 2

n

兺 r n/2ⳮ1(an F3n Ⳮ bn F4n) n⳱1 2

(Eq 12)

where: F1n ⳱ ⳮ(s Ⳮ (s F2n ⳱ ⳮ(s Ⳮ (s F3n ⳱ ⳮ(s Ⳮ (s F4n ⳱ ⳮ(s ⳮ (s

ⳮ ⳮ ⳮ Ⳮ ⳮ ⳮ ⳮ Ⳮ

1) 1) 1) 1) 1) 1) 1) 1)

sin[(s ⳮ 1)h] sin[(s Ⳮ 1)h] cos[(s ⳮ 1)h] cos[(s Ⳮ 1)h] cos[(s ⳮ 1)h] cos[(s Ⳮ 1)h] sin[(s ⳮ 1)h] sin[(s Ⳮ 1)h]

(Eq 13)

and, using the method of holographic interferometry: N

lt r n/2ⳮ12n E n⳱1 {an sin[(s ⳮ 1)h] Ⳮ bn cos[(s ⳮ 1)h]

w⳱ⳮ

Fig. 8

Results of calculation of the test problem. I, number of steps

兺

(Eq 14)

Methods for Determination of Inhomogeneous Residual Stress Fields / 131

G1, µ1

y

G2, µ2 r θ

1

Fig. 9

x

2

Crack with a tip on the boundary of heterogeneous materials

where E is the material’s elastic modulus, l is Poisson’s coefficient, and t is the thickness of the part. Since the local geometry of the crack-tip zone does not correspond to the mathematical slitting, the place of crack-tip position (r ⳱ 0) in certain measure is conditional. In connection with that in Ref 16 and 17, the specification of the cracktip position, corresponding to the experimentally obtained fields of stresses or displacements in the crack zone, was provided. Therefore, the corrections on the crack-tip state (dx,dy) are the finding parameters also as an,bn. That specification also is important because the errors in the determination of the crack-tip state can appreciably influence the finding values of SIFs. If the photoelastic coating method is used, the obtained system of equations is nonlinear, which requires the application of corresponding methods for their solution (for example, the NewtonRaffson’s method). The summary approach is provided to the creation of the analytical solution of the elastic theory task, corresponding to the initial experimental information. In difference of the other approaches to the solution of the determination of the stress-intensity factors task, this method is true in view of the uniqueness of the elastic theory task solution. In Ref 18, on the basis of the numerical tests, the possibility of an application of the given approach to the determination of the SIFs under combined loading in the case of loading of crack banks with the nonhomogeneous stresses changing with the high gradients is discussed. The task about the piecewise-continuous broken field of normal and shear stresses was considered test one; the stresses act on the banks of a crack in an infinite plate. The appeared stress-strain state was defined on the basis of the precise analytical solution of the corresponding task of elastic theory (Ref 7). The values KI and KII were determined using the approach with the displacement field. The results of the investigation show that the relative difference between the precise values of the SIFs and values, based on the mentioned approach, consist of less than 5%. It happens even in the cases in which the point-of-stresses rupture lies in close distance from the crack tip D/a ⱖ 0.05 (D is a point of slitting and a is the crack length).

These results justify the recommendation of the mentioned approach for the determination of the SIFs caused by creation of a crack indicator in the investigated parts. Calculating residual stress from experimentally obtained dependencies KI(x) and KII(x) on the basis or relationships in Eq 5 to 9 does not call for specially developed techniques due to correctness of the problem solved. Both direct numerical methods and standard software complexes can be used for computation. Preference should be given to those procedures that provide for spline approximation of KI(x) and KII(x)— dependencies at the first stage of experimental data processing. Peculiarities in Studying Piecewise-Homogeneous Materials. Equations 6 to 8, used to calculate residual stress from experimentally obtained dependencies KI(x) and KII(x), correspond to the case in which an edge indicator crack is located in a layer of bielastic bands. Hence, it follows that in studies of residual stress, an indicator-crack tip should be at some distance from the boundary between heterogeneous materials. If the crack tip is on the juncture of heterogeneous materials (Fig. 9), then the respective boundary value problem of elasticity theory has an asymptotic solution, different from that for the case of a crack located inhomogeneous milieu. The characteristic equation to determine the degree of k stress singularity, in this case obtained by Zak and Williams, is of the following type (Ref 20): 2(k2 ⳮ k1)(k1 Ⳮ 1) cos kp ⳮ 2k 21 ⳮ 2k1k2 Ⳮ 2k1 ⳮ k2 Ⳮ 1 Ⳮ 4k1(k2 ⳮ k1)(k Ⳮ 1)2 ⳱ 0 (Eq 15)

where k1 ⳱ (G1 /G2 ⳮ 1)/4(1 ⳮ v1) and k2 ⳱ k(1 ⳮ v1)/(1 ⳮ v2); k ⳱ G1 /G2; G1,G2 are shear modules of materials. The k value to be found is the sole real root of Eq 15 in the range (ⳮ1, 0). Thus, stresses in the crack tip have the peculiarity of the r k type, with k being different from k0 ⳱ ⳮ0.5, which corresponds to the case of crack located in the homogeneous material. The following table presents k values calculated on the basis of Eq 10 for l1 ⳱ l2 ⳱ 0.3 and different ratios G1 /G2: G1 /G2 0.2 0.6 1.0 2.0 4.0 6.0 10.0

the juncture D. It is evident that at k* → k at D → 0; k* → k0 ⳱ ⳮ0.5 with growing D. With those considerations, the following procedure for study of residual stress in piecewise homogeneous materials (bielastic band) can be accepted: 1. Two analogous specimens are used in the research. Residual stresses in each layer are determined on separate specimens. If residual stress along the boundary of heterogeneous materials does not change, the study can be made using only one specimen, with the first and second indicator cracks located at the distance that rules out their mutual influence. 2. Dependencies KI(x) and KII(x) in the range 0 ⱕ x h are determined experimentally for each layer. In this case, the SIF-determination methods developed for study of cracks in the homogeneous material are applied. 3. Experimentally obtained dependencies KI(x) and KII(x) for the first and second layers are used to calculate residual stresses ry(x) and sxy(x) in the range 0 ⱕ x h with the aid of Eq 17 to 20 in the following section. 4. Values of residual stress on the boundary between heterogeneous materials are determined by extrapolating the found dependencies ry(x) and sxy(x) to a corresponding locus of the boundary. The specified method excludes the necessity to determine SIF for the case when the crack tip is located either on or close to the boundary between heterogeneous materials. Calculation formulae for determining residual stress in the piecewise-homogeneous (bielastic) band are as follows. If the tip of the indicator crack is in the first layer (a h), the expressions for calculating residual stress are of the following form: KI ⳱ 冪paW1(a) KII ⳱ 冪paW2(a)

ⳮ

As the crack tip nears the boundary of heterogeneous materials, the singularity degree of k* stress changes depending on elastic properties of materials and the distance from the crack tip to

0

[sW1(s)/冪(x2 ⳮ s2)]ds

a

冮

0

[W1(u)m1(x,u)]du

x 僆 [0,a] (Eq 17)

where m1(x,u) ⳱

冮

0

␣u[A1(…)(␣xch ␣x Ⳮ sh ␣x)

Ⳮ A2(…)(2ch ␣x Ⳮ ␣sh ␣x) ⳮ M(␣u)ch ax]da

k ⳮ0.366 ⳮ0.450 ⳮ0.5 ⳮ0.575 ⳮ0.654 ⳮ0.699 ⳮ0.754

x

冮

ry(x) ⳱ (d/dx)

(Eq 16)

Aj (…) ⳱ Aj (␣h, ␣h1, ␣u, k, l1, l2) k ⳱ G1/G2 4

兺 Ai fji ⳱ qj i⳱1

( j ⳱ 1,4)

f11 ⳱ 2(1 ⳮ l1)C2 ⳮ S21 f12 ⳱ (1 ⳮ 2l1)S2 ⳮ C21 f13 ⳱ k[S11 ⳮ 2(1 ⳮ l2)C1] f14 ⳱ k[(1 ⳮ 2l1)S1 ⳮ C11] f21 ⳱ C21 Ⳮ (1 ⳮ 2l1)S2

f22 ⳱ S21 2(1 ⳮ l1)C2

f23 ⳱ k[(1 ⳮ 2l1)S1 Ⳮ C11 f24 ⳱ ⳮk[2(1 ⳮ 2l2)C1 Ⳮ S11]

132 / Measurement and Prediction of Residual Stress and Distortion f31 ⳱ S2 ⳮ C21 f32 ⳱ ⳮS21 f33 ⳱ S1 ⳮ C11 f34 ⳱ S11 f43 ⳱ ⳮf32 f42 ⳱ S2 Ⳮ C21 f43 ⳱ ⳮf34 f44 ⳱ S1 Ⳮ C11 q1 ⳱ Y1 Ⳮ MS2

q2 ⳱ Y2 ⳮ MC2

q3 ⳱ Y3 Ⳮ MC2

q4 ⳱ Y4 ⳮ MS2

Y1 ⳱ [2(1 ⳮ l1)I0(␣u) ⳮ Y4]e ⳮah Y2 ⳱ ⳮ[2(1 ⳮ l1)I0(␣u) Ⳮ Y2]e ⳮah Yq ⳱ (c ⳮ ␣h)I0(␣u) Ⳮ ␣sI1(␣u) M(␣u) ⳱ I0(␣u)ⳮ L0(␣u) Ⳮ ␣u[I1(␣u) ⳮ Lⳮ1(␣u)] Cj ⳱ ch␣uhj Cj1 ⳱ ␣uhjCj Sj ⳱ sh␣uhj Sj1 ⳱ ␣uhjSj Cj ⳱ 1,2 h2 ⳱ h; h1 ⳱ H ⳮ h; q⳱ 3,4 at g ⳱ 3, C ⳱ 1

at g ⳱ 4, C ⳱ 2

Ij ( j ⳱ 0,1) ⳮ modified Bessel functions of the first type Lj ( j ⳱ ⳮ1,0) ⳮ modified Struve functions (Eq 18) sxy(x) ⳱ (d/dx)

x

冮

0

[sW2(s)/冪(x2 ⳮ s2)]ds

a

冮 [W (u)m (x,u)]du m (x,u) ⳱ 冮 au[M(au)ch ax Ⳮ

2

On the basis of the analytical relations between the contour residual stresses and the stresses (or strains, displacements) arising in the specimen, and which can be measured on the cut-out contour, the residual stresses can be determined. The previously mentioned stages of the proposed approach were put to the base of all the rupture methods of the residual stresses measured. However, a main feature of the cutout indicator method consists in the suggestion about arbitrary distribution of the residual stresses on the contour, on which the cut is carried out. General Relations. To define the residual stresses by use of the cut-out indicator method, it is necessary to receive the contour residual stresses by some characteristics of stress-strain state, which were obtained with the help of the experimental methods in some area adjoining the contour of the cutting, without its inclusion. That means the task inverse to the first general boundary problem of the elastic theory is solved. As a basic relation, the Muskhelishvili equation of the elastic theory can be used in the view:

2

0

u(r) Ⳮ x(r)/x⬘(r)u⬘(r) Ⳮ w(r) f1 Ⳮ if2 (Eq 21)

2

0

ⳮ A2(…)(axch ax Ⳮ sh ax) ⳮ A1(…)ax sh ax]da

(Eq 19)

where M(␣u) is determined on the basis of the relationships in Eq 7, while the formulas for Eq 16 and 17 are: ( j ⳱ 1,2,3,4)

d1 ⳱ Y 1* ⳮ MC2 d2 ⳱ Y 2* Ⳮ MS2 d3 ⳱ Y *3 ⳮ MS2

d4 ⳱ ⳮY *4 Ⳮ MC2

Y *1 ⳱ Y *4 ⳮ Y0 Y *2 ⳱ Y *3 ⳮ Y0 Y *4 ⳱ Y0/2(1 ⳮ l1) ⳮ Y3 Y0 ⳱ 2(1 ⳮ l1)I0(␣u)eⳮah Y3 ⳱ [␣hI0(␣u) ⳮ ␣uI1(␣u)]eⳮah

f1 Ⳮ if2 ⳱ i

t

冮

t0

(Xn Ⳮ iYn)dS

(Eq 22)

The expansion into a Fourier series under the mapping onto the circle of plane specimen, bounded by given contour c (Ref 7) can be used for the solution of the first general boundary problem of the elastic theory:

4

兺 A1 fji ⳱ dj i⳱1

on c-loaded contour. Here u and w are the stress functions; x(r) is the function, which conformally maps the contour c on the circle; f1 Ⳮ if2 are the functions of loading on the contour and

(Eq 20)

Arbitrary Cut-Out Indicator Method The cut-out indicator method is based on an application of the boundary equation of elastic theory. The main idea of this experimental-analytical method is that the cut of a plane specimen is made along the fixed contour, out of which arises an additional stress-strain state. This state appears because of stresses releasing along the contour of the cutout. This (additional) field of stresses, strains, and displacements can be measured on the basis of the known interferencialoptical methods (method of optically sensitive coating, methods of holographic, speckle-interferometry, method of electronic digital speckleinterferometry, and so on, Ref 8). The discrete values of strains can be obtained by the other experimental methods (for example, with the help of a small-base gages measurement).

u(f) ⳱

兺0 ak f k

w(f) ⳱

k 兺0 a⬘f k

(Eq 23)

The functions of conformal mapping and loading can be presented in the following form: Ⳮ

x(r)/x⬘(r) ⳱

兺 bkrk

(Eq 24)

ⳮ

Ⳮ

f1 Ⳮ f2 ⳱

兺 Akrk

(Eq 25)

ⳮ

The possible loadings are limited by ones, which can be adequately offered by expansion into a Fourier series. After the transformation, the system of linear equations is obtained: ¯ [C]a¯ ⳱ A

(Eq 26)

where [C] is the matrix of coefficients and a¯ and ¯ are the vectors of expansion coefficients u, w, A and f1 Ⳮ if2. It should be noted that the different functions of the conformal mapping permit the use of the

given relations for an arbitrary cutout (e.g., the infinite plate with arbitrary cutout and arbitrary cutout from the plate with any shape, including the circular hole and the mathematical cutcrack). Experimental Data Treatment. The determination methodology of the internal stresses using the method of round and nonround holes and cutouts requires the experimental definition of functions u and w of Kolosov-Muskhelishvili’s potentials on the basis of relations for the stresses: XX Ⳮ YY ⳱ 2(u⬘(z) Ⳮ u⬘(z)) YY ⳮ XX Ⳮ 2iXY ⳱ 2(z¯u⬙(z) Ⳮ w⬘(z))

(Eq 27)

or for the displacements: 2l(u Ⳮ iv) ⳱ xu(z) ⳮ zu⬘(z) ⳮ w(z)

(Eq 28)

The given functions are searched in the form of corresponding Fourier series, and the task of their determination is reduced to the finding of coefficients under the expansion into series. As initial information, the displacements data u and v in the plane of plate, the normal displacements data (w ⳱ rx Ⳮ ry ⳱ XX Ⳮ YY), the maximum shear stresses data (smax) can be used. If two or more components of stresses, strains, and displacements near the cut-out indicator are known, the treatment and optimization of the data are maximally simplified. If the normal displacements are known, with the help of them and one of Kolosov-Muskhelishvili’s relations, the function u can be obtained. To find the function w, it is necessary to use the data of the other components of displacements. If the experimental determination of all three components of the displacements and their numerical interpolation on cutting contour is possible, then the determination of the contour residual stresses is possible using the relations of displacements and loading functions on the contour. In this case the nonlinear (including plastic) residual stresses can be defined because the given relations are valid for the nonlinear area as well (Ref 7). Evaluation of Method Accuracy. The correctness of the residual stresses calculation on the basis of the experimentally determined fields of displacements, strains, and/or stresses is provided with the use of received analytical relations, which connect the experimental data with the searching values on the cut-out contour. It can be provided also by the possibility of corresponding calculation procedures optimization and the possibility of treating the substantial masses of the experimental information. The different approaches and procedures can be used for the numerical calculations. It should be noted that the given approach is more simple than the general method described in previous sections, and the method of growing cracks, which allow for simple optimization of the calculating procedures used. In Ref 13, on the basis of numerical tests, the precision evaluations of the residual stresses de-

Methods for Determination of Inhomogeneous Residual Stress Fields / 133 termination using the experimental data, obtained by method of holography and optically sensitive coatings (the fields of the normal and tangential displacements, also the difference of stresses), were fulfilled. The task about piecewise-continuous broken field of the residual stresses in infinite plate was considered as a test. The round hole is an indicator of stresses. The arising stress-strain state is defined by means of the precise analytical solution of the corresponding task of an elastic theory (Ref 8). The numerical tests were carried out for the three types of experimental information, characterizing the stress-strain state in the area of circular cutout: sums and differences of stresses, values of normal w and radial u displacements, and values of normal w and tangential v displacements were used. The results confirm the effectiveness of the hole-indicator method for the practical application for the investigations of appreciably nonhomogeneous fields of the residual stresses in plane elements of constructions. Features of Practical Application of the Method. Technology of the creation of cut-out indicators is similar to usual technology, applied for the investigations of the residual stresses by the small circular hole method (Ref 8). Experimental information about the fields of stresses or displacements in the area of holes (cut-outs) indicators is presented in the following section.

Experimental Methods and Equipment It is possible to apply different stress-strainstate parameters determined experimentally in studying stress fields, deformation, and displacement as the source data to examine locally inhomogeneous fields of residual stress. This section presents some problems in obtaining experimental data necessary for determining residual stress on the basis of methods and respective computation procedures whose fundamentals are given in preceding sections. Determining inhomogeneous fields of residual stress within the considered framework requires significant amounts of data be obtained with regard to strain fields or displacements in local sur-

Fig. 10

Outline of photoelastic coating

face zones of investigated objects that develop after a notch is introduced (exception in this case is represented by the Volterra integral equation method described previously). These circumstances prevent one from applying methods of measuring strain state at individual spots, among them the small-base tensiometry (with the use of small gages) widely used in the study of residual stress. In view of the requirements to the scope and accuracy of experimental data needed to analyze residual stress by considered methods, it is possible to conclude that coherent optical methods (holography interferometry, speckle interferometry, etc.), as well as the photoelastic coating method (Ref 8), are most efficient for obtaining experimental data. Photoelastic Coating Method. In terms of equipment employed, the photoelastic coating method (Ref 8, 21) is one of the simplest and most reliable ways to study strain fields on the structure surface under static loads and to investigate stationary interim processes. Once developed, this method has been actively pursued to study residual stress using various techniques that employ workpiece cutting, and in particular, in combination with the circular hole drilling (Ref 8, 22–26, et al.). Still, this method has several peculiarities, and it is subject to associated errors that sometimes can significantly influence the validity of results. Respective problems are considered in studies (Ref 22, 24) where one can find ways to reduce errors or take them into account while applying the photoelastic coating method. Accuracy of strain-stress measurement on the surface of photoelastic coating objects is known to depend on several factors: errors from measurements of optical propagation difference, effect of coating hardness, and uneven thickness of coating and effects of irregular strain distribution over the coating thickness. It was pointed out in some papers that when measurements in stress concentration zones are taken, the most significant among these factors that determine experimental error are represented by the influence of deformation irregularity over the coating thickness due to high gradients of strain measured on the surface of the studied workpiece. M. Akhmetzyanov (Ref 24) suggests that the respective adjustment of optical measurement results for the coating requires that mean deformations be determined separately by coating thickness and second order equations be solved numerically in partial derivatives for the region studied. F. Zandman (Ref 21) recommends repeat experiments with reduced thickness of photoelastic coating, this, on the one hand, significantly extending the range of conducted experiments, yet, on the other, being practically unfeasible while studying residual stress. In keeping with the aforesaid, the following method is proposed for choosing the thickness of photoelastic coating, optimal with regard to obtaining the maximum value of optical effect with an acceptable value of result error. Selecting the Thickness of Photoelastic Coating in the Study of Holes and Notches. The value

of the optical effect in the photoelastic coating is proportional to its thickness (i.e., as the coating thickness grows, the error in optical measurement decreases). On the other hand, the growth in the thickness of photoelastic coating leads to the increase of errors related to the influence of coating hardness and to that of strain being distributed unevenly over the coating thickness. A simulation problem in the study (Ref 21) called for computations whose results allow for the quantitative assessment of aforementioned errors while examining within high gradients of stress, which are always present when methods described in the preceding sections are applied. Such assessment makes it possible to establish the optimal thickness of the optically sensitive coating from the required measurement accuracy with regard to the level of the measured optical effect. The simulation problem is outlined in Fig. 10. It is represented by a two-layer plate with a circular hole, the plate being subjected to the uniform all-directional tension load far enough from the hole. A thin layer with thickness h corresponds to the photoelastic coating, while a thicker layer corresponds to the steel specimen. The change in parameter h/c leads to the change of strain gradient (e1 ⳮ e2)/r at constant thickness of coating. Consideration is given to the parameter change in the range 0 h/c ⱕ 20. Calculations were made for the following mechanical properties of materials: ratio of elasticity moduli E1 /E2 ⳱ 0.015, values of Poisson’s factors l1 ⳱ 0.36; l2 ⳱ 0.3 (for epoxy photoelastic material and steel). The obtained results allow evaluation of the method error that emerges in zones of high gradients of stress and is caused by uneven distribution of strain over the coating thickness, this evaluation being made by comparing difference values of main strains on the studied surface (e1 ⳮ e2)z⳱0 and mean strains over the coating thickness (e1 ⳮ e2)* ⳱ (1/h) h0(e1 ⳮ e2)(z)dz. Main results of calculation are given in Fig. 11 and 12. These results make it possible to lay down domains of relationship for parameters h/c and r/ c where the value of considered error, dmax ⳱ [(e1 ⳮ e2)* ⳮ (e1 ⳮ e2)]/(e1 ⳮ e2), does not exceed the specified value. On the basis of obtained results and in view of known quantitatively evaluated errors conditioned by other previously mentioned factors, the following general conclusions can be drawn and recommendations made as to the application of the elastic coating method when taking measurements in zones of high gradients of stress for steel workpieces studied. If relationships of mechanical properties for materials of studied parts are different from specified ones, it is necessary to obtain estimated values analogous to those implemented. The results also can be used to estimate measurement error on the notch contour at non-axisymmetrical stress distribution as well as for noncircular holes, notches, and fillets. To do this, the value of the maximum gradient of stress in

134 / Measurement and Prediction of Residual Stress and Distortion the measurement zone must be estimated on the basis of available solutions, boundary layer problems of elasticity theory with similar geometry, and types of effective load, or those given directly from experiment data. The value for the radius of “equivalent” hole “c” and parameter h/c then can be determined. It follows from Fig. 11 and 12 that coatings with thickness less than 0.3 of hole radius (h/c 0.3) or fillets provide for high accuracy of measurement. Calculation results demonstrate that in this case, the error dmax does not surpass 5 to 6% on the hole contour and comprises less than 3% at distance 0.15 R from the contour. When optical measurement results are extrapolated to the hole contour—this usually done while processing data from the photoelastic method to rule out “fringe effect” in the optically sensitive material (Ref 21, 24)—the mentioned error will not exceed 2%.

When residual stress is investigated by the standard method of hole drilling, the minimal values of hole radii are commonly assumed to be approximately 3 mm (0.12 in.). Corresponding evaluations show that in this case 1 mm (0.04 in.) coatings should be used to provide for the necessary level of optical effect at sufficiently small deformations. When the arbitrary notch method described in the section “Arbitrary CutOut Indicator Method” is applied, the radius of the hole (indicator of residual stress) is, as a rule, at least 7 to 10 mm (0.28 to 0.4 in.), this enabling 2 to 3 mm (0.08 to 0.12 in.) coatings to be used for measurements. Should the relationships of mechanical properties for the studied object material and photoelastic coating differ significantly from accepted relationships, respective simulation problems have to be calculated to evaluate errors. To this end, it is possible to apply standard software

13 12 11

(e1 ⳮ e2)T ⳱ (1 Ⳮ l)r冪a/r/E冪2

10 δmax, %

8 7 6

(e1 ⳮ e2)0 ⳱ (1 Ⳮ l)2rc 2 /Er 2

5 4 0

0.2

0.3

0.4

0.6 0.8 1.0

2

3

4

5

6 7 8 9 10

h/c

where (e1 ⳮ e2)0 is the difference of main deformations, which was found after solving the problem analytically. Gradients of main deformation difference are determined from the following expression:

Relationship of maximum error dmax on hole contour to the parameter h/c

d(e1 ⳮ e2)0 /dr ⳱ ⳮ(1 Ⳮ l)4rc 2 /Er 3

δmax = 3%

1.0

(r/c – 1)

4%

5% 6% 8%

11% 0

0

1

2

3

4

5

6

7

8

9

10

(h/c)

Fig. 12

(Eq 29)

where (e1 ⳮ e2)T is the difference of main deformations in the crack zone. For the circular hole with radius c in the unlimited size plate under infinite all-directional tension r at r ⳱ c:

9

Fig. 11

r1 ⳮ r2 ⳱ 2KI /冪8pr

For the inner crack with length 2a in the unlimited size plate being stretched and under infinite tension stress r, KI ⳱ r冪pa. With regard to the photoelasticity law for the photoelastic coating method, the following equation is obtained (Ref 1):

14

3

complexes that allow computation of stressstrain state for bielastic parts using the leastsquare method. Selecting the Thickness of Photoelastic Coating while Determining the SIF. Results given in Fig. 11 and 12 can be used to determine the optimal thickness of coating when the indicatorcrack method is applied. This is possible because the recommended technique for determining SIF from measurements made on the coating excludes from consideration the zone closest to the crack tip and makes it possible to reliably determine KI and KII from processed results of measurement in the range r/a ⱖ 0.05/0.1. Stress distribution in the zone of crack tip, which corresponds to an asymptotic solution, takes the following form at h ⳱ p/2:

Domains of relationship for parameters r/c and h/c where value dmax does not exceed the specified value

(Eq 30)

By comparing right sides of Eq 29 and 30, it is possible to determine the radius of hole c at which there are equal gradients of main deformation difference on the hole contour and on the boundary of crack vicinity used as domain of source data when determining SIF (r/a ⱖ 0.05/ 0.1). Corresponding assessments demonstrate that if the vicinity of the crack tip is used for SIF determining (as shown in the following sections), the value r/a ⱖ 0.05, and at r/a ⱖ 0.07, c ⳱ 0.2a. Hence, it follows that at crack length a ⳱ 15 mm (a ⳱ 0.59 in.) it is acceptable to use 1 mm (0.04 in.) coatings if the domain for obtaining source information r/a ⱖ 0.07 is adopted. It should be noted that this result is obtained with allowance made for stress fields in the crack tip vicinity being represented asymptotically; therefore, values of stress gradients in the crack zone actually are overestimated. Optic Interferometry Methods. Considering all types of notches discussed in the three previous main sections, parameters of stress-

Methods for Determination of Inhomogeneous Residual Stress Fields / 135 strain state to be determined in the vicinity of notches (residual stress indicators) can be represented by components of surface displacement field in the object studied, these components appearing after a notch is introduced. The most effective ways to register local changes in the surface form are coherent-optical interference methods. Compared with the photoelastic coating method (Ref 27), these have certain advantages since they provide for measurements directly on the surface under study. It should be noted, however, that the equipment used in this case is much more complex compared with that applied with the photoelastic coating method. The same applies to the experiment technique, including special requirements to notches-indicators in preparing which any displacements of the workpiece as the rigid ensemble should be ruled out. Different approaches aimed at studying residual stress in cut parts by coherence optics have been well developed so far. Various schemes are used to obtain displacement fields after a notch is made: the real-time method, double exposure, and sandwich-hologram method (Ref 29–34). Most of these works, as well as some publications in digests (Ref 25, 26), are dedicated to the study of residual stress employing the hole drilling method; the paper (Ref 28) considers layerwise grinding while the work (Ref 19) considers the method of successive crack buildup. Study of residual stress that employs coherent optics is systematically presented in monographs (Ref 35, 36). The study in Ref 34 is quite distinctive among

6

these publications. This work presents a method that, apart from resolving components of normal displacement, makes it possible to reliably determine and use tangential components of displacements for residual stress evaluation, this fact significantly expanding research potential. With regard to peculiarities of investigating locally inhomogeneous fields of residual stress, the most promising measurement tool seems to be the electronic digital speckle interferometry that combines the known benefits of coherent optical methods (contact-free nature, high-sensitivity, lack of preliminary procedures on the studied object) with efficacy of direct computer presentation, storage, and processing of data (Ref 8, 37). In this context, the design and performance capabilities of the special interferometer developed for research of residual stress is discussed subsequently. The interferometer provides for separate recording of all three components of the displacement vector (Ref 38). It is worth mentioning that a special small-size portable unit was developed from this design to enable research both inside and outside the laboratory. A plane laser beam passes through a glass prism (1) (Fig. 13). In the classical Michelson interferometer, a deflected wave front is used to measure the normal component of the displacement vector W with the aid of a semi-transparent mirror (2) that developed two beams out of the plane wave, these beams lighting both the studied area on the object (3) and the diffusely reflecting base surface (4). Images of resulting speckle structures are focused with the lens (5) onto the charge-coupled device (CCD) (6)

5 4

CCD

z γ

2

8

10

placed in the imaging plane (c), with a digitized signal from the latter being registered in the form of computer files. On passing through holography elements, the beam is transformed into three plane waves, two of which lighten the studied surface by means of mirrors (8) and (9) at 45 angles to the normal in the plane of axis x. The semitransparent mirror (10) transforms the central beam in two waves, which, when reflected from mirrors (11) and (12), illuminate the surface under study at 45 angles to the normal in the plane of axis y. To measure displacements in the object after its notching, well-known optical designs of speckle interferometers sensitive to components can be used in the plane (U and V) and away from the plane (W). Such complex experimental installation actually combines three interferometers, with optical designs for determining U and V being completely identical yet turned by 90 round the normal to the object. Each of the three components in the spatial vector of displacement is determined in arbitrary order and independently from the two remaining ones. Figure 14 shows a plane fragment of the optical design for determining components W and U. To measure the normal component of the displacement vector W, there is a classical Michelson interferometer with the semi transparent mirror (1) that makes two beams out of the plane wave A, these beams illuminating along the normal both the studied region on the object (2) and the diffusely reflecting base surface (3). The tangential component U is determined using the optical design with two inclined beams B and B (with beam A closed) placed in the same plane with the normal. Images of the total speckle structures formed are focused with the lens (4) onto the CCD matrix (5) placed in the imaging plane (c), with digitized signals from the latter being registered in the form of computer files. Deducing image intensity distributions (speckle structures) recorded before and after the object deformation and corresponding to each type of interferometer finally results in the system of interference fringes

12

y 1 7 13

9

11

x

3

Optical design for the special speckle interferometer. 1, glass prism; 2 and 10, semi-transparent mirror; 3, object; 4, reflecting base surface; 5, lens; 6, charge-coupled device; 7, diffracting screen; 8, 9, 11, and 12, mirrors; 13, rotated parallel-sided plate

Fig. 13

Fig. 14

Fragment of optical design for the special speckle-interferometer


Fig. 15

Interference patterns in the zone of hole-indicator. (a) Normal displacement w. (b,c) Tangential displacements u and v

whose orders are connected to values of displacement components by linear relations: x

C

B(x, ε) 1

B

A B

ε

0.5

A D C D

0

0.5

1

Layout of tracking points in the vicinity of notch tip; behavior of the Volterra integral equation kernel at these points

Fig. 16

Fig. 17

Fringe pattern in the photoelastic coating (figures represent fringe order)

w ⳱ kNi/2 u ⳱ kNj/2 cos ␣ w ⳱ kNk/2 cos ␣

(Eq 31)

where k is the wavelength of the emission used; Nl, l ⳱ i,j,k are orders of interference fringes on corresponding speckle interferograms, that is, geometric loci of equal displacement points, normal to the surface (if displacement is determined from the plane) and tangential (inside the plane that contains direction vectors of lighting beams). The speckle interferometer can be applied successfully to study locally inhomogeneous fields of residual stress, as a means of measuring the strain response after a notch is introduced. High sensitivity of speckle interferometry enables one to measure reliably even with small diameter holes (2–3 mm, or 0.08–0.12 in.). To demonstrate interferometer capabilities, Fig. 15 displays typical speckle interference patterns that characterize displacements in the zone of the circular hole indicator with a 2 mm diameter, obtained when studying residual stress in the weld zone. The method allows for values of displacement both on the notch (hole) contour and those at some arbitrary range from it as input data while solving the inverse problem, with no distortion in scale commonly inherent to the cognate method of holographic interferometry. Electron-digital speckle interferometry makes it possible to accumulate data as computer files for comparing different states attendant to the notch-crack length expansion and to the increase of indicator hole size if necessary. It is worth noting that compared with holography interferometry, electron-digital speckle interferometry is about two times more sensitive to tangential components of displacement. Noteworthy, also, is the fact that when electron speckle interferometry is applied, displacement fields are registered directly in digital form, convenient for further mathematical processing of results from experimental procedures considered in previous sections.

Residual Stress Investigations Examples Study of Residual Stress in the Flat Specimen Made of Hull Plate Steel Using the Volterra Integral Equation. Following is an example of determining residual stress in practice, on the basis of the general approach presented in the section “Study of Residual Stress as Inverse Problem of Experimental Mechanics.” A flat specimen cut in a circular direction out of the cylinder-shaped shell of a water-moderated reactor pressure vessel was examined. The base material of the pressure vessel was alloy steel. The shell inner surface was faced with corrosionpreventive cladding 9 mm thick. The calculation procedure is based on applying the Volterra integral equations (Eq 1 and 2). Regular points A, B, C, and D close to angle points and over the symmetry axis (Fig. 16) were selected as typical measurement points when applying these equations. Oriented to measurements made with the elastic coating method, the value smax was used on the symmetry axis as the value to be measured, and the value sxy in the vicinity of angle points. Values B(x,e) obtained close to the notch tip are actually independent from the notch length; that is, B(x,e) B(x ⳮ e), while derivatives with respect to x and e coincide; that is, B⬘x(x,e) B⬘e(x,e). Conditionality of the system of linear equations (Eq 3) depends on the kernel structure determined by a measurement point chosen. To obtain a better conditionality, it is rational to choose a kernel with prevailing elements of the main diagonal that corresponds to the closer vicinity of the notch tip (e.g., point A or B) (see Fig. 16). The method of elastic coating was applied in measurement taking. The 1.8 mm coating of optically sensitive material based on epoxy rosin (Ref 8, 24) was glued over the specimen. The notch on the coated specimen was gradually expanded by 1 mm steps with the 0.5 mm diskmilling cutter. Optical measurements of fringe orders m and isocline parameters u at typical points (Fig. 17) that track the notch tip growth

Methods for Determination of Inhomogeneous Residual Stress Fields / 137 were made with the reflection polariscope “Photolastic Inc.” Figure 17 gives the picture of the typical fringe pattern in the notch tip zone for l ⳱ 7 mm. Figure 18 presents the dependency sA max(x) obtained from processed data of optical measurements as well as the residual stress profile ry(x) calculated using Eq 3. Study of Residual Stress in Bimetal Using the Crack-Indicator Method. As an example of applying the indicator crack method in practice, results from the study of residual stress in a flat specimen taken from bimetallic cylindrical

MPa

y x 7h

h

A

100

τmax(x)

σy(x)

A

τmax, σy, MPa

200

0

x/h

2

1

casings of power installations are presented here. The specimen was cut out of a full-fledged template from the material used in the reactor casing of a nuclear power plant. The cladding (stainless steel 08Cr18Ni10Ti) was applied to the base material of the vessel (low alloy steel 10CrNi1Mo) by explosion welding. Thickness of the cladding layer was 7.5 mm. The manufacturing process for large-scale members from such material envisages butt welding of bimetallic elements. The weld zone was studied for residual stress (Fig. 19). During this study, methods and procedures (way of crack creating, method of determining SIFs, and that of calculating residual stress) described in the section “Indicator Crack Method” were used. To determine values of SIFs in indicator cracks, the photoelastic coating method was used. Figure 20 gives typical fringe patterns that emerge in the zones of edge indicator cracks, these patterns being obtained when investigating the first specimen. Experiment results demonstrate that at all measuring points, KII(xi) values make up less than 7% of KI(xi) values. Hence, it follows that r¯ y(x) s¯ xy(x).

–100 Determining residual stress in the hull plate still specimen with corrosion-preventive facing. Data points indicate optical measurements in the photoelastic coating taken at notch-tracking points, with the notch being expanded stepwise, through 1 m steps

Fig. 18

4

8

42 2

42

Fig. 20

Photograph of fringe patterns in zone of crackindicator tip (crack length is 12 mm)

1 50 40

(a)

30

κr (x)

K I , MPa •

m

20 10 0

2

4

6 8

10

12

100 200 300 400

σ–y(x)

500 σx , MPa

Fig. 19

Drawing of (a) weld zone and (b) photograph of specimen surface

Results of residual stress study in the weld zone of bimetallic material from nuclear power plant reactor casing

Fig. 21

Principal results of the study are given in Fig. 21 as plots of relations KI(x) and residual stress ry(x) for bimetals under consideration. REFERENCES 1. A.N. Tikhonov and V.Y. Arsenin, Solutions to Ill-Posed Problems, V.H. Winston & Sons, Washington, D.C., 1977 2. J.V. Beck, B. Blackwell, and Ch.R. St. Clair, Jr., Ill-Posed Problems of Heat, Wiley Interscience, 1985 3. C.L. Lawson and R.J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ, 1974 4. V.O. Sergeyev, Regularizing the Volterra Equations of the First Type, Proceedings of USSR Academy of Sciences, Vol 282 (No. 3), 1971, p 531–534 (in Russian) 5. A. Vajdanatan and A. Finny, Determination of Residual Stresses from Stress Intensity Factors Measurements, Trans. ASME, Ser. C, 1971, p 131–135 6. G.R. Irvin, Fracture, Handbuch der Physik, Springer (Berlin), Vol 6, 1958, p 551–590 7. N.I. Muskhelishvili, Some Main Problems of Mathematical Theory of Elasticity, Nauka, Moscow, 1966 (in Russian) 8. A.S. Kobayashi, Ed., Handbook on Experimental Mechanics, Vol 2, Prentice-Hall Inc., Englewood Cliffs, NJ, 1988 9. V.D. Kuliev and I.A. Razumovskii, Determination of Residual Stresses in Bimetalls, Sov. Phys. Dokl. RAN (Proceedings of the Russian Academy of Sciences), Vol 315 (No. 1–3), American Institute of Physics, Nov 1990, p 985–987 10. I.F. Obraztcov, V.D. Kuliev, and I.A. Razumovskii, Fracture of Bimetallic Materials with an Edge Crack, Sov. Phys. Dokl. RAN (Proceedings of the Russian Academy of Sciences), Vol 308 (No. 1–3), American Institute of Physics, Sept 1989, p 859–861 11. Y. Murakami, Ed., Stress Intensity Factors Handbook (in 2 volumes), Pergamon Press, 1987 12. V.V. Panasyuk, Ed., Fracture Mechanics and Strength of Material Handbook, Vol 2, Kiev, Naukova Dumka, 1988, p 619 (in Russian) 13. M.V. Medvedev and I.A. Razumovsky, Methods for Studying Locally Nonuniform Fields of Residual Stresses by Cutting the Parts, J. Mach. Manuf. Reliab. (Russia), No. 5, 1998, p 70–76 14. G.W. Smith, Use of Photoelasticity in Fracture Mechanics, Experimental Evaluation of Stress Intensity Factors, Mech. Fracture, Vol 7, G. Sih, Ed., The Haughe, 1981, p 163–189 15. H.P. Rossmanith and R. Chona, Survey of Recent Development in Evaluation Stress Intensity Factors from Isochromatic Crack Tip Patterns, Proc. Int. Conf. Fracture Mech. ICEM (Cannes), 1981, p 348–354 16. R.J. Sanford and J.W. Dally, A General


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Method for Determining Mixed-Mode Stress Intensity Factors from Isochromatic Fringe Patterns, Eng. Fract. Mech., Vol 11, 1978, p 621–633 N.A. Makhutov and I.A. Razumovsky, Determination of Stress Intensity Factors for Three-Dimensional Cracked Parts by Use of Polarization Optic Methods/Testing Equipment for Experimental Investigations of Mechanical Properties of Material and Structures, Proc. Second Intern. Conf. (Moscow), 1989, Vol 2, IMEKO, p 5–13 I.A. Razumovsky and M.V. Medvedev, Procedure of SIF Determination from the Patterns of Normal Displacement, Proc. Intern. Society for Optical Eng., International Society for Optical Engineering, Vol 2791, 1995, p 129–133 N.A. Makhutov, V.J. Kulijev, I.A. Razumovsky, and N.S. Cherpakova, Experimental Analytical Method for Investigating of Local-Inhomogeneous Residual Stresses with the Use of Edge Crack as Indicator, Proc. Intern. Society for Optical Eng., International Society for Optical Engineering, Vol 2791, 1995, p 115–118 A. Zak and M. Williams, Crack Point Stress Singularities at Bimaterial Interface, J. Appl. Mech. (Trans. ASME), Vol 30 (No. 1), 1963, p 142–143 F. Zandman, S. Redner, and J.W. Dally, “Photoelastic Coatings,” SESA monograph, No. 3, p 373 F. Zandman, Photoelastic Coatings Technique for Determination Stresses Distribution in Welded Structures, Weld. J., Vol 39 (No. 5), 1960, p 23–29 M. Nisida and H. Tacabayashi, “Thickness

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Effects in ‘Hole Method’ and Application of Method to Residual Stress Measurement,” Handbook on Experimental Mechanics, Vol 2, A.S. Kobayashi, Ed., Prentice-Hall, Inc., 1988 A.Y. Alexandrov and M.Kh. Akhmetzyanov, Polarization-Optical Methods for Mechanics of Strained Solids, Nauka, Moscow, 1973, p 572 (in Russian) Residual Stress and Methods of Control, Proc. of All-Union Symposium (Moscow), Institute of Mechanics, USSR Academy of Sciences, 1982, p 278 (in Russian) Residual Technological Stress, Proc. of the Second All-Union Symposium (Moscow), Institute of Mechanics, USSR Academy of Sciences, 1985, p 240 (in Russian) I.A. Razumovsky, Photoelastic-Coating Technique for Study of Zones with Large Stress Gradients, Sov. Mach. Sci., Academy of Sciences of the USSR, No. 2, 1984, p 80– 84 V.G. Seleznev, A.N. Archipov, and T.V. Ibragimov, Holography Interferometry in Residual-Stress Determination, Ind. Lab. (Russia), translated from Russian original, (c/b Consultants Bureau New York and London), Vol 42 (No. 6), 1976, p 976–984 B.S. Kasatkin, A.B. Kudrin, and L.M. Lobanov, Experimental Methods for Deformation and Stresses Research, Kiev, Naukova Dumka, 1988, p 359 (in Russian) L.M. Lobanov, B.S. Kasatkin, V.A. Pivtorak, and S.G. Andrrushenko, Determination of Residual Stresses by Holographic Interferometry Using One Hologram, Sov. Phys. Dokl. RAN (Proceedings of the Russian Academy of Sciences), Vol 271 (No. 1–3),

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Yule, American Institute of Physics, 1983, p 555–556 A.A. Rassokha, Technique Residual Stress Investigation by Holographic and Speckle Interferometry, Probl. Prochn., 163, 1983, p 111–115 (in Russian) D. Nelson and J. McCrickerd, ResidualStress Determination through Combined Use of Holographic Interferometry and Blind-Hole Drilling, Exp. Mech., 26, 1986, p 371–378 L. Wang and J. Ke., The Measurement of Residual Stress by Sandwich Holographic Interferometry, Opt. Lasers Eng., No. 9, 1988, p 111–119 V.S. Pisarev, V.P. Shepinov, and A.Yu. Shikanov, Reflectance Hologram Application of Interferometers to Determine Residual Stress by Probing Hole Method, J. Theoretical Phys., Vol 66 (No. 1), 1966, p 99– 113 (in Russian) Y.I. Ostrovskii, V.P. Shchepinov, and Yu.I. Yakovlev, Holographic Interferometry in Experimental Mechanics, Springer Series in Optical Sciences, Vol 60, Springer-Verlag (Berlin), Heilberg, 1991, p 248 V.P. Shchepinov and V.S. Pisarev, Strain and Stress Analysis by Holographic and Speckle Interferometry, Chichester: John Wiley & Sons, 1996, p 496 R. Jones and C. Wykes, Holographic and Speckle Interferometry, Cambridge University Press, 1984 A.A. Apalkov, I.N. Odintzev, and I.A. Razumovsky, Application of Speckle Interferometry for Residual Stress Measurement, Ind. Lab. (Russia), translated from Russian original, (c/b Consultants Bureau New York and London), Vol 66, 2000



Residual Stress in the Forming of Materials Z. Wang and B. Gong, University of Toronto, Canada

ALL METAL PRODUCTS, except casting components, are subjected at some point in their manufacturing process to at least one metalworking or metal forming operation. Such operations can be very diverse, but all have the same primary objective: to produce a desired shape change. Several different operations may often be necessary; for example, a specific steel chosen to make tubes for manufacturing golf clubs is first hot forged, rolled, extruded into tubular shape, and then cold drawn with specific dies into final shape, apart from all the subsidiary treatment. Metal forming can be further divided into hot forming and cold forming. This article addresses cold forming and its resultant residual stresses. Cold forming (working) is defined as a forming process or plastic deformation operation carried out at temperatures below the recrystallization temperature of the workpiece material, but more often it is simply referred to as the forming process at room or ambient temperature. The most commonly used cold forming operations (drawing, extrusion, rolling, and forging, deep drawing, and pressing) are briefly discussed below. Drawing. Large quantities of metal or alloy products such as rods, tubes, and wires with various special sections are finished by the cold drawing process. Bars. Large bars, up to 150 mm (6 in.) in diameter or sometimes more, are frequently given a light sizing pass, reducing the diameter by about 1.5 mm (1⁄16 in.) to improve surface finish and dimensional tolerance (Ref 1). Light reductions are also made in the production of brightdrawing angles, channels, and strips. Many of the smaller-sized round bars, however, are drawn with much greater reductions of area, even up to 50% per pass. The general configuration of dies for rod and wire drawing is shown schematically in Fig. 1. A theoretical approach can be used to predict the maximum reduction of area possible in a single pass. In drawing round bars, for instance, the limiting reduction would be as high as about 63% (Ref 1). Wires are usually drawn through a large number of dies before reaching the final size, and may be reannealed several times as drawing proceeds. For wire drawing of high-carbon steel

(⬃0.5 to 0.8 wt% C), for example, six or more dies are needed. Power-driven capstans are provided between each die and the one ahead of it. Final drawing speed often reaches 7.5 m/s (1,500 ft/min). Dies are often made of tungsten carbide. The reduction at each die in a range of ⬃5 to 30% is determined by the size of the current die and also the preceding one, and can be altered by changing one of the dies. The deformation in wire drawing is not uniform, causing nonuniform hardness distribution along the radius direction. This phenomenon is particularly severe in the last couple of dies. The higher the die angle, the more severe the phenomenon (Ref 2). The total reduction after sequential passes could be more than 90%, allowing the tensile strength of the final wires to be doubled compared with that of the as-received rods (Ref 3). Tubes. Most tubes are made by hot extrusion to hollows, followed by one or multiple drawing passes at room temperature. Several major cold drawing processes are used for the production of tubes, as shown diagrammatically in Fig. 2. In the first three processes (Fig. 2a-c), the major part of deformation is the reduction of wall thickness. But it is also possible for the diameter to be reduced, accompanied usually by a small increase in wall thickness, by sinking the tube without internal support (Fig. 2d). The heaviest reduction in tube size may be reached with a moving mandrel, because the friction at the inner surface can also carry a portion of the drawing load. Most tube drawing with a mandrel or plug involves some reduction in internal diameter, if only an initial clearance in the bore is allowed. Extrusion. In this process a cylinder or billet of metal is forced through an orifice by means of a ram so that the elongated and extruded metal has a transverse shape that coincides with the die orifice. Cold extrusions are usually with the final forming processes. Low- and medium-carbon steels, low-alloy steels, and stainless steels are the common materials that can be cold extruded. In cold extrusion, a punch applies pressure to the slug or preform, causing the work metal to flow in the required direction (Fig. 3). The relative motion between punch and die is obtained by attaching

either one (almost always the die) to the stationary bed and the other to the reciprocating ram. The pressure can be applied rapidly by a sharp blow, as in a crank press or header (impact extrusion), or more slowly by a squeezing action, as in a hydraulic press. Rolling is a process in which the thickness of the material is reduced by passing between a pair of revolving rollers, which are generally cylindrical in shape for producing flat products such as sheets or strip. Their surfaces can also be grooved or textured in order to change the profile as well as the emboss pattern of the products. Specifically, cold rolling is carried out for special purposes such as the production of good surface finish or special mechanical properties. According to statistics, more materials are rolled for further manufacturing applications than are treated by all other processes. Forging, Deep Drawing, and Pressing. Forging compresses metal between a hammer and an anvil or in a pair of dies. Large-size materials such as castings and ingots are usually forged at high temperatures at which the yield strength is reduced as far as possible. Cold forging, often combined with cold extrusion, is mainly used for smaller-size stock. Deep drawing is an extension of pressing in that the metal blank is given a substantial third dimension after flowing through a die (Fig. 4). Simple pressing is carried out by loading a blank between a punch and a

Fig. 1

Schematic of a converging die for rod and wire drawing

142 / Residual Stress Formation in the Shaping of Materials die so as to indent the blank and give the product a measure of rigidity. Can ends in food and beverage containers are the most widespread examples. Advantages. Overall, metal forming processes such as extrusion, drawing, rolling, and forging offer many advantages compared with other production engineering methods. The de-

formation is carried out at constant volume with no loss of material in the form of chips. In the case of cold forming, a more favorable grain flow and dislocation structure are achieved, which could enhance mechanical strength and fatigue strength significantly. In particular, forming can improve the dimensional accuracy and surface finish of metal.

Residual Stress in Metal Forming When a metal is being plastically deformed, internal stresses frequently are created due primarily to deformation incompatibility—that is, the different strain levels experienced in different locations at the same time. This difference in the actual strain level in different locations may be caused by multiple reasons, including (1) a difference in strength between different but coexistent phases in the material, (2) different actual strains accommodated at different locations due to die/mold shape or constraints from the gripping force on the testpiece or workpiece, and (3) a possible temperature gradient in different locations. These internal stresses may remain in materials after the deformation/forming processes in the form of residual stresses. The most typical and simple example of the effect of residual stresses on materials behavior is the Bauschinger effect, a behavior reflecting

Fig. 4

Fig. 2

Tube elongation by drawing with internal support by (a) mandrel, (b) plug, (c) floating plug, and (d) without internal support by sinking

Generation of residual stress in sheet bending. (a) Geometry of a bent sheet. (b) Stress-strain relationship. (c) Distribution of residual stress through thickness

Fig. 5

Fig. 3

Schematic of deep drawing

Schematic of forward extrusion

Residual Stress in the Forming of Materials / 143 the effect of reversing the direction of straining in a testpiece. If a metal specimen is plastically deformed first in one direction—e.g., in tension—the yield stress measured in the reversed loading—i.e., in compression—is generally lower than that measured in tension. Similarly, an initial plastic compression produces a tensile yield stress lower than the original compression yield stress. Such an effect is due, in part, to the internal stresses—known as residual stresses— developed during the initial deformation. In general, residual stresses can be defined as the selfequilibrating internal stresses existing in a free body that has no external forces or constraints on its boundary (Ref 4). As mentioned above, these stresses arise from the elastic response of the material to an inhomogeneous distribution of nonelastic strains. Residual stresses are usually subdivided into macrostresses and microstresses, according to the distances over which they show significant variation. The former vary continuously or smoothly over distances of the order of the dimensions of the body, and the latter show marked variations in pattern and magnitude over distances of the order of the dimensions of microstructural elements such as grains and particles. Both types result from inhomogeneous deformation caused by external forces. Note that in this article, residual stresses produced in cold forming processes are mainly referred to as macrostresses. It is generally realized that the shape of the deformation zone, which is the region undergoing plastic flow in the material, exerts a strong influence upon the magnitude and distribution of residual stresses. Deformation zone geometry for forming processes such as drawing, extrusion, and rolling can be characterized by a single parameter, D, defined as the ratio of the mean thickness or diameter, h, of the work metal to the contact length between tool and work metal: D⳱

h L

Bending with superimposed tension. With sufficient tension, the neutral axis moves out of the sheet so that the strain is tensile across the entire section (a). With the stress-strain curve shown in (b), the stress distribution in (c) results. After removal of the moment, elastic unloading leaves very minor residual stresses, as shown in (d). Source: Ref 5

Fig. 6

(Eq 1)

For drawing or extrusion, according to Fig. 1, the contact length, L, is equal to (h0 ⳮ h1)/(2sin␣) and the mean thickness or diameter, h, is equal to (h0 Ⳮ h1)/2. Thus, D ⳱ [(h0 Ⳮ h1) sin␣]/(h0 ⳮ h1)

(Eq 2)

For axisymmetrical drawing, where h is the diameter, the reduction is given by r ⳱ (d 20 ⳮ d 2f )/d 20. Hence, D⳱

sin ␣(1 Ⳮ (1 ⳮ r)1/2)2 r

(Eq 3)

Similarly, one can demonstrate that for flat rolling, D⳱

(2 ⳮ r)(h0 /rR)1/2 r

(Eq 4)

In the formulas for drawing and extrusion, D increases with decreasing reduction and increasing

Fig. 7

Residual stresses in lightly drawn steel rods. Source: Ref 5

144 / Residual Stress Formation in the Shaping of Materials die angle; in the case of rolling, it increases with ratio of the strip thickness to the roller radius (Ref 5). Nearly all cold-formed products contain residual stresses. In most cases, these residual stresses are undesirable because they often lower the elastic limit of the material and may cause warpage during subsequent machining operations. The usual pattern of residual stresses with the surface in tension are particularly undesirable. Once a product with such a residual stress state is put in service under a certain external load, the nominal applied stress would then be superimposed onto these residual stresses of tension sense on the surface and in the subsurface. Hence, the real stress on the surface and in the subsurface would become higher than the nominal applied stress leading to a significant reduction in fatigue life of the product. Furthermore, even if without such a superposition of stresses, surface residual stresses alone would increase the susceptibility to stress corrosion. In practice, these residual stresses can be eliminated by heat treatment such as annealing or stress relieving. However, these treatments are costly and time consuming because of the extra operation; more importantly, heat treatment may considerably soften the work-hardened materials. From the point of view of forming, on the other hand, it is possible to reduce the residual stress or even to produce “useful” residual stress by optimizing forming parameters to control the deformation zone. Furthermore, for some processes, an additional deformation can also reduce residual stresses significantly. This will be discussed in later sections on wire drawing. Nevertheless, it is of utmost importance to understand the distribution and magnitude of residual stresses in cold forming products. There are usually two major approaches to the study of residual stresses: direct experimental measurements and theoretical simulations. Experimental approaches such as hole-drilling, x-ray, and neutron diffraction methods usually give reliable and even straightforward results. However, hole drilling requires destructive testing, and the latter two methods are expensive and time consuming. In recent years, the finite-element method (FEM) has received considerable attention and has proved a powerful tool for the analysis of metal forming processes, including residual stress analysis. In the following section, the generation of residual stress due to inhomogeneous deformation is illustrated by a few simple examples. Residual stress distributions studied either experimentally or theoretically in workpieces under various cold forming processes are presented and discussed in detail.

can be readily demonstrated by the example of the plastic bending of a piece of sheet. Figure 5(a) represents a sheet bent in the manner shown, where the subject sheet is assumed to be composed of many contact thin layers stacked along

the thickness direction. The stress is a maximum in tension at the upper surface of the sheet, layer 5. It decreases to zero at the neutral layer 0 and increases to a maximum in compression at the lower surface. If the stress does not exceed the

Fig. 8

Influence of area reduction on residual stresses after drawing with one die. Source: Ref 6

Fig. 9

Residual stresses after drawing with different area reduction in the second die. Source: Ref 6

Residual Stresses in Specific Cold Forming Processes Bending of Sheet The development of a system of internal stress as the result of inhomogeneous plastic straining

Residual Stress in the Forming of Materials / 145 yield strength of the materials at any point, removal of the applied bending force will permit the sheet to return to its original shape and thus no internal stress can remain. If, however, the maximum stress exceeds that for yielding, then the layers will extend or be compressed by an amount that depends on the extent to which the yield stress is exceeded. This amount is greatest at the surfaces and decreases in the layers nearer the neutral axis. While the bending load is still applied, the stress distribution across the thickness of the sheet will be as represented by Fig. 5(b), with layers 2 to 5 being on the plastic portion and layer 1 on the elastic portion of the stress-strain curve in tension. If the bending moment is now released, the beam will spring back toward its original flat profile, but not entirely, since this would require the complete reversal of both elastic and plastic strain. As a matter of fact, the amount of springback will be very different along the thickness direction of the sheet because of different plastic deformation. Suppose layer 5 is isolated from layer 4; in this case, the unloading process of the layer will follow the dashed line of point 5 in Fig. 5(b). Considering the interaction of layer 5 with layer 4, the unloading path of point 5 is actually along the solid line, since layer 4 has less plastic deformation or displacement than layer 5 and thus tends to resist the plastic extension of layer 5. As a result, layer 5 feels compression; the compression stress level would be DeE, where De is the residual strain shown in Fig. 5(b) and E is the Young’s modulus of the material. For layer 4, the situation is a bit complicated as layer 3 will resist the extension of layer 4, but layer 5 promotes the extension. The combined result will produce less compression residual strain. It is predictable that at a certain layer, these two influencing factors will become balanced, resulting in zero residual stress (strain) state, as shown by layer 3 in Fig. 5(b). Likewise, layers below the zero residual stress layer, such as layers 2 and 1, could feel extension. The overall pattern of the residual stress distribution is shown in Fig. 5(c). Two important points should be noted here: First, for equilibrium, the effect of tension must be balanced by that of compression; second, the surface that originally plastically extended finally remains in compression, while that which was plastically compressed is left in tension. This analysis can also be applied to the development of residual macrostresses in workpieces inhomogeneously deformed/formed by other processing methods. For instance, rolling sheet with insufficient camber produces material with thin edges, so that, since lateral spread is relatively difficult, the edges must be elongated in the direction of rolling by a greater amount than the central fibers of the sheet. The longitudinal residual stress should therefore be compressive near the edges, with the central fibers in balancing tension. A somewhat similar residual stress distribution—compressive at the surface and tension in the central regions—may be ex-

pected in cold-drawn rods due to the greater elongation in the surface layers when compared with those near the center. In reality, the problem is much more complex than what is presented above. Residual stresses are rarely unidirectional, and the inhomogeneity of the deformation usually produces a bi- or triaxial stress system. Springback in the case of sheet bending would not only create severe residual stresses but also cause problems in tool design. Fortunately, this kind of problem often can be avoided. Taking stretch forming as an example, the tooling does not apply a pure bending moment as assumed above. Rather, tension is applied simultaneously with bending. With increasing tensile forces, the neutral plane shifts toward the inside of the bend, and in most operations this tension is sufficient to move the neutral plane completely out of the sheet so that the entire cross section yields in tension. For such a case, the strain and stress distributions are shown in Fig. 6, leaving very minor residual stresses.

Drawing of Wire, Rod, and Tube The nature of residual stresses introduced by drawing strongly depends upon the shape of the deformation zone (D parameter), as discussed previously. With D-values equal to 1 or lower (i.e., with high reduction and small die angle), the flow pattern of the materials or the deformation is relatively uniform and the residual stresses created are minor. In general, as D is increased to values above unity, the surface of the product wire is left in residual tension (axial

Fig. 10

direction stress) and the center in compression. The magnitude of the residual stresses usually increases with increasing D. However, the typical pattern of residual stresses may be completely different if D is very large—that is, if the reduction is so small that the actual deformation zone does not penetrate to a considerable depth of the wire interior. In that case, the surface can be left in residual compression, as shown in Fig. 7 for lightly drawn steel rods (Ref 5). The residual stress in cold-drawn steel rods and wires can now be well described by using FEM verified by experimental measurements (Ref 6, 7). Specifically, residual stresses in single-pass drawing have been found to be not only dependent on the reduction in area and die angle, but also affected by a light deformation through an additional die immediately after the preceding one. As an example, Fig. 8 shows the influence of the value of area reduction (eA), after drawing with one single die, on the four components of the residual stress—namely, axial, radial, tangential, and equivalent stresses. Parameters and conditions for this analysis are as follows: Material Die angle Final rod diameter Area reduction

CK15 steel 2␣ ⳱ 25⬚ d1 ⳱ 15mm eA

Take eA ⳱ 18% as an example. Under this condition, the axial residual stress in the core section is in the compression condition, while residual stress in tension can be seen in the sur-

Residual stresses after drawing, with three different distances between the two dies. Source: Ref 6

146 / Residual Stress Formation in the Shaping of Materials face region. A lower reduction (eA ⳱ 10%) results in a higher residual stress on the surface, but a lower one in the core. Along the radial direction, all residual stresses are in the compression condition, being highest at the core and close to zero at the surface. Figure 9 shows the influence of the area reduction in a second die on the residual stress distribution. The area reduction in the first die is 10%, the distance between the two dies is 5 mm (0.02 in.), and the die angle is 2␣ ⳱ 25⬚. The small deformation of only eA2 ⳱ ⬃0.6 to 1% in the second die results in an effective reduction in stress levels, especially for axial and equivalent residual stresses. Figure 10 demonstrates the influence of distance between the main die and the second die (5, 13, and 21 mm, or 0.2, 0.5, and 0.8 in., respectively) on the residual stresses for an initial wire diameter of 16 mm (0.6 in.). The area reductions in the first and the second dies are both constant (eA1 ⳱ 10% and 1%, respectively). The stress distributions for the two inter-die distances, 13 and 21 mm (0.5 and 0.8 in.), are very similar. However, the equivalent residual stress for the 5 mm (0.2 in.) distance is much lower. This is because the plastic deformation zones in these two dies are connected due to the small distance between the two dies, and thus the inhomogeneous deformation pattern produced by

the primary die is not only affected but also controlled completely by the secondary die (Ref 6). The residual stress pattern in multistage colddrawn steel wire is quite similar to that of singledie drawing. Figure 11 shows the distribution of longitudinal residual stresses in 1H18N9 wire, a high-chromium, high-nickel alloy steel, from center to surface (Ref 8). Chemical composition of the steel is similar to that for 300 series stainless steels according to the SAE specification (0.12% C, 9.0% Ni, 2.0% Mn, 0.3% Mo, 18.0% Cr, 0.3% W, 0.15% V). The 1H18N9 steel wire was drawn through six or eight passes from 2.0 to 1.0 mm (0.08 to 0.04 in.), with a total reduction in area of 75%. The tensile strength after drawing is 1540 MPa (220 ksi), and the yield stress is about 1380 MPa (200 ksi). Residual stresses, measured using the electrolytic etching method, were very high (close to the yield stress) both at the wire surface and in the interior. To relieve these high residual stresses, two destressing operations were tried: multiroll straightening and additional light deformation drawing (3.8%). Figure 11 also shows the influence of these two methods. It is apparent that additional light drawing can significantly reduce residual stresses. The pattern of residual stresses in cold-drawn tubes, on the other hand, seems sensitive only to the area reduction. Figure 12 shows axial and tangential residual stresses at the outer surface of tubes before and after cold drawing (Ref 9). The tubing was made from ferritic steel (DIN St 35) with an initial outer diameter of 28 mm (1.1

in.) and a wall thickness of about 3.5 to 4 mm (0.14 to 0.16 in.). The tool used for drawing consisted of a die and a mandrel (see Fig. 2a). The reduction in area is represented by a nature strain, defined as u ⳱ ln(A0 /A1), where A0 and A1 are the initial and final cross-sectional areas, respectively. Residual stresses were measured using the x-ray technique and calculated from the {200} and {211} reflections. Before deformation, the residual stress state at the outer surface is compressive and of rotational symmetry. As a result of the plastic processing during cold drawing (u ⳱ 0.23), both the axial and tangential residual stresses shift toward the tensile direction. With further increasing in values of u, they are reduced in both directions. When u ⳱ 0.34, even compressive stresses, although small in magnitude, occur.

Extrusion and Rolling Similar to the case of the drawing process, residual stresses produced by extrusion and rolling processes are strongly dependent on deformation zone shape. Figure 13 compares residual stresses created by open-die extrusion without ejection and by the single-die drawing process, and shows very similar patterns and magnitudes of residual stresses upon the same amount of forming ratio. If the extrusion is rapid enough, temperature gradients caused by inhomogeneous deformation may cause an added effect upon subsequent cooling. Nevertheless, this is not the major cause of residual stresses (Ref 5). The ef-

Influence of destressing in multiroll straightening and additional drawing (3.8%) on the distribution of longitudinal residual stresses in 1H18N9 steel wire. Deformation, 75% (six passes). Source: Ref 8

Fig. 11

Fig. 12

Residual stresses at the outer surface of the tubes. Source: Ref 9

Fig. 13

Comparison between residual stresses after open-die extrusion without ejection and after drawing with one die. Source: Ref 6

Residual Stress in the Forming of Materials / 147 fect of die angle, reduction in area, and deformation zone parameter D on surface residual stresses in extruded steel rods is shown in Fig. 14. The numbers marked in the figure are the axial residual stress values on the surface in kg/ mm2, and the solid lines represent the constant D-lines. Apparently, higher die angles and lower extrusion rates produce higher residual stresses. The residual stress pattern within the kernel of the cold extruded rods, on the other hand, seems dependent only on area reduction (Ref 9). Residual stresses at the surface of rolled strip are shown in Fig. 15 (Ref 5). The residual stresses are normalized by the yield strength in the figure, and the abscissa is D2. With the increase of D, residual stress goes up and could even reach the yield stress of the material. High residual stresses, coupled with damage at the centerline, can result in spontaneous splitting or “alligatoring” of the work material as the material leaves the deformation zone (Ref 5). This type of failure is most likely in early breakdown rolling of ingots because the section thickness is usually large relative to the roll diameter, while the reduction per pass is low. Furthermore, the ingot structure will not have benefited from prior deformation.

Residual Stresses in Cold-Formed Steel Members Steel elements (members) produced by cold forming are a valuable alternative to hot-rolled sections. They offer weight savings because of their wall thinness, as well as a greater variety of shapes. The cold forming processes commonly used for steel members are rolling and press braking. The latter is a procedure in which sheet metal is bent to a desired angle. Rolling, used mainly for large-section series because it is continuous, increases both yield strength and ultimate strength. Press braking is economical for a limited series of section, the length of which is restricted by the length of the press machine itself. As a typical example, the distribution of residual stresses in steel members formed by press braking and rolling methods, respectively, are shown in Fig. 16(a) and (b) (Ref 10). Tensile strength for the rolled steel member is 480 MPa (70 ksi) and for the press-braked member is 350 MPa (50 ksi). At the top of Fig. 16 are geometric locations for residual stress measurement, which was performed using electric discharge machining (EDM). It should be noted that a measured negative residual strain corresponds to a tension residual stress, and a measured positive residual

strain corresponds to a compression residual stress. The figure provides following information: 1. Compression residual stresses (positive residual strain) were found on the inside surface of the sections, and tension residual stresses (negative residual strain) were found on the outside surface. 2. The magnitudes of the surface residual stresses of the sections ranged between ap-

Fig. 17

Residual stresses in a sunk tube of mild steel. Source: Ref 11

Fig. 18

Residual stresses at the middle height of a cup wall. Source: Ref 11

Fig. 14 Effect of die angle and reduction on residual stresses in extruded steel rods. Numbers are the axial residual stress on the surface in kg/mm2, and the constant D-lines are calculated from Eq 4. A0 and A1 are the initial and final cross-sectional areas, respectively. Source: Ref 5

Residual stresses at the surface of rolled strip. The residual stresses are normalized by the yield strength, and the abscissa is D2. Source: Ref 5

Fig. 15

Fig. 16

Residual strain. (a) Press braking. (b) Rolling. Source: Ref 10

148 / Residual Stress Formation in the Shaping of Materials proximately 25 and 70% of the yield stress of the material. 3. The magnitudes of the residual stresses on the flat portions of the section were found to be approximately uniform along the section perimeter. 4. The magnitudes of the residual stresses on the corner regions were higher than those on the flat portions—up to 30% of the yield stress of the material. 5. At the same location, the magnitudes of the residual stresses on the inside and outside surfaces of the flat portions of the section were quite close. The fact that residual stress in the corner regions was higher than in the flat portions is understandable, since more and nonuniform cold work was introduced in the corner regions. Thus, the yield stress at corners increased, which in turn increased residual stress. The residual stress pattern and magnitudes in cold-formed steel members are quite different from those in hot-rolled shapes, where the maximum residual stress is about 30% of the yield stress of the material and the residual stresses are assumed to be uniformly distributed throughout the plate thickness. Therefore, the direct application of the design standard for flexural buckling strength of cold-formed steel columns used

Table 1 Original tube Die

Lubricant Drawing speed

in the AISI specification (1986) would not be appropriate, because this standard was based on the residual stresses measured in hot-rolled steel shapes (Ref 10).

Residual Stresses in Deep-Drawn Cups, Sunk Tubes, and Radial Forging Products

Condition

0.15% C steel; outside diam, 30 mm (1.2 in.), wall thickness, 1 mm (0.04 in.) Die hold diam, 24 mm; half-die angle, 20⬚; die profile radius at the exit, 20 mm (0.08 in.) Machine oil mixed with MoS2 1 m/min (3.3 ft/min)

Fig. 20

Residual stress distribution on the outer surface of the workpiece. Source: Ref 12

Fig. 21

Residual stress distribution on the inner surface of the workpiece. Source: Ref 12

Fig. 22

Residual stress distribution with respect to thickness. Source: Ref 12

Deep drawing conditions

Parameter

Value

Die throat diam Punch diam Blank diam Blank holding force Die profile radius Punch profile radius Blank thickness Maximum punch load

Table 3 ditions

Schematic of the dies used in a radial forging machine. Source: Ref 12

Tube sinking conditions

Element/parameter

Table 2

Fig. 19

66.4 mm (2.6 in.) 64.0 mm (2.5 in.) 120 mm (4.7 in.) 5 tons 3 mm (0.12 in.) 3 mm (0.12 in.) 1 mm (0.04 in.) 9 tons

Forging geometry and process con-

Geometry

Workpiece geometry Outside radius Inside radius Mandrel radius Outside radius of forged tube Reduction in area Die configuration Length of die land Die inlet angle Process conditions Friction Friction Contact stiffness

Value

33 mm (1.3 in.) 7.94 mm (0.31 in.) 7.94 mm (0.31 in.) 30 mm (1.2 in.) 18.3% 12.7 mm (0.5 in.) 6⬚ Rigid Coulomb friction 0.05 4.0 ⳯ 106 N mmⳮ2

The residual stresses in deep-drawn cups and sunk tubes are related to season cracking phenomena that occur in cylindrical products. The cracks usually appear in the longitudinal direction. Therefore, the cause of cracking must be circumferential residual stress or hoop stress in the tube walls. The residual stresses in these kinds of products are considered to be caused by the axial unbending of the wall at the die exit (see Fig. 4). To demonstrate the relation, Fig. 17 shows the residual stress distribution through the wall thickness of a sunk, low-carbon steel (0.15% C) tube (Ref 11). The tube sinking conditions are listed in Table 1. The yield stress of the sunk tube is 570 MPa (80 ksi). The circles and squares in the figure are measured residual stresses obtained using the Sach’s method. The solid and dashed lines are from numerical analysis, and r* 1 and r* t represent residual stresses in the longitudinal and circumferential directions, respectively. The experimental and theoretical methods give a very close result. The residual stress pattern and magnitude are very similar in the longitudinal and circumferential directions. At the inner surface, the residual stress in compression is rather severe, while at the outer surface it is relatively lower in tension. The residual stress distribution in a colddrawn cup is similar to that in the sunk tube case. Figure 18 plots the residual stress distribution at the middle height of a cold-drawn cup of mild steel (0.23% C); the corresponding deep drawing conditions are given in Table 2. The notations in the figure have the same meaning as those in Fig. 17 (Ref 11). Radial forging is a cost-effective and materialsaving forming process for reducing the cross sections of rods, tubes, and shafts. The advan-

Residual Stress in the Forming of Materials / 149 tages of radial forging are smooth surface finish, considerable material or weight saving, preferred fiber structure, minimum notch effect, and increased material strength. Components processed by radial forging generally have higher residual stresses and thus undergo some deflections after forging. The residual stress distribution in high-strength metal is of great importance since its presence, if above a particular level, can shorten the service life of critical components used under severe conditions. A hollow shaft is an example of a common machine element manufactured by radial forging. A radial forging die is shown schematically in Fig. 19. The residual stress distribution in a steel tube (MIL-S-1195) produced by cold forging has been simulated using a three-dimensional FEM model (Ref 12). The forging geometry and parameters are listed in Table 3. Figures 20 and 21, respectively, show the stress distributions at the outer and the inner surfaces along the axial direction, from which it can be seen that the outer surface was dominated by tensile residual stresses with maximum value at the rear part of the workpiece. The axial stresses experienced a minimum (ⳮ48 MPa, or ⳮ7 ksi) at

the front part of the workpiece and increased along the axial direction to the maximum stress (300 MPa, or 45 ksi) at the rear part of the workpiece. However, the inner-surface stresses consisted mostly of compressive residual stresses, with only small tensile stresses at the front part of the workpiece. Figure 22 shows the residual stresses as a function of workpiece thickness. The axial stresses varied greatly between the inner and outer surfaces, but the radial and hoop stresses did not change significantly with thickness. The maximum tensile stress occurred at the outer surface of the workpiece along the axial direction. REFERENCES 1. G.W. Rowe, Principles of Industrial Metalworking Processes, Edward Arnold Ltd., London, 1977 2. E.P. Riley-Gledhill, Recent Development in Wire Making, Steel Times, Vol 214 (No. 1), 1986, p 12, 14 3. B. Gong and Z. Wang, “Investigation of Cold-Drawing Process—Mechanical Prop-

4. 5. 6. 7.

8. 9. 10. 11. 12.

erty Relationship of High C Steel Wires,” unpublished technical report, University of Toronto T. Mura, Micro-Mechanics of Defects in Solids, Martinus Nihoff, The Hague, 1982 W.F. Hosford and R.M. Caddell, Metal Forming, Prentice Hall, 1993 J. Gerhardt and A.E. Tekkaya, Advanced Technology of Plasticity, Vol II, SpringerVerlag, 1987, p 841 J. Gerhardt and A.E. Tekkaya, in Residual Stress in Science and Technology, E. Macherauch and V. Hauk, Ed., DGM Informationsgesellschaft, 1987, p 875 A. Skolyszewski, J. Luksza, and M. Packo, J. Mater. Process. Technol., Vol 60, 1996, p 155–160 C. Genzel, W. Wreimers, R. Malek, and K. Pohlandt, Mater. Sci. Eng., Vol 205A, 1996, p 79–90 C.C. Weng and T. Pekoz, J. Struct. Eng., Vol 116, 1990, p 1611–1625 K. Saito and Y. Shimahashi, in Metal Forming Plasticity Symposium, H. Lippman, Ed., Springer-Verlag, 1979 D.Y. Jang and J.H. Liou, J. Mater. Process. Technol., Vol 74, 1998, p 74–82



The Effect of Final Shaping Prior to Heat Treatment T. Ericsson, Linko¨ping University, Sweden

Final Shaping Processes Grinding is a chip-forming machining method. Many similarities when it comes to residual stress creation exist between grinding, milling, turning, and planing (Ref 1). The creation of residual stresses by grinding has been treated in many studies, (Ref 1–7). The cutting

energy used in the machining process results in temperature increase and plastic deformation. Three factors that can cause residual stresses can be distinguished: ● Plastic deformation involving a smearing of

the material in the plane of the surface tends to give compressive residual stresses. ● Temperature increase that momentarily causes an expansion, which is constrained by the bulk material. The resulting thermal stresses may exceed the yield stress at the actual temperature and, therefore, the surface material will be upset. During the subsequent cooling, tensile residual stresses are created. ● If the workpiece is made of hardenable steel, martensite may form due to the rapid heating and cooling, causing compressive residual stresses. The total resulting residual stress depends on the balance between these three factors (Fig. 1). The residual stress is given as a function of grinding power, but it could equally well have been described as machining power. The higher the grinding power, the more dominant the tensile residual stress contribution rthermal due to factor 2 will be. For the highest powers, martensitic hardening may occur, shifting the residual stress in the compressive direction. The residual stress creation during grinding has been modeled mathematically (Ref 4, 7). Important parameters are the cutting speed; the depth of cut and the feed rate, which results in cutting forces; the mechanical properties of the workpiece; and the heat conductivity of the grinding wheel and the workpiece. The importance of the latter is well illustrated when comparing the residual stresses after grinding with an alumina wheel and cubic boron nitride (CBN) wheel, respectively. The much better heat conductivity in the CBN wheel causes less temperature increase and, hence, more compressive residual stresses (Ref 4). Examples of residual stress depth profiles are given in Fig. 2 for a 0.45% C steel in two heat treatment conditions and in Fig. 3 for the steel AISI 1055. Typically, the affected depth is relatively shallow, usually considerably less than

100 lm. The magnitude depends on the material and grinding conditions. In principle it should be less than the yield strength of the affected material. For AISI 5100, values between 600 MPa (87 ksi) in tension and compression have been reported (Ref 9). Milling. In contrast to grinding, there is a well-defined cutting geometry in milling. Similar to grinding, a particular tool is not continuously in action. Down-cut milling, up-cut milling, and face-milling are distinguishable (Fig. 4). In all cases the residual stresses are due to the balance between the three factors mentioned previously. The mechanical process usually is divided into chip formation and smearing of the workpiece surface. Chip formation (i.e., metal separation) tends to give tensile residual stresses while smearing (i.e., plastic deformation) of the surface tends to give compressive ones. Most of the generated heat is stored in the chip and is removed from the workpiece. Factor 2, the tem-

+

σtherm Residual stress

FINAL SHAPING OF PARTS, including operations such as grinding, cutting, milling, turning, drilling, and processes such as shot peening and blasting, involves local plastic deformation. This means that they invariably are accompanied by residual stress formation. The residual stress can be compressive or tensile and at times even have large shear components. The primary concern regarding residual stresses has been the effect on the mechanical properties— in particular, fatigue, contact fatigue, wear, and stress-corrosion cracking (SCC). However, the presence of residual stresses also means the presence of elastic deformation, although usually on a very small scale. If this deformation is included in the final shape, distortion may result if the residual stresses are released by, for instance, heat treatment. The degree of distortion depends on the magnitude and geometric extension of the residual stresses. A highly stressed but thin surface layer is less disturbing than the presence of a large zone with smaller residual stresses. Therefore, it is also important to consider residual stresses from preceding operations such as straightening. This article first discusses the mechanism for residual stress formation due to the most important final shaping operations and typical examples of residual stress distributions. This is an area that is fairly well understood and for which mathematical models for calculating the residual stress are becoming available. Next, the effect on shape of relaxing the residual stresses, a less-studied topic, is discussed. Only for applications with extreme requirements of shape precision has this been done. Examples based on published work about bearing rings and turbine blades are presented. Recent experimental studies of straightening of bars also are reviewed.

0 σres σmech – a

b

c

d

Grinding power Contributions to the residual stress after grinding as a function of the grinding power. rtherm is the thermoelastic part, rmech is the mechanical part, and rres is the total residual stress. In region a, only elastic deformation occurs; in region b, thermoplastic deformation; in region c, thermoplastic plus thermomechanical deformation; and in region d, rehardening occurs. Source: Ref 2

Fig. 1

The Effect of Final Shaping Prior to Heat Treatment / 151 400

Residual stress, N/mm2

200

0

–200 Ck 45 Surface ground with CBN as-quenched 700 HV10 To the grinding Parallel direction Transverse

–400

–600

Quenched and tempered 420 HV10

–1000

To the grinding direction

Parallel Transverse

–800

0

25

50

75

100

125

150

Distance from surface, µm

Fig. 2

Residual stress distributions in the longitudinal and transverse directions after CBN grinding of steel SAE 1045 (Ck 45) in two heat treatment conditions: as-quenched and quenched and tempered. Source: Ref 5

perature effect, is favored in down-cut milling and face milling with inclined cutting axis and factor 1, the smearing effect, in up-cut milling and face milling with perpendicular axis (Ref 1). The depth of the affected layer is usually thicker than in grinding. Typical examples are shown in Fig. 5(a) and (b) for down-cut milling and upcut milling of recrystallized 0.45% C steel.

Stress grinding direction, MPa

500 Neutron X-ray

400 300 200 100 0 –100 –100

0

100

200 300 Depth, µm

400

500

Stress cross direction, MPa

500 Neutron X-ray

400 300 200 100 0 –100 –100

0

100

200 300 Depth, µm

400

500

The residual stress distributions in the longitudinal and transverse directions after grinding of steel AISI 1055 using grinding wheel speed 40 m/s and depth 3.8 lm. Both neutron and x-ray diffraction were used. Source: Ref 8

Fig. 3

Turning. A difference between milling and turning is that the tool is in continuous cut in turning. In turning, tensile stresses often are found near the surface, and compressive stresses appear deeper into the material (Fig. 6). The stress distribution is affected by friction in the cutting process, which tends to cause tensile stresses in the surface near layer and by plastic deformation, which causes compressive stresses in the deeper layers. Figure 7 shows the residual stress distribution after face grooving (turning) a cylindrical bar of the nickel-base alloy IN718 (Ref 10). The affected depth after turning is larger than after grinding; up to about 200 lm can be found after turning. Computer models have been developed for turning (Ref 11). Shot Peening. The primary objective of shot peening is not to shape the material but to strengthen it. In shot peening, shots made of steel, ceramics, glass, or other materials are thrown on the steel surface by an air jet or centrifugal forces. It results in a plastic deformation of the surface, which gives rise to residual compressive stresses. Depending on the size (diameter), hardness, density, and speed of the shots; the hardness of the workpiece; and the coverage of the surface by shots, the magnitude and depth distribution of the residual stress will vary. The process is well understood, and fairly accurate methods are used to calculate the residual stress by FEA (finite-element analysis) (Ref 12–15). However, it is more instructive to give a qualitative explanation based on Fig. 8 (Ref 16). The residual stress field is caused by two parallel processes. One process is the formation of a Hertzian pressure due to the vertical forces connected with the impacts of spherical shot balls. As indicated on the left side of Fig. 8, the resulting shear stress has a maximum at a certain depth. If the pressure is high enough, plastic elongation will occur and, therefore, compressive residual stresses will be produced. The other

process is a direct plastic deformation of the surface as indicated on the right side of Fig. 8. Thus, plastic elongation of the surface layers occurs. The former effect is more pronounced for a hard workpiece material, and the latter for a soft one. A few examples of residual stress profiles are shown in Fig. 9(a) and (b). It is obvious that the depth of the affected layer increases with the radius and speed of the shot balls. Depths approximately equal to the ball diameter have been reported in steel. The magnitude of the stresses is less than the yield stress. Work hardening can cause the residual stresses to exceed the yield stress of the unpeened material. The largest compressive residual stresses can be achieved by strain peening when the workpiece is strained in tension during the peening. Shot peening also causes shape changes, which can be considerable for thin sections. This effect is used in a manufacturing process known as peen forming in the aeronautical industry. It also is used to monitor the shot-peening intensity by help of so-called Almen strips. The bending of standardized steel strips then is measured. Pressure rolling is another mechanical strengthening process with some similarities to shot peening. It usually is applied to workpieces with cylindrical symmetry. A roll is pressed against the workpiece to obtain high-compressive residual stresses. Very deep affected zones can be obtained, more than 1 mm (0.04 in.) (Fig. 10). Straightening of bars, tubes, and plates often is carried out to meet the requirements of straightness tolerances. The methods for straightening are described in Ref 17 and 18. Examples include stretching, pressing, rolling, peening, heating, or other deformation methods. These procedures involve plastic deformation in local areas of the part and bring about the generation of residual stresses and sometimes work hardening of the steel. Figure 11 illustrates how after bending partially into the plastic regime, residual stresses are generated due to elastic recovery. During subsequent machining and/or heat treatment, the residual stresses can become released and cause distortions. Normally, the plastic deformation goes fairly deep into the material. The most common straightening methods depend on bending and usually are carried out in several small steps, either by pressing or rolling. Stretching of bars and shapes is less frequent because it is difficult to get the same productivity as for bending (Ref 19). However, stretching is attractive because it introduces less residual stresses than bending does. For strips, a combination of bending and stretching frequently is applied.

Distortion after Final Shaping After this survey of residual stress effects caused by important final shaping operations, distortion, which can arise during subsequent heat treatment if the residual stresses relax completely or partially, should be considered. The

152 / Residual Stress Formation in the Shaping of Materials thickness of the surface layer with residual stress and the magnitude of the stresses are then decisive. To estimate if any noticeable effect is to be expected, Stoney’s formula (Ref 20) can be used.

This formula permits calculation of the bending of a strip due to a surface layer with a coating with residual stress. It is in analogy with the Almen strips:

Face-milling

Residual stress

Down-cut milling

Cutting axis perpendicular

Up-cut milling

Cutting axis perpendicular

冤6 1 ⳮ m • h

r⳱ⳮ

1

h2sub

E

•

film

冥

1 R

where r is the stress in the surface layer, E is the elastic constant, m is the Poisson constant, hsub is the thickness of the substrate, hfilm is the thickness of the surface layer, and R is the radius of curvature of the strip. For the present application, it is of interest to calculate the “bending out” d of a strip of length 2l (Fig. 12). It is similar to the bending of an Almen strip used to measure the shot-peening intensity. For small d it holds that: d • 2R ⳱ ᐉ2

+

+

+ σr′′ σr′′

⊥

σr –

σr′′

⊥

–

d ⳱ ⊥

σr

⊥

σr

σr

–

–

Distance from surface

Fig. 4

Characteristic residual stress distributions in steels due to different milling processes. Longitudinal (solid line) and transverse (dashed line) residual stresses are shown. Source: Ref 1

400

400

200 Longitudinal 0 Transverse 200 400 0

Fig. 5

SAE1045, normalized

Up-cut milling



SAE1045, normalized

0.02 0.04 0.06 Distance from the surface, mm

Down-cut milling 200 Longitudinal 0 Transverse 200 400 0

0.08

0.02 0.04 0.06 Distance from the surface, mm

0.08

Residual stress distributions in longitudinal and transverse directions after up-cut milling (left) and down-cut milling (right). Source: Ref 1

800

Residual stress, N/mm2

f = 0.18 mm/r

f = 0.36 mm/r

f = 0.71 mm/r

400

σr′′

σr′′

σr′′

0 ⊥

400 0

0.1

⊥

σr

⊥

σr

0.2

0.3

0

0.1

σr 0.2

0.3

0

0.1

0.2

0.3

Distance from the surface, mm

Fig. 6

(Eq 2)

Inserting Eq 2 into Eq 1:

+

σr

(Eq 1)

Residual stresses in the parallel (solid line) and transverse (dashed line) directions caused by turning of SAE 1045 for different cutting feeds. The cutting speed is 90 m/s and no cooling. Source: Ref 1

3(1 ⳮ m) ᐉ E hsub

2

冢冣

• r • hfilm

(Eq 3)

The important quantity when comparing the effect of different manufacturing processes, is the product r • hfilm. The stress, r, cannot exceed the yield stress of the workpiece material. In principle, it should be considered that work hardening in the affected layer could increase the stress value. It is also obvious that the thickness of the workpiece has a strong effect because d depends on the inverse square of the substrate thickness, hsub. According to this analysis, grinding should be the least risky operation to cause distortion and straightening, shot peening, and pressure rolling the most risky, with milling and turning in-between. Shot peening, however, rarely is followed by heat treatment because the beneficial effect against fatigue or SCC may be lost due to residual stress relaxation. Some careful studies about distortion due to prior final shaping are reviewed next. Experimental and computational studies of distortion of some components have been performed. Bearing rings are an example of a product that is extremely sensitive to distortion and for which distortion-related costs can be very high. It is the background to some very careful studies about the origin of distortions (Ref 21–23). Reference 21 points out that one source of distortion is the presence of uneven residual stresses that have been generated and stored in the material during the manufacturing route. Although the rings are perfectly round after turning or cold rolling, they will become distorted during heating to the austenitizing temperature due to the release of the residual stresses. This is exemplified in Fig. 13, which shows the residual stress variation around a ring made of SAE 52100 and the yield stress at different temperatures. At room temperature no plastic deformation due to the residual stresses is expected, but at 600 C (1112 F) it will occur at certain positions, causing out-of-roundness. In another example, rings were manufactured from cold-rolled, straightened, and peeled tubes.

The Effect of Final Shaping Prior to Heat Treatment / 153 The cut-off rings were distorted and the measurement of ovality of a series of parted-off rings showed that the ovality followed the helix movement of the manufacturing operation of the tube (Fig. 14). In a further study, seven tube-manufacturing routes were investigated regarding their ovality of rings after soft annealing and after hardening. Residual stresses were measured at the outer surface of each ring at three different

locations spaced 120 apart. Figure 15 shows depth profiles of residual stresses in the best case and the worst case. It is evident that the residual stress is much smaller in the best case, and that the deviation in residual stress between the three locations in the worst case is considerable. The depth of residual-stressed layer is around 400 lm in this case. When the standard deviation of ovality after hardening is plotted versus the range of

measured residual stress, a clear correlation is found (Fig. 16). It is also pointed out by the authors that there is a clear difference between cold-rolled and hot-rolled tubes, probably due to the different hardnesses, which could be regarded as the potential for storing uneven residual stress. In a further study, an attempt was made to discriminate between the influence of the manu0

1000

200 Residual stress N/mm2

800 Radial Tangential

600


400 200

400 600 800

1000

0 200

1200 0

400

0.5

0

20

40

60

80

100

120

160

140

Residual stresses in the radial (transverse) and tangential (longitudinal) directions caused by face grooving of IN 718. The cutting speed is 1200 m/s and the feed, 0.5 mm/revolution. Source: Ref 10

Hertzian pressure as a consequence of the vertical forces connected with the impact of shot balls

a

Stretching of a surface layer as a consequence of surface hammering

Residual stress N/mm2

0

Distance from the surface, µm

200 400 600 800

1000 1200 0

a po

Elastic deformation of surface

Unpeened Shot velocity = 23 m/s Shot velocity = 81 m/s

Coverage = 100% – Shot diameter d = 0.6 mm


0.5

Influence of shot-peening parameters on residual stress distributions. (a) Shot diam 0.3 mm and 0.6 mm. (b) Shot velocity 23 m/s and 81 m/s. Source: Ref 16

Fig. 9

Plastically extended layer

y τH

σy′

0.47 a

200

z

z

Residual stress

Residual stress

0

0

Residual stress, N/mm

εpl

σz′

Tangential 400

Axial 600 37CrS4 800 0

Fig. 8


200

800

Fig. 7

Shot velocity = 53 m/s Coverage = 100%

400

600

1000

Shot diameter d = 0.3 mm Shot diameter d = 0.6 mm

z

z

Effect is possible with a soft shot and a hard workpiece

Effect is marked with a hard shot and a hard workpiece

Schematic illustration of the formation of residual stresses as a consequence of two different processes in shot peening: Hertzian pressure and direct stretching of the surface. Source: Ref 16


1.0

Residual stress distributions in tangential (rolling direction) and axial directions in a pressure-rolled round bar with 20.7 mm diam made of SAE 5132 (37CrS4) steel. The x-axis shows the distance from the surface in mm. Source: Ref 9

Fig. 10

154 / Residual Stress Formation in the Shaping of Materials facturing route and the heat treatment. An intermediate normalizing treatment was carried out, and the rings were measured after soft annealing, normalizing, and hardening. Figure 17 shows the shares of the out-of-roundness as influenced by the different steps. For both, the average and the maximum out-of-roundness the share for the hardening process itself is relatively small. The authors comment that normalizing or tempering just below Acm gives a good possibility to demonstrate the effect of residual stresses present in the components before hardening. It should also be pointed out that the out-of-roundness measured after soft annealing probably is not due to machining residual stresses, but to straightening or cold rolling before the actual machining, which can introduce much deeper residual stress layers. Part of these stresses were mechanically released when material was removed. This part is further analyzed in the following section. Modeling and Measurement of the Effect of Bending. The effect of the residual stresses generated during plastic deformation of tubes before machining and heat treatment to bearing rings

Fig. 13

Influence of the temperature on the yield strength on the occurrence of plastic deformations during heating of rings from hot-rolled tubes of SAE 52100, soft annealed condition. Source: Ref 21

Reference line 250 rings measured in total

DH

H

2

8

6

4

10

Compression Tension 1 B C

3

9

7

5

10 9

A

8 7 6 5 4

Ss

Sy

Ring No.

3 2

The principal stress distribution in a rectangular bar during loading to plastic yielding to the depth, DH (curve A); the elastic recovery (curve B); and the resulting residual stress (curve C)

Fig. 11

1

Fig. 14

Changes in the orientation of the maximum ovality in relation to a reference line of rings parted-off from a cold-rolled tube of SAE 52100. Source: Ref 21

300

300 2l

hsub

R

200

100

0° 120°

0 240° 100 200

0

200 Distance from surface, µm

Fig. 12

The bending of a strip due to a thin surface layer with the residual stress r

Fig. 15

Worst case Tangential residual stress, MPa

hfilm

Tangential residual stress, MPa

d

Best case

400

200 240° 100 120° 0 0° 100 200

0

200

400

Distance from surface, µm

Tangential residual stress distributions under the surface in soft machined rings from different manufacturing routes. Source: Ref 21

The Effect of Final Shaping Prior to Heat Treatment / 155 has been studied by computer modeling and experiments (Ref 23). The heat treatment was soft annealing because it was undesirable to add quenching stresses. All experiments and simulations were performed for the bearing steel SAE 52100. Three-point bending was performed on 490 mm (19 in.) long tubes with 81 mm (3.2 in.) outer and 65 mm (2.5 in.) inner diameter. The tubes were placed on two fixed supports of 1300 mm (51 in.) radius and bent with a punch of the same radius. Rings of 77 mm (3 in.) outer and 66 mm (2.6 in.) inner diameter and 15 mm (0.6 in.) height were produced by turning. The rings were soft annealed under controlled heating to 820 C (1508 F) and slowly cooled. The total cycle time was 20 h. The computer simulation was carried out using the finite element modeling (FEM) code ABAQUS in combination with a heat treatment simulation code DistSIMR. To model the bending, an elastic-plastic model with isotropic hardening and von Mises flow criterion was used. The material removal was divided into four steps. First was the cutting of a tube section to be turned; the second and third steps were the turning of the inside and outside of the tube, respectively; and the fourth, cutting of the ring by

removing all the material not belonging to the ring. In the simulation of the soft annealing, no phase transformations needed to be included. Most of the plastic deformation during heat treatment takes place at high temperature, and a creep model was used to describe this deformation. The simulation of the turning occurs in four steps. First, a short section is cut from the tube and distortion is calculated from the elastic spring back. Next, the inside is turned, and it is assumed to produce a circular shape that is later distorted when the elastic stresses are equilibrated. After that the outside is turned and the springback is limited. Finally, the ring is cut from the tube. This step releases substantial constraints from the ring and the shape becomes strongly distorted. During the turning, one end of the ring is constrained, simulating chucking. There, the calculated distortion is smaller than at the other end. In the course of the subsequent soft annealing, the remaining residual stresses are relieved and some additional out-of-roundness distortion occurs. In Fig. 18 calculated distortions are shown for the outer ring profile at three positions after turning from bent tube and after soft annealing. The positions correspond to 5, 10, and 16 mm (0.2,

0.4, and 0.6 in.) from the midpoint of the bent tube. As expected, the section nearest the center has the largest out-of-roundness. In Fig. 19 the measured out-of-roundness distortion expressed as the peak-to-valley radius variation is compared for five rings with the calculated distortion. The agreement is good. It should also be pointed out that the distortion of a ring made from an undeformed tube was very small. Two conclusions can be drawn from these results. First, substantial out-of-roundness can be generated from the internal stresses. Second, the distortion caused by the soft annealing is relatively small compared with the distortion due to the mechanical release of residual stresses. Although this study treats bending of a straight tube, the general conclusions are valid for straightening of a bent tube. An effect of the condition of the heat treatment equipment was also noticed in the first study about bearing rings cited previously (Ref 21). A furnace characterized as the “best in class” gave only about half the ovality as a standard furnace. Important factors are uneven heating and/or poor support. Preheating rings prior to the introduction into the austenitizing furnace has been reported to be beneficial if considerable

Standard deviation ovality (after hardening), µm

70 Cold rolled peeled, straightened Calculated outer profile at top

Cold rolled, ground SAE 52100

60

After turning

Cold rolled, straightened

Cold rolled peeled

50

50 µm

After turning and soft annealing

Calculated outer profile at center After turning

Calculated outer profile at bottom

50 µm

After turning


50 µm


Cold rolled, as-rolled Hot rolled, peeled

40 Hot rolled, as-rolled 30 50

150 200 100 Range of measured residual stress, MPa

Fig. 18

Correlations between the residual stress ranges in tubes and the standard deviation of the ovality of rings after hardening. Source: Ref 21

Calculated accumulated distortion of the outer ring profile at three positions. The distortion is given after turning from bent tube and after soft annealing. Source: Ref 23

Fig. 16

SAE 52100, rings turned from bent tube Outer radius, peak/valley

SAE 52100, rings turned from bent tube Inner radius, peak/valley

Stress relaxation during normalizing 40.0%

Maximum (total: 126 µm)

Soft machining 46.0%

Stress relaxation during normalizing 26.0%

150

200 Out-of-roundness, µm

Average (total: 50 µm)

Out-of-roundness, µm

200

Simulation

100

50

Hardening 14.0%

Soft machining 47.0%

Hardening 27.0%

Origin of the out-of-roundness of rings after hardening of rings from cold-rolled tubes in SAE 52100. Source: Ref 21

Fig. 17

Simulation

100

50 Experiment

0

150

Before soft annealing

Experiment After soft annealing

0

Experiment

Experiment

Before soft annealing

After soft annealing

Measured and calculated peak and valley out-of-roundness distortion of bearing rings made from tubes deformed in three-point bending. The distortion is given after turning and after soft annealing. a) Outer radius. b) Inner radius. Source: Ref 23

Fig. 19

156 / Residual Stress Formation in the Shaping of Materials Table 1 Residual stresses and residual stress differences in cross sections of bars 80 ⴒ 80 mm of SAE 4142 Ballring cooling bed

Trailer table

Treatment

Residual stress, MPa (ksi)

Maximum difference, MPa (ksi)

Residual stress, MPa (ksi)

Maximum difference, MPa (ksi)

Hot rolled Hot rolled Ⳮ roll straight Hot rolled Ⳮ press straight

ⳮ45 (ⳮ6.5) ⳮ32 (ⳮ4.6) Ⳮ68 (9.9)

28 (4) 50 (7.3) 102 (14.8)

Ⳮ49 (7.1) Ⳮ41 (5.9) ⳮ84 (12.2)

43 (6.2) 81 (11.7) 123 (17.8)

Cooling after hot rolling has been carried out on a ballring bed or a trailer table and subsequent straightening in a press or parallel roll machine. Accuracy of measurements, Ⳳ30 MPa. Source: Ref 26

residual stresses exist in the machined parts to be heat treated (Ref 24). The preheat not only allows the relaxation of residual stresses without gross plastic deformation but also minimizes thermal shocking as the parts are subsequently loaded into the high-temperature furnace. Shot Peening of Gas Turbine Components. Shot peening normally is not a process that is followed by heat treatment, but shot-peened

Magnetoelastisk parameter

140 120 100 80 60 40

Over before Over after Under before Under after

20 0

1

2

Left end

3

4

Center

5 Right end

Position along the length of the flat bar The Barkhausen noise parameter measured before (open symbols) and after (filled symbols) parallel roll straightening of flat bars, 215 ⳯ 22 ⳯ 5000 mm, of the tool steel UHB Chipper. Measurement points are equally spaced over the length of the bar. Circles from the top surface and the squares from the bottom surface. Source: Ref 27

Out-of-roundness, mm

Fig. 20

0.5 0.4

Ring thickness 2 mm 1 2 3

0.3 0.2 0.1 0 1: radius 40 mm

2: radius 34 mm

3: radius 28 mm

Distortion of cut-out rings of the high-speed steel SS44 after crossed-axis-roll straightened round bars with 81 mm diam. The filled and open symbols are for bars that showed little and large ovality, respectively, before straightening. The thickness of the rings is 2 mm. Source: Ref 27

Fig. 21

components may be required to operate at high temperature. In a recent work (Ref 25) on shotpeened turbine blades made of Inconel 718, the potential magnitude of mechanical distortion, which could result from thermal stress relaxation of compressive layers induced by shot peening, is calculated using FEM. It is stated that any shot-peened thin section component could be subject to distortion, and that the worst is expected when the section thickness is of the order of the depth of the compressive layer induced by shot peening. Uneven relaxation such as full relaxation on only one side of a blade is extra damaging. This can arise if there are large temperature differences between the two sides. Two cases were modeled: uniform relaxation from both sides of the blade, and relaxation on the concave side only. As expected, the latter case created the maximum distortion. Based on experiments it was concluded that thermal relaxation progresses in two stages: a primary, very rapid stage, and a secondary, more gradual stage. The rate and amount of relaxation are directly correlated with the degree of cold work caused by the shot peening. A high degree of cold work gave a more rapid and complete relaxation of the residual stress. Straightening. Few reports about measurements of residual stresses due to straightening exist in the literature. Such measurement should not only give the residual stress values on the surface but should include depth profiles to be really meaningful. Residual stresses have been measured (Ref 26) before and after straightening of 6 m (20 ft) long bars with a quadratic cross section, 80 ⳯ 80 mm (3 ⳯ 3 in.) and 110 ⳯ 110 mm (4 ⳯ 4 in.). Examples of the results are shown in Table 1 for the steel SAE 4142 (42CrMo4). After hot rolling, bars were cooled on two types of cooling beds—ballring bed and trailer table, respectively. The former gave out-of-straightness between 20 and 30 mm (0.8 and 1.2 in.) and the latter, between 40 and 60 mm (1.6 and 2.4 in.). The bars were either press or roll straightened. The residual stress was measured by x-ray diffraction in five points in cross sections, near the corners and in the center of the cross sections. In Table 1, typical residual stress values are shown together with the total variation between residual stress values in a cross section. Notice that these stresses are not in the longitudinal direction but in the plane of the cross section. The

residual stress values are in the range 30 to 80 MPa (4 to 12 ksi) and the variations 30 to 130 MPa (4 to 19 ksi). The measurement uncertainty was less than 30 MPa (4 ksi). The variations are bigger after the straightening. The report does not tell exactly where the measurement points are situated, but they are probably a few millimeters from an edge. The yield stress was not given, but it is normally about 400 MPa (58 ksi) in the as-hot-rolled condition. In a large collaborative research project carried out by the Swedish steel industry (Ref 27), measurements of straightness, distortion, and FEM of straightening have been carried out for different steels and equipment. In one series of studies the residual stresses in flat bars before and after parallel roll straightening were measured on the top and bottom surfaces along the bar. The Barkhausen noise technique was applied using Stress Scan 500 equipment. The measurements only give approximate stress values, the higher the value, the higher the residual stress in the tensile direction will be. An example is shown in Fig. 20 for rectangular bars 215 ⳯ 22 ⳯ 5000 mm (8.5 ⳯ 0.9 ⳯ 197 in.) made of a tool steel UHB Chipper. The residual stress varies along the length of the bar, being mainly compressive on the top and bottom surfaces before straightening, and tensile on the top surface after straightening. At the two ends of the bar the residual stress does not change so much due to straightening and is slightly compressive. Not shown here is that the residual stress varied across the width of the bar. In a further study on rectangular bars 63 ⳯ 4.7 ⳯ 400 mm (2.5 ⳯ 0.19 ⳯ 15.7 in.) made of the same steel, the bars were carefully ground in steps from one side and the bow measured after each step. A conclusion was that most of the bow was due to operations before straightening. For round bars with 81 mm (3.2 in.) diameter made of the high-speed steel SS44 the out-ofroundness of rings with different diameters turned and cut-off from the bar was measured (Fig. 21). The bars to be turned were 70 mm (2.8 in.) long and cut from long straightened bars. These bars had been rotary straightened in a crossed-axis-roll machine. The figure presents data for several bars with large and small out-ofroundness before straightening. It is obvious that the cut-out rings with the largest diameter had the largest out-of-roundness. This indicates that the residual stresses have been largest near the surface of the bars. The change in average diameter (not shown here) was quite small, around 0.1 mm (0.004 in.), indicating that the out-ofroundness was due primarily to unsymmetric residual stresses in the hoop direction created during straightening. The distortions so measured on the rectangular and the round bars after machining (grinding and turning, respectively) should be better understood. This is important for being able to minimize them in order to increase the custom satisfaction of delivered bars. A step was taken in this direction by carrying out an FEM simulation

The Effect of Final Shaping Prior to Heat Treatment / 157 100 80 60

Height, mm

40

8.

20 0 20 40

0.004

0.012

0.02

9.

60 80 100 200

Fig. 22

0

200

400 600 Axial position, mm

800

1000

1200

10.

The calculated plastic deformation in the depth of flat bars with thickness 30 mm and length 2500 mm. The legend shows the effective plastic strain. Source: Ref 27

11.

functions at elevated temperature. The same should hold for a subsequent heat treatment.

12.

of parallel-roll straightening using DYNA2D. The model includes four upper and four lower rolls and comprises 2501 elements and 1600 nodes. The flat bar has the dimension 30 ⳯ 2500 mm (1.2 ⳯ 98 in.). The width is not considered in the two-dimensional model. Figure 22 illustrates how the plastic deformation grows during the straightening and reaches 2% effective strain at the surface and 0.4% in the center after passing the last rolls. The residual stresses (not shown here) can also be calculated. The deep plasticized zone indicates that the residual stresses can extend deep into the material. A main conclusion is that straightening can be simulated and the effect of material operation parameters studied.

Conclusions A survey has been presented about the generation of residual stresses due to machining such as grinding, milling, and turning, and surface deformation processes such as shot peening, pressure rolling, and straightening. The text illustrates by typical examples of residual stress profiles. The so-called Stoney’s formula is used to show that due to the thin affected layers after machining only small distortions are expected after relieving the residual stresses when a machined component has a dimension (thickness) much larger than a few hundred microns. Shot peening and, in particular, straightening should give more distortion when relieving the residual stresses due to larger affected depths. These conclusions are supported by careful studies on manufacturing of bearing rings and straightening of bars. It is also pointed out that preceeding heat treatments and straightening operations could give much more substantial distortions due to the presence of deep and irregular residual stress fields. A modeling study of stress relaxation of shot-peened material demonstrates that severe distortions can occur when a relatively thin part

REFERENCES 13. 1. B. Scholtes, Residual Stresses Introduced by Machining, Advances in Surface Treatments, Vol 4, A. Niku-Lari, Ed., Pergamon Press, Oxford, U.K., 1987, p 59–71 2. E. Brinksmeier, Process Near Control of the Residual Stress State of Ground Workpieces with Magnetic Methods, Residual Stresses, V. Hauk, H. P. Hougardy, E. Macherauch, and H.-D. Tietz, Ed., DGM Informationsgesellschaft Verlag, Oberursel, Germany, 1993, p 863–872 3. J. Grum and P. Zerovnik, Residual Stresses in Steels after Different Heat Treatments and Grinding, Fifth International Conference of Residual Stresses, Linko¨ping University, Linko¨ping, 1997, p 250–255 4. E. Brinksmeier, A Model for the Development of Residual Stresses in Grinding, Advances in Surface Treatments, Vol 5, A. Niku-Lari, Ed., Pergamon Press, Oxford, U.K., 1987, p 173–189 5. R. Herzog, A. Sollich, and H. Wohlfahrt, Residual Stresses of Heat Treated Steels with Different Hardness after Grinding with Cubic Boron Nitride (CBN), International Conference on Residual Stresses, ICRS-2, G. Beck, S. Denis, and A. Simon, Ed., Elsevier Applied Science, London, 1989, p 740–746 6. A. Sollich and H. Wohlfahrt, Residual Stresses in Quenched and Tempered Steels after CBN-Grinding with and without Prestress, Advances in Surface Treatments, Vol 5, A. Niku-Lari, Ed., Pergamon Press, Oxford, U.K., 1987, p 919–926 7. P. Belardi, E. Capello, and Q. Semeraro,

14.

15.

16.

17.

18.

19.

20.

21.

Surface Integrity in Cylindrical Grinding of 39NiCrMo3 Steel, Sixth International Conference on Residual Stresses, ICRS-6, IOM Communications, London, 2000, p 217– 224 D.F. McCormack, W.B. Rowe, X. Chen, A. Bouzina, M.E. Fitzpatrick, and L. Edwards, Characterising the Onset of Tensile Residual Stresses in Ground Components, Sixth International Conference on Residual Stresses, ICRS-6, IOM Communications, London, 2000, p 225–232 B. Scholtes, Residual Stresses in Mechanically Surface Deformed Materials, DGM Informationsgesellschaft Verlag, Oberursel, Germany, 1991 (in German) C. Schlauer, Ongoing Ph.D. thesis work, Department of Mechanical Engineering, Linko¨ping University, Sweden, 2001 L. Olovsson, L. Nilsson, and K. Simonsson, An ALE Formulation for the Solution of Two-Dimensional Metal Cutting Problems, Comput. Struct., Vol 72, 1999, p 497– 507 D. Deslaeff, “Numerical Modelling of Shot Peening: A Three-Dimensional and Dynamic Approach,” Ph.D. thesis, Universite´ de Technologie de Troyes, 2000 (in French) S.A. Mcguid, G. Shagal, and J.C. Stranart, Finite Element Modeling of Shot Peening Residual Stresses, J. Mater. Process. Technol., Vol 92–93, 1999, p 401–404 K.I. Mori and K. Osada, Application of Dynamic Viscoplastic Finite Element Method to Shot Peening Process, Trans. NAMRI/ SME, Vol XXII, 1994, p 29–34 K. Schiffner and C. Droste gen Helling, Simulation of Residual Stresses by Shot Peening, Computers and Structures, Vol 72, 1999, p 329–340 H. Wohlfahrt, Shot Peening and Residual Stresses, Residual Stress and Stress Relaxation, Plenum Press, New York, 1982 Straightening of Bars, Shapes, and Long Parts, Forming and Forging, Vol 14, Metals Handbook, 9th ed., American Society for Metals, 1988, p 680–689 Straightening of Tubing, rev. by P. Delori, Forming and Forging, Vol 14, Metals Handbook, 9th ed., American Society for Metals, 1988, p 690–693 G. Horn, Modern Section Straightening Technology, Proceedings of Straightening of Long Products, 6 Nov 1991 G.G. Stoney, The Tension of Metallic Films Deposited by Electrolysis, Proc. R. Soc., Vol A82, 1909, p 172–175 J. Volkmuth, U. Sjo¨blom, J. Slycke, and A. Thuvander, Effect of Uneven Residual Stresses on Dimensional Changes and Variations of Through Hardening Bearing Steel Rings, Proc. 20th ASM Heat Treating Society Conference, 9–12 Oct 2000, ASM International, 2001

158 / Residual Stress Formation in the Shaping of Materials 22. J. Volkmuth, F. Hengerer, and Th. Lund, Influence of Casting Process and Casting Cross Section on the Out-of Roundness, Ha¨rterei-Technische Mitteilungen, Vol 6, 1995, p 352–358 (in German) 23. A. Thuvander, Out-of-Roundness Distortion of Bearing Rings due to Internal Stresses from Tube Bending, Submitted to Mater. Sci. Technol., 2000 24. H.W. Walton, Understanding and Control-

ling Distortion in Large Bearing Rings— Some Practical Aspects, Proc. 2nd Int. Conf. on Quenching and the Control of Distortion, G.E. Totten, M.A.H. Howes, S. Sjo¨stro¨m, and K. Funatani, Ed., ASM International, 1996, p 143–147 25. P.S. Prevey, D.J. Hornbach, and P.W. Mason, Residual Stress Relaxation and Distortion in Surface Enhanced Gas Turbine Engine Components, Proc. 17th Heat Treating

Society Conf., ASM International, 1997, p 3–12 26. E. Doege and F. Weber, The Effect of Production Conditions on Residual Stresses in Bars, Stahl und Eisen, Dusseldorf, Germany, Vol 111, 1991, p 85– 88 (in German) 27. J. Bergstro¨m, The Effect of Straightening on Material Properties, Jernkontorets forskning, TO 40–37, Jernkontoret, Stockholm, 1996 (in Swedish)



Factors Affecting Final Part Shaping J. Pan, Shanghai Jiao Tong University, P.R. China

THE FACTORS THAT AFFECT the final shape of components are quite complicated. Many resultant factors from each step of the design and manufacture processes, besides heat treatment and alignment processes, have various influences on the final shape of the components. Factors and the relationships between heat treatment and distortion of components are summarized briefly in Fig. 1. The complexity results not only from the large number of factors but also from complicated interactions among them. For example, with the contents of the alloying elements in a steel increasing, the heat conductivity of the steel decreases, and the difference in temperature increases in the component during heating and cooling processes, resulting in larger distortion. On the other hand, the hardenability of the steel increases with the increase of the contents of alloying elements. The proper cooling rate can be employed in its quenching process in order to decrease the distortion of a component made of the steel. Another example is an eccentric cylinder shown in Fig. 2. The distortion tendency of the component is large due to its thin wall and asymmetry. If the component is made of 45 steel and quenched in a salt solution, the tendency of distortion further increases because of the high cooling rate. The external diameter of the component is obviously expanded after quenching. The distortion of the component is very small if the component is made of 40Cr steel and marquenched in nitrate (Table 1). When a screw plate is molded by a rolling process, the shape of its tooth face is protruded due to the influence of plastic-flow resistance of the metal from which the screw plate is made. The shape of the tooth face is concave after quenching if a certain method is employed to decrease the cooling rate of the back side of the screw plate during quenching. For example, when the fixture shown in Fig. 3 was used during quenching, the tooth faces of the two screw plates were concave. If a steel plate with appropriate thickness determined by experiments is placed on the back sides of the screw plates to make the cooling rate of the back sides lower than that of the tooth faces, the cooling rate of the back of the screw plate will be relative to the cooling rate of the tooth faces. For a component, the asymmetry is another factor that increases the tendency of distortion.

The distortion of a component made of AISI 1045 steel, shown in Fig. 4, was heated at 830 ⬚C (1530 ⬚F), quenched in water for 3 s and then quenched in oil. The external with a diameter of 57 mm (2 in.) (D1) expanded by 0.17 to 0.27 mm (0.007–0.011 in.) and the internal diameter (d1) expanded by 0.37 mm (0.015 in.) (Ref 1). The distortion of D1 and d1 obviously could be reduced after quenching if the end of the component was put on a small sleeve with an external diameter of 80 mm (3 in.), internal diameter of 57 mm (2 in.), and height of 30 mm (1 in.). It can be seen from these examples that the influences of various factors affecting the final shape of the component sometimes superpose, and sometimes offset, one another. Thus, it is necessary to know every factor comprehensively when the reasons that cause the distortion are analyzed and the measures of controlling distortion are studied. But, it is true that under various conditions, a factor plays a different role in the distortion of a component; it can play an important role under one condition and an unimportant role under another condition.

Influence of Shape of Component on Heat Treatment Distortion Quenching Distortion of a Component with Simple Shape. Besides the volume change caused by the phase transformation during heat treatment, the shape of a component will deform with the functions of thermal stress and structure stress. The distortions of simple components caused by these stresses are shown in Fig. 5. The functions of thermal stress and structure stress are contrary to each other, as shown in Table 2. The quenching distortion of a certain component is the result of the common effects of thermal stress and structure stress. Generally speaking, the distortion of the component with simple shape, uniform thickness of the wall, and good symmetry is relatively small and regular. The more complex and worse the symmetry of the shape of a component is, and the larger the difference in thickness of the component, the larger the distortion of the component will be. The Cylindrical Component. The length and diameter of the component with axial symmetry after quenching will have a little change. The

distortion relates to the ratio of length to diameter (L/D), size, quenching condition, heating temperature, the composition of the steel, and so on. Thus, the quantity and direction of the distortion under various conditions are quite different. Some examples are listed in Table 3. For a medium-carbon cylindrical component, the length will increase while the diameter will decrease after being quenched. The distortion will increase with the heightening of the quenching temperature (Fig. 6). The distortion is also sensitive to the ratio of L/D (Fig. 7). If the medium-carbon steel cylinder has not been fully hardened, the distortion will decrease with the increasing of the diameter (Fig. 8). The distortion of 1045 steel after being heated to 840 ⬚C (1540 ⬚F) and quenched in nitrate bath is less than that in water (Table 6). Carbon content greatly influences the distortion of cylindrical carbon steel components (Fig. 9). The distortion of medium-carbon steel is greatest, while the distortions of both low-carbon and high-carbon steels are relatively small. For T12 steel after being quenched from 780 ⬚C (1430 ⬚F) and 1015 steel after being carburized and then quenched in water from 850 ⬚C (1560 ⬚F), the length decreased and the diameter increased. If the cooling condition is different between the two sides of the cylindrical component during the quenching process, there will be bending deflection. The face with a higher cooling rate will protrude in a longitudinal direction due to thermal stress, but will be concave because of transformational stress. The direction of the bending is dependent on the relative amount of thermal stress and transformational stress. Asymmetry. The asymmetrical axle component will experience bending deflection caused by uneven cooling of the two sides during quenching. If there were only thermal stress, the component would protrude to the side with the faster cooling rate when quenched. But, because of transformation stress, the component protruded to the side with the slower cooling rate when quenched. The amount of final distortion depends on the relative amount of these two stresses: ● The axle with keyslot (Fig. 10) is the most

popular asymmetrical component. The influ-

160 / Residual Stress Formation in the Shaping of Materials ences of keyslot on quenching distortion are shown in Table 4. ● The axle with cross slot experienced bending deflection after being quenched. The distor-

tion of a small axle made of AISI 52100 steel (Fig. 11) was more than 0.75 mm (0.03 in.) after being heated to 840 ⬚C (1540 ⬚F), quenched in nitrate bath for 5 to 10 min, then

cooled in air. The 1045 steel valve stem had such bending deflection as shown in Fig. 12 after being heated to 820 ⬚C (1500 ⬚F), quenched in water for 2 s, and then quenched

The shape of the component The design of the component The rationality of qualification and performance requirement

The technological process

The metallurgical quality of steel

Forging The manufacturing methods of the blank

Rolling

Casting

Weldment Cutting

The influences of pre-heat treating and original structure

The selection of heat treatment methods The factors that have influences on the final shape of the component

Equipment and medium Charging form

Heating Heating rules Control of heating

Equipment

Heat treatment

Composition Cooling (quenching)

Quenching medium Temperature The design of fixture Agitation Cooling methods Alignment during quenching

Tempering and aging

The factors of chemical heat treatment which cause distortion Alignment and destressing

The stability of the component after being heat treated

Fig. 1

Factors affecting the final shape of a component

The stability of microstructure

The residual stresses

Factors Affecting Final Part Shaping / 161 in oil. The shrinkage of the 4 mm (0.16 in.) slot was 0.145 mm (0.006 in.). ● The cylinder and screw with ringlike slot shrank in the longitudinal direction, as shown in Table 5. ● For components with a deep slot in the end side, quenching distortion of the slot is influenced by the quenching direction. As shown in Fig. 13, with the slot downward, width b increases after quenching (Fig. 13a); with the slot upward, width b decreases (Fig. 13b). In the latter cases, embedding a steel block with the width of b, the distortion is effectively controlled (Fig. 13c).

Influence of Shape on the Distortion of Hollow Cylinders Cylinder with Even Wall Thickness. The distortions of symmetric hollow cylinders with uniform wall thickness caused by thermal stress and transformational stress are shown in Fig. 5(d). The actual distortion of the component is the combined action of those two inner stresses. Example 1 is a long jacket made of 1045 steel. Its size is ␾70 ⳯ ␾50 ⳯ 70 mm (␾25 ⳯ ␾2 ⳯ 2 in.). The distortion after quenching is shown in Fig. 14. The internal radius and external radius swell while the height increases, as shown in Table 6. Example 2 is a hollow cylinder made of 52100 steel. The distortion after being heated at 830 ⬚C (1530 ⬚F), oil quenched, and tempered at 160 ⬚C (320 ⬚F) for 2 h is shown in Fig. 15. The deformation of the external radius is ⳮ0.02 to 0.04 mm (ⳮ0.0008–0.002 in.) while the deformation of the internal radius is ⳮ0.04 to 0.08 mm (ⳮ0.002–0.003 in.). The deformations of both ends are larger than that of the middle. The distortion of the symmetric hollow cylinder with even wall thickness after being heat treated relates to diameter, wall thickness, height, and so on. Figure 16 shows the relationship between wall thickness and the deformation of hollow cylinders made of 1045 and 5140 steels, respectively. The principal laws of the distortion of a hollow cylinder are:

∅35

2 ∅48

∅4 25

Fig. 2

Distortion of an eccentric cylinder bushing

Table 1

Distortion of 1045 steel eccentric cylinder bushing

Quenching technology

800 ⬚C (1470 ⬚F); quenching in water for 1.5 s; quenching in oil 810 ⬚C (1490 ⬚F); quenching in aqueous alkali with 180 ⬚C (356 ⬚F)

Hardness after quench, HRC

External radius, ␾48

Internal radius, ␾36

49 to 53

0.15 to 0.25

0.30 to 0.40

42 to 43

0.08 to 0.11

0.10 to 0.15

Source: Ref 1

Table 2

Comparison of distortions caused by thermal stress and structure stress

Distortion caused by thermal stress

Distortion caused by structure stress

Contracting along the largest-sized direction Elongating along the shortest-sized direction Surface protruding Smoothing of the edges and corners Exradius expanding, inradius contracting The end inner hole tending to horn type

Elongating along the largest-sized direction Contracting along the shortest-sized direction Surface concavity Sharpening the edges and corners External radius contracting, internal radius expanding The end inner hole tending to close up

∅80(D) ∅39(d) 3

● The internal radius and external radius of a

component made of 1045 steel swell and the height increases. ● If the component is fully hardened, the amount of swelling of the internal radius and external radius increases with the increase of wall thickness when the wall thickness is small. When the wall thickness is larger than 10 mm (0.4 in.). However, the amount of swelling of the internal radius and external radius decreases with the increase of the wall thickness if the component is not fully hardened. ● For the component with wall thickness less than 12 mm (0.5 in.), the amount of swelling of internal radius is approximately 0.7 to 0.9% of the swelling quantity of external radius when being quenched in nitrate bath. The

2 67

1 30

∅39(d1) ∅57(D1)

Fig. 3

Jig and fixture method for quench of screwplate. (1) screwplate, (2) ironplate, (3) jig

Fig. 4

Distortion of a stop ring made of AISI 1045 steel. Source: Ref 1

162 / Residual Stress Formation in the Shaping of Materials amount of swelling of the internal radius is less when being double-liquid (salt and oil) quenched, approximately 0.5 to 0.6% of that of the external radius. The deformation is much less when being marquenched, normally less than 0.15%, and tends to be reduced. ● After being tempered at medium temperature, internal and external radii of the component decrease, but the deformations are much less than that during quenching. ● When medium-carbon low alloy steel 5140 is quenched in oil or marquenched, the internal radius shrinks if the wall thickness is smaller than 10 mm (d ⬍ 10 mm) (0.4 in., d ⬍ 0.4 in.), while the internal radius, external radius, and height increase if the wall thickness is larger than 10 mm (d ⬎ 10 mm) (0.4 in., d

Initial state

L

⬍ 0.4 in.). The deformation is approximately 0.1%, which is much less than that of 1045 steel after being quenched in water. The distortion of the internal radius of the hollow cylinder made of 1045 increases with the increase of d. When the thickness of wall reaches a certain value, the amount of swelling will decrease with the increase of d. ● The distortion patterns of high-carbon steel 1080, 10100, and 10120 are generally the same. For quenching a hollow cylinder made of high-carbon steel, the swelling deformations of internal radius and external radius are less than that of medium-carbon steel. The higher the carbon content, the smaller the swelling deformation will be. When the wall thickness is larger than the thickness of the hardening layer, the larger the size is, the

L

L

smaller the swelling deformation of internal and external radii will be, and even the internal and external radii shrink. ● When high-carbon low-alloy steel 52100 is heated to 830 ⬚C (1530 ⬚F) and quenched in oil, its internal and external radii shrink, while the height increases. ● The inner hole of low-carbon steel 1015 shrinks after being carburized and quenched. The larger the internal radius, the larger the shrinking deformation will be. The shrinking deformation increases with the increase of height. The deeper the carburized layer is, the larger the shrinking deformation will be. The external radius shrinks when the wall thickness is smaller than 10 mm (0.4 in.) and swells when the wall thickness is larger than 10 mm (0.4 in.).

L L

D

D

D

d

d

D

D

Thermal stress

Structural stress

(a)

Fig. 5 Table 3

(b)

(c)

(d)

(e)

Distortion of some typical simple components

Examples of a smooth cylinder with varying sizes after being quenched DD, mm (in.) (a)

Steel No.

1045 4140

0.65% C, 0.85% Mn 1.52% C, 0.37% Mn 1.2% C 52100 Carburized 1015

Heat treating process

Top

Medium

Bottom

DL, mm (in.) (b)

Water quenching from 820 ⬚C (1508 ⬚F) Nitrate bath quenching from 840 ⬚C (1544 ⬚F) Water quenching from 830 ⬚C (1526 ⬚F) Oil quenching from 830 ⬚C (1526 ⬚F) Nitrate bath quenching from 830 ⬚C (1526 ⬚F) Oil quenching from 810 ⬚C (1490 ⬚F) Water quenching from 810 ⬚C (1490 ⬚F) Water quenching from 800 ⬚C (1472 ⬚F) Water quenching from 780 ⬚C (1436 ⬚F) Oil quenching from 830 ⬚C (1526 ⬚F) Oil quenching from 880 ⬚C (1616 ⬚F) Water quenching from 780 ⬚C (1436 ⬚F) Water quenching from 850 ⬚C (1562 ⬚F)

0.11 (0.0043) 0.0075 (0.0003) 0.013 (0.0005) 0.007 (0.00028) 0.016 (0.0006) 0.022 (0.00087) 0.033 (0.0013) ... 0.045 (0.0018) 0.020 (0.00079) 0.025 (0.00098) ... ...

ⳮ0.005 (–0.0002) 0 0.004 (0.00016) 0.01 (0.00039) 0.018 (0.0007) 0.020 (0.00079) 0.050 (0.0020) 0.048 (0.0019) 0.052 (0.002) 0.025 (0.00098) 0.030 (0.0012) 0.041 (0.0016) 0.038 (0.0015)

ⳮ0.005 (–0.0002) ... 0.008 (0.0003) 0.01 (0.00039) 0.023 (0.0009) ... ... ... ... ... ... ... ...

0.535 (0.0211) 0.097 (0.0038) 0.135 (0.0053) 0.104 (0.0041) 0.206 (0.008) 0.025 (0.00098) 0.110 (0.0043) 0.078 (0.003) ⳮ0.015 (–0.0006) 0.1 (0.0039) 0.19 (0.0075) 0.010 (0.0004) ⳮ0.105 (0.0041)

Ellipses, no experimental data. (a) D ⳱ 25 mm (1 in.). (b) L ⳱ 125 mm (5 in.), Source: Ref 1

Factors Affecting Final Part Shaping / 163 0.6

L D

0.5 0.4

● When low-carbon low-alloy steel 5120 is car-

● The internal radius of high-alloy tool steel

burized and quenched in oil, its internal radius shrinks, while the external radius and height have no obvious change.

Cr12Mo swells after being quenched. The thicker the wall is, the larger the swelling deformation will be. Normally, the external ra-

∆, %

0.3 %

Deformation in length Deformation in diameter Sample size: ⌽25, L/D = 5 ~ 6

0.43

0.2 0.1

+ 0.206

0.208

0.10

0

0.00084

−0.1 −0.2 700

750 800 850 900 Quenching temperature, °C

950

0 0.000014

Effect of quenching temperature on the distortion of medium-carbon steel cylinder

Fig. 6

0.024 −

0.012

0.15% C

0.45% C

1.0% C

1.2% C

0.45

L D

0.4

Fig. 9

0.35

Effect of content of carbon on the distortion of carbon steel cylindrical components

0.3

b

∆, %

0.25 0.2

h

0.15 0.1

L

D

0.05

Fig. 10

0 −0.05

0

1

2

3 L/D, mm

4

5

Table 4

Effect of length to diameter (L/D) on the distortion of medium-carbon steel cylinder

Fig. 7

Distortion of asymmetrical axle with keyslot

Quenching distortion of asymmetrical axles with keyslots

Type of steel and quenching method

0.7 Middle carbon steel: water

oil

0.6

Convex deformation toward the side with keyslot Medium-carbon steel marquenched in nitrate bath High-carbon steel marquenched in nitrate bath

L/D > 4.5 0.5

0.4

∆L,%

Direction of bend deformation

Deformation of keyslot

Medium-carbon steel quenched in water High-carbon steel quenched in water

0.3

The bend with convex or concave deformation is limited. The deformation of axes results from other factors.

Width of keyslot dwindles

Width of keyslot dwindles or expands slightly

Various alloying steels quenched in oil

0.2

0.1

0.0

Fig. 8

Convex deformation toward the side opposite keyslot

Width of keyslot expansion

Various alloying steels quenched in nitrate bath 0

20

40 60 D, mm

80

Effect of diameter of medium-carbon steel cylinder on its distortion

Convex deformation toward the side opposite to keyslot

Width of keyslot expansion

164 / Residual Stress Formation in the Shaping of Materials 6

3.2

20

∅20 10 220 355

Fig. 11

Bend distortion after marquenching of 52100 steel axle with keyslot. Source: Ref 2

4

∅20

∅12

Bend direction after quenching

Fig. 12

Distortion of valve stem after quench. Source: Ref 1 A

A

B

B

C

C

Table 5 Comparisons of distortion of a smooth cylinder and distortion of a screw with ringlike slot after quenching Distortion after quenching, mm (in.) Shape and size of workpiece

DD

Steel Size before quenching, mm (in.)

DL

1050

U28 ⳯ 119 (U1.102 ⳯ 4.685)

1050

U28 ⳯ 119 (U1.102 ⳯ 4.685)

Ⳮ0.03 (Ⳮ0.0012)

5140

U22 ⳯ 120 (U0.866 ⳯ 4.724)

–0.02 to –0.03 Ⳮ0.63 to Ⳮ0.69 (ⳮ0.0008 to ⳮ0.0012) (0.0248 to Ⳮ0.0272)

U22 ⳯ 120 (U0.866 ⳯ 4.724)

Ⳮ0.08 (Ⳮ0.0032)

5140

0

Ⳮ0.27 toⳭ0.32 (Ⳮ0.0106 to Ⳮ0.0126)

–0.18 to –0.15 (ⳮ0.0071 to ⳮ0.0059)

d(∅50) D(∅70)

–0.13 to –0.18 (–0.0051 to –0.0071)

Fig. 14 Source: Ref 3

Distortion of a long cylindrical jacket made of 1045 steel after quenching. Source: Ref 1

−∆b

∅25

∅60

50 +∆b

Fig. 13

Distortion tendency of axle with keyslot in the end side

Fig. 15 Ref 1

Distortion of hollow cylinder made of 52100 steel after quenching and tempering. Source:

Factors Affecting Final Part Shaping / 165 Table 6

Distortion of a long cylindrical jacket made of 1045 steel after quenching A-A

B-B

DD, mm (in.)

Dd, mm (in.)

DD, mm (in.)

Dd, mm (in.)

DD, mm (in.)

Dd, mm (in.)

820 ⬚C (1508 ⬚F), quenched in water 780 ⬚C (1436 ⬚F), quenched in water

Ⳮ0.36 (0.014)

Ⳮ0.44 (0.017)

Ⳮ0.22 (0.0087)

Ⳮ0.35 (0.0138)

Ⳮ0.30 (0.012)

Ⳮ0.36 (0.014)

Ⳮ0.29 (0.011)

Ⳮ0.39 (0.015)

Ⳮ0.24 (0.009)

Ⳮ0.35 (0.0138)

Ⳮ0.37 (0.015)

Ⳮ0.43 (0.017)

Source: Ref 1

0.4

0.4

a(∆D)

b(∆d)

0.3

0.3

0.2 ∆D, mm

0.2

0.1 1 0.0

−0.2

7

0

5

10

Concave dies normally have complex shape, and the size of each part is very different. Thus, the quench distortion of the cavity of concave dies is more complex than that of rings. It is the

25

−0.2

30

5

10

25

15 20 δ, mm

30

0.08

2

3

0.06

0.04

5

1

0.04

3 0.02

0.02 4

δ, mm

∆D, mm

7

−0.1

15 20 δ, mm

0.06

0.00

0.00

−0.02

−0.02 8

C(∆D) 0

5

10

2

−0.04

−0.04 −0.06

6

0.1

0.0

−0.1

Influence of Asymmetry

Quench Distortion of the Cavity of Concave Dies

5

5

1

When the cooling rates at the two sides of an asymmetric component differ, there will be bending deflection after the component has been quenched. The side with a high cooling rate will be concave when thermal stress acts on it, while the side with a low cooling rate will be concave when structure stress acts on it. Figure 20 shows several examples of asymmetric components. The bending deflection is dependent on the steels, cooling method, and cross section size, as shown in Table 7. The greater the size of the component is, the greater the tendency of bending deflection. Figure 21 shows examples of the asymmetry of the parts shown in Fig. 20. The quenching distortion of an asymmetric alloying steel thin structural gear heated by high frequency induction is shown in Fig. 22. When the frame of a height ruler made of 9CrSi steel is heated to 860 ⬚C (1580 ⬚F) and quenched in oil in the longitudinal direction, the notch size decreases because of the notch direction during immersion; the outer side is cooled quickly, while the inner side is cooled slowly (Fig. 23).

C-C

Heat treatment process

∆D, mm

dius shrinks. The shrinking deformation decreases with the increase of wall thickness. When the external radius is smaller than the height, the deformation of height is larger than that of diameter. Otherwise, the deformation of height is smaller than that of diameter. Influence of Keyslot on the Distortion of a Hollow Cylinder after Quenching. The change of keyslot width is the same as internal radius, observed with the inside radius in the tubular example just discussed. The keyslot becomes wide if the internal radius swells. On the other hand, the keyslot becomes narrow if the internal radius shrinks (Fig. 17). The smaller the wall thickness is, the larger the distortion of keyslot will be. Uneven Distortion of Internal Radius. For hollow cylinders with keyslot, the distortion of internal radius is uneven. The shape of the inner hole after being quenched becomes elliptical. Eccentric Hollow Cylinder. Because the wall thickness of an eccentric hollow cylinder is quite different in various directions, the deformation is different after being quenched, as shown in Fig. 18. Component with Different Cross Sections. The deformations of internal and external radii at both ends of the component are different because of the difference in wall thickness. Meanwhile, the adjoining parts restrict each other, thus the deformation is as shown in Fig. 19.

15 20 δ, mm

25

d(∆d)

−0.06 30

0

5

10

15 20 ∆D, mm

25

30

Fig. 16

Effect of wall thickness on the distortion of hollow cylinder after quenching, U70 ⳯ 35 mm (U2.756 ⳯ 1.378 in.). 1: 5140, heated at 840 ⬚C (1544 ⬚F), quenched in oil; 2: 5140, heated at 840 ⬚C (1544 ⬚F), quenched in oil, tempered at 410 ⬚C (770 ⬚F); 3: 5140, heated at 840 ⬚C (1544 ⬚F), quenched in 140 ⬚C (284 ⬚F) nitrate bath; 4: 5140, heated at 840 ⬚C (1544 ⬚F), quenched in 140 ⬚C (284 ⬚F) nitrate bath tempered at 410 ⬚C (770 ⬚F); 5: 1045, heated at 840 ⬚C (1544 ⬚F), quenched in 5% NaCl water; 6: 1045, heated at 780 ⬚C (1436 ⬚F), quenched in 5% NaCl water; 7: 1045, heated at 840 ⬚C (1544 ⬚F), quenched in 150 ⬚C (302 ⬚F) nitrate bath. Data Source: Ref 1

result of the combined effect of thermal stress, transformation stress, and volume variation caused by phase transformation that affect the shape and size of the dies after quenching. For example, the die with a thin wall or thin edge exhibits less temperature difference and less thermal stress during the quenching process, and is fully hardened easily, leading to greater transformational stress so that the cavity expands. As the wall of the die increases, the thermal stress will become the major cause of cavity shrinkage.

If the thickness of the wall is not uniform, the thinner position is easy to expand and the thicker is easy to shrink (Fig. 24).

Influences of Treating Procedure and Machining Process on the Final Shape of Component Coordinating of Cold-Working and HotWorking. The coordinating of machining and

166 / Residual Stress Formation in the Shaping of Materials heat treating has obvious influence on the quenching distortion of a component that is easy to deform. The elastic chuck made of 1080 steel shown in Fig. 25 is easy to deform when quenching because of its bad rigidity. The distortion will be reduced if position A is not cut before being quenched but is cut after quenching. Influence of the Sequence of Heat Treating and Machining. Example 1: Ball Screw. The length of long and thin ball screw made of AISI 52100 steel (Fig. 26) extends after being quenched. The thinner the component is or the deeper the hardening layer is, the larger the elongation will be. When screw rollaway nest is machined before the component being quenched, the distance of screw should be shrunk. When the component is quenched, its length will be increased to reach the length required. For the ball screw with lead less than 10 mm (d ⬍ 10 mm) (0.4 in., d ⬍ 0.4 in.), such method as quenching the smooth pole and then the machining screw can be employed. It is useful to get the exact final shape. Example 2: High-Speed Gear Wheel. The high-speed gear wheel shown in Fig. 27 is made of alloy carburized steel. The rotating speed is 4000 rpm. Thin wall structure and size precision are required to reduce the centrifugal force. If the spoke is first machined and then carburized and quenched, it is easy to have obvious heat treating distortion. The following technique, however, can guarantee the precision of the final shape and size of the gear wheel and meet the requirement of a high-speed gear wheel: 1. Forge 2. Anneal 3. Machine (the machining allowance at both ends is 3 mm (0.12 in.); machining the external circle to the required size, the machining allowance of internal circle is 3 mm (0.12 in.), hobbing 4. Carburize

5. Temper at high temperature 6. Machine (cut the carburized layers at both ends to the required sizes; cut the carburized layer of the internal circle) 7. Quench and temper at low temperature 8. Machine the spoke to the required size; fine machine inner hole 9. Stabilize (150 ⬚C, or 300 ⬚F) 10. Machine key slot; grind inner hole, gear grind

next process. If the deflection cannot meet the requirement, the component has to be aligned first and then heated to 650 ⬚C (1200 ⬚F) to relieve stress. If these two stress relieving times are replaced by one stress relieving, or the stress relieving temperature is up to 620 ⬚C (1150 ⬚F), the deformation of the component after nitriding is larger than 0.05 mm (0.002 in.).

Influence of Machining Allowance and Stress-Relieving Procedure

Influence of Residual Stress Caused by Cutting on Heat Treating Distortion

The main axle of boring lathe is made of 38CrMoAl steel. The external radius is 105 mm (4 in.) and the length is 2010 mm (79 in.). The required hardness after being quenched and tempered is 24 to 28 HRC; after nitriding, the surface hardness is more than 900 HV, and the depth of the nitriding layer is 0.4 to 0.5 mm (0.0157–0.0197 in.). The machining procedure follows: 1. Rough machine; the machining allowance of external circle is 3 to 4 mm (0.12–0.16 in.) 2. Quench and temper at high temperatures 3. Align 4. Stress relieve (650 ⬚C, or 1200 ⬚F, 15 h) 5. Fine machine; the machining allowance of external circle is 0.25 mm (0.01 in.) 6. Stress relieve (650 ⬚C, or 1200 ⬚F, 10 h) 7. Grind; the machining allowance of external circle is 0.06 mm (0.002 in.) 8. Nitride 9. Half-fine grind; the machining allowance of external circle is 0.02 to 0.03 mm (0.0008– 0.0012 in.) 10. Artificial age (450 ⬚C, or 840 ⬚F, 6 h) 11. Fine grind to the required size The deflection should be checked after each stress relieving to meet the requirement of the

The residual stress caused by the cutting process causes distortion in the subsequent heating process due to stress relaxation. Residual stress will be high and the distortion will increase if the front rake angle and inner angle of the tool edge are not up to the standard or the cutting load (depth of cut and feeding) is too large. Long and thin components are especially sensitive to these factors. Improper clamping of the component also can cause more residual stress. For example, there is a gear wheel made of 18Cr2Ni4W steel. Its external radius is 240 mm (9 in.), internal radius is 224 mm (8.8 in.), modulus is 4 mm. The ovality is more than 4 mm (0.16 in.) after the component is nitrided at 500 ⬚C (930 ⬚F) for 40 h. It has been found that the four-jaw chuck used for clamping during heating caused greater residual stress. The following measures should be employed to keep the ovality at less than 0.04 mm (0.002 in.): ● Use plastic clamping apparatus, bring pres-

sure to bear on circle evenly

● Increase cutting frequency and decrease cut-

ting depth

● Perform stress relieving annealing during cut-

ting process

Larger expansion

2 ∅35

∅48

Height, h = 25 (a)

Fig. 17

(b)

Distortion of a hollow cylinder with inner keyslot, after quenching. (a) The keyslot becomes wider with the increase of internal radius. (b) The keyslot becomes narrower with the decrease of the internal radius.

Fig. 18 in water

Distortion of inner hole of an eccentric hollow cylinder made of 1045 steel, after quenching

Factors Affecting Final Part Shaping / 167

Methods of Manufacturing Blanks and the Influences of Their Original Structures Castings. Influences of the original structures of castings are as follows. Segregation in the Castings. The segregation results in many zones with different composition in the same casting, which causes the physical properties of these zones, such as heat conductivity, specific heat, elastic modulus, yield limit, melting point, and phase transformation temperature to be inconsistent. The thermal stress and transformation stress in the workpiece will

increase. Segregation is particularly troublesome for sand casting. If the blank is obtained by metallic mold casting, this disadvantage can be improved to some extent. The segregation in the blank, however, becomes comparatively much less in the case of pressure casting or centrifugal casting. Grain Size. Grain coarsening in sand casting is also a problem, resulting in increased distortion during subsequent heat treatment. However, much finer grains can be obtained by the methods of metallic mold casting, pressure casting, or centrifugal casting. The Morphology of Eutectic Structures. The morphology of eutectic structures is very sensi-

Bend distortion of long asymmetrical parts with small cross section. The lower sides were cooled quickly.

Fig. 19

Table 7

With the increase in asymmetry, the bend distortion increases.

Fig. 20

Distortion of a hollow cylinder with varying wall thickness

Direction of bend distortion caused by asymmetry under different conditions

Condition

Bending direction

The side that cooled slowly

The side that cooled quickly

Carbon steel, quenched in water or salt water Bad hardenability of steel or component with large cross-section area; the hardened layer is thin

Fig. 21

Asymmetry of the parts in Fig. 20

Fig. 22

Distortion of an asymmetric thin structural steel gear heated by high-frequency induction, after

Carburizing of low-carbon alloying steel Medium-carbon alloying steel or alloying tool steel, quenched in oil or nitrate Good hardenability of steel or component with small cross-section area; it could be hardened completely using small cooling rate Carburizing of low-carbon steel (1015, 1020, etc.)

The side that cooled slowly

The side that cooled quickly

quenching

168 / Residual Stress Formation in the Shaping of Materials tive to the cooling rate during solidification. The heating and cooling rates within the casting are uneven because of the existence of the coarse dendritic grains. Thus, the larger the casting, the greater the residual stress will be. On the other hand, residual stress will increase if the workpiece shape is favorable for the occurrence of inhomogeneous shrinkage. For example, the concave surface of the sliding guide often appears in cast-iron lathes. Influences of Methods of Castings. Blanks made by pressure casting or centrifugal casting are expected to possess sound structure, reduced segregation, and fine primary grains, all of which are beneficial to reducing heat treatment distortion. Stress Relieving Treatment and Pre-Heat Treatment. Stress relieving, which is performed to stabilize the shape and size of the casting, can eliminate residual stress within the casting. The tendency of the distortion in casting can be reduced by the pre-heat treatment. For example, intercrystalline segregation can be improved by diffusion annealing; the primary coarse grains can be refined by annealing or normalization. However, improvement of banded segregation and eutectic morphology cannot be reduced by pre-heat treatment. Hot-Rolled Steels or Forgings. Influences of the original structures of hot-rolled steels or forgings are as follows. Zone segregation in the steel ingots cannot be eliminated completely by rolling or forging, though the shape of the segregated zone possibly can be changed. For example, square-shape segregation often appears in the cross section of hotrolled steel. Therefore, heat treatment distortion will be intensified because of this segregation. Segregation of Carbide. The morphology of ledeburite in the ingots of high-carbon and high-

alloy steel can be changed by hot rolling or hot forging. However, carbide segregation cannot be eliminated completely. The carbide morphology varies with the amount of the deformation caused by hot rolling or forging and the methods of forging. Therefore, it can be divided into different carbide-segregated grades according to the morphology of carbide. Carbide segregation not only causes inhomogeneous carbide distribution, but also leads to the increase of the alloy elements and carbon contents in the austenite near the carbide-rich zones. This leads to inhomogeneity of heat conduction, and martensitic transformation becomes asynchronous, increasing the tendency of heat treatment distortion. Deformation Caused by Banded Segregation of Carbide. The banded segregation of carbide is often observed in the rolling and forging of high-carbon and high-alloy steel. After quenching, large volumetric expansion parallel to the bands may occur in the workpiece; less expansion, or even contractions, occur perpendicular to the bands (as shown in Fig. 28). The effects of direction of the banded carbide on quenching

Fig. 24

distortion of dies in various shapes are shown in Fig. 28. Influence of Forging. The segregation of carbide in hot-rolled tool steel with ledeburite structure is found to be beltlike distribution, which has a significant effect on the quenching distortion. The amount of expansion along the bands tends to increase, but the increment of the swelling perpendicular to bands is relatively smaller. Banded segregation can be eliminated by forging because the grade of the banded carbide can be reduced greatly by upsetting and drawing alternately and repeatedly, which is favorable to reducing the quenching distortion. Beltlike structures of ferrite and pearlite in the hypoeutectoid steels cause nonuniform distortion because of the differences between the quenching distortion along the bands and that in the perpendicular direction. Cold-Rolled Steel Sheet Stampings. The deformation along different directions caused by quenching is inconsistent because of the fiber structures existing in cold-rolled steel sheet. The cold-rolled 1015 steel sheet, for example, elongates 0.2% in the longitudinal direction, yet con-

Examples showing distortion of cavity

Cut after quenching 30

Quenching direction

30

Fig. 25 70

Elastic chuck made of 1080 steel

S

∅

L

Fig. 23

Distortion of keyslot of height ruler made of 9CrSi, after quenching in oil

Fig. 26

Schematic of a ball screw made of AISI E52100 steel. S, screw distance

Factors Affecting Final Part Shaping / 169 tracts 0.05% in the transverse direction after quenching at 860 ⬚C (1580 ⬚F). Having been quenched at 80 ⬚C (176 ⬚F) in hot oil (hardening layer is about 0.25 mm, or 0.01 in.) after carbon nitriding at 860 ⬚C (1580 ⬚F), the deformation of the forging-formed 1015 steel ferrule is shown in Fig. 29. The figure shows that the ellipticity

approaches 0.005 to 0.10 mm (0.0002–0.0039 in.) because of the deformations caused by stretch forming. The fibrous orientation is changed along the arc and thus results in different deformations in the different diametrical directions, which leads to an evident ellipse. But on the same conditions, the ellipticity is below

Shape before carburizing

∅220

Fig. 27

Schematic of a high-speed heavy-loaded wheel

0.04 mm (0.0016 in.) if the ferrule is made of 1015 steel sheet with fine equiaxed grains.

Influence of Heat Treatment on the Final Shape of Component The influences of pre-heat treating and original structure on the heat treatment distortion are shown in Fig. 30. The prenormalizing or quenching and tempering can refine the crystal grain of the original structure. Thus, uniform microstructure can be obtained to reduce the distortion of the component when quenching. Especially under rapid heating conditions of such processes as high-frequency quenching, it is necessary to heat the component to a higher temperature if there is a large block of ferrite in the original structure. But the component can be quenched to obtain the suitable hardness at a lower temperature if it is prenormalized or quenched and tempered properly. This is useful to reduce the distortion of the component after high-frequency quenching. If there are beltlike ferrite and pearlite in the original structure, the distortion of those parallel to the beltlike structure is quite different from those perpendicular to it. For example, if a sample prepared by 0.13% C steel is quenched from 860 ⬚C (1580 ⬚F), the elongation parallel to the lamellar structure is 0.17%, while the contractibility along the direction vertical to the lamellar structure is only 0.015%. However, the size variations for both directions are similar (Ⳮ0.04% and Ⳮ0.025%, respectively) after being normalized. If quenching and high-temperature tempering are employed as pre-heat treating, the final distortion of the semi-finishing product can be reduced. Moreover, the scattering of distortion can be limited to a relatively small scope. When the semi-finishing gear wheel is quenched and tempered before high-frequency quenching, the structure can be refined and uniformed so as to be transformed to uniform austenite quickly when induction heating. This process is useful in reducing distortion. The specific volume of globular pearlite is larger than that of lamellar pearlite. The volume

1.75

25

Fig. 28

Influence of banded segregation of carbide on quenching distortion of workpieces made of high-carbon and high-alloy tool steel. Arrows indicate the direction of carbide segregations.

∅28.5

Fig. 29

Distortion of a forging-formed 1015 steel ferule

170 / Residual Stress Formation in the Shaping of Materials change of uniform and fine globular pearlite after quenching is the smallest among various annealing microstructures of tool steel. The spheroidizing grades of high-carbon alloy tool steel such as 9Mn2V, CrWMn, and 52100 exhibit large influence on the thermal straightening property. When the original structure is uniform fine globular pearlite, the component is straightened easily when the component has been quenched to 200 to 260 ⬚C (390–500 ⬚F). Dimensional stability is quite good; that is, the shape of the component is not changed easily after the component has been aligned and cooled to room temperature. If components such as the long slideway and screw, for which alignment is necessary, have not been spheroidized and annealed properly, their thermal alignment properties will be very poor. The cutability of the original structures influences the residual stress caused by machining and thus affects the distortion of the component indirectly after being heat treated. For the highcarbon tool steels, the cutability of globular pearlite is the best. For medium- and low-carbon steels, however, cutability becomes poorer after being spheroidize annealed. As for medium- and low-carbon steels, as well as medium- and lowcarbon low-alloy steels, the cutability is the best

if the original structures are fine lamellar pearlite and free ferrite that are distributed uniformly along the crystal boundary of austenite. The cutability will worsen if there is globular cementite or free ferrite in block form or Widmansta¨tten structure or granular bainite in the original structures. Influence of Heat Treating Method to Tendency of Distortion. For many components, there are many different methods of heat treatment that meet the requirements for application. However, the distortions caused by these methods are quite different, as shown in Table 8. Thus, the selection of a heat treating method is an important factor affecting the final shape of the heat treated component. The general rules are: ● The lower the heating temperature, the

smaller the distortion will be. For example, component distortion is minimal if the temperature can be controlled to 200 to 300 ⬚C (390–570 ⬚F) when an ion implantation method is used. But the component distortion is obvious if kept at a high temperature such as 1000 ⬚C (1830 ⬚F) for several hours when boronizing or metallic cementing to reduce distortion. ● Distortion after the component is quenched

The difference of specific volume between the original structure and quenching structure

The influences on the uniformity of structure

Pre-heat treating and original microstructure

The influences on the austenitizing temperature

locally or surface quenched is less than that of being immersion quenched. ● Normally, among various surface-quenching methods, the higher the heating rate and the more shallow the depth of hardening is, the smaller the distortion will be. The distortion is the least if self cooling after rapid heating is used. The comparison of several surface quenching methods is shown in Fig. 31. ● For chemical heat treatment, when the types of penetrating elements are similar, the lower the temperature or the shorter the time, the smaller the distortion will be. For example, distortion of a nitrocarburized component is less than that of a carburized component. The distortion of a ferrite nitrocarburized (560 ⬚C, or 1040 ⬚F, 2–4 h) component is smaller than that of austenite nitrocarburized components (600–700 ⬚C, or 1110–1290 ⬚F, 2–4 h). The distortion of a ferritic nitrocarburized component is less than that of ferritic nitriding. Normally, the distortion of an isothermal nitrided component is less than that of twostage nitriding.

Influence of Heating on the Final Shape of the Component Influence of Heating Medium. The influence of heating medium on the distortion of a heat treated component is reflected mainly by two factors, heating rate and heating uniformity. Generally, the distortion is less when the component is heated at a low heating rate, while the distortion increases when the component is heated at a high heating rate. Distortion is also less when the component is heated in the medium with good heat transfer uniformity. The sensitivities of these two factors relate to specific production conditions. The distortion of a large hob made of high-speed steel after being heated

The influences on cutting ability and residual stress

The influences on hot alignment ability

Fig. 30

Heat treat method

Influence of pre-heat-treating and original microstructure on the final shape of component

Power frequency quenching

Mid frequency induction hardening

Flame quenching

Ultra-high frequency hardening Electrical heating and quenching

High frequency hardening

Laser quenching Electron beam hardening

Big

Fig. 31

Table 8 Deformation tendency of various heat treat methods

Distortion comparison of various surface quenching methods

Small

Metallic cementation Boriding Solid quenching Carburizing quenching Nitrocarburizing Chemical vapor deposition Local quenching Induction heating-surface quenching Flame heating-surface quenching Nitriding Nitrocarburizing of austenite Electron beam heating-quenching Physical vapor deposition Nitrocarburizing of ferrite (Tufftride, TruTec, Springfield, OH) Nitrocarburizing Short-time nitriding Laser heat treatment Ion implantation Ion implantation enhanced vapor phase deposition Carburizing at low temperature

Deformation tendency

Very big Big

Medium

Small

Very small

Slight


Temperature of the component going into the furnace

The influences of heating rules

Fig. 32

The control of heating rate

Holding temperature

Keeping warm

Holding time

Pre-heating

Pre-heating temperature

Heating temperature and keeping warm time

Pre-heating time

Influences of heating rules on distortion

Table 9

Influences of heating media on heat treatment distortion

Medium

Heating rate

Heating uniformity

Gas, various protective gases or air

Slow

Liquid

Fastest

Depends mainly on the structure of the heating furnace; depends on the radiation uniformity at high temperature and on gas-flowing uniformity at low temperature Different faces can be heated evenly.

Melting metal

Fastest

Different faces can be heated evenly.

Melting salt bath

Faster

Different faces can be heated evenly.

Fluidized bed

Fast

Vacuum

Slowest

The heat transfer coefficients of the side, bottom, and top are quite different. The heating uniformity is bad. Depends on radiation of heating. The uniformity is bad when a large number of components are loaded.

1

Comments

…

It is useful to reduce the distortion caused by the weight of the component with the effect of buoyancy. It is useful to reduce the distortion caused by the weight of the component with the effect of buoyancy. The buoyancy is approximately 40% of the above, so it also can decrease the distortion caused by the weight of the component. For an internal electrode salt bath furnace, the long and thin component is easily deformed with the effect of electromagnetism stirring. …

…

1

2 3

1

Unreasonable

Fig. 33

Unreasonable

Reasonable

Influence of loading pattern on heating uniformity. (1) Workpiece. (2) Heating elements. (3) Refractory materials

in a vacuum furnace is less than when heated in salt bath because the heating rate of the hob in the vacuum furnace is lower. But for the highspeed steel drills with a small diameter being loaded in batches, the distortion after being heated in a vacuum furnace is greater than that in salt bath. The influences of heating medium on quenching distortion are shown in Table 9. Influence of Rules of Heating. For the components that deform easily, distortion may be reduced if the heating rate, especially in the phase transformation temperature range, is reduced. For example, the distortion of high-speed steel or high-alloy tool steel components may be reduced when put into the furnace with lower temperature, kept at 800–850 ⬚C (1470–1560 ⬚F), and then heated to the quenching temperature. It is better for these steel components to be preheated at 500 ⬚C (930 ⬚F) in an air furnace and 800–850 ⬚C (1470–1560 ⬚F) in a salt bath, and then pre-heated at high temperature in a different salt bath. Normally, the pre-heating time is double the heating time. The influences of heating rate and time on the heat treatment distortion are complex. Generally, heating at a relatively low temperature and shortening the heating time properly not only reduces the distortion caused by the weight of the component when heated, but also reduces the distortion caused by the temperature difference during the subsequent quenching processes. But for some alloy tool steels, acceptable amounts of retained austenite can be obtained if the component is quenched at a specified temperature. This process is called “micro distortion quenching.” If the quenching temperature is lower than that temperature, the volume of the component will increase. If this is not done, shrinkage will occur. The quenching temperature may be decreased when sufficient hardness is obtained by the following methods. Changing the Original Structure of the Component. The lower-limit temperature may be used for quenching and tempering hypoeutectoid steel because of the relative ease of austenite nucleation. This is observed during the high-frequency induction heating process. However, the component should be heated at a higher temperature to ensure complete austenitization if block-free ferrite is present in the original microstructure. In the original microstructures of eutectoid and hypereutectoid tool steels, the finer and better distributed the globular pearlite is, the lower the austenitizing temperature will be. For exTable 10 Influences of increasing quenching temperature on the distortion of mold hole Type of steel

Distortion of mold hole

Medium-carbon High-carbon Low-carbon (carburizing) Medium-carbon low-alloy High-carbon low-alloy High-alloy

Expand Contract Expand Expand Expand Contract

172 / Residual Stress Formation in the Shaping of Materials ample, the austenitizing temperature of 52100 is 850 ⬚C (1560 ⬚F) if the microstructure is the normal globular pearlite (the average diameter of cementite is about 1 lm). The austenitizing temperature may be decreased to 810 ⬚C (1490 ⬚F) if the component has been pre-heat-treated to form super-fine carbide (the average diameter of cementite is smaller than 0.3 lm). Changing the Chemical Composition of the Surface Layer. The component that has been nitrided in advance can be quenched at 700 ⬚C (1290 ⬚F) to harden the surface layer. The component can be quenched at 600 to 650 ⬚C (1110– 1200 ⬚F) to obtain a high hardness when it is being nitrocarburized to form austenite with 1.0 to 2.8% N in the nitrocarburized layer. The distortions of the component with a thin wall after being treated by these methods are minimal. The influence of heating on distortion is shown in Fig. 32. For the mold with a cavity inside, however, the relationship between distortion and heating temperature is comparatively complex, as shown in Table 10. The distortion caused by weight of the part will increase if the aging period is prolonged unnecessarily. The heating period influences dissolution of carbon and alloy elements in austenite and therefore affects the transformation stresses. Heating Equipment and Loading Pattern. The influences of heating equipment and loading pattern on the distortion of the component are described here. Heating Uniformity. Nonuniform heating will increase the temperature difference, resulting in large thermal stresses inside the component. Generally, uniform heating is easy in a continuous furnace, while uniform heating in a periodic furnace is relatively poor, especially if the batch is large. The components being heat treated in a passing-type furnace are relatively small and therefore are easily heated evenly. The uniformity of heating is fairly poor because the charging basket in a periodic furnace is larger and can load more components, especially when loaded concentratedly. For furnaces with working temperatures above 600 ⬚C (1110 ⬚F), radiation is the main heat transfer process. Therefore, the location of the heating elements relative to the load exhibits a large influence on the uniformity of heating. Heat radiation conditions throughout the furnace may vary greatly. For example, the heat radiation is intensive near the furnace door and, thus, the temperature is lower here. In this case, the power distribution of the heating furnace also influences the uniformity of furnace temperature. For a combustion-heated furnace, direct flame impingement onto the component should be avoided. Radiant tube may be used to improve heating uniformity. For furnaces with working temperatures lower than 600 ⬚C (1110 ⬚F), such as those used for solution treatment and agency of aluminum-alloys, convection is the main heat transfer process. The uniformity of air flow is critical with

respect to the uniformity of heating. It is necessary to have a circulating fan with enough power, an air duct, and a conducting plate to guarantee uniformity of air flow around the component during heating. Racking. The loading pattern (racking) will promote the uniformity of heating, as shown in Fig. 33 and 34. The loading pattern that best reduces distortion caused by the weight of the component should be used. Random loading leads to poor heating uniformity. For long and thin components, vertical loading should be used in a pit furnace. Meanwhile, movement of the heated parts should be smooth and steady when removing the component from the furnace to reduce distortion caused by swaying and colliding. Charging basket and fixtures should have enough rigidity and hot strength so that their distortion, caused by their repeated operation, does not distort the component. The selection of the supporting point also has a great influence on the distortion of the component, as shown in Fig. 34. Smooth running of the machine driving system for uploading and downloading. The machine driving system for transmitting the component into or out of the furnace must start and brake steadily to avoid moving up and down and colliding.

Influence of Cooling on Distortion The cooling process has the greatest influence on the final distortion of the component. There are many complicated factors that affect the distortion, such as the type and the design of the cooling equipment, the quenchant, temperature and agitation of the quenchant, quenching method, cooling or immersing time, and the pressure in the cooling process. Type and Design of the Cooling Equipment The influences of cooling equipment on the quenching distortion are as follows. Cooling Equipment. Types of cooling equipment and influencing factors include: ● Quenching tank for immersion: volume and

size of quenching tank, fluid flow and agitation condition of quenchant, and fluid maintenance ● Gas quenching equipment: cooling gas and pressure, flow rate of gas, design of dynamics of flow field, and heat transfer ● Gas jet and fog jet cooling equipment: structure of nozzle, site and arrangement pattern of the nozzles, water pressure and flux, air pressure and flux, and adjusting and controlling system for pressure and flux Quenching tanks, including water-based polymer quenching tanks, oil-quenching tanks, stepquenching tanks, and isothermal-quenching tanks, are the most popularly used quenching equipment. The volume of the quenching tank directly affects the heat dissipation. If the tank is too small, the quenchant temperature will vary considerably, leading to nonuniform temperature distri-

bution during the quenching process, which will influence quench distortion. In a normal quenching tank, quenchant flows from the upper overflow vent, heat exchanger, and is then returned to the tank by the pump. The tank design influences the uniformity of the cooling of the component and thus influences the quenching distortion. The volume of the quenching tank shown in Fig. 35(a) is comparatively small. Cold quenchant is put into the tank from the right bottom and flush through the component unevenly. This brings about the nonuniform cooling of the component and increased distortion. Cold quenchant flows into the tank from the holes of the pipe located at the bottom of the quenching tank shown in Fig. 35(b). The quenching uniformity has thus been improved. There is a quenching ring in the tank, as shown in Fig. 35(c). The liquid quenchant is sprayed on to the component from the holes on the liquid sprayer using a highpressure pump. This kind of tank is suitable for large cylinder components. The cooling of the component is uniform and component distortion can be reduced. Several stirrers are arranged at the right side of the tank shown in Fig. 35(d). The quenchant flows evenly from the bottom by means of the baffle. The design of the tanks shown in Fig. 35(b), (c), and (d) is useful in reducing the distortion caused by the nonuniform flow of the quenchant and the unidirectional flow through the component. Gas-Quenching Equipment. High-pressure gas quenching has increased very quickly in recent years due to its cleanliness (no pollution) and minimal distortion. The cooling rate of highpressure gas quenching is less than that of oil, and it is not necessary to move the component when using high-pressure gas quenching in a vacuum furnace. These factors are beneficial in reducing quenching distortion. However, under some circumstances, the distortion of vacuum quenching is more than that of oil quenching or salt-bath quenching. The distortion of vacuum quenching is related to cooling uniformity, while cooling uniformity is related to the hydrokinetic feature of equipment and the loading of components. For example, in some high-pressure gas-quenching equipment, gas has been input and output from the top and the bottom. Two kinds of methods have been employed. Gas has been input from the top and output from the bottom; gas has been input from the bottom and output from the top. Nozzles can move right and left to improve the cooling uniformity. Nevertheless, cooling of the upper-side and the lowerside of the component is not the same. For the component with tabular shape, the distortion is less if it is placed in the furnace as shown in Fig. 36(a), while there is bending deformation if the component is placed as shown in Fig. 36(b). When several plates are piled in the furnace (Fig. 36(c)), the flow velocity in every interval increases due to the effect of a narrow slot, which can cause the uneven cooling of the component and the final distortion. In the designing of some gas-quenching furnaces, nozzles are positioned evenly in the chambers. This improves the


Incorrect

Correct

Incorrect

Incorrect

Correct

Incorrect

Correct

Unreasonable Reasonable

Unreasonable

Fig. 34

Reasonable

Reasonable

Influence of a supporting point on the distortion of a component

C

P

(a)

C

P

C

P

(c)

(b)

2

1

Fast cooling 2

3

1 5

3

4

4

5

C (d)

P (e) 1. cylindric tank 2. mixer 3. flow-guiding pipe at side 4. flow-guiding pipe at bottom 5. thermocouples

Fig. 35

Structure of quenching tank on the cooling uniformity. C, heat exchanger; P, pump. (f) Source: Ref 6

(f) 1. slipping slot connected with furnace 2. high pressure nozzle 3. quick cooling mesh belt 4. slow cooling mesh belt 5. liquid surface

174 / Residual Stress Formation in the Shaping of Materials quenching distortion of large blocks, while it can result in the uneven cooling of cutting tools that are quenched in the loading basket (Fig. 36(d)). Moreover, the gas distribution along longitudinal direction is also uneven and, thus, long and thin components tend to deform when they are batch loaded (Fig. 36(e)). Jet-Hardening and Fog-Quenching Equipment. Factors in jet-hardening and fog-quenching equipment that have influence on the quenching distortion of a component are as follows. Design of Nozzles. The sizes of jet angle and jet stream, the uniformity of jet intensity, the quality of atomization, and so on all can influence the cooling uniformity of the component. The positions of nozzles and their relative positions to the component are also important factors that can influence cooling uniformity. Ring injectors can be used in the quenching of axle parts. The cooling uniformity not only depends on the distribution uniformity of jet stream, but it also is influenced to a great extent by the racking position of the central lines of the axle and ring. If the central line of the axle deviates from the central lines of the ring, bending will occur, as shown in Fig. 37(a) and (b). An ideal jet-hardening system (Fig. 37(c)), should meet the following three requirements:

air flux change at different positions. This design can meet the requirement for quenching of a large batch of small parts. Computer simulation may be used to optimize the jet-hardening and fog-quenching process and equipment design.

Influence of Quenchant Cooling characteristics of various quenchants and their influence on quench distortion are dis-

(a)

(b)

cussed in other chapters of this book. The cooling intensity of the quenchant is not only related to the physical and chemical properties of the quenchant, but also related to some outside factors, as shown in Table 11. The comparison of several major quenchants is shown in Table 12. Generally, the greater the cooling intensity, the deeper the hardened layer, the greater the distortion will be. However, there is no exact relationship between these variables. This is due to the influence of the fastest cooling rate, the relative degree of the cooling rates within pearlite

(c)

● The axle is vertically hung. ● There is an accurate locating system to ensure

that the central line of the axle coincides with that of the ring. ● Component can rotate smoothly in the cooling process. The pressure and flux of water have intensive influence on the cooling rate of jet hardening, while the cooling rate of fog quenching is sensitive to the proportion of air to water. Various cooling rates can bring about various distortions. The Influence of the Control System. In jet hardening, the Grossman Quench Severity factor may be as high as 6.0 if water pressure is 6 atm, while the cooling rate under 1 atm is similar to that of brine solution. The cooling rate of fog quenching varies, depending on the proportions of air and water, between the cooling rate water and air quenching. In this case, the cooling abilities of jet hardening and fog quenching may be adjusted on a wide range. If quenching equipment is provided with a control system with regulators of water pressure, water flux, air pressure, and air flux, it is possible to obtain various cooling intensities at different temperature ranges to reduce distortion optimally. There are two design schemes for adjustable jet-hardening and fog-quenching equipment:

Degression of pressure (d)

(e)

Fig. 36

Effect of high-pressure gas quenching equipment on the cooling uniformity

Fig. 37

Effect of site of spray nozzle on the distortion of axle component after quenching

● The relative positions of components and

nozzles are fixed, while such parameters as water pressure, water flux, air pressure, and air flux change with time. This design can be employed to the quenching of large components with regular shapes. ● Components are placed on the conveyor using a continuous cooling process, and thus water pressure, water flux, air pressure, and

(a)

(b)

(c)

Factors Affecting Final Part Shaping / 175 Table 11

Factors that influence the cooling intensity of liquid quenchants

Factor

Function(s)

Physical and chemical properties of quenchants Heat of vaporization The larger the heat vaporization is, the stronger the cooling intensity. The heat of vaporization of water at 100 ⬚C (212 ⬚F) is 2260 kJ/kg while the heat of vaporization of mineral oil is about 210 kJ/kg. Therefore, the cooling intensity of water is much more powerful than that of oil. Vapor pressure The lower the vapor pressure is, the more difficult the gasification, and therefore the lower the cooling intensity is. Boiling point Lower boiling point brings about the increasing of cooling rate in range of martensite transformation. Surface tension The smaller the surface tension is, the less the stability of vapor film is, and the stronger the cooling intensity. Specific heat The higher the specific heat is, the stronger the cooling intensity. Viscosity The smaller the viscosity is, the stronger the cooling intensity will be. The separation behavior of solute Vapor film can burst when the inorganic (NaCl, NaOH, Na2CO3, etc.) dissolved in water-based quenchant is separated at the surface of hot component, which can at the surface of hot increase the cooling intensity of quenchant. component Inverse-solvent power Polymer quenchant has the power of inverse-solvent. Polymer film can be formed around hot component so as to separate water from the component, and thus decrease the cooling intensity of quenchant. The cooling intensity can be adjusted by changing the concentrating of polymer. Outside factors The temperature of quenchant

The cooling intensity of water solution drops intensively with the increasing of the temperature and the temperature corresponding to the fastest cooling rate obviously moves to lower. However, the cooling rate of oil increases slightly with the increase of temperature due to the decreasing of the viscosity of oil. Agitation can drop down the stability of vapor film and thus increase the cooling intensity of quenchant. The higher the flow rate is, the greater the influence. The uniformity of fluid flow around component has great influence on distortion. The higher the gas pressure is, the bigger the heat of vaporization, and therefore the faster the cooling rate. For spray hardening, the higher the pressure is, the more powerful the cooling intensity. When component is cooled in cycling gas, its cooling intensity increases with the increase of gas pressure. The cooling rate of coarse surface is faster than that of smooth surface. The salt or borax sticking to component surface can promote the burst of vapor film.

Circulation and agitation

Gas pressure above liquid The pressure of quenchant

The surface condition of component

Table 12

Comparison of several commonly used quenchants in cooling rate and distortion

Quenchant

Cooling rate

transformation period and martensite transformation period, or strictly speaking, the cooling curve. There is a strong relationship between surface heat transfer coefficient, surface-to-arc temperature gradient, and distortion. For example, the cooling intensity of 10% NaOH solution or 10% NaCl solution is much higher than that of water and, therefore, the hardened layer is also much deeper. However, the distortion of the component being quenched by 10% NaOH water solution or 10% NaCl water solution is just slightly less than that of water because the cooling rates of those quenchants within martensite transformation period are similar. The depths of hardened layers after being quenched in 50% NaOH water solution is greater than that of water but the distortion is less. The reason is that the viscosity of NaOH water solution with high concentration is large and its cooling intensity within martensite transformation period is only 1 ⁄6 of the cooling intensity of water. The maximum cooling rate and characteristic temperature of high-speed quench oil with additives are obviously higher than that of straight unaccelerated oil, while its cooling rate within a low-temperature range is slower than that of ordinary mechanical oil due to the greater viscosity. Therefore, although the depth of hardened layer quenched by high-speed quench oil is deeper than that of unaccelerated quench oil, the distortion is similar. The distortions of a C-ring test specimen made of 5140 steel (Fig. 38) quenched in various quenchants are shown in Table 13.

Influence of Quenching Methods

Distortion

Large

10% NaCl water solution

Large

10% Na2CO3 water solution

Large

50% NaOH water solution

Large

Water

Large

Polymer quenchants

Medium

25% NaNO3 Ⳮ 20% KNO3 Ⳮ 20% NaNO2 Ⳮ 35% H2O

Medium

Accelerated quenching oil

Small

Alkaline salt bath

Very small

Nitrate bath

Very small

Ordinary mechanical oil

Small

Air

Very small

Cooling in One Medium. The factors that influence component distortion are quenchant selection, quenchant temperature, agitation rate, and uniformity of agitation. The influence of quenchants on the distortion of cavity of coldforging dies is shown in Table 14. The selection of quenchant should account for the following two opposing factors, depth of hardened layer and quenching distortion. According to the dimension of the workpiece and

6

037

10% NaOH water solution

Table 13 Quenchant

Water 10% NaCl 1% NaOH 50% NaOH 75% NaOH Source: Ref 1

The influences of quenchants on the distortions of C-style sample Temperature, ⬚C (⬚F)

Cycling rate, m/s (ft/s)

Hardness after quenching, HRC

Gap opening, mm (in.)

20 (68) 20 (68) 20 (68) 20 (68) 15 (59)

0.5 (1.6) 0.5 (1.6) 0.5 (1.6) 0.5 (1.6) 0.5 (1.6)

56–60 57–60 57–59 58–60 55–57

0.39 (0.015) 0.18 (0.007) 0.22 (0.009) 0.12 (0.005) 0.05 (0.002)

12 051

Fig. 38

C-style samples

176 / Residual Stress Formation in the Shaping of Materials Table 14

Influence of quenchants on the distortion trend of cavity of cold forging dies Types of steel

Quenching medium

Mediumcarbon steel

Highcarbon steel

Carburized low-carbon steel

Carburized low-alloy steel

Medium-carbon low-alloy steel

Low-alloy tool steel

Mediumalloy steel

Highalloy steel

Saline water Oil Alkaline salt Nitrate bath Air

Expand Shrink Expand Expand …

Shrink Shrink (b) Expand …

Shrink Shrink Shrink Shrink …

Shrink Shrink Shrink Shrink …

… Expand Expand Expand …

… (a) Expand (b) Expand

… (a) … (b) …

… (a) … (b) …

(a) For alloy tool steel, hot oil can increase the expanding trend, while cold oil can increase the shrinking trend. (b) Too much water in alkaline salt or nitrate bath, decreasing the bath temperature, and short keeping time will result in the expanding trend of cavity. Source: Ref 4

Table 15 Influence of various stirring degrees on the cooling intensity of quenchants (Grossman factor, in.ⴑ1) Agitation degrees

No agitation Mild agitation Moderate agitation Good agitation Strong agitation Violent agitation

Air

Oil

Water

Saltwater

Nitrate

0.008 … … … … 0.2

0.25–0.30 0.3–0.35 0.35–0.40 0.40–0.50 0.50–0.80 0.80–1.00

0.9–1.1 1.0–1.1 1.2–1.3 1.4–1.5 1.6–2.0 4.0

2.0 2.2 … … 4–5 …

0.5 … … … … 2.25

Source: Ref 5

Table 16

Factors that influence distortion of a component during marquenching

Factor

Function(s)

Cooling rate above isothermal temperature Isothermal temperature above martensite point below martensite point Isothermal time or keeping time

Affecting thermal stress obviously Affecting structural stress obviously Affecting the quantity of residual austenite Having certain influence on structural stress Affecting the quantity of retained austenite Intensively affecting structural stress Affecting the quantity of retained austenite

Cooling rate below isothermal temperature

Table 17

Factors that affect the distortion of spray hardening

Factor

Function

Water pressure Water flow Injector or nozzle design Spray hole or nozzle position Component shape and relative movement against nozzles

Table 18

Intensively affects cooling intensity Affects cooling intensity Affects cooling uniformity and rate Affects cooling uniformity Affects cooling uniformity

Distortion tendency of gears after carburizing and quenching

Gear parameter variation

Addendum circle diameter Bore diameter

Surface warpage and taper Tooth profile Helix angle variation

Distortion tendency of gears after carburizing and quenching

Addendum circle diameter of plate gear generally expands. Addendum circle diameter of gear shaft generally shrinks. Bore diameter generally shrinks. The amount of shrinkage increases with hardenability and case depth. Inner diameter of gears with anticarburizing bore expands slightly. For gears with nonuniform cross section, the bore shrinks more significantly in the thinner part, resulting in conical deformation of the bore. For disk gear with large outer diameter/height ratio, its end surface warps easily and gear rim tapers off easily. End surface of bevel gear warps. Tooth thickness increases after carburizing and quenching, particularly as approaching tooth tip or both end faces. Helix angle of helical gear after carburizing and quenching becomes smaller.

hardening ability of the steel, quenchant with a relatively lower cooling intensity should be selected to reduce distortion, provided the hardness after quenching is guaranteed. Temperature of Quenchant. The temperature of aqueous quenchant can affect its cooling character intensively. Increasing the temperature of the quenchant will increase the stability of vapor film and reduce the cooling rate in the range of pearlite transformation, while only decreasing slightly the cooling rate in the martensite transformation range. Therefore, increasing the temperature of the aqueous quenchant is not a good method to control component distortion. Although the boiling point of a quenching oil is typically relatively high, increasing the temperature of quenching oil usually will not obviously affect the stability of vapor film but can decrease the viscosity of oil. In this case, thermal stress, transformation stress, and retained austenite can be controlled by adjusting the temperature of the quenching oil. Thus, regulating the temperature of quenching oil is an effective method for controlling distortion. Agitation Rate. It can be seen from Table 15 that agitation has a great influence on the cooling intensity of the quenchant and thus affects the depth of the hardened layer and quenching distortion. Some good quenching tanks have an adjustable circulation rate, and it is possible to change the cooling rate rationally. For example, the following technical method can reduce the quenching distortion without influencing the depth of the hardened layer: 1. Moderate agitation rate should be used when the temperature of the component is above 650 ⬚C (1200 ⬚F). 2. Strong agitation should be used when the temperature of the component is between 450 and 650 ⬚C (840 and 1200 ⬚F). 3. Agitation slows when the temperature of the component is below 400 ⬚C (750 ⬚F). 4. Stop agitation at the final period of cooling. Uniformity of Circulation. Nonuniform stirring will create the difference in flow rate between the two sides of the component and thus cause the nonuniform cooling of the component, resulting in an increased amount of distortion of the component. Two-Step Quenching. The component is quenched in quenchant with strong cooling intensity during pearlite transformation period and then quenched in medium with weak cooling intensity during martensite period. An example of a twostep quenching is first, the component is quenched in salt water and then oil. The factors that affect the distortion of a component are type of quenchant and cooling time in those two media. Pre-cooling quenching is a commonly used method to reduce distortion. It includes delayed quenching, isothermal precooling quenching, quenching for decreasing temperature after carburizing, and so on. The factors that influence pre-cooling quenching on the distortion of a component are:

Factors Affecting Final Part Shaping / 177 ● Time: Quenching distortion often can be re-

before being placed into the quenchant. Both isothermal temperature and keeping time influence the distortion of the component. ● Temperature and holding time of quenching for decreasing temperature after carburizing: It can effectively reduce the distortion of a carburized component if the component is kept in a carburizing furnace for a certain period of time when the temperature of the furnace is dropped to approximately 840 to 870 ⬚C (1540–1600 ⬚F) (depending on type of steel). Marquenching is an effective way to reduce quenching distortion. In this process, the component first is quenched into an isothermal bath. After its temperature becomes uniform, the com-

Temperature, °C

duced if the component is kept in the air or protective gas for a certain period when moving from the heating furnace into the quenchant. The longer the keeping time is, the less the distortion will be. However, the keeping time can be too long so as not to affect the hardness and the depth of the hardened layer of the component. ● Temperature and time of isothermal precooling: It is useful to decrease the temperature difference between the inside and outside of the component and thus reduce distortion. To be sure the component is isothermal, it should be kept in a fluid bed or salt bath or an isothermal furnace for a certain period of time

Ms

2 1 Time, lg τ

Fig. 39

Marquenching and isothermal quenching

3

ponent is cooled to room temperature. There are two types of marquenching. In the first type, the component is quenched into a bath in which the temperature is above the martensite point, and in the other, the quenching bath temperature is below the martensite point. Curve 1 in Fig. 39 indicates marquenching below the martensite point, while curve 2 indicates broken hardening above the martensite point. The factors that affect the distortion of a component are shown in Table 16. Isothermal Quenching. The cooling curve of isothermal quenching is shown as curve 3 in Fig. 39. The microstructures after isothermal quenching are bainite with a certain quantity of retained austenite. In this case, there is only a small variation in specific volume, which results in a small amount of the distortion of the component. The factors that influence isothermal quenching distortion are isothermal temperature and time. Spray Hardening. A significant cooling rate can be achieved when high-pressure water is sprayed onto the surface of the component, making spray hardening suitable for large-sized components. The cooling intensity of spray hardening can be changed in a wide range by adjusting the pressure and flow of water. With the help of computer simulation of transient temperature field and phase transformation in the spray hardening process, nozzles can be positioned and pressure and flow of water can be regulated so that a better hardening effect can be obtained. This method is generating increased interest. The factors that affect the distortion of spray hardening are shown in Table 17.

Influence of Tempering, Deep Freezing Process, and Stabilization

Before tempering

After tempering

Influence of Tempering. There exist some factors that will cause a volume change in quenched steel during its tempering process. In the tempering process, while the carbide is separating from the martensite, the carbon concentration of the ␣-phase decreases, causing contraction. Meanwhile, the transferring of the retained austenite causes expansion. Normally, the former takes greater effect than the latter, so the final volume changing tends to be decreased (compare with quenched state). However, the temper process should not be expected to make up the distortions caused by annealing. Initially, the tempering temperature is insufficient, which can totally reverse the volume change caused by the quenching process. More importantly, the plastic distortion caused by inner stresses during the quenching process cannot be changed by tempering. The distortion incurred during temper is far less than that in quenching. Therefore, the final distortion after the quench-temper process is decided primarily by the distortion in the quenching process. Factors that influence the distortion in the temper process are: ● Temperature: At higher temperatures, where

more obvious contractions occur for carbon

178 / Residual Stress Formation in the Shaping of Materials

The higher nitrogen content of the layer, the larger deformation. The thicker nitrided layer, the larger deformation.

The volume of nitrided layer expands.

The more nitride formation elements the steel contains, the larger deformation. The higher nitriding temperature and longer nitriding time, the larger deformation. The higher nitriding potential, the larger deformation. The worse uniformity of nitriding layer, the larger deformation.

Internal stress before nitriding.

Effect of residual stress caused by machining. Effect of the prestress relieving

Distortion of nitrided workpiece.

Effect of loading method Creep caused by the weight of workpiece.

Effect of fixture design The thinner wall thickness, the larger deformation due to the volume expansion of nitrided layer. The greater difference of wall thickness, the larger deformation during nitriding.

Shape factor The worse shape symmetry, the larger deformation during nitriding. The worse rigidity, the larger deformation due to creep.

Fig. 41

Distortion of tube-type parts after carburizing and quenching

Effect along the direction of gravity. Effect on the gravity of workpiece.

Effect of loading tools on heat treatment distortion

Influence of the Deep Freezing Process. When quenched steel is cryogenically treated, the retained austenite will transform to martensite. Thus, the size of the workpiece will have only a little expansion, and the size stability of the workpiece will be raised. Influence of Stabilization. Temper makes the microstructure of steel stable and reduces the residual stress (or make the stress state stable), which can improve dimensional stability. In most situations, the dimensional stability can be obtained only through a temper process. Some precision tools tempered at a low temperature, however, need to be heated several times, for an extended period, and kept at a temperature slightly below the temper temperature. Low-temperature aging can reduce the residual stress while stabilizing the retained austenite to increase dimensional stability of precision tools.

Factors Affecting Chemical Heat Treatment Distortion

Effect on the heating uniformity.

Factors Affecting the Distortion of a Carburized Workpiece. Besides shape, quenching methods, quenchant selection, and hardenability, other factors relevant to the carburizing process also can influence the final size and shape of the workpiece significantly:

Effect on the cooling uniformity.

● Surface carbon content and carbon concen-

Effect on the homogeneity of chemical heat treatment case.

Effect on the stability of loading/unloading.

Fig. 42

Effect on the weights of other workpieces in the same furnace.

steel and low-alloy steel, the volume can shrink back to what it was before the quenching process when tempering at a temperature above 500 to 600 ⬚C (930–1110 ⬚F). For the high-alloy tool steel, however, after the temper process at the temperature where the second hardening occurred, the amount of the volume contraction will be reduced due to the transferring of the retained austenite. ● Time: The volume contraction is mostly being processed in the initial period of the temper process and will begin stabilizing after 1 to 2 h. ● Pressure: When the workpiece is being pressed during the temper process, its shape can be fixed due to the function of its elastic stress being relaxed. The typical example is the tempering of a piston ring. The method involves keeping the notch opening by iron mass during the temper process. Under the same principle, the workpieces can be flattened after the temper process, during which they are pressed (Fig. 40).

Effects of loading tools on heat treatment distortion

tration distribution of carburized layer: Surface layer with high-carbon content has a lower martensite-transition point, greater amount of retained austenite, and larger volumetric increase during martensite transformation. Transformation stress of carburized parts varies with case carbon content and carbon concentration distribution in the carburized layer. ● Case depth of carburization: The deeper the case depth of carburization, the greater the

Factors Affecting Final Part Shaping / 179 transformational stress after quenching, and the greater deformation of the parts ● Control accuracy of carbon potential: The more accurate the control of carbon potential is, the more consistent the deformation of carburized parts will be. ● Carburizing temperature and time: Deformation caused by creep increases as carburizing temperature and time increase, and the influence of temperature is more significant. Therefore, for carburizing parts with thin wall or shallow case depth, the carburizing temperature should be lowered.

(a)

Fig. 43

● Quenching methods after carburizing: Dis-

● Heterogeneous case depth or local carburiz-

tortion of carburized parts through direct quenching is usually less than that through reheating and requenching because of less times of heating and cooling in the former process. ● Core hardness of carburized parts: Core hardness reflects the degree of hardening. With the increase of core hardness, the deformation changes from being caused by thermal stress to that being caused by transformational stress.

ing: Heterogeneous case depth or local carburizing will result in nonsymmetrical distribution of structural stress and, therefore, lead to distortion.

(b)

(c)

(d)

Comparisons of the distortion of slender shaft resulting from gravity. (a) Large distortion. (b) Medium distortion. (c) Little distortion. (d) Illustration of universal joint hanger ∅16

These factors, along with the size and shape of the parts, result in the distortion of carburized and quenched parts. For example, distortion patterns of tube-type parts after carburizing and quenching are described as follows. Distortion of low-carbon steel or low-carbon alloy-steel-tube-type parts with a wall of 5 to 15 mm (0.20–0.60 in.) thickness after carburizing and quenching is shown in Fig. 41. The bore tends to shrink. Larger bore diameter and deeper case depth will result in greater shrinkage of the bore. The height and outer diameter of tube-type parts are generally reduced slightly (their reduction is smaller than that of the bore). When the bore has key grooves, carburizing and quenching will result in the width reduction of the key grooves. Distortion tendency of gears after carburizing and subsequent quenching is illustrated in Table 18. Factors Affecting the Distortion of Nitrided Workpiece. Nitriding is a method of heat treatment that causes the least distortion. In industry, nitriding is used on many important precise machine components, which have rigid requirements of deformation. Factors influencing the distortion of nitrided parts are described subsequently.

Effects of Auxiliary Equipment and Loading Methods on the Final Shape of Components

100

12

Effects of loading tools and arrangement patterns on the final heat treatment distortion are

∅20 ∅90 (a)

(b)

(c)

Fig. 44

Supporting pattern of shaft gear in furnace

(d)

Do

Di

3 × 120°

Incorrect

Fig. 45

Loading methods of a gear

Correct

180 / Residual Stress Formation in the Shaping of Materials shown in Fig. 42. Charging batcher, supporting frame, and hanging tools determine the direction and magnitude of thermal stress and affect the transportation stability during uploading and unloading. Moreover, many factors, such as heating uniformity, flow resistance of furnace gas during chemical heat treatment, and flow state of quenchant during cooling, are related to the loading patterns. Therefore, the design of loading tools has evident influence on the heat treatment distortion, which is discussed in the following paragraphs. Effect of Loading Tools on Distortion Caused by Gravity. Creep caused by gravity during heating is one of the significant causes of heat treatment distortion, and loading tools have decisive effect on it. The effects of furnace tray, supporting frame, and hanger on heat treatment distortion are shown schematically in Fig. 42. The distortion caused by gravity can be eliminated if the hanger is used to keep the slender workpieces in a vertical state. In Fig. 43, deformation of (a), (b), and (c) decrease successively. In Fig. 43(d), a universal joint hanger is designed to ensure the workpiece is suspended vertically. The shaft gear illustrated in Fig. 44 is carburized and then quenched in trays. Different types of supporting patterns can affect distortion significantly. Placing the shaft gear in the horizontal position on the base plate, as shown in Fig. 44(b) and (c), will cause large deformation due to gravity. In Fig. 44(d), the stem of ␾16 mm is plugged in the grid of fixture, surrounded with three height-adjustable supporting bolts to ensure it is in the vertical position; the distortion will be reduced greatly. For normal disk-shaped parts with through hole in the center (Fig. 45), suspension from the center hole can reduce deformation. However, if there is only a small difference between the outer diameter (Do) and the inner diameter (Di), suspension from the center hole will cause large deformation (it may become elliptic). In this case, other options should be used, such as hanging from around the outer circle of the part, or just placing it in the horizontal position on a flat, stiff base plate (Fig. 46). A disk gear for mass production should be placed in the horizontal position, so as to make full use of furnace chamber space and improve productivity. Influence on Heating and Cooling Uniformity. If the workpieces are placed disorderly in baskets, the heating and cooling uniformity will be greatly affected. For example, during carburizing and quenching automobile gears in a sealing chamber furnace or continuous furnace, special baskets are designed for distributing the parts evenly and allowing appropriate space between them (Fig. 47). The four sides of the basket can prevent the heater from irradiating the parts directly, and act as diversion of circulated furnace gas and quenchant during cooling, which are in favor of improving heating and cooling uniformity. The bottom of the basket should have good stiffness to make it more stable, which can also

∅80 ∅30

1 30

67 2

∅57

Fig. 48

Auxiliary sleeve used for reducing quenching distortion. (1) workpiece, (2) auxiliary sleeve

(a)

Fig. 46

(b)

(c)

Loading method of ring-shaped parts with a large hole in the center (a) circumferentially hanging, (b) centrally hanging, and (c) horizontally placed

3

4 5 2 1

Fig. 47

Schematic layout of basket and parts. (1) pedestal, (2) basket, (3) cramp bar, (4) locating pedestal, (5) parts


NH3

3 1 2 4

A

A

A-A

Fig. 49

Schematic of the unimproved layout of bolt nitriding. (1) furnace chamber, (2) ammonia inlet, (3) parts, (4) heater

be designed as a dismountable locating pedestal if necessary. The surface of the locating pedestal and parts should be machined to be smooth. For some easily deformed parts with walls of heterogeneous thickness, properly designed auxiliary fixtures can improve heating and cooling uniformity, and therefore, reduce heat treatment distortion. As mentioned previously, while quenching of 1045 steel stop ring, a sleeve underneath during quenching can significantly reduce distortion (Fig. 48). Effect of Loading Methods on the Uniformity of Chemical Heat Treatment. During chemical heat treatment, loading tools and loading methods will affect case homogeneity, which is also an important cause of heat treatment distortion. Well-designed baskets and properly distributed workpieces can make furnace gas flow evenly, and therefore improve case homogeneity, as shown in Fig. 48. For another example, in unimproved furnaces, as shown in Fig. 49, the bolts used in a plastic machine are nitrided in a pit furnace. Gas flow around the bolt is rather heterogeneous because of the small size of the furnace chamber, unevenly distributed interface, and one side of the bolt being closer to the furnace wall than the other. As a result, bending deformation of nitriding bolts is beyond the tolerance limit. In the improved design, as shown in Fig. 50, the following measurements are adopted: ● Enlarging chamber volume ● Installing centrifugal impeller on furnace lid ● Adding a diversion tank in furnace chamber

5

4

3 6

2

1

These improvements greatly improve atmosphere and heating uniformity, and therefore, the distortion is controlled within the tolerance limit. Function of Forced Distortion Devices in Heat Treatment. Some devices employed in quenching can control the workpiece distortion by use of internal stress emerged in heat treatment, though they exert no external force on the workpiece. For example, in Fig. 13, a workpiece with a groove in the end face was quenched with the groove upward, and groove width shrank evidently. If a smooth steel block is plugged in the groove, which is heated and quenched with the parts, and then taken out after subsequent tempering when stress relaxed, distortion can be greatly reduced. In actual production processes, to avoid bending distortion, quench press machines are used to quench parts such as gears, friction plates, and even butterfly springs formed during quenching. Moreover, for mass production of disk gears, quench press machines are also applied to the quenching treatment. The disk gear shown in Fig. 51 was quenched in a pulsating quench press machine. At the same time, end face warpage and bore distortion were corrected. The compressive forces were (Ref 4): ● Ring pressure at position B: 11,740 N (2,639

lbf)

Fig. 50

Schematic of the improved layout of bolt nitriding. (1) guide flow tank, (2) furnace chamber, (3) guide flow ring, (4) annular ammonia inlet, (5) furnace lid, (6) fan

● Pressure at position A: 16,003 N (3,598 lbf) ● Expansion pressure at position C: 3,910 N

(879 lbf)

182 / Residual Stress Formation in the Shaping of Materials All of the properties and quality of the quench press machine, the design and manufacture quality of the compression die, the magnitude of compressive force, and so on, will contribute to the distortion of the workpiece quenched by a press machine, as shown in Table 19.

B

A

32

REFERENCES 18

C

D

∅110 ∅220

Fig. 51

Table 19

Disk gear quenched in pulsating quench press machine. (A) pressure from outer hold-down ring, (B) pressure from inner hold-down ring, (C) pressure from expansion heap, (D) pressure from bottom die ring

Factors affecting workpiece distortion quenched by press machine

Factor

Unsuitable fit between conical expansion rod and cone face of central die Untidy work surface of central die or gear bore surface Inadequate dimension of central die and limiting ring or inappropriate dimension of limit ring Insufficient pressure of central die Excessive pressure of central die or oversized inner diameter of limiting ring Insufficient pressure of inner hold-down ring Excessive pressure of outer hold-down ring Excessive taper of lower mold surface Insufficient pressure of outer hold-down ring Excessive pressure of inner hold-down ring Inadequate taper of lower mold surface Source: Ref 4

Influence

Elliptical bore Elliptical bore Elliptical bore Elliptical bore Nonsmoothness of inner end surface Nonsmoothness of inner end surface Nonsmoothness of inner end surface Nonsmoothness of inner end surface Nonsmoothness of outer end surface Nonsmoothness of outer end surface Nonsmoothness of outer end surface

1. Z. Peiyu, The Control of Heat Treamtment Distortions of Common Machine Parts, Mechanical Industry Publisher, Beijing, China, 1990 2. X. Dawei, F. Zhijun, and X. Huizhi, The Heat Treatments of Fine Long Parts, Mechanical Industry Publisher, Beijing, China, 1991 3. Y. Lunian, The Control of Distortion in Steel Heat Treatments, Mechanical Industry Publisher, Beijing, China, 1987 4. Heat Treatment Handbook, 2nd ed., Vol 2, Heat Treatment Institute of China Mechanical Engineering Society, Beijing, China, 1991 5. Heat Treating, Cleaning and Finishing, Vol 2, Metals Handbook, 8th ed., American Society for Metals, 1964, p 18 6. G.E. Totten and M.A. Howes, Steel Heat Treatment Handbook, Marcel Dekker Inc., New York, 1997



Effects of Process Equipment Design F.T. Hoffmann and T. Lu¨bben, IWT Foundation Institute for Material Science, Germany R. Hoffmann, IVA Industrieo¨fen, Germany K. Heess, Karl Heess GmbH, Germany

IN MANY CASES, fabrication of parts ends with a heat treatment process to set the required properties. Unwanted effects that may appear after the heat treatment process are dimensional alterations and distortion as a result of a processinduced inner stress state of the parts. The origin of the stresses may be in each part of the manufacturing process of the parts (i.e., construction, production process of the material, manufacturing processes, and heat treatment processes) between and at the end of the production process. Further on stresses generated in different stages of the production process can additively or compensatively superpose during the manufacturing process. At the last heat treatment will be the production process that will release the residual stresses as distortion. Distortion can increase to such an extent that the parts can no longer be used, or that at least reoperation processes will be necessary. These additional necessary processes will be costly because they have to be done in the high-hardness state after finishing the heat treatment processes. Accordingly, more or less material has to be charged so that the distortion, which is to be expected, can be adjusted by, for example, partial grinding operations. The exact knowledge of the overmeasures is of high importance because too small additional measures will lead to defective goods. On the other side, too high overmeasures will increase the costs. The results are higher grinding costs and an increase of the heat treatment costs. For instance, carburizing time has to be increased to set a higher carburizing depth. Another problem is that distortion will differ from part to part and that the scattering of the values is based on multifarious reasons. Distortion as a result of the manufacturing process is not a new problem. It is documented in literature broadly and has been the subject of research work in various technical fields. However, the state of the art is very inhomogeneous and conclusions cannot be made, or only with unacceptable uncertainties. A new starting point to minimize distortion is the awareness that distortion is not only the problem of the material or a single step in the manu-

facturing process but a property of the whole manufacturing system. Thus, it has to be seen as a system property of the whole manufacturing process, including: ● Construction: Construction prearranges the

●

●

●

●

distortion potential. This means the liability to changes in shape and form (e.g., by changes in cross sections materials selection). Steel producing: Melting and solidification and the following deformation processes appoint the local inhomogeneity of the chemical composition, which result in a local different transformation behavior. This leads to different microstructures and so to a inhomogeneous distortion behavior, in extreme cases, to crack formation. Forming: The state of microstructures and residual stresses in a part is influenced by the state of the material (chemical composition, inhomogeneity of the microstructure, segregations, etc.) before forming and by the deformation parameters. They influence the following machining operations and the subsequently appearing distortion and dimensional alterations: Machining: Machining (turning, milling, drilling) adds specific distortion potentials to the distortion system by generating mostly inhomogeneous residual stress states. Heat treatment: Heat treatment implies a specific distortion potential. As a finishing manufacturing process, it releases the total distortion potential, accumulated as residual stresses, inhomogeneities of material, and microstructure up to this moment, as dimensional alterations and distortion. The origins of distortion are quite complex and connected with the total manufacturing process and should not be attributed solely to the heat treatment process.

Therefore, to minimize distortion, the whole production process has to be observed. In the following chapters, the heat treatment process, and especially the influence of process equipment, are discussed

Identification of Distortion Generating Process Equipment Distortion can be increased by different steps of heat treatment processes. In the majority of cases, quenching steps are brought into connection with the generating of distortion because quenching is the last step of the process. However, a high amount of distortion will be generated before quenching or cooling is started. To avoid or to minimize distortion, it is important that the parts being heat treated are heated and cooled uniformly so that a homogeneous temperature distribution results over all the cross sections. On the other hand, if cooling and heating are as homogeneous as possible, but the component is very inhomogeneous (chemical composition, microstructure, residual stress state before heat treatment) or the shapes of the parts show very different transverse sections, bores, holes, and so on, distortion will not be avoided without using special methods such as press quenching. Therefore, if there are problems dealing with distortion and there is the presumption, that distortion could have been released by equipment, it should be checked simultaneously if material or shape could also be responsible for the failure. With respect to the process and the equipment, a general remark is that heating and cooling must be done as uniformly as possible.

General Possibilities to Influence Distortion Generation by Process Equipment Distortion is generated by elastic and plastic deformations during the production process of the part. Origins may be an inhomogeneous microstructure of the material due to its metallurgical history or nonuniform or unbalanced conditions during heating or cooling processes during the manufacturing process. The former case cannot be influenced by normal process equipment. Beyond this, these in-

184 / Residual Stress Formation in the Shaping of Materials homogeneities are unidentified if the quality control has not been done sufficiently.

Influences of the Heating System The insulation of the furnace has to be uniform. Cold spots may lead to an undershooting of the dew point, which will result in the formation of moisture. Also, the insulation material has to be fitted to the atmosphere to avoid side reactions between atmosphere and insulation material. Otherwise, the local homogeneity of the treatment may be influenced negatively, which may lead to an inhomogeneous impact of the atmosphere to the parts (e.g., followed by inhomogeneous carbon content in the case of carburizing or oxidizing in protective atmospheres). In turn, this will influence the transformation behavior and may increase distortion during the quenching or cooling step of the process. Heat Irradiating Areas in Ratio to the Size of the Batch. If parts are located too closely to heating devices, local differences in temperature may occur. Different temperatures will influence locally the carburizing or nitriding behavior in the case of thermo-chemical processes or in the transformation behavior if temperature differences result in a different amount of solved alloying elements. These inhomogeneities promote distortion. Therefore, the ideal distance of heating devices from the batch should be as far away from the parts that approximately a 15⬚ radiation angle still can be realized. However, it should not be closer to the parts than 150 mm (6 in.). If this rule of design is fulfilled, the usable space will be significantly bigger than the workspace, and bigger parts than allowed for ideal charging can be used. In respect of ideal heating conditions for a uniform heat treating a furnace should not be overloaded. The ideal size of a charge will be smaller than the potentially usable space. Thus, an unfavorable charging is preprogrammed, also in respect of the operating efficiency of the process. A furnace, if not constructed as a tube, has six sides. Normally, only two sides are stoked. The temperature homogeneity can be enhanced by heating more than two sides. However, this will not be possible for all areas; for example, specific problems will occur at walls with feeding units. Also, temperature inhomogeneities can be caused by metallic parts forming a temperature dip. In addition, each flange worsens the temperature homogeneity. Inner doors are thinner, in consequence of their function. It has to be considered that the heat loss in areas with doors is higher than in the better-insulated surrounding areas. Number and surface area of the heating devices influence the temperature homogeneity by the necessary surface temperature to reach the desired batch temperature. The surface temperature of the heating devices should not exceed that of the batch temperature by more than 30 K. The

distance to the batch is especially important at point-shaped heat sources. Gas Atmosphere. Heat transfer into the parts is induced by enforced convection. Gas velocity at the surface of the parts, homogeneity of the gas velocity at the surface and in the inner regions of the batch, and differences of the velocity in the inside and outside of the batch will influence the heat transfer and, therewith, the temperature homogeneity. Theoretically, more uniform conditions should be reachable by baffles. Because of the high temperatures, however, only simple-shaped constructions can be used. Optimal rules of design cannot be applied. Thermocouples. The location of thermocouples must allow for correct temperature measurement; the tip of the thermocouple has to be placed near the workpieces in the furnace. It has to be exposed to the same heating environment as these pieces. The uniformity of the temperature in the furnace must be checked before installing control thermocouples. Special Problems at Thermochemical Treatments. The revolution of the process gases serves only for equalization of the atmosphere. It is not strong enough to manage a good temperature equalization. The limitation of the degree of revolution is given by the strength of the fan material. Metals have a low strength at process temperature, and carbon fibre composite (CFC) materials are not usable in conjunction with oxygen-containing atmospheres. Inside a furnace it has to be distinguished between lowand high-temperature areas. The limit will be at approximately 700 to 800 oC (1290–1470 ⬚F). Above this temperature, radiation will be the main heat transfer mechanism, and this is the main reason that revolution will not enhance the temperature uniformity. Hot and cool spots must be avoided. Hot spots will result in a higher dissociation of the process gas; at cold spots, soot can be formed. Local different gas compositions may lead to differences in element profiles, and soot on the parts will hinder the carbon transition. Both effects influence the transformation behavior of the material during quenching and, therewith, distortion behavior. A further influencing parameter on atmosphere homogeneity is the disposition of the gas-inlet points. Atmosphere uniformity must be reached before the atmosphere comes into contact with the parts to be heat treated. As mentioned previously, for the uniformity of the carburized layer, temperature and atmosphere homogeneity are responsible. However, the choice of treatment temperature also may be of high influence (e.g., if parts with differences in cross section should be carburized or carbonitrided to small carburizing depths). High temperatures in connection with those geometries can result in high temperature differences. As a result, overcarburized spots and spots with toolow carburizing depths will occur. In these cases, low carburizing temperatures offer higher uniformity of carburizing depth, but longer treatment times are necessary. Additionally, large sections of the parts stay ferritic during carburizing and will not be hardened—only the sur-

face near cross sections that will pick up carbon transform to austenite. Special Problems of Pit-Type Furnaces. Atmosphere homogeneity in a furnace is a prerequisite to avoid unequal case conditions during thermochemical treatments and so prerequisite to avoid distortion. To reach a good homogeneity the flow field must be optimized. In the case of pit-type furnaces, this can be done by guide cylinders. If the length to diameter ratio of the furnace is small (1:1 or 2:1), there is no need for such a measure. But, at higher ratios, guide cylinders are necessary to receive a uniform atmosphere distribution. Further improvement at higher temperatures (e.g., carburizing) is achievable by usage of gas lances. At low temperatures (e.g., nitriding), stronger fans can be used. Special Problems of Vacuum Furnaces. Temperature homogeneity is predominantly determined by the disposition and layout of the heating elements. The number of the heating devices is substantial for the equability but also for the costs. Thus, depending on the size and construction of the furnace, a minimum number is necessary. Charging with large distances between the parts in too-large furnaces will be good for homogeneous heating but worse with regard to the costs.

Influences of the Quenching System Quenching is the most dangerous process step of heat treatment to generate distortion. Thus, nonuniform agitation/quenching or nonuniform circulation of quenchant around a part results in inhomogeneous cooling rates that create shape distortion. The extent of distortion also increases with the intensity of cooling. As discussed previously, however, uneven hardening, with the formation of soft spots, increases distortion. Similarly, uneven case depths in case-hardening steels have the same impact. As a general rule, cooling should be done as slowly and as homogeneously as possible. When quenching in fluids, there should be a good revolution of the quenching media also within the batch. Influences by charging should be considered as well, for example, the hardenability of the parts, their form and size, and their distances from each other (batch density). The composition of the charge will influence distortion greatly, too. Forces by the self weight of the parts can deform the parts if they are not held up sufficiently. In dependence of the shape of the parts, weight forces are dependent on the manner of charging. Long, slim parts, therefore, should be hung. If parts have to be laid down, they must be supported sufficiently. Grids. Metallic grids will not stay even, which also can influence distortion by weight forces (gravity). In consequence of uneven grids, the charge will not stay in a plane. When distortion of a grid increases, it can be turned. Dense charging will cause the same behavior as the behavior of a large compact part. Therefore, the inner areas of the batch will be cooled down more slowly than the outer regions.

Effects of Process Equipment Design / 185 The best possibility to adapt quenching to the requirements of the parts or the batch is given by gas quenching. By gas type, pressure, flow rates, and other influencing parameters, the quenching rate can be adapted to the parts. However, there are a lot of additional parameters that influence quenching behavior and therewith distortion, that are not fully recognized at each process. Some of these influences are: ● ● ● ● ● ● ●

Heat radiation emitting and absorbing areas Inflow of heat-emitting areas Cooling of the quenching gas Pressure as function of quenching time Power of the fan (flow velocity of the gas) Flow field in the charging area Local turbulences

The design of the gas flow is essential for the homogeneity; impinging jets with high velocity

rmax

rmin

Roundness chart of a bearing ring (184 ⳯ 200 ⳯ 25 mm diam, or 7.2 ⳯ 7.9 ⳯ 1 in. diam, SAE 52100) after free quenching in a high-speed quenching oil. The difference between maximum and minimum radius (roundness), r, is 0.436 mm (0.017 in.).

Fig. 1

Roundness chart of a bearing ring (184 ⳯ 200 ⳯ 25 mm diam, or 7.2 ⳯ 7.9 ⳯ 1 in. diam, SAE 52100) after quenching in a quenching press. The difference between maximum and minimum radius (roundness) is 0.057 mm (0.002 in.).

Fig. 2

results in a high heat flow, tangential inflow in a low heat transfer. The homogeneity of the heat flow increases with increasing flow rate. Gas quenching is the only quenching method that allows adaption of the quenching intensity to the special needs of single parts or a batch. Also, different quenching rates at one part can be realized (e.g., by quenching in a nozzle field). In this way, distortion, or at least the scatterband of distortion, can be minimized.

Distortion Minimizing by Quenching in a Hardening Press In actual industrial practice, the heat treatment process frequently is carried out with large charges. In such operations, many workpieces are simultaneously heated, then simultaneously cooled. Such multiple-workpiece treatment procedures have the obvious advantage of substantially increasing output rate; however, the cooling curves of each individual workpiece are different. Thus, in order to ensure that the required minimum effective cooling rate is achieved, it is necessary, in such cases, to orient the procedure on the basis of the slowest-cooling section of the processed charge. A corresponding selection of quenching conditions (involving, for example, the use of a high-efficiency quenching oil) leads, in such cases, to the cooling of all other portions of the charge at an excessively high rate. Therefore, in such a situation, it currently is impracticable to establish an optimal charge-processing procedure. In cases in which the workpieces undergoing treatment are distortion sensitive (such as, thin-walled roller-bearing rings), extreme deformation may occur (Fig. 1). In the current state of industrial technology, workpieces of such sensitive types can be treated successfully only through the use of expensive and time-consuming grinding operations, which produce workpieces with the required end dimensions. However, some workpieces may be in such bad shape that they cannot even be subjected to post-production treatment, and in such cases, the benefits of any previously applied treatment procedures are lost. One potential solution to this problem is the use of hardening fixtures. An essential feature of such an installation is that each workpiece is subjected to an individual cooling regimen, while the deformation is maintained at a very low level by applying external forces. A comparison between Fig. 1 and Fig. 2 shows the accuracy (roundness) generated through the use of this procedure and clearly indicates the high level of effectiveness of the hardening fixture installation in procedures of the type in question. The primary goal of the fixture-hardening procedure is the enhancement of end-product quality, through achieving a uniform hardness distribution for the processed workpieces, minimal level of deformation, as well as a substantial reduction in the need for the use of supplemental finishing procedures, such as grinding.

Fixture hardening is characterized by the fact that it is carried out through the use of an integrated hardening press unit, into which the heated manufactured workpiece, either singly or in batches, is inserted and then subjected to a precisely regulated, optimized cooling regimen, while simultaneously being subjected to a specific applied force. For example, in the case of the quenching of round workpieces, a radial force is applied to prevent the workpiece from undergoing any significant changes in shape during the structural-transformation process. Changes in workpiece dimension, which are common products of structural-transformation procedures, in the context of fixture hardening (which involves the use of applied external forces) may, within this context, be converted to variations in the geometric relations (for instance, in the case of ring-shaped workpieces, to variations in wall thickness). The dimensions of freely hardened workpieces differ markedly from those of fixture hardened; in the latter case, it is possible to adjust workpiece dimensions in such a manner that the fixture-hardened workpieces uniformly exhibit the required dimensions. However, whatever quenching method is selected, it is vital to bear in mind the close relationship obtained between the hardening operation itself and previous production steps. In the case of rotationally symmetrical, ringshaped workpieces, as a general rule, a mandrel is employed, which aids in the centering of the workpiece, as well as the maintaining of the roundness of the inner ring surface during the quenching procedure. Therefore, at the beginning of and/or at some point during the quenching procedure, an external force is applied to the workpiece. This applied external force leads to the plastic deformation of the workpiece, and by this means, effectively prevents the workpiece from undergoing the loss of roundness that can be generated by nonuniform cooling rates of its various crosssectional regions and released stress. The selection of the specific mandrel system to be employed in a given operation is determined by such factors as the material of which the workpiece is composed, its geometrical characteristics, and the hardening process used. Thus, in cases where the workpiece undergoing treatment exhibits shrinkage at the conclusion of the procedure, a solid mandrel can be used (Fig. 3). During the hardening process, the workpieces shrink on the mandrel and then must be pressed off. Solid mandrels are simple and inexpensive to manufacture and yield extremely good shape results when employed in operations of the type described. In order to obtain the higher precision values required in geared workpieces or cogs, the use of smooth-surface mandrels can be effectively supplemented with cog-cut mandrels. In such cases, the workpiece undergoing treatment can be positioned in the cog mandrel in either the tooth flank or the root of the gear tooth (Fig. 3). Special cogged mandrels also ensure conformity to dimensional specifications in free-cut cogs or gears, which, with the use of conventional

186 / Residual Stress Formation in the Shaping of Materials smooth-surface or expanding mandrels, can be partially lost since the free-cut cog or gear regions do not mesh precisely with the mandrel employed. Another problem typically encountered in the hardening of fully hardenable workpieces is a substantial volume increase as a result of the formation of a martensitic structure throughout the entire workpiece, which in turn, leads to an undesirable expansion. As a result, during the first part of the quenching process, the workpiece shrinks on the mandrel, and when the Ms point (the temperature at which martensite starts to form from austenite on cooling) is attained, the

workpiece dissociates from the mandrel again. As a result, deformation can appear again during the generation of martensite. Plastic deformation of the workpiece during the martensite generation cannot be prevented through the use of a solid mandrel. In order to eliminate the difficulty just described, an expanding mandrel system is commonly employed, which allows a slight variation of the diameter (Fig. 3). Through the expansion of the segments of the mandrel over a cone, the workpiece, while undergoing martensitic structure generation, has its inner diameter “pressed out round” as a result of plastic deformation.

Smooth mandrel

Fixed mandrel

Expanding mandrel Toothed mandrel

Basic fixing

Fig. 3

Fig. 4

Flank fixing

Digest of actual mandrel system at press quenching

Synchronizing cone Fixed mandrel receptacle with retention and mandrel ejection device

Ring gear Expanded mandrel receptacle with separated retention

Synchronizing ring Receptacle on conical fixed mandrel with retention, conical outer retracing, and mandrel ejection device

Sliding sleeve Fixed mandrel takeup, with retention, mandrel ejection device, and optional external pressing

Examples of fixtures for hardening of ring-shaped bodies

However, the expanding mandrel is substantially more expensive to produce than a standard type fixed mandrel; if the expanding mandrel is not produced to conform with precise dimensional tolerance limits, there will be a substantial adverse effect upon the dimensional precision of the end product. In addition, the diameter variability of expanding mandrels is very limited, because if mandrel-segment radii and workpiece radii were different, they would touch tangentially only. Through the applied force, the workpiece maintains a polygon-shaped inner diameter, determined by the number of segments (as a general rule, from 5 to 10 segments). In accordance with the specific geometry of the workpiece to be treated, fixture components in addition to the mandrel may be employed, such as mounting and support rings, down holders, or devices for applying force to the outer diameter. These components usually are used only in combination with solid mandrels since the simultaneous application of force to the inner and outer diameters at the same time can result in undefined dimensional variations. Pressure to the outer surface is frequently applied to workpieces, which, owing to their constituent materials and/or geometries, undergo a significant increase of their internal diameter in the course of the structural-transformation procedure. Particularly in the case of thin-walled rings, often it is not possible to obtain the required levels of both shape and dimension stability in conventional fixture-hardening systems without the application of pressure to the outer surface of the workpiece undergoing treatment. Figure 4 shows schematic representations of fixtures for use in the hardening of various types of ring-form workpieces. The final decision regarding the use of a fixture-hardening system is conditioned primarily by the degree of precision that is required of a given end-product workpiece. As noted, both the material of which the workpiece is composed and its specific geometric configuration are important factors in this context. Other factors also have an essential influence on the accuracy of the hardened workpieces. Thus, for any given workpiece, it is critical to establish precise values for amount of compressive force to be applied, cooling time, and handling time. Programmable control units, operating in conjunction with personal computers, make possible the convenient storage of workpiece- and material-specific treatment parameters in a database. In such an automated system, any significant variations from production charges can easily be evaluated and effectively compensated. In addition, in automated systems of this type, it is possible to control procedures by comparing actual values with desired values, which is of vital importance from the standpoint of quality control. The treatment of individual workpieces at fixture-equipped processing stations also makes it possible to establish workpiece- and material-specific data records, which would not be possible in a system in which the simultaneous treatment of an entire batch was carried out.



Residual Stresses in Nitriding Z. Kolozsva´ry, S.C. Plasmaterm S.A., Tg-Mures, Romania

A NUMBER OF technological processes are based on the diffusion of nitrogen in steel or of nitrogen combined with other elements, including carbon, oxygen, and sulfur. The basic difference between nitriding and carburizing is that, in carburizing, the specific properties of the case against the core are obtained by a controlled carbon-rich martensite in the diffusion layer. No difference occurs in the structural nature of the case against the core, and all the property modifications may well be predicted considering the changes in carbon content. (Carbide-forming elements modify only the hardenability of the case and its stability.) Nitriding has a completely different mechanism. Due to the very low solubility of nitrogen in iron, the nitrogen diffused in the surface layer will form nitride precipitates with iron (mainly c⬘-Fe4N) and with the alloying elements of the steel, according to their chemical affinity to nitrogen. The mechanism of hardening is different

Fig. 1

Coarse, needle-shape nitride precipitates in the diffusion layer of low-carbon steel

from that of carburizing, and is practically based on a precipitation process. The greater the occurrence of uniform, finely dispersed precipitates of stable nitrides (of aluminum, titanium, chromium, niobium, etc.), the higher the hardness in the diffusion layer. Because of the high nitriding potential in the nitriding atmosphere, however, a compound layer will almost inevitably form on the steel substrate. This compound layer consists of c⬘(Fe4N) and e-(Fe2ⳮ3N)-type nitrides on the surface, rarely as a monophase layer. Modern technologies offer close process control, resulting in a more or less monophase layer, or even bright nitriding (without a compound layer), but in industrial practice duplex compound layers generally are characteristic. This is especially true for gaseous treatments, less so for plasma processing. Simultaneous action of carbon and oxygen results in mostly compact, hexagonal etype, crystals with varying amounts of nitrogen and carbon, or nitrogen, carbon, and oxygen. A few characteristics are common to all nitriding/nitrocarburizing procedures. First, the process temperature is between 450 and 570 C (840 and 1060 F), which means no austenitic transformation occurs and the structure remains basically ferritic or, more exactly, in the ferritic domain. Due to the lack of phase transformation, no specific residual stresses appear. Second, this lack of phase transformation means that the structure of the steel before nitriding strongly affects both the mechanical parameters of the treated parts and the stress-strain state after nitriding. Normalizing, annealing, and quenching and tempering will influence the substrate properties, as well as the post-treatment residual stress level and resulting deformation. Best results are generally obtained for quenchedand-tempered structures prior to nitriding, presuming the tempering temperature is higher than that of nitriding or nitrocarburizing. In this case, practically any influence of carbide precipitation, spheroidization, or carbide coagulation can be neglected. Third, the low treating temperature also modifies the thermodynamics and kinetics of layer formation. The activity of the steel surface plays a determining role in the whole process; thus, machining and finishing operations may influence the stress-strain state of the surface layer.

The compound layer is mainly responsible for the tribological properties of the nitrided/nitrocarburized engineering components, whereas the substrate with its diffusion layer provides loadbearing capacity and improved fatigue properties. Structure, composition, and morphology of the compound layer cover a rather large spectrum as a function of process parameters, and some discrepancies may be found in the literature concerning the properties of compound layers depending on their composition. The effect of oxygen in the layer and on layer formation is still being debated (Ref 1–5). To outline the problem of residual stresses in nitrided/nitrocarburized layers, a short summary of their structure and properties follows.

Structure of Nitrided Layers Gaseous Nitriding in NH3-N2-H2 Mixtures. Basically, nitrogen diffusion in steel results in a low-nitrogen ferrite according to the Lehrer phase diagram (Ref 6, 7) and precipitated nitrides of the alloying elements, especially chromium, aluminum, molybdenum, and titanium. The most desirable structure consists of fine, uniformly dispersed nitride precipitates in the ferritic matrix. However, due to the low solubility of nitrogen in iron, even with close control of process parameters, some Fe4N occurs, mostly in the form of coarse nitride needles. Usually, a brittle c⬘-(Fe4N) compound layer also appears on the surface, which is later removed by various chemical or mechanical processes. These structures are obtained at low temperatures of 510 to 530 C (950 to 990 F) with a subsequent slow cooling. Thus, residual stresses primarily originate due to the modification of chemical composition and crystal structure by precipitation in the diffusion layer (Fig. 1). Nitrocarburizing (Ferritic). The combined effect of nitrogen, carbon, and oxygen results in a mainly e-type or e Ⳮ c⬘ compound layer of 5 to 25 lm on the steel substrate, supported by a diffusion layer. Contrary to gaseous nitriding, the main purpose of nitrocarburizing is to improve the tribological properties, and it can also be applied to unalloyed or low-alloyed steels. A certain amount of porosity in the compound layer is generally present due to the mechanism

210 / Residual Stress During Hardening Processes of layer growth. The hardness of the diffusion layer is given by the nitride precipitation phenomena in the matrix, just as for gaseous nitriding. However, because of the generally higher treating temperature (540 to 570 C, or 1005 to

Microstructure of compound and diffusion layer in plain carbon steel. Gaseous nitrocarburizing, 570 C (1060 F), 2 h

Fig. 2

Microstructure of diffusion layer in low-alloy structural steel. Gaseous nitrocarburizing, 570 C (1060 F), 2 h

Fig. 3

1060 F), the increase in hardness is less prominent even for special alloy steels, as the precipitates are coarser and less uniformly distributed (Fig. 2, 3). The interdependence of tribological/mechanical parameters and chemical composition of the compound layer is not completely elucidated. The nitrogen/carbon ratio in the e-type layer has been extensively investigated (Ref 6, 8, 9), but it remains difficult to provide accurate parameters for industrial processes. The presence of oxygen is also of utmost importance, increasing the layer growth rate due to increased surface activity (Ref 5, 10, 11). The problem of residual stresses is more sophisticated in this case, because consideration must be given not only to stresses in the compound layer or in the substrate, but also to some particular phenomena that appear in the interface between the compound layer and the substrate. Another important factor is the dissolution of carbide particles in the e compound layer from the pearlite grains of the substrate (Fig. 4). Salt bath nitrocarburizing results basically in the same structure discussed above, but due to the dissolution phenomenon in the bath an equilibrium in the layer growth process will occur— one that is dependent not only on the bath active composition but also on its contamination, especially with iron (Ref 12). Usually extremely fine salt inclusions also can be found in the compound layer’s outmost film, as it may be observed in studying the fracture toughness of compound layers (Ref 13). This dissolution process modifies not only the stress state in the

Fig. 4

layer, but first of all that of the interface between the compound layer and substrate (Fig. 5). Plasma Nitriding and Plasma Nitrocarburizing. Plasma-assisted processes involve cathode sputtering, which significantly affects both the interface (at the beginning of the process) and layer formation. Very accurate and close control of the process parameters in plasma nitriding and nitrocarburizing is possible, so different structures and properties can be obtained. When a low treating temperature (up to 510 C, or 950 F) is maintained a thin but very hard layer will appear with extremely fine, dispersed nitride precipitates in the steel substrate. In this case, the compound layer is either very thin c⬘-type or may be avoided altogether. As in gaseous nitriding, such a process may only be applied for alloy steels (Fig. 6). For improved tribological properties, the compound layer plays the key role. Different data are available in the literature on the tribological properties of compound layers of different structures and composition (Ref 10, 11, 14, 15). There appears to be good agreement among the specialists that plasma-nitrided alloy steels will show the best properties with a relatively thin, but uniform monophase c⬘ compound layer on a hard substrate. On the other hand, some researchers claim that the ductility and fatigue wear resistance of enitrocarbide compound layers are better than those of c⬘. Usually the controversy finds its roots in the fact that it is very difficult to control the porosity of the e layers, and this porosity has a negative effect on service properties. The most

Dissolution of carbide particles in the compound layer from the pearlite grains of the substrate. Transmission electron micrograph (TEM)

Residual Stresses in Nitriding / 211 favorable nitrogen/carbon ratio in the compound layer is not completely known, and the reproducibility of the case composition is rather problematic, even with up-to-date process control. A certain amount of carbon may also be found in plasma-nitrided duplex compound layers (c⬘ Ⳮ e) due to the reverse diffusion of carbon from the substrate into the compound layer. This retrodiffusion may be very important on the interface, where the e nitrides absorb important quantities of carbon, causing even the dissolution of carbide lamellas from the pearlite grains in a ferritic/pearlitic substrate (see Fig. 4). Certainly, as plasma nitrocarburizing becomes a common practice, it is possible to obtain a monophase, compact e compound layer with an optimized nitrogen/carbon ratio (Fig. 7 a–c) (Ref 8, 16). The residual stresses in the compound layer and in the substrate are strongly connected to the nature of compound layers. Whenever a thick, more or less monophase e-type compound layer is desired, the higher treating temperatures result in less significant substrate hardness and in a lower residual stress level. The influence of a compound layer on fatigue properties may not be neglected, however, as it reduces the stress concentrators in the surface. Slightly different phases appear when stainless steels are plasma nitrided (Ref 7, 13, 17– 21). The problem in this case is to obtain a simultaneous increase in tribological properties, without significant loss in corrosion behavior. Passivated or oxide surface films offer only a partial solution.

stresses as compared to those in carburized layers. Due to the complex mechanism of “hardening” in nitriding (the presence of a compound layer), investigations are more difficult and the mathematical modeling must consider numerous factors. Most of the data in the literature are connected to the residual stresses in the diffusion layer, and generally relate to gaseous nitriding. Surprisingly few data can be found on residual stresses in nitrocarburizing, especially for compound layers. From the experimental data on tribological and fatigue properties it is obvious that not only the compound and the diffusion layer play

Fig. 5

Compound Layer Several theories related to the origin of residual stresses in nitrided layers associate these stresses mostly with the diffusion layers (Ref 22–25). The main causes of the residual stresses are considered to be: ● Changes in chemical composition in the dif-

fusion zone

● Phase transformation in the diffusion zone,

and precipitation phenomena

● Volume changes caused by the phase trans-

formation and the growth of precipitates

● Thermal effects due to different coefficient of

expansion during layer formation The residual stresses connected to the compound layer formation are rarely considered; however, their effect on the fatigue limit of treated parts may be significant, especially if the film thickness of the layer is comparable to the total wall thickness (engineering components for precision mechanical applications). These residual stresses originate from: ● Volume changes during the formation of dif-

ferent phases in the compound layer

● Internal stresses caused by molecular nitro-

gen formation in the porosity

Residual Stresses in Nitrided Layers Residual stresses and their computer modeling have been extensively studied for case hardening. However, a rather limited number of papers deal with the problem of residual stresses in nitriding and related technologies. No doubt one of the reasons for this is the lesser effect on distortions and generally lower level of these

an important role in properties of treated parts, but that specific phenomena on the interface between the compound layer and substrate are also critical.

Fig. 6

Microstructure of plasma-nitrided low-alloy steel (18MnCr10). 560 C (1040 F), 8 h

Modified interface between the compound layer and substrate as result of carbide dissolution. TEM

Dependent on process parameters, the porosity is generally associated with the high nitrogen potential for the e-type compound layer. This porosity usually is concentrated at the outer zone of the compound layer, sometimes causing tensile residual stresses to appear there (Ref 14, 26, 27). Investigations have shown that compressive residual stresses exist in the compound layer during layer growth, and these stresses increase during cooling as a result of the volume misfit generated by different thermal expansion coefficients of the compound layer and the diffusion zone (Ref 28). These observations apply particularly to c⬘ structures but are also true for compact e structures. The internal stresses in the compound layer are of the second and third type (Ref 3, 29). Considering the definition of residual stresses given by Macherauch et al. (Ref 29), residual stresses of the third type are particularly important on the interface, where they occur due to high dislocation density at grain-boundary inhomogeneities and to formation of the new crystal structure (e or c⬘). Very few measurements of residual stresses in compound layers are known, partly because of technical difficulties—even by x-ray diffraction (XRD) methods—and partly because the diffusion layer seemed to play a more important role in the residual stress state of the surface. In situ measurements of residual stresses have been performed for a c⬘-Fe4N-type compound layer built on a steel surface during gas nitriding (Ref 28).

212 / Residual Stress During Hardening Processes Most of the data related to residual stresses in compound layers result from experiments in gaseous nitriding or plasma nitriding (Ref 27, 30– 32). The combined effect of nitrogen and carbon, and of nitrogen, carbon, and oxygen, has been extensively investigated (Ref 9, 10, 33–35), but these studies have focused primarily on their effect on wear and fatigue behavior and less on the residual stress state. When considering the residual stresses in compound layers, the layer structure cannot be neglected. Structures of c⬘ or etype (or, more exactly, pure c⬘ or mixtures of c⬘-e with different compositions) were investigated, with the aim of finding the most favorable effect on fatigue behavior. Combined wear and fatigue resistance is of critical importance for the mechanical industry (Ref 7, 15, 17, 36–38). In terms of fatigue behavior, a particular aspect may be connected to the penetration of the compound layer into the substrate: Electron-microscopic examination of nitrocarburized surfaces has shown that a significant “removal” of surface defects resulted from the finishing process, thus decreasing the stress concentrators that can initiate the first microcracks in long-cycle fatigue phenomena (Ref 34). Some discrepancies among the experimental results, including their interpretation and concluTable 1

sions, are also found in the literature. Frequently, the role of residual stresses in compound layers is considered of lesser importance, while other studies emphasize that the compressive stresses in the surface will practically disappear with removal of the compound layer (Ref 31, 39). As discussed in the article “Material Factors” in this Handbook, significant differences appear in the structure and morphology of nitrided (nitrocarburized) layers, a function of the technological process. These differences are reflected in the stress-strain state of the layers. However, it is very difficult to obtain comprehensive and reliable data on residual stresses in compound layers, and it seems even more problematic to measure the residual stress state at the interface between the compound layer and the substrate. Most experiments have been performed using the XRD method for measuring the residual stresses, but this presumes chemical or mechanical removal of subsequent films of the compound layer, certainly modifying its stress state as well. In situ measurements of residual stresses in compound layers have been performed on gasnitrided samples (Ref 28). Data in the literature show a wide range of values for residual stresses, but it is generally agreed that tensile stresses appear in e compound layers. According to one study, tensile stresses

Residual stress distribution in the e and cⴕ compound layers Residual stress(a), MPa (ksi) e-Fe2ⴑ3N

Distance from surface, mm (in.)

0 (0) 0.005 (0.0002) 0.01 (0.0004) 0.015 (0.0006) 0.02 (0.0008) 0.03 (0.001)

ⳮ54 (ⳮ8) ⳮ492 (ⳮ71) ⳮ594 (ⳮ86) … ⳮ590 (ⳮ86) …

cⴕ-Fe4N

Ⳮ48 (Ⳮ7) ⳮ264 (ⳮ38) … ⳮ432 (ⳮ63) ⳮ587 (ⳮ85) …

ⳮ327 (ⳮ47) ⳮ624 (ⳮ90) ⳮ721 (ⳮ104) … ⳮ705 (ⳮ102) …

ⳮ393 (ⳮ57) ⳮ528 (ⳮ77) … ⳮ764 (ⳮ111) ⳮ724 (ⳮ105) ⳮ640 (ⳮ93)

(a) The residual stress values given for the same layer structure were measured for layer thicknesses of 22 and 25 lm on 31CrMoV9 steel treated at 570 C (1060 F) for 16 and 32 h, respectively. Source: Ref 27

Fig. 7

up to 200 MPa (30 ksi) were found on Armco iron, whereas another found approximately 150 MPa (20 ksi) tensile or compressive stresses on C45 steel. Rozendaal et al. (Ref 40) measured tensile stresses up to 800 MPa (115 ksi) in the outer zone of e layer, which decreased toward the interface and changed to compressive stress. In c⬘ compound layers, the same authors measured compressive stresses between ⳮ60 and ⳮ600 MPa (ⳮ10 and ⳮ90 ksi). Oettel and Ehrentraut (Ref 26) studied the residual stresses in compound layers of different nitrided alloy steels. According to their data, compressive stresses between ⳮ350 and ⳮ1500 MPa (ⳮ50 and ⳮ220 ksi) are typical for c⬘ compound layers, whereas tensile stresses of 100 to 370 MPa (15 to 55 ksi) characterize the basically e structures. However, compact e (pore-free) layers may show compressive stress values up to ⳮ580 to ⳮ800 MPa (ⳮ85 to ⳮ115 ksi) at the interface with the diffusion layer. In general, thinner layers presented higher stress values, which may be explained primarily by their more compact nature and also by a lesser effect of the sophisticated influence of the relaxation process during the long treating cycle. Investigations performed by Spies (Ref 27) with Cr-Mo, Cr-Mn, and Cr-Mo-V steels have shown stress values of ⳮ500 to ⳮ600 MPa (ⳮ70 to ⳮ90 ksi) in e-Fe(2ⳮ3)N compound layers of 20 to 25 lm and 620 to 720 MPa (90 to 105 ksi) for c⬘. Increasing the treating time from 16 to 32 h, a compound layer thickness of 20 to 30 lm caused no significant decrease in residual stress level. The most significant data are shown in Table 1. All the available data indicate higher compressive stresses in compound layers of pure c⬘ than in e or c⬘ Ⳮ e layers. According to Spies (Ref 27), maximum residual stresses may attain ⳮ700 to ⳮ750 MPa (ⳮ100 to ⳮ110 ksi) in c⬘-

Plasma nitrocarburized EN-9 (070M55) steel. (a) Microstructure. (b) GDOS carbon and nitrogen profile. (c) X-ray diffraction pattern at the surface (showing almost pure ephase). 570 C (1060 F), 3 h, 4 mbar. Source: Ref 16

Residual Stresses in Nitriding / 213 Fe4N compound layers, whereas values of 550 to 600 MPa (80 to 90 ksi) were measured in eFe2ⳮ3N layers. In situ measurements in gaseous nitriding performed by Hoffmann et al. (Ref 28) resulted in a slightly lower compression stress level of about ⳮ450 MPa (ⳮ65 ksi). The carbon content of the substrate, especially the carbon level in the compound layer, has a considerable effect on residual stresses; increased carbon content results in an increased residual stress level (Ref 8, 28) (Fig. 8). However, the importance of carbon in the compound layer is more emphasized in e-Fe2ⳮ3(C,N) structures, due to the increased solubility of carbon in the compact hexagonal e-Fe2ⳮ3N crystals (Ref 8). The apparently lower residual stress values in e-type compound layers probably also can be explained by the ductility of this structure. These observations pertain to gas nitriding, where the compound layer consists almost exclusively of Fe4N nitrides. Very few data have been published on residual stresses in nitrocarburizing, where the compound layer consists mainly of e-carbonitrides with some oxygen (Ref 6, 8, 10). Investigations have shown that compressive stresses appear in the compound layer due to volume changes during e-crystal formation as a result of dissolved carbon from the matrix. This phenomenon is clearly shown in Fig. 9 (Ref 9). Due to the solubility of carbon in e-nitrides (carbonitrides), the carbide particles of the pearlite grains in the interface are dissolved in e-crystals; thus, the compound layer is “rooting” in the substrate at the boundaries of pearlite grains. This phenomenon causes compressive residual stresses not only in the compound layer, but also in the substrate in the interface region. It may also be partly responsible for increased fatigue resistance of nitrocarburized samples and for the significant increase in surface fatigue resistance when dynamic loading is combined with sliding wear. According to the literature, the incorporation of carbon and/or oxygen in the layer does not significantly affect the residual stresses in the usual composition ranges (Ref 10, 33). This may well be explained by the almost similar interstitial influence on lattice parameters of these elements. Mathematical modeling of residual stresses in

Residual stresses in c⬘-nitride during cooling from the nitriding temperature to room temperature. Source: Ref 28

compound layers has been little studied. Computer modeling of compound layer formation, which is of crucial importance for the mathematical formulation of stress patterns, was initiated in a few investigations (Ref 32, 41), but the results fail to answer a number of basic questions. Both the kinetics of surface reactions in nitriding and the thermodynamics of Fe-N-C have not yet been satisfactorily elucidated. The very good model proposed by Sun and Bell (Ref 42) for the diffusion of nitrogen and the formation of nitride precipitates in the matrix also gives only a few indications for the compound layers.

Diffusion Layer As was discussed earlier, a number of studies present different aspects of the residual stresses in nitrided layers (Ref 14, 22–24, 26, 28, 31, 32, 37, 43–49). The mechanism of nitriding causes practically no differences in the phenomena in the diffusion layer function of the applied technology. Due to its low solubility in the ferrite matrix, nitrogen will form Fe4N-type nitride needles or precipitates in the diffusion layer substrate. The presence of alloying elements will modify the composition of the nitrides, resulting in nitrides and carbonitrides of the alloying elements (Ref 44, 45). The treating temperature strongly influences both the structure and composition of the nitrides, but basically the kinetics of diffusion layer formation will remain the same for different industrial processes. Thus, the main causes of the residual stresses are connected to volume changes in the layer due to:

● Formation of iron nitrides in the compound

layer ● Dissolved nitrogen in the ferrite matrix of the

layer ● Precipitation of different nitrides in the dif-

fusion layer ● Decarburization in the diffusion layer ● Differences in thermal contraction between

the layer and the substrate during cooling ● Thermal volume misfits between the matrix

and precipitates, generating thermal residual stresses during cooling from the process temperature. (These volume misfits originate from differences in the linear thermal expansion coefficients of the precipitates and matrix.) Thus, it seems logical that the residual stress level increases with increased nitrogen content, respectively with increased number and volume of the nitride precipitates. This was clearly shown in the experimental work of several investigators (Ref 26, 28, 32, 40, 44, 45, 50). It is also important to emphasize that the residual stresses may attain a maximum value limited by the thermal-induced creep phenomena. Higher values should cause plastic deformations and thus a reduction of the stresses (Ref 45). Maximum stress levels are shown in Table 2. The maximum compressive stresses are determined primarily by the nitrogen concentration and less by the structural phase itself. Due to the maximum of 0.1% nitrogen solubility in ferrite, the stress level cannot be higher than ⳮ250 MPa (ⳮ35 ksi). In contrast to the development of re-

Fig. 8

Fig. 9

Dissolution of carbides from pearlite grains of the subsurface region in the e-type compound layer. TEM

214 / Residual Stress During Hardening Processes sidual stresses in carburizing, there is no significant influence of other factors associated with cooling (i.e., the changing solubility of nitrogen in iron, or other thermal stresses associated with quenching). Both the material composition and the process parameters covering the treating temperature and the nitriding potential influence the residual stress state of the nitrided steel. As might be expected, the steel composition influences not only the precipitates, but also the behavior of nitrogen in the diffusion layer. The effect of carbon content must also be considered. Specimens containing a large amount of strong nitride-forming elements—such as chromium, aluminum, and ti-

Table 2 Influence of nitride-forming elements on residual stress Residual stress (a) Element

Ferrite, 0.1N Fe4N AlN CrN Cr2N Dissolving Fe3C

Residual stress (b)

MPa

ksi

MPa

ksi

… … ⳮ820 ⳮ440 ⳮ210 …

… … ⳮ120 ⳮ65 ⳮ30 …

ⳮ2700 ⳮ2600 ⳮ1600 ⳮ1700 ⳮ1600 Ⳮ1250(c)

ⳮ390 ⳮ375 ⳮ230 ⳮ245 ⳮ230 Ⳮ180(c)

tanium—form a high-hardness case and high residual stresses in the layer. A direct correlation seems to exist between the microhardness of the diffusion layer and the residual stress level (Ref 49). Also, the higher the carbon content of the steel, the higher the compressive residual stress level (Ref 28). This is illustrated in Fig. 10 (Ref 45). The process temperature has an important effect on the residual stresses, by its influence both on the diffusion rate and on differences in precipitate formation during cooling. In situ measurements of residual stresses during the nitriding process revealed important data on not only stress relaxation by plastic deformation during nitriding, but also the influence of process parameters on induction of residual stresses in both the compound and the diffusion layers (Ref 28). The cooling process can be considered the most important step in generating residual stresses in the compound layer, whereas stresses are created in the diffusion zone mostly during nitriding and only a very slight change occurs in cooling. Figure 11 shows the general influence of treating

(a) % Me mass. (b) % N mass. (c) % C mass. Source: Ref 45

Fig. 12

Influence of treating time on residual stresses. Source: Ref 45

Increase of residual stresses as a function of the concentration of nitride-forming elements in steel. Source: Ref 45

K-oxygen K-no oxygen

5 Reaction rate, k 10–7

4

3

2

1

0 0

Fig. 11

Decrease of residual stress level with increasing nitriding temperature. Source: Ref 45

Influence of Residual Stresses on Fatigue Behavior of Nitrided Steel Components Residual Stresses and Bending Fatigue Resistance

6

Fig. 10

temperature on stress pattern (Ref 45). Nitriding time also influences the residual stress profile. A long nitriding cycle produces a deeper compressive stress distribution, but with lower maximum values in the near-surface region (Ref 37). The simultaneous stress generation and relaxation process can explain this, with the dominance of the relaxation in long treating time. The influence of treating time on the residual stress pattern can be clearly seen in Fig. 12 (Ref 45). In Fig. 11 and 12, notice the specific decrease in residual stresses in the near-surface region, which is caused first of all by the redistribution of carbon in the diffusion layer. In chromiumcontaining steels, an increase in carbon content in front of the diffusion layer is observed, together with decarburization in the surface and precipitation of cementite on the grain boundaries (Ref 24). In gaseous processes, oxygen in the treating atmosphere also has a remarkable effect on the kinetics of layer formation. Oxygen causes a surface activation, which has a positive effect on both nitrogen diffusion and uniformity in the surface layer. It has been proven that in the presence of a controlled oxidation, the surface layer contains no soft spots, which are frequently characteristic of passive surfaces resulting from machining operations (especially deep drawing, lapping, honing, etc.) (Ref 10, 35). This effect is shown in Fig. 13. Though no specific data are known on the influence of oxygen on residual stresses, it may well be assumed that enhanced nitrogen diffusion increases the residual stress level.

10

20 30 40 50 Undissociated ammonia, R, %

60

Effect of oxygen addition on the reaction rate (k) in gaseous nitrocarburizing, as a result of surface activation

Fig. 13

Nitrided surface layers (especially those that have been nitrocarburized) have a clearly positive influence on both the bending fatigue and surface fatigue behavior of steel components. However, this positive effect is the result of a rather complex mechanism. The surface of the components usually presents a complex structure after machining, with the characteristic Beilby layer. The inner zone of this layer, consisting mostly of deformed and partially damaged grains and crystals, is the source of microcrack initiation. These microcracks are extremely deleterious when friction combined with local hertzian loading appears (gears, bearings, etc.). The recrystallization associated with the dissolution phenomena in the surface film eliminate these stress concentration points, thus reducing the crack initiation hazard (Ref 38). On the other hand, the considerable compressive stresses in the near-surface region of the compound layer further reduce the crack initiation in this zone. Certainly, this effect is impor-

Residual Stresses in Nitriding / 215 tant first of all in long-cycle fatigue behavior. The compressive residual stresses in the diffusion layer are of primary importance in reducing the subsurface crack initiation, as well as the

crack propagation rate. However, remember that the compound layer also has a combined effect with the diffusion layer. This can be illustrated by comparing the fracture toughness of different

nitrided and nitrocarburized layers, using the reverse impending method (Ref 51). Figure 14 shows clear evidence of these differences, but unfortunately no residual stress measurements were performed on the test samples. The influence of nitriding and carbonitriding on bending fatigue properties was investigated for different steels and different process parameters (Ref 36, 52–54). The fatigue resistance of both unnotched and notched samples depends on the value and distribution of the residual stresses in the diffusion zone. This is practically correlated with the hardness and its distribution in the layer. For the same hardness values, a deeper nitride case will increase the residual stresses in the diffusion zone, thus causing an increase in long-cycle fatigue strength (Ref 54). According to Spies et al. (Ref 52, 54), an e-type compound layer results in higher residual stresses in the diffusion layer and in a higher fatigue limit (Tables 3 and 4). There is no doubt that all the data from the technical literature outline the efforts for a more fundamental, mathematical approach to the problem of residual stresses in nitrided steels and their influence on fatigue behavior. Though nitriding—with all its industrial versions—is a well-established and widely applied technology, the mathematical description of layer growth and the formation of local strength and macrostresses is far from that of carburizing. The explanation may be connected to the more sophisticated kinetics and thermodynamics of the process, but also to the practical fact that the prediction of residual stresses in nitrided components is less critical than for carburized components.

Residual Stresses in Contact Fatigue Behavior

Fig. 14

’TEMs showing typical crack pattern of surface layer. (a) Gaseous nitrocarburizing. (b) Salt-bath nitrocarburizing. (c) Plasma nitriding. (d) Plasma nitrocarburizing

Table 3

Influence of steel grade on residual stresses and fatigue life of structural steels Compound layer

Steel

Type

Thickness, lm

Case hardness, HV0.3

rE(a), MPa (ksi)

rAD(b), MPa (ksi)

Wo¨hler line exponent(c), k

45MnV3BY

c⬘ e(c⬘) c⬘ e(c⬘) c⬘ e(c⬘) e(c⬘)

8–10 20–22 8–10 22–24 10 22–25 25

535–550

ⳮ135 (ⳮ20) ⳮ185 (ⳮ27) ⳮ300 (ⳮ45) ⳮ350 (ⳮ50) ⳮ255 (ⳮ35) ⳮ315 (ⳮ45) ⳮ260 (ⳮ40)

499 (72) 528 (77) 574 (83) 593 (86) 608 (88) 670 (95) 615 (90)

15.8 19.9 19.3 29 11.2 15.8 15.3

20MnCr5N 20MnCr5QT

660–680 640–650 640–650 600

(a) rE, residual stress; depth below surface, 50 lm. (b) rAD, fatigue, when a nominal mean stress or residual stress is applied (long life alternating strength); bending fatigue test, P ⳱ 50%. (c) The Wo¨hler line exponent was calculated for long-cycle fatigue. Source: Ref 52

There is a considerable difference between the bending or torsion fatigue resistance and the surface fatigue behavior of treated steels. Failure of components exposed to contact fatigue occurs in different forms, such as pitting, exfoliation, or surface crack formation (which later can cause pitting or exfoliation). Surface fatigue also has a specific form when mechanical loading combines with a corrosive environment, as in many chemical industry applications. This fretting corrosion also must be considered on nitrided samples. Surface fatigue as the result of combined rolling and sliding load usually starts as microcracks at small angles to the surface, in the immediate subsurface region due to shear stresses. The greater the sliding loading effect, the closer to the surface are these microcracks. Contact fatigue behavior of nitrided/nitrocarburized components depends on both the compound and the diffusion layers. The compound layer has a positive influence on sliding wear properties of the components, whereas the diffusion layer is the support for hertzian, normal cyclic loads. This composed structure leads to a significant difference in the resistance of nitrided and, especially, nitrocarburized steels compared to carburized

216 / Residual Stress During Hardening Processes steels, because not only is the layer thickness smaller, but the hardness gradient in the layer presents different shapes for the two different surface layers. Due to these differences, nitrocarburized surfaces show better resistance to sliding wear, but lower normal loading capacity may be expected. Compressive residual stresses in the diffusion layer also improve contact fatigue resistance (Ref 37, 38, 41). According to Li et al. (Ref 37), the short-time plasma nitriding has a significant effect on the fretting fatigue resistance of En19 steel, increasing it by more than 250%. Other sources state that there are no practical differences between plasma-nitrided and gaseous-nitrided samples exposed to contact fatigue, presuming the same type of layer structure was obtained (Ref 31, 39).

Modeling and Prediction of Residual Stresses Modeling of the nitriding and nitrocarburizing process is much less developed than modeling of carburizing. Much experimental data exist concerning the structure and properties of ni-

trided/nitrocarburized layers, but only a few attempts have been made to develop a mathematical description of the layer-growth mechanism and the formation and distribution of residual stresses. Probable explanations for this situation may be connected to the complexity of the parameters to affect the process itself, and to the less critical effect on deformations and service behavior. No practical attempts have been made to mathematically model the compound layer formation and residual stress distribution. In contrast, a few remarkable studies may be found on modeling the formation and stress-state of the diffusion layer. A model elaborated by Buchhagen and Bell (Ref 32) for the simulation of residual stress development in the diffusion layer of low-alloy plasma-nitrided steels considers the thermally controlled creep process, with the residual macrostress being the driving force for stress relaxation. According to this model, the thermally induced stress was the temperature-dependent volume part of the constituents and their volumes per metal atom. These volumes were considered separately for heating to the process temperature and for cooling. Due to the missing quantitative

data on stress relaxation and on the redistribution of carbon in the diffusion layer, some assumptions have to be made using measured residual stress profiles and carbon profiles from analysis by glow discharge spectroscopy. The plasma-nitriding simulation program (PLASMA) developed by Sun and Bell (Ref 42) calculates the profiles of nitrogen concentration, volume fraction of the nitrides, and hardness as a function of distance from the surface. The modified program activates the stress simulation unit after every 10 min of the simulated nitriding time. The time-constant for the relaxation must be provided experimentally. Extensive work on computer simulation of the formation of diffusion layers in nitriding chromium-alloyed steels was carried out by Schreiber et al. (Ref 23, 43, 50). The model developed assumes that the nitrogen in the diffusion layer is dissolved partly in the ferritic matrix and partly in nitride precipitates. The nitrogen diffusion generally takes place with a constant surface nitrogen concentration; at the beginning of the process the compound layer is formed and the diffusion of the dissolved nitrogen will be determined by the equilibrium concentration on the phase boundary between the ferrite and the iron nitrides (the compound layer and the substrate) (Ref 23). The total solubility thus is much higher than in pure iron, because the strain caused by the nitride precipitates leads to elastic distortions of the matrix around the precipitated particles. This excess nitrogen is determined by the stress state caused by the misfitting nitrides and the maximum solubility of the strain-free lattice, C a0,N, and can be described by: r •V

冢R • T冣

C aN ⳱ C a0,N •exp r⳱

4•G •e•M 4 1 Ⳮ •G•K 3

C a0,N ⳱ A • exp

Fig. 15

Calculated nitrogen concentrations for iron and FeCr alloys. 550 C (1020 F) 10 h. Source: Ref 50

Table 4

(Eq 1)

(Eq 2)

ⳮQ

冢R • T冣

(Eq 3)

where A is a constant, Q is activation energy, R is a gas constant, T is temperature, V is the molar volume of nitrogen in iron, G is shear modulus, K is the compressibility of nitride precipitates, e is volume misfit, and M is the molar fraction of the precipitates.

Structure of nitrided layer and fatigue limit (␣K ⴔ 1) Hardness, HV0.3

rE (c)

Ncd (b)

Stress-intensity factor

rAD (d)

Steel (a)

Case

Core

mm

in.

MPa

ksi

MPa

ksi

Wo¨hler line exponent (e), k

Ratio of increase (f)

MPa

ksi

20MnCr5N 20MnCr5QT

630 600 600 590 470

190 260 250 250 250

0.42 0.24 0.44 0.56 0.60

0.017 0.009 0.017 0.022 0.023

ⳮ365 ⳮ360 ⳮ430 ⳮ235 ⳮ140

ⳮ53 ⳮ52 ⳮ60 ⳮ35 ⳮ20

490 640 670 745 760

70 90 100 108 110

14.1 13.0 9.3 9.2 18.5

1.55 1.22 1.28 1.49 1.60

15.7 16.7 18.9 21.9 23.7

2.3 2.4 2.7 3.2 3.4

C45QT

(a) Neds nitrided case depth. (b) Pretreatment: N, normalized; QT, quenched and tempered. (c) rE, residual stress; depth below surface, 50 lm. (d) rAD, fatigue, when a nominal mean stress or residual stress is applied (long life alternating strength); rotating bending test: P ⳱ 50%; diameter, 7 mm. (e) For high-cycle fatigue: P ⳱ 50%; (f) rAD nitrided/rAD unnitrided for P ⳱ 50%. Source: Ref 52

Residual Stresses in Nitriding / 217 The fraction of the precipitated nitrides, W(t), can be described by the following Avrami equation: W(t) ⳱ (1 ⳮ eⳮ(t/s) ) n

(Eq 4)

Assuming homogeneous nucleation and spherical particles, the precipitation rate constant is given by: s⳱

cP ⳮ c0 r2e • cm ⳮ c0 2 • DMe

(Eq 5)

where DMe is the diffusion coefficient of the alloying element; re is the equilibrium radius of precipitates; and cm, cP, c0 are the alloying element concentration in the matrix, in the precipitate, and at the phase boundary of the precipitate respectively. Assuming that the z-axis is perpendicular to the surface, the diffusion and precipitation process can be described using the following onedimensional inhomogeneous diffusion equation: dW 冢冣兺 k • 冢 dt 冣

dC d2C ⳱ ⳮDN • Ⳮ dt dz2

(Eq 6)

i

i

i

where DN is the diffusion coefficient of nitrogen and ki represents the nitrogen fraction in the precipitate of the alloying element i. The diffusion equation can be solved numerically. The boundary condition is given by the sum of nitrogen a concentration (C aN) in strained and (C0,N ) in strain-free lattice of ferrite. The calculated nitrogen concentrations for pure iron and FeCr alloys are shown in Fig. 15 (Ref 50). With the calculated volume fraction of precipitation as a function of the distance from the surface, the strain distribution due to volume change is given. The total strain increment consists of three components: vol detx ⳱ deel Ⳮ deplx x Ⳮ dex

(Eq 7)

The elastic strain component is given by Hooke’s law: rel x (z) ⳱

E • eel x (z) 1 ⳮ m

(Eq 8)

The strain due to volume change is given by the volume misfit between nitride and matrix (DV/ V) and the volume fraction of precipitated alloying element CME: evol ⳱ x

兺i (CME)i • 3 冢 V 冣i 1 DV

(Eq 9)

For plastic strains, thermally induced creep is taken into account and described with a Norton equation: depl x ⳱ A•

Fig. 16

Measured residual stresses in an FeAlC alloy with 0.6 wt% Al and 0.15 wt% C. 590 C (1095 F) Source: Ref 50

n

冢G冣 • dt r

where A and n are constants. Using the mechanical equilibrium condition for an endless plate with thickness d,

冮 r (z)dz ⳱ 0 el x

Fig. 17

Calculated residual stresses for an FeAlC alloy with 0.6 wt% Al and 0.15 wt% C, 590 C (1095 F). Source: Ref 50

(Eq 10)

(Eq 11)

the macrostress can be calculated. The measured and simulated stress profile data show a very good agreement. Figure 16 shows the macrostress distribution in the diffusion layer of an FeAlC alloy nitrided at 590 C (1095 F) for 4 and 36 h, respectively (Ref 50). The stress was measured by x-ray diffraction combined with chemical removal of the layer. The sample nitrided for 4 h presents a compressive stress maximum of 380 MPa (55 ksi) near the surface. After 36 h of nitriding, the compressive stress maximum decreases to 200 MPa (30 ksi) and shifts to a distance of about 550 lm from the surface. The maximum of compressive stresses near the surface disappears completely during prolonged nitriding. Figure 17 presents the simulation of macrostress distribution (Ref 50). The position, the value of the maximum, and the extension of the stress almost agree with the measured values. The calculated decrease of stress near the surface is lower than the measured one. This effect is

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Stresses, Informationgesellschaft Verlag, 1993, p 1001–1010 H. Oettel and B. Ehrentraut, Macroscopic Residual Stresses in Compound Layers of Nitrided Steels, HTM 40, Rudolph Haufe Verlag, Munich, Germany, 1985, p 183– 187 (in German) H.-J. Spies, “Residual Stresses in Compound Layers (Measurement with Cr-K␣Radiation),” University of Freiburg, Germany, unpublished report (in German) F.T. Hoffman, U. Kreft, T. Hirsch, and P. Mayr, In situ Measurement of Residual Stresses during the Nitriding Process, Proceedings of the Second International Conference of Carburizing and Nitriding with Atmospheres (Cleveland, OH), ASM International, 1995, p 289–293 E. Macherauch, H. Wohlfahrt, and U. Wolfstieg, Practical Definition of Residual Stresses, HTM 28, Vol 3, Rudolf Haufe Verlag, Freiburg, Germany, 1973, p 201– 211 (in German) E.J. Mittemeijer, The Relation between Residual Macro- and Micro-stresses and Mechanical Properties of Case-Hardened Steels, Case Hardening Steels: Microstructural and Residual Stress Effects, TMSAIME, 1986 J.M. Cowling and J.W. Martin, Effect of Internal Residual Stresses on the Fatigue Behavior of Nitrided En 41B Steel, Heat Treatment ‘79, The Metals Society, London, 1979, p 178–181 P. Buchhagen and T. Bell, Simulation of the Residual Stress Development in the Diffusion Layer of Low Alloy Plasma Nitrided Steels, Computational Mater. Sci., Vol 7, 1996, p 228–234 H.-J. Spies and F. Vogt, Gaseous Nitriding of High Alloy Steels, HTM 52, Vol 6, Rudolf Haufe Verlag, Freiburg, Germany, 1997, p 342–349 (in German) Z. Kolozsva´ry, Observation Concerning the Characteristic of Soft Nitriding in Controlled Atmosphere, Casting and Forging, No. 293, 1972, p 43–46 Z. Kolozsva´ry, A. Baraba´ssy, and V. Sańdor, Effect of Surface Activation on the Formation of Carbonitride Compound Layers and Their Properties, Proceedings of XVIIth International Conference of Heat Treatment (Barcelona), Asociacion Tecnica de Tratamentos Termicos, 1978, p 1–12 H.-J. Spies, M. Scharf, and N.D. Tan, Influence of Nitriding on the Durability of Steels, HTM 46, Vol 5, Rudolf Haufe Verlag, Freiburg, Germany, 1991, p 288–293 (in German) C.-X. Li, Y. Sun, and T. Bell, Consideration of Fretting Fatigue Properties of Plasma Nitrided En19 Steel, Surf. Eng., Vol 15 (No. 2), 1999, p 149–153 Z. Kolozsva´ry, Contribution to the Study of Surface Fatigue in Sliding Wear, Wear, No. 25, 1973, p 215–224 D.H. Jack and S. Winnik, Effect of Process

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Variables on the Fatigue Resistance of Nitrided Steel, Heat Treatment ‘79, The Metals Society, London, 1979, p 169–177 H.C.F. Rozendaal, P.F. Colijn, and E.J. Mittemeijer, Morphology, Composition and Residual Stresses of Compound Layers of Nitrocarburized Iron and Steels, Proceedings Heat Treatment 1984, The Metals Society, London, 1984, p 31.1–31.6 G. Schreiber and H. Oettel, Modeling of the Precipitation and Relaxation Processes: Diffusion Layers in Nitriding and Nitrocarburizing, Nitrieren und Nitrocarburieren, Weimar, 1996, p 167–175 (in German) Y. Sun and T. Bell, Proceedings of 9th International Congress on Heat Treatment and Surface Engineering, 26–28 Sept 1994 (Nice, France), F. Moreaux, Ed., PYC Edition, Ivry-Sur-Seine Cedex, France, 1994, p 385–394 G. Schreiber, H. Oettel, W. Darbinjan, and R. Wiedemann, Residual Stresses in the Precipitation Zone of Nitride Layers, Residual Stresses, European Conference on Residual Stresses, Frankfurt, 1992, p 965–974 H. Oettel, G. Schreiber, Residual Stresses in

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Nitriding of Steels, 6th Konferenz Metallkundl. Probleme d. Werkstoffentw., TU Bergakademie Freiberg, 1989, p 194–199 (in German) H. Oettel and G. Schreiber, Formation of Residual Stresses in the Diffusion Layer, Nitrieren und Nitrocarburieren, AWT Tagungsband, 1991, p 139–151 (in German) J. Zu¨rn, C. Razim, and J. Gosch, The Effect of Residual Stress in Case Hardening, Heat Treatment and Surface Engineering: Proc. 6th International Congress on Heat Treatment of Materials, 1988, p 279–283 W. Daves and F.D. Fischer, Numerical Simulation of the Development of Residual Stresses during Nitriding, Residual Stresses, Informationgesellschaft Verlag, 1993, p 957–964 B. Larisch, H.-J. Spies, and K. Ho¨ck, Bright Nitriding of Cr-Mo-Steels in Plasma and Gas, Proceedings of the Second International Conference of Carburizing and Nitriding with Atmospheres, (Cleveland, OH), ASM International, 1995, p 213–217 N.L. Loh and L.W. Siew, Residual Stress

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Profiles of Plasma Nitrided Steels, Surf. Eng., Vol 15 (No. 2), 1999, p 137–142 H. Oettel and G. Schreiber, Calculation of Macro-stresses in Nitrided Steels, 4th Conference on Residual Stresses, Baltimore, 1994, p 1285–1291 Z. Kolozsva´ry, S. Jańosi, V. Sańdor, A. Rusu, and T. Re´ti, “A New Approach in Characterizing the Mechanical Properties of Surface Layers,” presented at 18th ASM Heat Treating Society Conference and Expo, Rosemont, IL, 13–15 October 1998 H.-J. Spies, Fatigue Behaviour of Nitrided Steels, Steel Re., Vol 64 (No. 8/9), 1993 H.-J. Spies, K.H. Kloos, J. Adelmann, T. Kaminsky, and P. Trubitz, Modeling of Bending Fatigue resistance of Samplers Resembling Engineering Components with Standard Wo¨hler-bands, Mat. Wiss. Werkstofftech., Vol 27, 1996, p 60–71 (in German) H. Spies, N.D. Tan, and F. Vogt, Influence of Morphology of Nitrided Layers on the Fracture Toughness of Notched Samples, HTM 48, Vol 3, Rudolf Haufe Verlage, Freiburg, Germany, 1993, p153–161 (in German)



Induction Hardening J. Grum, University of Ljubljana, Ljubljana, Slovenia

INDUCTION SURFACE HARDENING offers a number of advantages over other heat treatment methods. The most important advantages are short heat treatment times, good repeatability concerning the hardened-layer quality, small or negligible subsequent distortion, and a minimum subsequent product surface oxidation. Induction hardening offers good possibilities for automation and can be incorporated into a manufacturing cell (Ref 1, 2). Induction surface hardening is applicable to axisymmetric or near-axisymmetric steel or cast iron machine parts that are produced in substantial volumes. There are two basic techniques for induction hardening of machine parts: “single shot” and “scanning.” The former employs selective heating and quenching to harden a specific area or areas of the machine part in one operation. The latter is usually applied to progressively harden long, continuous sections such as shafts and spindles. In this instance, the scanning inductor traverses the length of the section, heating only a relatively small area at any given time, and is followed closely by the quench arrangement, which is often an integral part of the inductor (Ref 1, 3). A basic characteristic of induction hardening is that heat is generated in the workpiece due to the skin effect. If a ferromagnetic material is surrounded by a load coil or inductor through which high-frequency alternating current passes, flow of eddy currents is induced in the surface layer of the workpiece due to the alternating magnetic field. The flow of these currents heats the workpiece. The mode of heating may be influenced by the workpiece arrangement in the inductor as well as by electric parameters. Heating is very fast and very reliable. Consequently, induction heating, that is, induction hardening, has become successfully established in automated production systems. Induction heating is suited to small, medium-size, and large, as well as extremely large, machine parts since, by varying energy input, heating to the required temperature and the specified case depth may be ensured. Flame hardening is suited mostly for individual hardening of parts with large dimensions and of comparatively uncomplicated shapes. A characteristic of flame hardening is that a gas mixture is burning at the blowpipe outlet and thus indirectly heating the part surface. The machines, de-

vices, and accessories used in flame hardening are comparatively simple and inexpensive, but the process requires an operator with much experience in blowpipe positioning if a uniform case depth without softer areas within the hardened layer is to be obtained (Ref 4, 5). Recent hardening processes related to surface hardening are laser hardening (Ref 6, 7) and electron beam hardening (Ref 8). In both cases, heat is generated in the surface layer of the workpiece due to the interaction of the beam and the material. From the heat treatment point of view, laser can be considered a versatile and flexible high-intensity heat source that can operate in air. It is capable of undertaking a range of processes, essentially simultaneously, since the laser beam can be directed through air by metal mirrors and switched and shared among a number of workstations. Manipulative techniques using mirrors allow the beam to be directed to the areas not accessible by other techniques, for example, the bores of tubes (Ref 6, 7). Deficiencies of laser hardening are a very lowenergy efficiency in transformation of electric energy into heat energy and a comparatively high cost of investment. Laser hardening has lately become successfully established for the following specific applications only: ● Hardening of small products of intricate

shapes, which are hard to adapt to induction heating ● Hardening of small internal surfaces such as small boreholes for which inductors small enough cannot be produced ● Hardening of parts with exacting shapes, with which admissible distortion is exceeded in induction hardening From the technology viewpoint, these surface hardening processes are very much alike since they all have to ensure adequate energy input and the case depth required. In the same manner, regardless of the hardening process applied, in the same steel the same microstructural changes, very similar microhardness variations, and similar variations of residual stresses within the hardened surface layer may be achieved. In induction hardening, the surface of suitable materials—usually plain-carbon or low-alloy steels or cast irons—is austenitized and then quenched to produce a hard martensitic surface

layer, which is usually tempered in a subsequent operation. Case depths normally range between 0.5 and 5 mm. Case hardnesses amount typically to around 700 HV after hardening and range between 600 and 650 HV after tempering at 180 to 220 C (Ref 1). Normally the hardening process also introduces compressive stresses into the surface layers, leading to an improvement in fatigue properties. Hardened parts—always ground because of their high hardness—require a minimum level of final grinding. This can only be achieved by a minimum oversize of a machine part after hardening, thus shortening the final grinding time and reducing costs of the final grinding to a minimum. With an automated manufacturing cell, one should be very careful when selecting individual machining processes as well as machining conditions related to them. Ensuring the required internal stresses in a workpiece during individual machining processes should be a basic criterion of such a selection. In those cases when the internal stresses in the workpiece during the machining process exceed the yield stress, the operation results in workpiece distortion and residual internal stresses. The workpiece distortion, in turn, results in more aggressive removal of the material by grinding as well as a longer grinding time, higher machining costs, and a less-controlled residual stress condition. The workpiece distortion may be reduced by subsequent straightening, that is, by material plasticizing, which, however, requires an additional technological operation, including appropriate machines. This solution is thus suited only to exceptional cases when a particular machining process produces the workpiece distortion regardless of the machining conditions. In such cases, the sole solution seems to be a change of shape and product dimensions so that material plasticizing during the machining process can be prevented. It is characteristic of induction hardening that machine parts show comparatively high compressive stresses due to a lower density of the martensitic surface layer. The compressive stresses in the surface layer act as a prestress on the most strongly loaded surface layer, which increases the load capacity of the machine part and prevents crack formation or propagation at the surface. The machine parts treated in this way

Induction Hardening / 221 are suited for the most exacting thermomechanical loads since their susceptibility to material fatigue is considerably lower. Consequently, much longer operation life of the parts can be expected. Residual internal stresses, that is, the so-called residual stresses, are the stresses present in a material or a workpiece/machine part when there is no external force and/or external moment acting upon it. The residual stresses in metallic machine parts have attracted the attention of technicians and engineers only after manufacturing processes improved to the level at which the accuracy of manufacture exceeded the size of deformation, that is, distortion, of a workpiece/ machine part. Thus it was in the 1850s that the effect of internal stresses on plastic strain, for example, of machine parts was already known. It was then that experts introduced measurement of individual dimensions of machine parts. For a given type of machining process, they connected the influence of the selected machining conditions with the size of deviations of dimensions. This was also the beginning of an expert approach to the selection of the most suitable machining conditions based on the criterion of minimum deviations of dimensions, that is, minimum machine part distortion. Still, at the time of publication, measurement of individual machine part dimensions is a very practical, uncomplicated, and reliable method of machine part quality assessment. The surface and surface-layer conditions of the most exacting machine parts, however, are monitored increasingly by means of the socalled “surface integrity.” This is a scientific discipline providing an integral assessment of the surface and surface layers and defined at the beginning of the 1960s. For high-quality machine parts and products subjected to heavy thermomechanical loads, different levels of description of the surface integrity were defined. A basic level of the surface-integrity description includes measurement of roughness and the analysis of microstructure and microhardness in the thin

104 Strip Strip heating, heating contour contour hardening, hardening single-shot hardening

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Typical power/frequency regions of induction heat treatment applications. Source: Ref 13

surface layer resulting from the machining process under given machining conditions. The second level of the surface-integrity description includes studies of residual stresses in the surface layer and of mechanical properties of the given material. The third level of the surface-integrity description includes tests making clear the behavior of the given part during machining. More detailed information on the levels of surface integrity description may be obtained in Ref 9 and 10. The previous paragraphs indicate that the knowledge of residual stresses in induction hardening alone does not permit a reliable assessment of the influence of the sum of the residual stresses present on the behavior of a machine part in an assembly under given thermomechanical loads.

Characteristics of Induction Hardening Induction heat treatment is a segment of the much larger technical field of induction heating, which combines many other industrial processes using the phenomenon of heating by induction (Ref 11–14). Induction heating is often one of the most effective heat treatment processes available for a variety of applications including surface hardening, through-hardening tempering and stress relief, annealing and normalizing, grain refinement, precipitation hardening or aging, and sintering of powdered metals. In most of these applications, induction heating is used to selectively heat only the portion of the workpiece that requires treatment (Ref 1, 15, 16). This usually means that the process can be accomplished in a relatively short time and with high efficiency because energy is applied to the workpiece only where it is needed. One of the main features of induction heating compared with conventional heating procedures is that heat is generated in the workpiece itself. In conventional heating procedures the heat input achieved is only 5 to 200 kJ/m2 • s energy, whereas in induction heating this energy input is 300 MJ/m2 • s. In induction heating, heat penetrates the workpiece with the aid of highfrequency alternating current; the choice of frequency depends on heating requirements. Induction heating power supplies are frequency changers that convert the available utility-line frequency power to the desired single-phase power at the frequency required by the induction heating process. They are often referred to as converters, inverters, or oscillators, but they are generally a combination of these. The converter portion of the power supply converts the linefrequency alternating-current input to direct current, and the inverter or oscillator portion changes the direct current to single-phase alternating current of the required heating frequency. Many different power supply types and models are available to meet the heating requirements of a nearly endless variety of induction

heating applications (Ref 13). The specific application will dictate the frequency, power level (Fig. 1), and other inductor parameters such as coil voltage, current, and power factor (cos u) or Q factor. In induction surface hardening, it is necessary to carefully plan individual characteristic phases of manufacture of machine parts, which are: ● Design of a machine part from a blank to its

final shape with additions for final grinding

● A technique and conditions of surface induc-

tion heating

● A technique and a quenching process ● Tempering the surface layer after hardening ● Final machining of the machine part by grind-

ing The selection of a blank is related to various steel semi-finished products or various primary forming processes such as casting, working, and so forth. Various shapes of blanks do not influence the selection of the conditions of induction heating, but they result in different variations of residual stresses, which have to be considered together with quenching residual stresses. Because of the character of the forming process itself, particularly the prescribed thermomechanical conditions of forming the blank, the expected stress state is obtained. Further forming of blanks by cutting also produces changes in the stress state depending on the machining process applied and the machining conditions. Very often with very complex workpieces, the thermomechanical conditions can cause a certain distortion of workpiece dimensions in addition to residual stresses. No studies treating a relationship between the stress state in the workpiece after primary forming and that after secondary forming could be traced. The primary reason is that the primary forming, that is, blank shaping, is usually carried out in one company and the secondary forming, that is, manufacture of a final product, in another. It has also been proved that with suitable heating conditions in different heat treatment processes, certain heat effects characteristic of a certain annealing process that affect the range of residual stresses can be obtained. The difference between induction heating and furnace heating is related to considerable changes of heating times and rates up to the hardening temperature and, consequently, to heating costs. Induction hardening is most often used for surface hardening of machine components and has the following advantages over other procedures (Ref 1, 5, 11): ● Heating times are relatively short. ● Heating procedure is not strictly governed by

hardening temperature. All that matters is that the heating process does not end at a temperature low enough for transformation into austenite to occur. The maximum temperature of heating is limited by the solidus-line temperature, since the process is to be carried out while the material is in a solid condition. With a short heating time, there is no danger that at higher austenitization temperatures the

222 / Residual Stress During Hardening Processes austenite grains would grow, which also means that there is no danger of formation of coarse and brittle martensite . ● The quenching procedure is easy to perform, contributing to short surface hardening times. In progressive induction hardening, a spray coil is located right beneath the inductor, directly quenching the heated surface. In single-

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shot hardening, the inductor is designed so that it heats as well as quenches. The coil around the workpiece functions as an inductor in the heating phase, and after the austenitization temperature has been reached the current is interrupted and the coil starts functioning as a quenching spray. Induction hardening is a short procedure that does not require any additional protection against oxidation. Thus, compared with other similar procedures such as cementation, it does not require much subsequent machining. Because of the nature of the procedure, the workpieces are less susceptible to undesirable deformation after induction hardening, especially if they are symmetrical. The volume changes in the workpieces after hardening the surface layer can be very accurately predicted or estimated. The volume changes after induction hardening of thin layers are so small that quite often the function of the machine component is not affected. Especially in induction hardening of thin layers and workpieces with low mass, it is possible to achieve the desired critical cooling rate by self-cooling in air alone, that is, by heat conduction from the heated surface layer into the remaining cold part of the workpiece. With thicker layers and workpieces of greater mass, it is necessary to use such quenching agents that move the actual cooling rates close to the critical cooling rate. These requirements can be met with the right selection of quenching oils or polymer water solutions. Practical experience has shown that polymer water solutions are very suitable for quenching induction-heated surfaces, since with the right choice of concentration of the polymer water solution optimal quenching can be ensured. The induction hardening procedure enables the engineer, by simply adapting the shape of the induction coil, to ensure a desired shape of the hardened profile of the surface layer. Likewise, the engineer can surface harden only that part of the surface (local hardening) on which a certain increased level of hardness and wear resistance are wanted. One of the main advantages of induction hardening is that it makes it possible to harden a surface layer only on certain places, at defined penetration depth and shape. Induction hardening can be fully automated and is especially suitable for large series of workpieces. Induction hardening always leaves compressive residual stresses in the surface layer, which make machine components more resistant to dynamic loads. Compressive residual stresses in the surface layer after induction hardening prevent the occurrence of cracks in dynamically loaded components and prevent the growth of existing cracks on the workpiece surface if these are present due to hardening or hardening and grinding. Induction hardening is appropriate for smallsized workpieces, since by well-chosen tech-

nology of heating and cooling or quenching one can ensure a hardened surface layer and a refined core. Thus one can create the required wear resistance of the machine component on a certain location as well as the required load-bearing capacity of the component with only a slight loss in toughness of the core. In induction heating there are a number of parameters influencing the heating process with the given heat treatment. This article discusses the influence of individual parameters on surface induction hardening. In surface induction hardening the heating conditions should be treated as a system consisting of a high-frequency generator, an induction loop, and the workpiece, which has to be defined by the characteristic system parameters. The course of surface induction hardening depends on: ● The type of steel or cast iron ● Electrical and magnetic properties of the ma-

terial

● The effect of the primary material microstruc● ● ● ● ● ●

ture on the properties of the hardened microstructure The time/temperature relationship in induction hardening and possible tempering The selection of power density and current frequency The workpiece shape and the shape of the hardened surface layer A correct execution of the coupling between the induction loop and the workpiece Selection of appropriate heating and hardening processes Selection of the induction loop with or without magnetic-flux concentrator

Time/Temperature Dependence in Induction Heating The time variation of temperature in induction heating of the thin surface layer depends on the type and shape of the induction coil used, alternating-current frequency f (Hz), and power density Q (W/cm2). Power density is defined by the selected power of the high-frequency (HF) generator and the surface layer of the workpiece. Surface heating depends on the coupling between the induction coil and the workpiece. Figure 2 shows the influence of the selected power density and frequency on the reference depth of the skin effect in a ferromagnetic material. A higher power density results in a greater reference depth of the skin effect and a greater depth of the heated layer with the same maximum temperature obtained at the workpiece surface. (Ref 1). Figure 3 shows the interdependence between the heating parameters—that is, power density and generator frequency—as a function of the specified depth of hardened layer and the heating time required for single-shot techniques of surface induction hardening (Ref 1). Although the data supplied by the diagram provide basic in-

Induction Hardening / 223 formation, they make the selection of an optimal surface induction condition easier. With the scanning technique of surface induction hardening, however, instead of time, the speed of workpiece movement ensuring the depth of hardened layer required should be defined. Generally, it may be stated that longer heating times are required with smaller power densities and vice versa. Also, for the same depth of hardened layer, longer heating times are required with lower current frequencies. With regard to the depth of hardened layer selected between 0.5 and 10.0 mm, generator frequencies of 450, 10, and 3 kHz can be selected in the single-shot surface hardening technique, in which case appropriate power densities between 2 and 50 MW/m2 are obtained. With lower high frequencies such as 10 kHz, the same depth of surface hardened layer, that is, 2.0 mm, can be ensured only in the cases when the power density is changed to 50 MW/m2. The lowest generator frequency, that is, 3 MW/m2, shown in Fig. 3, cannot ensure the depth of hardened layer smaller than 2.5 mm. Immediately after tempering an intensive inverse heat flow is also expected. With the surface heat treatment processes, the influence of the selected heating and quenching conditions on the depth of hardened layer and the size of transition zone between the hardened microstructure and the unhardened layer is often studied. One simple and practical procedure to control surface heat treatment is measurement of the time variation of temperature from the beginning to the end of the heating process and then also from the beginning to the end of the quenching process. The heat process can be changed by changing the power density and the generator frequency, whereas the quenching process can be changed by selecting different quenching agents and quenching processes. Figure 4 shows the time variation of temperature at the surface during heating and quenching as well as in the core, which is due to heat conduction into the remaining cold workpiece material during heating as well as during quenching (Ref 17).

The total time variation of temperature during both heating and quenching is called the description of the surface heat treatment process by thermal cycles, which may be divided into those dependent on heating and those dependent on quenching. The same figure also shows thermal inversion in workpiece quenching when the core temperature during quenching is higher than the workpiece surface temperature. Denis and coauthors (Ref 18) presented different physical models to describe different processes occurring in the material during surface induction hardening. The authors analytically treated studies of a cylindrical specimen 16 mm in diameter and 48 mm in length and made of hypoeutectoid carbon steel with 0.43% C. The theoretical study was then verified by appropriate experimental methods. The experimental verification was to confirm the size of the expected error of individual characteristic quantities, for example, variation of temperature/time cycles, variation of through-thickness microhardness of the cylindrical specimen, and the throughthickness variation of residual stresses. Figure 5 shows the measured and calculated temperature cycles for the surface, the core, and in a radius r of 7 mm at a depth of 1 mm in the cylindrical specimen (Ref 18). A comparison of the temperature cycles shows that in surface induction hardening a thermal flow of 3 MW/mm2 in heating and that of 5.8 MW/mm2 in quenching were selected. Under such heating conditions, a maximum temperature of nearly 1000 C was attained while heating above 800 C was somewhat slowed down. The data in the diagram show that the time required for heating the specimen from the ambient temperature to that of 800 C is equal to the time required for heating from the latter to the maximum temperature obtained at the surface, that is, 1.6 s. A temperature cycle at the surface takes 3.2 to 3.3 s. The temperature differences between the surface and the core in

a given moment are the greatest during the heating process, DTmax 艑 600 C. During the quenching process, however, they can reach up to 360 C. Temperature gradients change much more in heating than in quenching. In material heating, there is also a great difference in yield stress of the material, which can produce plastic deformation of the material. Another very important finding of the authors (Ref 18) is that the theoretical model is appropriate since the results obtained were confirmed by the standard experimental methods such as temperature measurement with thermocouples, diamond pyramid hardness test, and measurement of residual stresses with x-ray diffraction. The difference between the measured and the calculated temperature cycles is very small. It occurs mostly in heating and reaches up to 60 C at maximum not taking into account the losses due to eddy currents. Figure 6 shows two temperature cycles. One of them takes account of the influence of the enthalpy of phase transformations in the physical model of surface induction heating and quenching for the surface and the core, and the other does not. A comparatively small influence of the enthalpy of phase transformations on the thermal cycles, however, confirms the small influence on the changes of the stress state of the cylindrical specimens during the process of surface induction hardening (Ref 18). Bru¨ckner and coauthors (Ref 19) determined the through-thickness temperature variation for a thin cylindrical plate with a diameter of 120 mm and made of steel Ck45 for hardening and tempering and for surface hardening with the finite element method. Figure 7, which shows the temperature changes from the surface toward the core, also shows that after 14 s a maximum temperature of 870 C is reached at the surface. It is higher than the temperature of magnetic transformation, which is around 750 C. The through-

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Variation of temperature cycles of surface and core in surface induction hardening. Source:

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Comparison of variations of calculated and measured temperatures cycles for cylindrical specimens 16 mm in diameter. Source: Ref 18

224 / Residual Stress During Hardening Processes thickness temperature variation confirms a slow change of temperature in the surface layer and ensures, after quenching, a slow transition from compressive to tensile residual stresses in the thin surface layer. This slow change of temperature in the transition zone should be obtained by an optimal heating condition to attain the desired variation of the stress state in the surface layer and to enhance fatigue strength. Figures 8 and 9 show the variation of temperature from the surface to the core in a round plate with 30 mm in diameter. Figure 8 shows the through-thickness temperature variations from the surface toward the core in a cylindrical

specimen after different heating times (Ref 19). In the diagram the austenitizing temperature, TA3 艑 800 C, and the highest temperature obtained at the surface, TA 艑 900 C, are indicated. With a final heating time t of 9 s and a volume power density Q of 2.4 ⳯ 103 MW/m3, the highest temperature difference DTsc max between the core (C) and the surface (S), that is, around 450 C, was obtained. The high temperature obtained increases slightly in the core due to the cooling process in the surface, which can have a beneficial influence on residual stress relief. Residual stress relief can be ensured by heat transfer from the central part of the specimen to the surface

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Variations of temperature cycles of surface and core considering enthalpy of phase transformations and without it. Source: Ref 18

immediately after quenching. In any case, it is desired that after quenching the temperature TT due to the inverse thermal flow does not increase above 180 to 220 C after core cooling by heat transfer toward the cold surface. This is the only way to ensure tempering of tetragonal martensite and a possible change of the residual austenite immediately after hardening. Figure 9 shows the variation of temperature from the surface toward the core with various volume power densities Q ⳱ 0.4 ⳯ 103, 1.2 ⳯ 103, and 2.4 ⳯ 103 MW/m3 (Ref 19). With smaller volume power densities also the maximum temperature differences between the surface and the core become smaller and the austenitizing times longer. Because of higher temperatures attained in the core, one should be aware of the fact that the inverse heat flow may be so high as to produce even a change in microstructure and thus, consequently, reduction of hardness in the surface layer. Figure 10 shows the influence of specimen mass on the heating time with the same volume power density and the same maximum final heating temperature of the surface Tmax, 900 C (Ref 19). The maximum temperature in the core should also be mentioned. With the longest diameter, for example, 120 mm, it equals the ambient temperature, whereas with the specimen diameter of 60 mm it raises to 150 C and with that of 30 mm to 450 C. The data on the variation of temperature from the surface toward the core permit a conclusion that for the specimen with the greatest mass and the diameter of 120 mm additional induction heating of the surface should be ensured to allow tempering of the surface layer. Melander (Ref 20) and the author quoted in Ref 21 first treated surface induction hardening of low-alloy steel with 0.4% C, 0.7% Mn, and 1.1% Cr for quenching and tempering as well as

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∆Tmax


600

7s

600

5s 400 3s 200

200

TAC

Q1

3



3

Q2

600

Q3

400

Q, W/m3 200

10 s

t =1s

6s 0

2s 0

0

20

40

60

0

5

10

15

3

0

Radius (r ), mm

0

5

tH,s

1

0.4 × 109

57.4

2

1.2 × 109

18.8

3

2.4 × 109

9.0

10

15

Radius (r ), mm

Radius (r ), mm Calculated time variation of through-thickness temperature in surface induction heating by the finite-element method. Source: Ref 19

Fig. 7

Calculated time variation of temperature through specimen cross section in induction heating with volume power density Q of 2.4 ⳯ 103 MW/m3 and different heating times. Source: Ref 19

Fig. 8

Calculated variation of temperature through specimen cross section in induction heating up to hardening temperature with different volume power densities. Source: Ref 19

Fig. 9

Induction Hardening / 225 surface hardening. For an analysis, a representative size of machine parts, for example, a cylindrical specimen 40 mm in diameter, was chosen. Induction-heating conditions were selected so that the temperature of the diameter TA1 was exceeded to a depth of 5.0 mm. This means that a change of microstructure and hardness was expected even to the depth of 5.0 mm, where only partial austenitization was obtained. Such induction-heating conditions were chosen that the surface layer was subjected to heating for up to 35 s. Time variations of temperature at the surface of the cylindrical specimen and in its subsurface in the depths of 2.0, 4.0, and 10.0 mm are shown in Fig. 11. Time/temperature diagrams differ from the previous figures since a distinctive deviation occurs in heating the specimen material when the temperature of magnetic 1000

t =9s

t = 12 s

t = 14 s

800

TAC Temperature (T ), °C

3

600

400

200 Material: Ck45 Q = 2.4 × 109 W/m3 0

0

15

30

45

60

75

Radius (r ), mm Calculated variation of temperature through specimen cross section in induction heating of specimens of different masses up to given hardening temperature. Source: Ref 19

Fig. 10

1000 Surface Depth 2.0 mm Depth 4.0 mm Depth 10.0 mm


800

process as well as the quenching process, various thermokinetic changes of microstructure affecting volume changes, development of internal stresses, and distortion of machine parts occur; therefore, knowledge of changes of material properties such as yield stress of individual phases which in the given moment compose the microstructure, permeability, and electric conductivity, as a function of temperature is indispensable. The entire process of evaluation, that is, modeling, of surface induction hardening is shown in Fig. 12. Modeling of the induction heating and quenching processes includes following essential numerical calculations (Ref 23):

domain TA2 is reached and exceeded. The course of surface heating indicates that the transformation temperature TA2 was obtained in 10 s. In spite of the same power density, further heating of the surface up to 850 C was very slow due to nonmagnetic character of the surface layer of steel and took another 28 s. Which models of induction heating are more suitable than others is difficult to assess. It turned out, however, that the heating process suggested more reliably ensured a homogeneous, fine austenitic microstructure giving, after quenching, the finest martensite with the highest possible hardness of the given steel. Because of the presence of alloying elements and high rates of cooling of the surface layer, in addition to fine martensite up to 3% residual austenite also appears. Based on the time/temperature variation of heating, it can be evaluated that the depth of hardened layer ranges between 2.0 and 4.0 mm. From the time/temperature variation in the depth of 10 mm it can be assumed that the specimen was heated through the entire volume, that is, to the very core of the specimen. Because of a different time variation of temperature of the fourth temperature cycle, it may be concluded that the maximum temperature obtained at the depth of 10 mm is lower than the magnetic transformation temperature of the given steel. Because of strong overheating of the cylindrical specimen toward its center, lower temperature gradients occur, resulting in a reduction of thermal stresses during the heating process. Because of a comparatively high temperature in the core, temperature gradients between the surface and the core are generally lower, producing a decrease of axial internal stresses generated during quenching and also a decrease of axial residual stresses. Langeot and Delalean (Ref 23) treated numerical simulation of the induction heating process for materials and machine parts from industrial practice. A general method of modeling is based on knowledge of the magnetic field surrounding the induction loop with the inserted specimen, that is, workpiece. Knowledge of the temperature field in the workpiece, namely, permits an analysis of momentary conditions in the material during working, for example, strain, stress state during induction heating and quenching, and residual stresses. During the heating

1. Determination of a relationship between the density of induced currents and the temperature field created in the specimen material (Joule heating effect) 2. Influence of a temperature on electrical and magnetic properties of the material 3. Determination of the influence of the induced currents or the magnetic field in the material on transformation of microstructural phases in the material 4. Determination of the influence of individual microstructural phases in the workpiece material on electromagnetic properties of the material 5. Description of mechanical characteristics of the material as a function of temperature 6. Description of the relationship between heat energy and mechanical strains 7. Description of volume changes due to phase transformations 8. Description of transformation plasticity in phase changes during heating and quenching 9. Influence of latent heat of phase transformations on individual characteristics of surface-induction hardening 10. Description of phase transformations as a function of thermokinetic processes during surface-induction heating as well as quenching 11. Influence of strain and distortion of machine parts on magnetic and electrical properties of the material

600 1

Magnetic field analysis Eddy current

400

Temperature 2 11

200 3

10

4

5 9

0

0

20

40

60

7

80 Phase transformation

Time (t ), s

Fig. 11 Ref 20

Time/temperature cycle during single-shot surface induction heating and quenching. Source:

8

Fig. 12

6

12 Material Mechanical properties Internal stresses Residual stresses Strain

Langeot’s method of mathematical modeling of surface induction heating and quenching. Source: Ref 23

226 / Residual Stress During Hardening Processes 12. Influence of the magnetic field in the material on the development and magnitude of strain and distortion The authors of Ref 23 focused primarily on the treatment of electric energy transforming into heat energy, making possible heating of the workpiece material. Heat energy in the workpiece material is represented by temperature fields in the workpiece near the induction loop. Unfortunately, the authors deal with the issues primarily from the viewpoints of electromagnetism and quality assessment of the numerical calculation procedure proposed for individual thermomechanical characteristics of the workpiece material during heat treatment. The thermomechanical characteristics are plotted graphically as temperature fields obtained during induction heating, and as graphical charts of microstructural changes and sizes, namely, shapes, of the hardened surface layer. A comparison of the numerical results obtained in the thermomechanical state during and after surface induction heating with those obtained by other authors is very difficult since standard presentations of the results of thermomechanical characteristics such as time variation of temperature and time variation of the stress state as well as the size and variation of residual stresses after hardening are missing. Inoue and coauthors (Ref 24) treated numerical simulation of single-frequency and dualfrequency surface induction hardening of gear wheels. Machine parts such as a gear wheel should show appropriate surface hardness and through-depth hardness profile of teeth as well as toughness so that tooth surfaces are highly wear resistant and the root of tooth is tough enough to withstand dynamic loads as well as unexpected mechanical loads. Gear wheels are, therefore, most often case hardened, but they can also be nitrided and surface induction hardened. Dual-frequency induction hardening is related to

the selection of an appropriate preheating procedure with a current having a mean frequency of 3 to 10 kHz and very fast further heating with a high frequency of 100 to 250 kHz, which should be followed by suitable spray quenching. Practical results confirmed that such a surface induction hardening process permits, in surface hardening, the best properties of machine parts in terms of hardness magnitude and variation in the hardened layer, high compressive residual stresses in the surface layer with a minimum distortion of machine parts, and a sufficiently tough core to be obtained. The authors had already reported on simulation of dual-frequency induction hardening based on a metallothermomechanical model (Ref 24). With this model, the influence of the magnetic field on heat generation in the workpiece due to eddy currents in relation to analyses of mechanical fields and microstructural changes was analyzed. Such an approach was needed since Joule heat is generated in the workpiece material during induction heating due to eddy currents, which depend on the current supplied to the coil, and the temperature dependence of permeability of the workpiece material should be taken into account as well. The numerical calculations were related to the formation of the magnetic field in the workpiece material; thus, it was necessary to elaborate a comprehensive electrothermomechanical model to relate electrical quantities to material heating and then, at the second stage, to relate temperature to the mechanical calculations required. The authors, therefore, suggest the establishment of a complete relationship between the magnetic and thermomechanical fields in the workpiece material. The thermomechanical analysis takes as a basis the temperature field formed due to the action of the magnetic field and relates to the temperature dependence of magnetic properties. The heat

Magnetic field Temperaturedependent electric conductivity and magnetic permeability

Heat generation due to induction heating Thermal stress Stress Strain

Temperature Mechanical work

Latent heat

Temperaturedependent phase transformation

Transformation stress

Stress-induced transformation

Microstructure

Fig. 13

Relationship between magnetic field and thermomechanical state of workpiece material in numerical modeling of surface induction hardening. Source: Ref 24

generated in the workpiece material by a temperature field permits establishment of a numerical relation between the formation and development of the microstructure, internal residual stresses, and distortion. In Fig. 13, the authors show the principle of relationship between the magnetic field generated in the workpiece material and the changes of thermomechanical properties of the material (microstructure, yield stress) for the determination of the stress-strain state of the workpiece material (Ref 24). A technique of numerical calculation consists of two separated analyses shown in Fig. 14—the metallothermomechanical analysis and the electromagnetic analysis to establish heat generation during heating and calculate thermomechanical fields for the characteristics selected (Ref 24). A heat increase in the workpiece was simulated by the electromagnetic analysis of the field for each step, taking into account momentary temperatures obtained in the material, its permeability, and conductivity. These data were then transferred to another group of analyses based on a description of the state of microstructure for the determination of stress-strain state of the machine part. The whole procedure was iterated starting with calculations of the ambient temperature and ending with a maximum temperature of induction heating, which was followed by quenching. Magnetic permeability generally depends on magnetic field intensity as well as on a momentary temperature of the material of the machine part at the spot considered. In the calculation, a constant permeability of the workpiece material is assumed in the first approximation. In heating, for each iteration change permeability and electric conductivity are taken as a function of temperature. Figures 15(a) and (b) show two different ways of induction heating of the gear wheels, dual frequency and single frequency (Ref 24). In both cases the heating process ends up in almost the same time, around 2.8 s. In dual-frequency heating, heating takes place in two phases, first with a power of 293 kW and the lower frequency, 3 kHz and then with a power of 339 kW and the higher frequency, 150 kHz. In the first phase, which takes 1.8 s, the edge of the gear wheel warms up to a temperature of 740 C, and after a pause of 0.9 s follows heating in the second phase, which takes 1.18 s, up to a final temperature of 858 C, which is followed by quenching. The entire heating cycle including the pause in between takes 2.88 s. In single-frequency heating, heating with a power of 165 kW and frequency of 25 kHz takes place without the pause and takes 2.8 s. It is followed by quenching. The maximum temperature obtained at the surface of the gear wheel at the end of heating was much higher than in dualfrequency hardening and amounted to 970 C. Figure 16 shows the measured and calculated temperature cycles in dual-frequency induction heating of gear wheels (Ref 24). The measured and calculated temperatures refer to the tip of tooth, the plane of division of the gear wheel, and the root of tooth. The temperature cycle of dual-frequency heating including the pause in-

Induction Hardening / 227 of the gear wheel and the smallest differences at the root of tooth. A comparison of the temperature cycles obtained in single-frequency induction heating shows important temperature differences among individual measuring points occurring with the calculated temperature cycles as well as with the measured ones. The temperature differences became smaller as soon as the temperature of magnetic transformation of the material was exceeded. Slowed heating of gear wheels above the temperature of magnetic transformation ensures longer heating times up to the hardening temperature, that is, the temperature of homogeneous austenitization. Such a heating procedure results in lower micro- and macrostresses during the heating process, which is highly important, since materials show a considerably lower yield stress at elevated temperatures. In dualfrequency induction heating of gear wheels, similarly as in single-frequency induction heating, it was found that there were low-temperature gradients through the entire depth of tooth; yet there were obvious differences in the obtained maximum temperature from which the gear wheels were quenched. With regard to distortion of the teeth of the gear wheel, thermal conditions during the quenching process are important. If the calculated temperatures and the temperatures measured at the same measuring point in a given moment are compared, it will be found that the temperature differences in dual-frequency induction hardening are very small. The temperature differences among different measuring points are at their minimum as well. Hence it follows that the quenching conditions were very favorable, and a very uniform thickness of the hard-

ened layer and a uniform microstructural state with minimum distortion of the teeth as well as of the gear wheels could be expected. Figure 18 shows the temperature distribution in the half-cut of a gear-wheel tooth in dualfrequency induction heating. Figure 19, however, shows the temperature distribution in the same cut of the gear-wheel tooth after singlefrequency induction heating (Ref 24). With dualfrequency induction heating it can be found that: ● A maximum temperature of 937 C is ob-

tained at the tip of the gear-wheel tooth.

● At the end of heating, a temperature higher

than the hardening temperature required was obtained from the tip to the root of tooth. ● The temperature is considerably lower than the hardening temperature only a few millimeters below the root radium, for example, at a depth of 6 mm around 150 C. In single-frequency heating it can be found that: ● A maximum temperature of 1042 C is obtained at the tip of tooth. ● A temperature higher than the quenching temperature is obtained along the entire gearwheel tooth, except at the root of tooth. ● A temperature below the hardening temperature is obtained from the root of tooth downward, and 6 mm below the root of tooth it still amounts to 300 C. A comparison of both heating modes shows that heating of the tooth is much more uniform in dual-frequency heating, and the variation of the stress distribution during quenching is much


dicates that low-frequency heating is performed up to the temperature of magnetic transformation and high-frequency heating up to the hardening temperature. It is essential for this dualfrequency induction-hardening procedure that after hardening tempered martensite is obtained in the hardened layer and gear-wheel distortion is smaller than in single-frequency induction heating. Figure 17 shows the measured and calculated temperature cycles in single-frequency induction heating of gear wheels (Ref 24). Because of progressive and uniform induction heating of the surface layer of the gear wheel after a longer single-frequency induction heating not including the pause, a temperature Ts somewhat higher than in dual-frequency heating was obtained at the surface of the gear wheel, namely, 1120 C. The surface temperature was much higher, although Curie temperature was exceeded and the root of tooth of the gear wheel was heated to a temperature higher than 800 C. Another very important finding, resulting from the time variation of temperature, is very similar temperature variations at different measuring spots at the tooth of the gear wheel regardless of whether it is the tip or root of tooth. It is also very important that the differences between the calculated temperatures and the ones measured at the same measuring point are small in heating and a little bit greater in quenching. This indicates that the model elaborated is suitable, particularly for heating and the measuring equipment for temperature measurement at individual measuring points. The greatest temperature differences between the measured and the calculated temperatures in quenching are found at the tip of tooth

Magnetic field anaylsis

Eddy current

150 kHz 339 kW

858 °C

740 °C 3 kHz 293 kW

1.8

Heat generation

2.7 2.88

Time (t ), s (a)

Electromagnetic properties

Temperature microstructure stress/strain Temperature

Temperature cycle Heat distribution Temperature distribution Volume fraction of martensite Residual stress distribution Distortion after hardening


970 °C

Thermomechanical analysis

25 kHz 165 kW

2.8 Permeability µ Conductivity σ

Fig. 14

Flow chart of the numerical calculation. Source: Ref 24

(b)

Fig. 15

Time (t ), s Dual-frequency (a) and single-frequency (b) induction heating of gear wheel. Source: Ref 24

228 / Residual Stress During Hardening Processes more favorable due to a lower temperature, which ensures lower residual stresses after hardening. Figure 20 shows a volume-fraction distribution of martensite calculated with the finiteelement method and using a relatively coarse grid for calculation of the conditions existing in dual-frequency heating of the gear-wheel tooth (Ref 24). Figure 21 shows a volume-fraction distribution of martensite in single-frequency heating. The temperature distribution in heating shows an exceptionally good relationship with the result of quenching, that is, with the volumefraction distribution of martensite through the gear-wheel tooth (Ref 24). The results obtained confirm that the mathematical model used was correctly chosen and the procedure of numerical calculation of the temperature field as well as of the volume-fraction distribution of martensite suitable. Simulation of the heating process can be monitored in time by a momentary temperature distribution in the gear-wheel tooth, which can point out possible weaknesses in heating as

well as quenching. The simulation can be enhanced by a denser grid—a greater number of calculated values, for example, of temperature, distribution of microstructural phases, and so forth, at the same area of the gear-wheel tooth. The paper treats a simulation with a very coarse grid, which provides a less accurate image of the heating process and the final result of quenching, that is, of reliability of the assessment of volume distribution of martensite after quenching, respectively. Figure 22 shows the temperature distribution transverse to the half-cut of the gear-wheel tooth in dual-frequency induction heating of the gear wheel, and Fig. 23 shows the same in singlefrequency induction heating (Ref 24). In the parallel figure, a gray scale indicating the time variations of power density per volume unit in individual fields of the gear-wheel tooth or the amount of heat generated in the gear-wheel tooth is shown. The greatest amount of heat generated at the end of heating (legend) was 96,500 MW/ cm3 with the dual frequency and 81,320 MW/-

°C × 103 Max 0.9372

20 mm

Temperature distributions in the tooth gear at t ⳱ 2.88 s induction heating (dual frequency). Source: Ref 24

Fig. 18

°C × 104 Max 0.1042

1200 20 mm

Simulated Measured


1000

Tip PCD

800

t = 2.88 s

0.9600 0.8800 0.8000 0.7200 0.6400 0.5600 0.4800 0.4000 0.3200 0.2400 0.1600 0.0800 Min 0.0399

0.1100 0.1000 0.0900 0.0800 0.0700 0.0600 0.0500 0.0400 0.0300 0.0200 0.0100 0.0000 Min 0.0030

Bottom

Temperature distributions in the tooth gear at t ⳱ 2.8 s induction heating (single frequency). Source: Ref 24

Fig. 19

600

400 Max 0.9970 1.0000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 Min 0.0000

200 0

0

1

2

3

4

5

6

Time (t ), s

Fig. 16

Measured and calculated time variations of temperature in dual-frequency induction heating of teeth followed by quenching. PCD, pitch circle diameter. Source: Ref 24

1200

Simulated volume fractions of martensite in the tooth gear after induction surface hardening (dual frequency). Source: Ref 24

Fig. 20

Simulated Measured


1000

Tip PCD

800

Bottom

Max 0.9970 1.0000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 Min 0.0000

600

400

200 0

0

1

2

3

4

5

6

Time (t ), s

Fig. 17

Measured and calculated time variations of temperature in single-frequency induction heating of teeth followed by quenching. PCD, pitch circle diameter. Source: Ref 24

Simulated volume fractions of martensite in the tooth gear after induction surface hardening (single frequency). Source: Ref 24

Fig. 21

Induction Hardening / 229 cm3 with the single frequency. The value of the entire analysis of thermal conditions increases if they are monitored in frequent time intervals and with as fine a grid as possible for their calculation. The theoretically calculated values of the heat distribution in the gear-wheel tooth can be verified only by relevant measurements carried out at thermally treated gear wheels. Thus, a micro-

[W/m3]

structure can be analyzed and hardness measured. The authors decided to measure hardness along the tip, the middle, and the root of tooth. Because of different tooth widths at different locations, namely, radii, a greater number of measurements with the same distances between the measuring points were made. Figure 24 shows the hardness variation at the tip, the pitch circle diameter (PCD), and the root of gear-wheel tooth after dual-frequency induction hardening (Ref 24). Along the entire tooth surface from the tip to the root of tooth the same hardness, 750 HV,

× 1011 Max 0.0965

t = 2.88 s

800

Hardness, HV

20 mm

0.1100 0.1000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 −0.100

600 400 Tip PCD Root

200 0

0

× 1010 Max 0.8132 0.9000 0.8250 0.7500 0.6750 0.6000 0.5250 0.4500 0.3750 0.3000 0.2250 0.1500 0.0750 0.0000 Min 0.0000 Generated heat distributions in the tooth gear at t ⳱ 2.8 s induction heating (single frequency). Source: Ref 24

Tip PCD Root

400 200

0

1

2

3

4

6

7

1.0 Tip PCD Root

0.8 0.6 0.4 0.2 0

0

1

2

3

4

5

Simulated volume fraction of martensite across the tooth gear after induction surface hardening (dual frequency). PCD, pitch circle diameter. Source: Ref 24

Fig. 26

M

Hardness, HV

800

0

5

Distance from surface (z ), mm

Volume fraction of martensite (Vf )

Fig. 23

M

[W/mm3]

600

4

Fig. 25 Measured hardness profiles across the tooth gear after induction surface hardening (single frequency). PCD, pitch circle diameter. Source: Ref 24

Volume fraction of martensite (Vf )

Generated heat distributions in the tooth gear at t ⳱ 2.88 s induction heating (dual frequency). Source: Ref 24

20 mm

3


Fig. 22

t = 2.8 s

2

1

Min 0.0000

1.0 0.8 0.6 0.4 Tip PCD

0.2 0

0

5

1

2

3

4

5

6

7


Distance from surface (z ), mm Measured hardness profiles across the tooth gear after induction surface hardening (dual frequency). PCD, pitch circle diameter. Source: Ref 24

Fig. 24

Simulated volume fraction of martensite across the tooth gear after induction surface hardening (single frequency). PCD, pitch circle diameter. Source: Ref 24

Fig. 27

was attained. It decreased slowly towards the tooth core. The hardness of the tooth core after hardening was 220 HV. The data on the hardness measured confirm that in dual-frequency heating the gear-wheel tooth is hardened only to a small depth, that is, approximately 0.4 to 0.6 mm at the tip, up to 1.5 mm in the middle, and approximately 1.0 mm at the root. In single-frequency induction heating, hardening layers are much thicker. Thus, the depth of hardened layer at the tip of tooth was 1.1 mm and the greatest depth in the root of tooth. Figure 25 shows the variation of hardness at the same measuring points at the gear-wheel tooth after single-frequency induction hardening (Ref 24). Along the entire length of the tooth surface from the tip to the root of tooth the same hardness, 800 HV, was attained. At the tip and the root of tooth it changed gradually with the depth. The results obtained show that in single-frequency induction hardening the thickness of the hardened layer increases with the increase in distance from the tip of tooth. Conditions are somewhat different in dualfrequency hardening in which the greatest depth of hardened layer was obtained in the middle of the tooth, and hardness decreased toward the tip and the root of tooth. It follows from the hardness variation transverse to the gear-wheel tooth that the core of the tooth was through-hardened and a uniform and very high hardness, even up to 800 HV, was obtained through the entire tooth width. Figure 26 shows calculated line changing of the volume fraction of martensite transverse to the tooth after dual-frequency induction hardening at the characteristic measuring points. Figure 27 also shows calculated line changing of the volume fraction of martensite transverse to the tooth, but this time after single-frequency induction hardening (Ref 24). The efficiency of the numerical calculation of the volume distribution of martensite can be assessed by the microhardness measured at the characteristic points. In the case given, major deviations occurred between the calculation of volume distribution of martensite and the hardness measured at the given measuring points only in dual-frequency induction hardening, whereas in single-frequency induction hardening the deviation was much smaller. Fujio and coauthors (Ref 25) monitored distortion of gear-wheel teeth and the variation of residual stresses after induction hardening of gear wheels. The authors treated the conditions in induction hardening and quenching of gear wheels made of carbon hardening and tempering steel S35 experimentally and theoretically. The experiments of induction hardening were carried out at gear wheels with an outer diameter of 196 mm and width of 150 mm and the tooth of 22.9 mm in height. The inductive loop surrounding the gear wheel had nine windings with an inner diameter of 226 mm and a width equal to the gear-wheel width, 150 mm. The output power of the high-frequency generator was 400 kVA and the frequency 10 kHz. The gear wheels were induction heated to a maximum temperature of 860

230 / Residual Stress During Hardening Processes C, which was reached in 187 s. During heating, temperature was measured at four measuring points, that is, at the tip of tooth 1, at the pitch circle at the tooth surface 2, in the tooth core 3, and at a depth of 25 mm from the tip of tooth 4. Figure 28 shows the gear-wheel tooth with the marked measuring points for temperature measurement with thermocouples (Ref 25). The time variation of the temperature measured in heating the gear wheel at the same measuring points is shown in Fig. 29(a) and (b) (Ref 25). It follows from both figures that the magnetic transformation occurred above 700 C. In the calculation,

1

2

heat fluxes of the temperature range below the Curie temperature, q01 ⳱ 75 W/cm2 and that above the Curie temperature, q02 ⳱ 10 W/ cm2 —were taken into account. A comparison of the calculated and of the measured time variations of temperature in heating shows that there are certain differences. The maximum temperature differences exceed even 100 C, which is, according to the authors, still acceptable. These data on the time variation can, therefore, be used efficiently in quality assessment of induction hardening of gear wheels in terms of microstructure, microhardness as well as residual stresses, and/or distortion of the gear-wheel tooth. The investigation conducted thus gave useful information on the tooth condition after induction hardening. The following figures show isotherms transverse to the gear-wheel tooth calculated for the induction heating process. Figure 30 shows the heating process after 20, 60, and 187 s when it ends (Ref 25). It is very important that: ● The gear-wheel tooth is heated only by 80 C

25 mm 3

4

Fig. 28

Tooth gear and position at given measuring points for thermocouple fitting. Source: Ref 25


1000

(from 780 C after 60 s to 860 C after 187 s of induction heating) in a comparatively long heating time, that is, 127 s, when the Curie temperature of magnetic transformation of steel was reached. ● Isotherms are running almost in the direction of gear-wheel tooth radius. ● The entire gear wheel obtains martensitepearlite microstructure due to the temperature fields in it. Figure 31(a) shows the time variation of the temperature measured at the individual measuring points of the gear-wheel tooth during quenching with a pressurized water jet (Ref 25). Data on the temperature variation show that the cooling temperatures were very similar at mea-

suring points 1 and 2, somewhat lower at measuring point 3, and the lowest at measuring point 4, where after 40 s of quenching it still amounted to around 350 C. Figure 31(b) shows the calculated time variation of temperature at the same measuring points of the gear-wheel tooth during quenching taking into account selected heat transfer coefficients ␣0 of 5000 and 10,000 kcal/m2Ch (Ref 25). The calculated time variations of temperature differ from the measured ones only at those measuring points with higher cooling rates. The time variation of temperature refers only to the selected measuring points; therefore, assessment of the stress state during the quenching process and of distortion of gear-wheel teeth or of a tooth is very difficult. The authors focused on an analysis of the conditions during the quenching process using a calculated distribution of temperature shown as isotherms (␣0 ⳱ 5000 kcal/m2Ch) at the half-cut of the gear-wheel tooth. Figure 32 shows the variation of isotherms during the quenching process after 0.1, 1.0, and finally 10 s of cooling (Ref 25). In quenching it is very important that the temperature gradients are high enough to prevent plastification, that is, distortion, of the gear wheel during quenching. Such quenching conditions including high-temperature gradients result in decrease of favorable compressive residual stresses after hardening. It follows that a sufficiently high cooling rate has to be ensured at the tooth surface as well as to the required depth of hardening. That means that temperature gradients in the gear-wheel tooth have to be attained so that gear-wheel teeth are hardened with the minimum cooling rate required, thus ensuring the required martensite transformation in it. A sequence of images showing isotherms in very short time intervals from the beginning of

800 1 2

600

3 4

400 200 0

0

80 120 Time (t ), s

40

860 °C ºC

780 °C ºC

End of induction heating

600 °C ºC 840 °C ºC

160 187200 500 °C ºC

(a)


820 °C ºC

700 °C ºC

1000 400 °C ºC

800 1

800 °C ºC

2

600

3 4

400

q q

200

01 02

= 75 W/cm2

300 °C ºC

= 10 W/cm2

600 °C ºC

780 °C ºC

Curie point TA = 721 °C 2

0

0

40

80 120 Time (t ), s

760 °C ºC

160 187200

200 200 ºC °C

500 °C ºC

740 °C ºC

(b) Temperature profiles of tooth gear during induction surface heating process. (a) Measured. (b) Calculated. Source: Ref 25

20 s

Fig. 29

Fig. 30

60 s

187 s

Temperature distributions during induction surface heating process. Source: Ref 25

Induction Hardening / 231 quenching allows assessment of the size of distortion of the tooth and residual stresses to be expected after quenching. Figure 33(a) shows the measured volumefraction distribution of martensite and Fig. 33(b) the calculated volume-fraction distribution of martensite when different values of heat transfer coefficient ␣—5000, 7500, and 10,000 kcal/ m2Ch—are taken into account (Ref 25). The main difficulty encountered in the calculation is how to determine the heat transfer coefficient in order to obtain a description of real quenching conditions. It should be considered that quenching is very intensive since it is carried out under a pressurized water jet; the gear wheel has been induction heated whereas the core is cold.

negligible influence on the results of heat treatment. The quenching system for induction hardening is defined by eight parameters (Ref 26): heat time/scan rate, power level, power frequency, part position/rotation, quench flow, quench temperature, quench time, quench concentration. Important simultaneous changes of one or more of these parameters can produce unwanted effects on the workpiece, which in extreme cases result in an unsuitable microstructure, deviations in the depth of hardened profile, unsuitable hardness variation (too low hardness, soft spots), and exceeding distortion of the machine element.

Quenching Systems for Induction Hardening

In practice, there are machine parts of different shapes and size, requiring different depth of hardened layer. In these cases, the type of material chosen and its through-hardenability should be considered. Thus, with alloyed steels having good through-hardenability and/or machine parts with a comparatively thin hardened surface layer, the martensite microstructure can be obtained without the application of a quenchant. In such cases, heat sinks from the surface into the cold workpiece core so that the critical self-cooling rate obtained at the surface is higher than the critical cooling rate.

500 °C ºC 100 °C 1000 ºC

600 °C ºC 850 °C ºC

Control of the quenching process of the gear wheel from high hardening temperatures ensures the martensite microstructure. The cooling rate should be high enough to prevent formation of unwanted softer microstructures such as pearlitic or bainitic; therefore, it is very important that in a development of new systems of induction hardening, quenching systems are designed properly (Ref 22, 26). Process parameters should be accurately controlled to ensure permanent and reproducible results after hardening of machine parts. It is also indispensable to define individual parameters and determine their permissible deviation in operation, presuming that the deviations have a

700 °C ºC

200 °C ºC

800 °C ºC

300 °C ºC

750 °C ºC

400 °C 750 °C ºC 500 °C ºC


1000 800

0.1 s

600 Stop of spouting water under a pressure 3

400 200 0

0

10

Fig. 32

1s

10 s

Temperature distributions during cooling process. Source: Ref 25

4 2

1

20 Time (t ), s

30

Martensite volumetric fraction, %

40

90-100 50-90 0.1-50 0-0.1

(a) 1000 Temperature (T ), °C

α 0 = 5000 kcal/(m2 °Ch) α 0 = 10,000 kcal/(m2 °Ch)

800 4

600 3

400

2

200 1

0 0

10

20

30

40

Time (t ), s

α 0 = 5000

(b) (a) Temperature profiles of tooth gear at given measuring points during cooling process. (a) Calculated. (b) Measured. Source: Ref 25

Fig. 31

Fig. 33

α 0 = 7500

α 0 = 10,000 kcal/m2 Ch

(b) Martensite distribution of hardened gear. (a) Measured. (b) Calculated at the maximum cooling rate. Source: Ref 25

232 / Residual Stress During Hardening Processes Two common quenching methods using a quenchant are spray quenching and immersion quenching. Particularly popular spray quenching techniques offering different possibilities are:

60 Ratio (inlet:outlet)

1:1

Flow (q ), gpm

50

1:1.7

40

● Spray with progressive scan heating (scan

hardening)

1:3

30

● Spray after heating in position (single-shot

hardening)

20

● Spray quenching out of location after heating

1:5

10 0

0

10

20

40

30

60

50

Pressure (p), psi

Fig. 34

Effect of inlet:outlet ratio on quench flow versus pressure. Source: Ref 26

6

Hole size (d), in.

3/16

5

Flow (q ), gpm

4 5/32 3 1/8 2 1.45

3/32

1

1/16

0.5 0

0

10

20

30

Fig. 35

40

50

60

70

80

Pressure (p), psi

15

Effect of hole size on quench flow versus pressure. Source: Ref 26

1000

Curve 1:10% 800


Curve 3:20% 600 Curve 2:15% 400 Curve 4:25% 200

0

0

20

40

60

80

100

120

140

Cooling rate (v), °C/s

Fig. 36

Polymer additive ratio affects cooling rate. Source: Ref 26

Spray quenching is carried out immediately after heating with a short pause. It is used with machine parts made of steels with good hardenability and with a comparatively thin hardened layer. Immersion quenching is carried out after the inductor has been disconnected from the high-frequency generator. Gradual hardening is very efficient and prevents the influence of inverse heat from the core toward the surface so that no reverse heat flow and no heating of the already cooled surface occur. This problem is characteristic of large parts of which the workpiece surfaces should be hardened selectively. In the past, straight oils and water-soluble oils were used for quenching after surface induction heating. Straight oils and water-soluble oils produce mild quenching effects, which reduce difficulties due to distortion and/or crack initiation. Straight oils require immersion quenching to minimize the risk of oil ignition whereas watersoluble oils are more suitable for spray quenching. Other quenchants used are water, polymeric water solutions of different concentration, water soluble oils, salt water, and so forth. Polymeric water solutions are inflammable quenchants. They are prepared in various concentrations to be suitably adapted to various cooling rates. For spray quenching various flow rates of quenchants can be selected. They depend on the size of inlet openings and the number of outlet nozzle boreholes in one, two, or more rows at the quenching ring. The fluid-flow rate can also be regulated by pressure. Technical literature provides data on shaping of quenching nozzles as well as on the selection of the quenchant flow rate required. Figure 34 shows the dependence of the flow rate on the quenchant pressure and the size and number of outlet boreholes (Ref 26). It is very important that a sufficient flow rate of the quenchant is chosen to ensure sufficient heat removal from the workpiece surface layer during quenching. The flow rate is controlled also by the number of boreholes for the flow and spraying of the quenchant, respectively. Figure 35 shows a dependence of the quenchant flow rate on the borehole diameter of the quenching nozzle, and the pressure required (Ref 26). An appropriate arrangement of the boreholes in the ring permits a uniform heat removal after spray and proper and uniform cooling. The borehole cross sections should amount to only 15% of the total ring surface available and of the inductor in the singleshot type application, respectively. Rotation velocities of the workpieces in surface induction heating are relatively high and can be selected between 800 and 1000 rotations/min, whereas

the rotation velocity of the workpieces during quenching is considerably lower, namely, 40 to 60 rotations/min. Very high rotation velocities of the workpieces are required when a uniform and reproducible depth of hardened layer are to be ensured and particularly with relatively short heating times. Figure 36 shows dependence of changes of cooling rates on the momentary temperature at the workpiece surface for four different concentrations of polymeric water solutions (Ref 26). The selection of an appropriate concentration of the polymeric water solution for the selected steel and the depth of hardened layer required should ensure minimum distortion of the workpiece, which is the final purpose of any heat treatment. Thus, the required heat removal from the heated surface layer of the workpiece, considering the thickness of the heated layer, should be ensured by an appropriate quenching system.

Time Variation of Stresses and Residual Stresses in a Material With certain heat treatments, the required microstructural changes and an appropriate magnitude and variation of hardness are obtained. It is also required that distortion of a machine part is as small as possible so that the final size of a machine part can be obtained with minimum precision machining. Consequently, it is very important that distortion be kept under control. That means that an appropriate technology of machining and appropriate heat treatment processes should be selected, and internal stresses lower than the yield stress ensured at any moment and at any location of a machine part during heating and/or cooling. Analytical methods give an insight into heat treatment conditions if the time variation of internal stresses is monitored and the dependence between the cooling time and the specimen temperature at each point is known. With regard to the specimen temperature determined in this way, at each point on the specimen yield stress can be determined as well. Consequently, with different heat treatment conditions, different values of physical quantities can be selected. They are reflected in the changed conditions in the material, which makes it possible to study distortion of the machine part during cooling and determination of the magnitude of residual stresses. Figure 37 shows the time variation of axial stresses at the surface and in individual depths, that is, from 2.0 to 4.0 mm under the surface and in the middle of the cylindrical specimen (Ref 21). It follows from the time variation of temperature in the diagram in Fig. 26 that the austenitizing time was shorter than 15 s, which means that after this time quenching of the surface followed (Ref 21). In surface heating, tensile stresses occurred at the surface due to thermal extension of the surface layer, but when the temperature of transformation of the microstructure from pearlitic to austenitic was exceeded,

Induction Hardening / 233 additional compressive stresses occurred at the surface. The compressive axial stresses transform into tensile stresses in the zone of undercooled austenite. In the transformation of undercooled austenite into martensite, the compressive stresses increase with the increased martensite fraction. In the core, the opposite sign of the stress was obtained, namely, the tensile stress. At the end of quenching, the compressive residual stresses were obtained in the surface hardened layer amounting to around ⳮ1600 N/mm2 and the tensile stresses in the core amounting to around Ⳮ870 N/mm2.

1000

Figure 38 shows a distribution of the individual components of the residual stresses, that is, the axial component rz, the tangential rT, and the radial rr (Ref 21). The axial and the tangential components of the residual stresses were compressive at the surface and amounted to ⳮ1600 N/mm2. Then they gradually reduced so that at a depth of 5.0 mm, the residual stresses changed their sign to become tensile stresses. A maximum value of the residual stresses was up to 1000 N/mm2. The radial stress at the surface was 0, but it gradually increased to a depth of 5.0 mm to attain Ⳮ500 N/mm2. Denis et al. (Ref 18) calculated and measured the distribution of residual stresses through the entire radius of a cylindrical specimen of 16 mm in diameter and 48 mm in length. The specimen was made of carbon steel with 0.45% C and of pearlitic-ferritic composition.

0

−500

60

−1000

50

Pearlite

Surface Depth 2.0 mm Depth 4.0 mm Center

−1500

−2000

0

20

40

60

80

Time (t ), s

Volume fraction (Vf), %

Internal stress (σ), N/mm2

500

Axial stress distribution at various depths below the surface during single-shot induction surface hardening. Source: Ref 21

Fig. 37

High-carbon martensite Ferrite

40 Low-carbon martensite

30

20

10

0

Austenite

0

2

1

3

4

Depth below the surface (z), mm 1000 Calculated distribution of microstructures across the cylinder radius at the end of cooling. Source: Ref 18

Fig. 39

0 1000

−500

Residual stress σRS, N/mm2

Residual stress (σRS), N/mm2

500

−1000 σz σT σr

−1500

−2000

200 0 200

20

40

60

σr

600 T

1000 1400 0

0

σz

600

80

1

Calculated Measured

2

3

4

5

6

7

8

Depth below the surface (z ), mm

Depth below the surface (z), mm Residual stress distribution after single-shot induction surface hardening. rz, axial component; rT, tangential component; rr, radial component. Source: Ref 21

Fig. 38

Calculated and measured residual stress profile of particular components after induction surface hardening. rz, axial component; rT, tangential component; rr, radial component. Source: Ref 18

Fig. 40

The cylindrical specimen was surface induction heated to a temperature of 980 C and then quenched in salt water. Figure 39 shows the calculated distribution of individual microstructural phases from the surface to the center of the cylindrical specimen at the end of cooling (Ref 18). The initial microstructure was preserved to a radius r of 5.5 mm. In the radii between 5.5 and 6.6 mm, the pearlitic-ferritic microstructure and low-carbon martensite appeared. With the radii exceeding 6.6 mm, a fine martensitic microstructure with around 6.0% residual austenite was obtained due to intensive cooling. With the selected conditions of induction heating and fast cooling of the specimen, no homogeneous martensite was formed in the surface hardened layer. Figure 40 shows the calculated and measured variations of individual components of residual stresses (Ref 18). The calculated variations of residual stresses represent high compressive stresses at the surface, that is, the axial component of residual stresses rz amounting to ⳮ803 N/mm2 and the tangential one rT amounting to ⳮ588 N/ mm2. On the contrary, the tensile residual stresses were calculated after hardening in the core, that is, with the preserved pearlitic-ferritic microstructure. Thus the axial component of residual stresses rz calculated for the core amounted to Ⳮ370 N/mm2 and the tangential component rT to Ⳮ62 N/mm2. The diagram in Fig. 40 indicates that the maximum tensile stresses were attained in the transition zone between the hardened and the unhardened layer (Ref 18). At a greater depth, very low stress gradients occurred and in the opposite direction, that is, in the thin surface layer to a depth of 2.5 mm, very high gradients of residual stresses occurred. The variations of residual stresses were determined experimentally by x-ray diffraction. The great changes of the gradient of the measured residual stresses in the thin surface layer can also be confirmed by the measurements made. The results of the measured and calculated variation of residual stresses in the surface hardened layer agree sufficiently with small local deviations. In order to determine the local deviations of the variation and of residual stresses, numerous calculations were made with varying physical parameters of the material and taking account of different process parameters, too. A particular problem with steels having ferritic-pearlitic and pearlitic-ferritic microstructure is that heating of short duration does not ensure complete homogenization of austenite. Figure 41 shows the influence of inhomogeneity of austenite on the level of residual stresses, which is particularly noticeable in the martensite zone (Ref 18). The initial inhomogeneous austenitic microstructure resulted in the appearance of the martensitic transformation with a small fraction of residual austenite. With regard to the volume fraction of martensite and residual austenite, plastification of the material occurred, which produced internal stresses and the variation of residual stresses, particularly in the thin surface hardened layer.

234 / Residual Stress During Hardening Processes Figure 42 shows the calculated distribution of residual stresses due to heating of the specimen with heating rates of 200 and 800 C/s to a temperature of 1050 C followed by cooling with a cooling rate of 1500 C/s (Ref 18). With the high heating rate v, 800 C/s, a very steep transition of residual stresses from the compressive zone to the tensile one was obtained, which resulted in a decrease of fatigue strength. With the considerably lower heating rate, 200 C/s, it turned out that the variation of residual stresses in the thin surface layer was essentially more favorable than that with the high heating rate. The variation of the tangential and axial components of residual stresses permits the following findings: ● With the lower heating rate, the residual

stresses at the surface are lower by 100 to 200 N/mm2. ● The stress gradient for the tangential and axial components rt and rz is very small in the subsurface, that is, from a depth of 0.7 to 4.5 mm. ● The transition from compressive to tensile residual stresses does not occur earlier at a depth of 2.6 mm due to a small stress gradient.

residual stresses with the favorable rate of surface induction heating VH1, 200 C/s, which gives the maximum temperature obtained at the surface Tmax, 1050 C (Ref 18). This was followed by quenching with two cooling rates, 1500 and 300 C/s. The variation of the tangential and axial components of residual stresses permits the following findings:

The radial component of residual stresses is 0 at the surface. In the subsurface it is tensile. Thus it amounts to around 50 N/mm2 with the higher heating rate, that is, 800 C/s, and to 400 N/mm2 with the lower one, that is, 200 C/s. Figure 43 shows simulation of the variation of

sidual stresses are obtained at the surface, that is, the axial component of ⳮ800 N/mm2 and the tangential component of ⳮ1050 N/mm2. With a low gradient, the axial and tangential components of the stresses vary; they change their sign to the tensile zone only in the depth between 2.6 and 2.8 mm. With the lower cooling rate, considerably lower compressive residual stresses are obtained at the surface, that is, an axial component of ⳮ275 N/mm2 and a tangential component of ⳮ390 N/mm2. A comparison of the axial and the tangential components of residual stresses indicates that because of the considerably reduced cooling rate the latter is lower in the thin surface layer even by a factor of 3. The gradients of residual stresses with the higher or lower cooling rate are favorable since a slow decrease of compressive to tensile residual stresses results in a minor susceptibility of a machine part to fatigue under dynamic loads.

● With the higher cooling rate, compressive re-

●

● 1000

2 Residual stress σRS , , N/mm

600

σz

r

●

200 0 -200

●

-600

T

-1000 -1400

0

1

2

Heterogeneous austenite Homogeneous austenite

6 3 4 5 Depth below the surface (z ), mm

7

8

Calculated residual stress profile of particular components after induction surface hardening for heterogeneous and homogeneous austenite at austenitizing temperature. rz, axial component; rT, tangential component; rr, radial component. Source: Ref 18

Fig. 41

1200

z Residual stress σRS, N/mm2

800

σr

400

0

400

σT

800

1200

0

1

2

Tmax = 1050 C Heating rate 200 C/s Heating rate 800 C/s Cooling rate1500 C/s

3 4 5 Depth below the surface (z ) , mm

6

7

8

Simulated residual stress profile of particular components at maximum surface temperature (Tmax ⳱ 1050 C) with various heating rates vH1 ⳱ 200 C/s and vH2 ⳱ 800 C/s) and at given cooling rate vc of 1500 C/s. rz, axial component; rT, tangential component; rr, radial component. Source: Ref 18

Fig. 42

Bru¨ckner et al. (Ref 19) discussed their investigations conducted on residual stresses due to surface induction hardening as well as the time variation of internal stresses. They applied the finite-element method to the calculation of the time variation of individual components of internal stresses rz, rr, and rt. Figure 44 shows the time variation of all these components after heating times of 1, 4, 6, and 9 s in the cylindrical specimen with 30 mm in diameter, which was heated with a heat flow Q3 of 2.4 ⳯ 106 kW/m3 (Ref 19). Radial stresses rr vary with time. They are always 0 N/mm2 at the surface. Then they gradually increase toward the center of the cylindrical specimen. After the heating time t of 4 s they reach the highest value in the core, 210 N/mm2, and after the heating time of 9 s they reach the value of 100 N/mm2. The radial stresses during heating and cooling may be critical if they essentially exceed the yield stress, which may produce lamination of the surface from the core. Axial stresses rz vary with time as well. They are the highest after the heating time t of 4 s, 500 N/mm2 in the core and around 130 N/mm2 at the surface. The time variation of temperature through the radius of the cylindrical specimen indicates that these stresses occur at around 500 C at the surface and at around 150 C in the core. It can be concluded that because of high axial internal stresses in the core and considerably lower ones at the surface, they rarely produce distortion of a machine part or even its fail-

Induction Hardening / 235 ure. It is interesting that after a heating time of 1 s the tensile stress in the core ra is around 250 N/mm2 and at the same time a little higher, that is, 280 N/mm2, at the surface. The transition from a compressive stress to a tensile stress shifts toward greater depths with time.

Tangential internal stresses vary with time, similar to axial and radial ones, but the absolute values are somewhat lower than that of axial stresses. This means that tangential stresses in the core are tensile and the highest after the heating time of 4 s (rTc ⳱ 200 N/mm2). At the sur-

1500

σz

Residual stress σRS , N/mm2

1000

r 500

0

500

1000 1500

Tmax = 1050 °C Heating rate 200 °C/s Cooling rate 1500 °C/s Cooling rate 300 °C/s

σT 0

3 4 6 5 Depth below the surface (z ) , mm

2

1

7

8

Simulated residual stress profile of particular components at maximum surface temperature (Tmax ⳱ 1050 C) with heating rate of 200 C/s, and at various cooling rates (vC1 ⳱ 200 C/s and vC2 ⳱ 800 C/s). rz, axial component; rT, tangential component; rr, radial component. Source: Ref 18

Fig. 43

4s

200

500

σr , N/mm2

Material: Ck 45 Q = 2.4 × 109 W/m3 4s

400

6s 1s

Surface

100 9s

face the highest compressive stresses occur after a heating time of 1 s (rTs ⳱ 270 N/mm2). The investigation showed that values of tangential and radial stresses at individual heating times are very similar in the core, but the differences between axial and tangential stresses there are greater, that is, by a factor 2 in the axial direction. Taking into account the magnitude of time variation of tangential internal stresses during the heating process, internal stresses should probably also be monitored during the quenching process. The diagram in Fig. 45 shows the time variation of tangential internal stresses using the finite-element method in the selected moments, that is, t ⳱ 9 s (at the beginning of cooling), t ⳱ 9.1 s, t ⳱ 10.5 s, t ⳱ 12.5 s, t ⳱ 18 s, and t ⳱ 53 s (Ref 19). At the beginning of the quenching process, there are very low compressive tangential internal stresses rT, ⳮ50 N/ mm2, at the surface. Then they gradually change to become of a tensile character and amount to 260 N/mm2 after the cooling time of 10.5 s. As cooling continues, after a total time of 18 s and a quenching time of 9 s, compressive stresses rT at the surface amount to ⳮ320 N/mm2, and then slightly increase, during cooling, up to ⳮ390 N/ mm2. The variation of tangential residual stresses after quenching is very favorable since compressive stresses change slowly from the surface to a depth of 6.0 mm, where the sign for the stresses changes and the maximum tensile residual stresses is reached in a length of 8.5 mm. Melander (Ref 20) proceeded from a magnetic field and a temperature field to a phase composition at the given temperature and, consequently, internal stresses and residual stresses formed due to heat treatment, respectively. The entire procedure of calculating the characteristics mentioned is based on suppositions that:

Surface 0

6s

300

0

5 10 Radius (r ), mm

10.5 s

Material: Ck 45 Q = 2.4 × 109 W/m3

200 4s Internal stress (σT ), N/mm2

Surface 100

1s

100

9s 0

0

−100

−100

−200

−200

0


15

−300

100

12.5 s 9.1 s

0 9.0 s −100

−200

−300

18 s

−400 0


53 s 0

15

Internal stress time distributions in particular components during surface induction heating process. rz, axial component; rT, tangential component; rr, radial component. Source: Ref 19

Surface

6s

−300

Fig. 44

300

15

200 9s

200

σT , N/mm2

Internal stress (σz ), N/mm2

1s

5

10

15

Radius (r ), mm

Fig. 45

Tangential internal stress component distribution during quenching process. Source: Ref 19

236 / Residual Stress During Hardening Processes ● The workpiece is of infinite length and has a

● Electromagnetic properties: magnetization

● Regardless of the measuring point, the tem-

cylindrical, axially symmetric shape. ● Heat conductivity does not depend on the workpiece length. ● The magnetic field varies. For the calculation, equations for: ● Magnetic field ● Heat conduction ● Phase transformations ● Stresses Input data to the physical model and computer program consist of: ● Basic mesh of nodes and their start temperature

curve (B-H) ● Curie temperature TA2, surface magnetic field strength H0(T), and frequency f ● Surface heat flux q(T) ● Material properties: thermal conductivity kk(T), specific heat c(T), density q, heating diagram (ITh diagram), and cooling diagram (ITc diagram), latent heat L

perature difference between the measured temperature and the calculated temperature is exceptionally small. ● At the individual measuring points, the differences between the calculated temperature and the measured temperature are greater in the heating cycles. ● The greatest difference between the measured temperature and the calculated temperature in the heating cycle is found at the measuring point at the surface, that is, with the radius r of 18.5 mm.

1000

r = 18.5 mm

800


r = 14.5 r =0

600

400

200

0 10−1

1

102

10 Time (t ), s

Measured temperature cycles (dashed lines) and calculated temperature cycles (solid lines) at different radii of cylindrical specimens. Source: Ref 20

Fig. 46

Residual stresses (σRS ), N/mm2

800

400

0

The computer program for solving the temperature field and phase content consists of heating and cooling phases: 1. During heating, the eddy current loss is responsible for the temperature field rise. The heat flux through the surface is due to the surrounding air. The phase transformation into austenite is calculated using a heating diagram (ITh diagram). When the steel part has been heated for a given time or to a desired temperature, heating is switched off. 2. Water quenching can be preceded by air cooling for some seconds or vice versa or other quenchants can be used. The material that transformed into austenite during heating is now transformed into ferrite, pearlite, bainite, or martensite depending on the cooling diagram (ITc diagram). The material untransformed during heating is assumed to remain untransformed during quenching. Throughout the calculations, material parameters are chosen from the input curves at the temperature at hand. 3. Temperatures and phase content as a function of time in every point in the body are the results obtained. These values together with mechanical data are used as input data to the stress program. Stresses are calculated by the finite element method. Figure 46 shows the measured and calculated temperature cycles in the middle of the cylindrical specimen with 40 mm diameter and 120 mm length (Ref 20). In the middle of its length, that is, at a distance of 60 mm, two thermocouples are mounted in the radial direction. They measure the temperature during heating and cooling. The first thermocouple is located at a radius r of 11.5 mm and the second at a radius of 18.5 mm. In the figure the temperatures measured are indicated by a dotted line and the calculated ones at the same measuring points by a solid line. The differences obtained at the given time t are surprisingly small, namely:

Figure 47 shows the variations of individual components of residual stresses along the radius r of 20 mm (Ref 20). The author’s calculations show that: ● Axial residual stresses are compressive at the

surface (rz ⳱ ⳮ850 N/mm2), the transition to the tensile zone is found 6.0 mm below the surface, and the maximum axial tensile stress rz, 400 N/mm2, occurs at a depth of 10.0 mm. ● Tangential residual stresses vary in a very similar way and have similar values (rT ⳱ ⳮ880 N/mm2) in the surface layer, whereas tensile residual stresses in the central part rT amount to 200 N/mm2. ● There are no radial residual stresses rr at the surface, but in the central part they slowly increase up to 200 N/mm2. The authors also experimentally verified the magnitude of axial residual stresses at three measuring points in the thin surface layer and calculated the mean value. The measurement of axial residual stresses was performed with x-ray diffraction. Table 1 shows measured residual stress values at various measuring points (Ref 20). The average of three measurements at three measuring points gave ⳮ852 N/mm2 at the surface and ⳮ1377 N/mm2 in the subsurface at a radius of 19.91 mm. The deviations between the measured and the calculated values are comparatively great. The authors attribute them to measurement errors as well as to the errors in calculation due to inappropriately selected values of physical parameters. Fujio et al. (Ref 25) in their third report on induction hardening focused on studies of distortion of gear wheel teeth and of residual stresses in gear wheels. The authors measured the outer diameter and the root diameter of the gear wheel across two opposite teeth and the root

−400 σz σT σr

−800

−1200 0

5.0

Table 1

Residual stress (rz), N/mm2

10.0

15.0

20.0

Radius (r ), mm Calculated residual stress in particular components after surface induction surface hardening. rz, axial component; rT, tangential component; rr, radial component. Source: Ref 20

Fig. 47

Measured residual stress values by x-ray diffraction at various measuring points

Radius (r), mm

Point 1

Point 2

Point 3

Mean value

20.03 20.00 19.96 19.59 19.91

ⳮ858 ⳮ1019 ⳮ1443 ⳮ1109 ⳮ1315

ⳮ779 ⳮ1278 ⳮ1250 ⳮ1204 ⳮ1423

ⳮ920 ⳮ1156 ⳮ1292 ⳮ1206 ⳮ1394

ⳮ852 ⳮ1151 ⳮ1328 ⳮ1173 ⳮ1377

Source: Ref 20

Induction Hardening / 237

Change of tip diameter (∆DT ), mm

0.3 0.2 0.1

Gear No. 2

0 0.3 0.2 0.1

Gear No. 3

0 0.3 0.2 0.1 0

Gear No. 4 114

316

57918 20 22 Tooth number

1124

1326

Experimental Theoretical

Fig. 48

Gear No. 2

0.2 Change of whole depth (∆WD ), mm

Change of tip gear wheel diameter after quenching. Source: Ref 25

0.1

Gear No. 3

0.2 0.1

Gear No. 4

0.2 0.1 0

1

5

10

15

20

25

Tooth number Experimental Theoretical

Fig. 49

Change of tip whole depth of gear wheel after quenching. Source: Ref 25

parts of the teeth with a micrometer before and after quenching. The same dimensions were also calculated theoretically, taking into account the volume changes due to phase transformations, and serve as a basis of determination of deviations. Figure 48 shows a change of the outer diameter of the gear-wheel tooth of gear wheels 2, 3, and 4 (Ref 25). The gear wheel has 26 teeth, which means that the deviation was measured between the first and the twenty-sixth tooth, 3 and 16, and so forth, so that 13 total measurements were made. The results of the measurements are shown as points in the diagram. The dotted line represents the theoretically calculated increase in diameter due to heat treatment. Figure 49 shows a change of tooth height of gear wheels 2, 3, and 4, as in the previous case (Ref 25). The dotted lines in the individual diagrams represent the theoretical deviations of height of the individual teeth by 0.18 mm and the deviations found by measurement, which are mostly greater than the theoretical values. The greatest deviation can be found with gear wheel 4. It even exceeds 0.2 mm. Figure 50 shows changes of the root diameter. Calculations show that after heat treatment the root diameter reduces by around 0.02 mm (Ref 25). The measured values of the same diameter, however, remained unchanged for gear wheels 2 and 3 and decreased by 0.1 mm at maximum for gear wheel 4. A comparison of the outer tooth diameter and the tooth root diameter, taking account also of the tooth height, shows that distortion of individual gear wheels is considerably more complicated and cannot be described by the selected measurement methods; therefore, also changes of tooth profiles along tooth height were measured. Figure 51 shows tooth profile error curves after induction surface heating and after quench-

ing (Ref 25). Prior to quenching, the left tooth surface was marked with the letter “a” and the right tooth surface with the letter “b.” Measurements of the height profile are shown for two teeth, that is, those marked 1 and 14, of gear wheels 2 and 3. Considering that the tooth height is 10 mm and the deviations are plotted in millimeters, their absolute value can be evaluated. It ranges between 9 and 100 lm at each tooth surface concerned. Residual stresses due to surface induction hardening of the gear wheels were calculated along the tooth surface during the heating process as well as the quenching process. Figure 52(a) shows distributions of internal stresses during the heating process after 20, 60, 100, and 187s (Ref 25). The profile variation of internal stresses indicates that: ● In the initial heating phase, the internal

stresses in the root of tooth are compressive and reach up to ⳮ700 N/mm2; with further heating they change into tensile internal stresses ranging from 200 to 300 N/mm2. ● They are considerably lower in the zone reaching from the root to the pitch circle; up to a heating time of 60 s, they are tensile and reach up to 700 N/mm2; with further heating they gradually change to compressive stresses attaining ⳮ100 N/mm2. ● They are obviously very low and insignificant in the upper part of the gear wheel tooth, that is, from the pitch-circle diameter to the tip of tooth; therefore, they are not plotted. Deformations are for this very reason the greatest at the tip of gear-wheel tooth. Figure 52(b) shows changes of internal stresses during the heating process and the cooling and quenching processes (Ref 25). It is characteristic of the quenching process that considerably higher internal stresses occur during the

Tooth tip Gear No. 2

0.1

Gear No. 3

Change of root diameter (∆DR ), mm

0 −0.1

Gear No. 2

−0.2 0.1 0 −0.1

Gear No. 3

Tooth root

−0.2

(a)

(b) Left

Tooth No. 1

Right (b)

(a)

(a)

(b) Left

Tooth No. 1

(a)

(b) Left

Tooth No. 14

Right (b)

(a)

(a)

(b) Left

Tooth No. 14

Right (b)

(a)

0.1 0

Gear No. 4

−0.1 −0.2

1,214,15

4,517,18

7,820,21

10,1123,24

13,1426,1

Tooth number Experimental Theoretical

Fig. 50

Change of root gear wheel diameter after quenching. Source: Ref 25

Fig. 51

Right (b)

Tooth profile error curves after induction surface heating (a) and after quenching (b). Source: Ref 25

(a)

238 / Residual Stress During Hardening Processes

The magnitude of residual stresses was measured with x-ray diffraction and strain gages. Figure 53 shows the results of measurement of stresses in the pitch circle, that is, at the middle of the tooth surface for both teeth and in the root of tooth where critical residual stresses occur (Ref 25). Using x-ray diffraction, the authors found that: ● The highest residual stresses occur in the root;

at the surface they amount to around ⳮ540 N/mm2, then increase to ⳮ750 N/mm2 at a depth of 30 lm to reach ⳮ870 N/mm2 at a depth of 60 lm.

20 s

60 s

100 s

187 s

(a)

1s

0.1 s Stress σ 0 (b)

10 s

300 s

daN/mm2

50

Principal stress during induction surface heating and quenching process. (a) Heating process. (b) Quenching process. Source: Ref 25

Fig. 52

A general conclusion can be drawn that the experimental as well as theoretical results agree very well and provide a lot of useful information especially to a technologist in manufacture of gear wheels. In Ref 24, Inoue et al. treated the variation of tangential residual stresses in the root of tooth after single-frequency and dual-frequency surface induction hardening. Figure 54(a) shows the variation of the tangential residual stresses in the tooth root where usually the highest residual stresses in gear wheels are found (Ref 24). The calculated residual stresses and the measured ones after dual-frequency hardening refer to the root width of gear-wheel tooth. The residual stresses are measured with the x-ray diffraction. Individual measurements are marked by points. The calculated residual stresses at the root surface of tooth show the same values as the measured stresses, but the variations of the two differ strongly, particularly at a depth greater than 0.5 mm. The calculated variation of stresses in the root cross section of tooth shows a linear dependence to a depth of 2.0 mm. At the surface, the calculated tangential residual stresses amount to ⳮ650 N/mm2, and, with a small stress gradient, they change so that at a depth of 1.2 mm there is a transition to tensile stresses, which at a depth of 1.9 mm attain around 400 N/mm2. The calculated variation of tangential residual stresses is ideal since the stresses are compressive and show a sufficiently high value at the surface, slowly decreasing with depth. Such a variation ensures high fatigue strength of the material, and the latter ensures, in turn, a longer life of a machine part. Figure 54(b) shows the variation of tangential residual stresses after single-frequency induction surface hardening (Ref 24). Resulting from a better and a more uniform heating of the central part of the gear wheel across the tooth height, a martensite-bainite microstructure forms after quenching, and very low compressive residual stresses are obtained through root depth of tooth. The tangential compressive residual stresses are very low and amount to around ⳮ200 N/mm2. Because of a very small stress gradient, they change to give, at a depth of 0.25 mm, the transition of the compressive residual stresses into the tensile ones reaching 100 N/mm2. Such a variation of the residual stresses is unfavorable because it does not provide sufficient compressive residual stresses in the surface layer, which produces a decrease in fatigue strength of gearwheel teeth. Because of a symmetric variation of the residual stresses at both sides of the tooth, that is, the left and the right tooth surfaces, and a symmetric load state of the gear-wheel tooth in operation, the tooth may often be subjected to a considerable tensile load, which results in damage to the tooth root or even a tooth failure.

Figure 55 shows shape distortion after singlefrequency and dual-frequency induction surface hardening in the half-cut of the gear-wheel tooth (Ref 24). Figure 55(a) shows simulation of distortion by showing first the initial shape of the tooth half-cut prior to hardening (dotted line) and the modified shape after dual-frequency induction surface hardening (continuous line). Figure 55(b) shows simulation of distortion in the same way as Fig. 55(a), but for the conventional single-frequency induction surface hardening. In the figure the calculated actual size of distortion is shown to be 50 lm with an equivalent geometrical scale of 2.0 mm. A comparison of

Residual stress (σRS), da N/mm2

and 1 s, the internal stresses are of the tensile character along the entire tooth height; they are the highest in the root of tooth and gradually decrease toward the tooth tip. ● Between the quenching times of 1 and 10 s, the sign of the internal stresses changes, the latter gradually becomes compressive and ranges between 100 and 150 N/mm2 in the upper part of the tooth and up to 600 N/mm2 in the root of tooth. ● At the end of quenching, that is, after the cooling time of 300 s, the internal stresses change considerably only in the root of tooth and attain up to ⳮ1500 N/mm2.

middle of the tooth surface, that is, at the pitch circle; at the surface they amount to around ⳮ90 N/mm2, then gradually increase with a greater depth to reach ⳮ400 N/mm2 at a 60 lm depth.

−100 −80 Root point −60 −40 Pitch point −20 0

0

30 60 Distance from tooth profile (z ), µm

90

Residual stress measurements on root and pitch point below the tooth surface. Source: Ref 25

Fig. 53

800 Residual stresses (σRS), N/mm2

● In the initial quenching phase, that is, in 0.1

● The residual stresses are a bit lower in the

400

0 −400 Calculated Measured

−800 −1200

0

2.5 0.5 1.0 1.5 2.0 Distance from surface (z ), mm

3.0

(a) Residual stresses (σRS), N/mm2

quenching process and are more important in the root of tooth. The figures show the magnitude and variation of internal stresses after the cooling times of 0.1, 1, 10, and 300 s, when the gear wheel is finally cool. The series of graphical representations of the internal stresses at the tooth surface indicates that:

800 400

0 −400 −800

Calculated Measured 0

2.5 0.5 1.0 1.5 2.0 Distance from surface (z ), mm

3.0

(b) Measured and calculated residual stress distributions below the surface for dual (a) and single (b) frequency. Source: Ref 24

Fig. 54

Induction Hardening / 239 both cases of hardening from the viewpoint of tooth distortion clearly shows that distortion in single-frequency surface induction hardening is twice that obtained after dual-frequency hardening. This difference in tooth distortion can be attributed to the fact that in single-frequency surface induction hardening, the martensite transformation occurs in the whole tooth. Consequently, the volume change of the tooth is greater and so is distortion. In dual-frequency surface induction hardening only the tooth contour gets hardened. Consequently, the volume change of the tooth is smaller and so is distortion; that is, it amounts to only half of that obtained after single-frequency hardening. In Ref 28, Fujita et al. dealt with the development of an experimental procedure for assessment of surface durability of two hardened materials in a pair. Since the 1980s, steels have been used most frequently for surface hardening in manufacture of various gear wheels since this hardening process is faster and very economical. In order to clarify surface durability of surface hardened gear wheels, investigations were conducted on surface defects, rolling fatigue life, and determination of the optimal thickness of a hardened layer under sliding/rolling conditions

5 × 10−2 mm (a)

of gear-wheel teeth. For testing of surface durability of surface induction hardened machine parts, specimens with 60.3 mm in diameter and made of steel S45C with 0.45% C were selected. The steel was hardened from an austenitizing temperature of 850 C for 1 h and then quenched in water by high tempering at 650 C for 2 h. Finally, the surface layer was induction hardened under different conditions so that the depths of hardened layer were 1.75, 2.95, and 5.00 mm. After surface hardening, tempering at a temperature of 150 C was carried out for 2 h. Figure 56 shows the hardness distributions of induction surface hardened roller specimens IA, IB, and IC (Ref 28). The surface hardnesses of roller specimens are designated HVIA, HVIB, and HVIC, respectively. The hardness of induction surface hardened layer is about 750 HV, and the core hardness is 200 HV in any specimen. The case depth is greatest in specimen IA and followed by specimens IB and IC. The variations of hardness under different conditions of induction surface hardening show almost the same hardness at the surface and a very similar throughthickness variation of hardness of the hardened layer. Figure 57 shows the residual stress distributions of induction hardened rollers. The variation of the calculated tangential residual stresses agrees with the expectations based on the variation of hardness and the hardened-layer thickness (Ref 28). The influence of the variation of residual stresses on surface durability depends on the load applied to the machine part concerned. With a continuous compressive load, plastification of the subsurface can occur; therefore, it is necessary to ensure a sufficient thickness of the hardened layer and a sufficient strength of the subsurface layer. The sufficient thickness of the hardened layer can be achieved by selecting appropriate conditions of induction

Table 2

Case depths of roller specimens

Specimen mark

Effective case depth zef, mm

Total case depth zT, mm

1.32 2.20 3.02

1.75 2.95 5.00

IA IB IC Source: Ref 28

200

5 × 10−2 mm

100

(b)

800 IA IB IC

600

0 Residual stress (σT ), N/mm2

Distortion of tooth gear after induction hardening with dual (a) and single (b) frequency. Source: Ref 24

Fig. 55

Vickers hardness, HV

surface hardening and the sufficient strength of the subsurface by selecting appropriate steel or a steel to which a hardened-and-tempered core has been added. Machine parts are mostly subjected to combined compressive and transverse loads that produce surface wear and subsurface plastification. In the third case, that is, when the side of a gear wheel is subjected to an alternating bending load, the magnitude of compressive residual stresses in the surface layer is important too. An appropriate heat treatment ensuring compressive residual stresses in the surface can result in an increase in fatigue strength and, consequently, a longer life of a machine part. Thus it can be concluded that the knowledge of residual stresses is most important in connection with those machine parts that are subjected to alternating or pulsating loads, that is, dynamic loads. In this way, compressive residual and applied stresses are ensured at any moment so that no cracks can appear or propagate. The whole procedure proposed by the authors is, with the residual stresses known beforehand, connected with a search of the optimal thickness of the surface layer in consideration of the radius of curvature of the sliding/rolling cylindrical specimen. Table 2 (Ref 28) shows the effective and total case depths of each roller specimen determined from hardness and residual stress distributions after various induction surface hardening con-

446 HV

−100 −200 −300 −400 −500

Heat treatment conditions

−600 −700

IA Water quenching at fixed position IB Coil: φ65 × 10 IC Tempering 2 h × 150° Material: S45C

−800

400 1.75

2.95

−900

5.0

−1000

200 0

Fig. 56

1.0 2.0 3.0 4.0 5.0 Distance from roller surface (z ), mm Hardness distribution of induction surface hardened roller specimens. Source: Ref 28

0

1

2

3

4

5

Distance from roller surface (z ), mm

Fig. 57

Tangential component of residual stress distributions of induction surface hardened roller specimens. Source: Ref 28


Induction surface hardened depth (z ), mm

ditions. Figure 58 shows the optimal induction surface hardened depth for surface durability calculated by the proposed method for various relative radii of curvature, assuming that there are no mass effects in heat treatments of induction surface hardening and no size effects for surface

10 700 HV at subsurface hardened layer 210 HV at core

8 6

Total case depth

4 2

Effective case depth

0 0

10 20 30 40 Relative radius of curvature (R ), mm

Fig. 58

50

Optimal induction surface hardened depth for surface durability. Source: Ref 28

Hardness Martensite

8

800 700 600

6

500 4

400 300

2

200

Microhardness, HV0.5

Martensite fraction (Vfm ), %

10

durability even though the radius of roller varies (Ref 28). The effective case depths were obtained by interpolating or extrapolating the calculated total case depths considering the relation of Table 2. It is clear that as the relative radius of curvature increases, the optimum inductionsurface-hardened depth increases and the optimal total case depth increases almost rectilinearly up to the relative radius of curvature of 40 mm. Beck and Simon (Ref 29) treated theoretical fundamentals of calculation of stresses due to different heat treatment processes. Among others they dealt also with surface induction hardening. The calculations of temperature fields, and finally stress fields, in machine parts during their heating and quenching are made in accordance with a physical model and the finite-element method. Numerical calculations and possibilities of simulation of surface induction hardening require very extensive and lengthy calculations, but give a very good insight in the heat treatment process as a whole. The results obtained until now in the field of the simulation of surface induction hardening are accurate enough so that the time variation of the stress state in a machine part can be predicted efficiently, which permits optimization of heating and/or quenching technology. In 1984 Melander (Ref 27) was the first to show some results of his numerical calculations and verify them experimentally. Figures 59 and 60 show theoretical and experimental results concerning the martensite fraction, and the variations of microhardness and residual stresses in the induction surface hardened layer (Ref 27). In Fig. 59, the continuous line indicates the calculated variation of the martensite fraction and the dotted line the variation of microhardness in the

thin surface hardened layer (Ref 27). The alloyed chrome-molybdenum heat treatment steel AISI 4142 shows very good agreement between the calculated martensite fraction and the microhardness measured in the surface layer. Figure 60 shows the through-thickness variation of calculated axial residual stresses (solid line) and the through-thickness variation of the measured axial residual stresses (dotted line) of a surface hardened layer. Although parameters of surface induction hardening are not known, it can be confirmed that with regard to the martensite fraction and the microhardness attained, the variation of the calculated axial residual stresses is within expectations. The variation of the measured axial residual stresses in the thin surface hardened layer to a depth of 0.75 mm is surprising. There, the deviation between the calculated and measured values of the residual stresses is exceptionally strong. The variation of axial residual stresses depends on the variation of the martensite fraction in the surface hardened layer and the increase in the specific volume of the surface layer with the martensitic microstructure. The measured variation of hardness indicates that a probable variation of axial residual stresses is closer to the one calculated. The first group of diagrams (Fig. 61) shows the time variations of through-thickness temperature in single-shot induction heating with the high-frequency generator with powers of 40, 60, 100, and 180 kW and a medium-frequency current (Ref 30). Characteristic temperature transformations TA1 and TA3 for equilibrium heating are plotted in the diagram. Induction heating is a very fast process; therefore, the temperature transformations mentioned shift to higher temperatures. In order to obtain homogeneous austenite in the surface layer, it is necessary to heat

100 0 0

1 2 3 Depth below the surface (z ), mm

4

Measured hardness (dotted line) and calculated martensite distribution (dashed line) after induction surface hardening. Source: Ref 27

Fig. 59

400 200 0 −200 −400 −600 −800

Calculated Measured

−1000 −1200 0

1 2 3 Depth below the surface (z ), mm

4

tH, s

Heating time

tH, s

Heating time

tH, s

tH, s Ac3 Ac7

25 7

15

20

4.5 20

7 30 2.5 15

10

10

7

0

Fig. 61

7 15

4.5

(a) Measured axial stress distribution (dotted line) and calculated (solid line) after induction surface hardening. Source: Ref 27

Fig. 60

Heating time

Heating time


Residual stress (σzRS), N/mm2

600

1150 1100 1050 1000 950 900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50

8

16

24

4.5 32

0 (b)

8

4.5 2.5 16 24 32 0 8 16 Depth below the surface (z ), mm (c)

24

32

0

8

16

24

32

(d)

Time/temperature variations in single-shot heating at various HF generation powers. (a) P1 ⳱ 40 kW. (b) P2 ⳱ 60 kW. (c) P3 ⳱ 100 kW. (d) P4 ⳱ 180 kW. Source: Ref 30

Induction Hardening / 241 the surface layer up to the hatched temperature range. The results shown in Fig. 61(a) to (d) make it possible to draw the following conclusions: ● The heating curves differ strongly. ● The temperature does not reach the hatched

temperature range in 30 s only with the power of 40 kW. ● The hatched temperature range is reached in a shorter heating time with all other powers higher than 60 kW. ● More intensive heating of the surface layer occurs (shown in a more steep hardness curve in the hatched temperature range) with all powers higher than 60 kW. The first question raised by an engineer would be how to evaluate the through-thickness variations of hardness and residual stresses with reference to the time variation of temperature. The second question would be how to select induction-heating parameters to obtain optimal properties of the surface hardened layer with a minimum energy input. An answer is that one must take into account the initial steel microstructure and choose an appropriate quenchant to ensure, in the surface layer, a cooling rate equal to or a bit higher than the critical cooling rate required. The second group of diagrams (Fig. 62) shows the time and through-thickness variations of temperature of the specimen at heating with different powers and different velocities of workpiece movement, that is, v1 ⳱ 140 mm/min, v2 ⳱ 220 mm/min, v3 ⳱ 370 mm/min, and v4 ⳱ 680 mm/min in scan hardening (Ref 30). In the first case, that is, with v1, the hardened layer is obtained with the powers of 74 and 50 kW. In the second case, that is, with a higher velocity of

movement v2, the hatched temperature range is reached only in heating with the powers of 78 and 59 kW. In the third case, that is, with v3, the hatched temperature range is reached only in heating with the power of 112 kW, whereas in the fourth case, that is, with the highest velocity v4, this temperature range is not reached in spite of a very high power, namely, 151 kW. In his contribution Kegel (Ref 31) treated the conditions in surface induction heating and quenching of flat steel with a thickness of 3 mm. In 1943 Seulen and Voss published a study on surface induction hardening in shot hardening and scan hardening (Ref 30). Figure 63 shows the time variation of temperature in surface induction heating with a power density Q of 6.5 kW/cm2, a high frequency f, that is, 250 kHz, and the selected heat transfer coefficient ␣ of 40,000 kcal/m2 Ch after 0.02, 0.04, 0.05, 0.08 (dotted line), and 0.8 s (continuous line) (Ref 31). The other group of curves (continuous lines) indicates the time and through-thickness variations of temperature due to quenching of the flat specimen with a water jet. A starting point for a study of the conditions of cooling with a water jet is the time and through-thickness dependence of temperature at the end of 0.1 s heating, when a maximum temperature, that is, 1050 C, was reached at the specimen surface. The time/temperature curves of through-thickness cooling of the specimen indicate that: ● The surface temperature changes quickly due to the influence of the quenchant and heat removal using a cold quenchant. ● The temperature toward the specimen core increases due to the cold core and the heat conducted from the surface to the colder core material; thus it increases at a depth of 2 mm from the initial 130 C even up to 340 C.

Figure 64 shows the variation of rate of induction heating of the surface layer (dotted line) (Ref 31). At the beginning of heating, that is, after 0.02 s, the heating rate at the surface amounts to 12,500 C/s and at the end of heating, that is, after 0.1 s, decreases to 6800 C/s. The cooling rate at the surface and in the subsurface is around 3700 C/s after 0.15 s and then gradually decreases so that after 1.0 s it amounts to only 200 C/s. It is very important that in the depths greater than 0.8 mm heating of the subsurface occurs. It reaches a maximum rate, that is, around 2300 C/s, just before surface cooling with the quenchant (water). After 0.1 s of heating and additional 0.05 s of cooling, cooling of the surface layer to a depth of 1.2 mm and then heating in greater depths are obtained. Heating in the greater depths occurs due to heat convection from the thin surface layer toward the cooler core material. One method of induction surface hardening appropriate for large gear modules is known as tooth gap hardening, a progressive hardening method. In this case, the coil is placed so that it ensures uniform gap between the coil and the flanks of two adjacent teeth. The tooth gap hardening method is very demanding and requires a lot of experience and knowledge to achieve the desirable properties of the gear. This method is also known as contour hardening. It is an ideal method for heat treatment of gears as it increases the hardness on the surface of the tooth while only slightly decreasing the load-bearing capacity in the root of the tooth. Gears heat treated in this way exhibit very good behavior in operation as compressive residual stresses are present in the root of the tooth. Gears with induction hardened flanks, given that the dimensioning is carefully carried out, can achieve highest fatigue

1300 1200 74

1100 1000

56

900 Temperature (T ), °C

78

112

Power kW 35

TAC

59

800

3

700

TAC

92

1

600

151

500

80 140

400

60

39

300

128 92 81 60 40

200 40 100 0 (a)

Fig. 62

4

8

12

16

0 (b)

4

8 12 16 0 4 8 12 Depth below the surface (z ), mm (c)

16

0

4

115

8

12

16

(d)

Time/temperature variations in scan hardening at various traveling speeds and various HF generation power. (a) v1 ⳱ 140 mm/min. (b) v2 ⳱ 220 mm/min. (c) v3 ⳱ 370 mm/min. (d) v4 ⳱ 680 mm/min. Source: Ref 30

242 / Residual Stress During Hardening Processes strength. To verify the results of induction surface hardening, it is necessary to take up certain measures for controlling the quality of the hardened layer. For this purpose, hardness and microhardness measurements supported by microstructure analysis are commonly used. A disadvantage of this procedure is also that, due to the method of heating and quenching (nonuniformly overheated left and right tooth flank), one might get slightly higher dimensional deviations than in the case of simultaneous hardening of both flanks of the same tooth (Ref 11). Figure 65 shows the deviation in the dimensions of the tooth after induction surface hardening in heating with a coil that encircles the gear tooth. Measurements of gear teeth and gear gaps after induction surface hardening show an increased

volume in the tooth root and thus a smaller gap and increased volume at the tip of the tooth (increased gear diameter). These volume changes result in a slightly smaller width of the tooth above the pitch circle and slightly increased tooth width below the pitch circle of the gear. These dimensional deviations are relatively small and negligible in the case of gears with small diameter or small module, but might become more important in gears with larger modules and greater tooth width (Ref 32, 33). Surface hardening of gears is one of the most frequent applications of induction surface hardening. The first part of this article discusses different methods of induction heating of gears; these methods depend not only on gear size, but also on the properties expected of gears after heat treatment. Gears are axisymmetric machine elements; therefore, volume changes due to the transformation into martensite microstructure in-

1200 1000

Profile before hardening


0.1 s

Profile after hardening

800 0.08

0.2

600

0.3

0.06

0.4

400 0.5 0.7

200

1.0 0.02

0 0

0.04

1 2 Depth below the surface (z ), mm

3 Distortion of individual tooth shape after induction surface hardening caused by volume changes. Source: Ref 32

Fig. 65

Time/temperature profiles in surface induction heating of steel plate with 3 mm thickness at given heating conditions. Source: Ref 31

Fig. 63

Stress Profiles in Machine Parts in the Loaded State

12,500

0.1

Cooling rate (v ), °C/s

6000 4000 2000 1.0 0.5

0.3

0 −2000

Compression


0.02 s

0.04

Tension

10,000 8000

+ −

−

Depth below the surface (z ), mm

0.2

0.15

−4000 0.12 −6000 0.7

−8000 0

Fig. 64 Ref 31

1 2 Depth below the surface (z ), mm

3

Surface induction heating and cooling rate in thin surface layer at given conditions. Source:

duced by heat treatment are to be expected. Also, the teeth themselves are symmetrical, which means that careful application of uniform heating of particular gear teeth and uniform quenching, regardless of the method applied, should not cause distortion after heat treatment. In induction surface hardening, compressive residual stresses are created in the surface, which in addition to hardness and wear resistance of the surface, creates a considerably high fatigue strength and resistance to bending loads. Figure 66 shows a part of a gear in cross section with residual stress distribution in the surface hardened layer of the gear tooth. Also in this case, one obtains a residual stress distribution typical of induction hardening, that is, compressive residual stresses in the hardened layer with a martensite microstructure, followed by tensile residual stresses, and at greater depth again compressive residual stresses. It is known that the size and distribution of residual stresses can be influenced by power density. A number of authors have done research into the effects of power density or energy input used in heating with the purpose of determining optimal induction hardening conditions leading to good mechanical properties of gears. Lower power density at the same current frequency requires longer heating times at the same depth of the hardened layer and results in higher compressive residual stresses with a moderate transition of residual stresses from the compressive into the tensile region. In induction hardening of gears, it is necessary to ensure the most uniform depth of the hardened layer to achieve a symmetric distribution of residual stresses in the gear tooth cross section.

Fig. 66 Ref 32

Residual stress distribution in the induction surface hardened layer of the gear tooth. Source:

Heat treatment engineers have to be very careful in choosing the conditions of induction surface hardening to benefit from the distribution of residual stresses achieved in dynamically loaded parts. In industrial practice, induction surface hardening should satisfy the requirement of fatigue resistance of machine components. This worsening of the properties of the machine part is mainly attributed to tensile residual stresses in the hardened layer and undesirable hardness distribution in the transition zone from the hardened into the unhardened part of the subsurface. These effects are quite natural and are in the first phase a result of very rapid local heating of the thin surface layer while in the second phase this is accompanied by forced quenching, which ensures a critical cooling rate and the occurrence of martensite microstructure. Both phases in the induction surface hardening can increase the risk of fatigue especially if the latter is assessed only from the point of view of surface hardness. For successful estimation of the quality of the hardened layer, it is thus recommended one selects the optimal synergistic effects between the input electric energy and the interdependence between the induction coil and the workpiece surface,

Induction Hardening / 243 connected with the occurrence of eddy currents in the workpiece surface layer, which leads to heating. Due to complex synergistic effects in induction heating or hardening, it is necessary to carefully study each influence on the properties of the hardened surface layer (Ref 11, 34). Fatigue strength in machine components that have been induction surface hardened is increased if the summed up load tensions and residual stresses in the surface layer are compressive. In order to ensure the highest fatigue strength of a component, it is necessary to provide: ● In dynamically loaded components, the sur-

face is prone to fatigue occurrence, so the sur-

Heated above hardening temperature−quenched Heated below hardening temperature−quenched Core not heated

(a) Residual stress

+σRS

Tension

Martensite

−σRS Compression

Tempered structure

Residual stress

(b) +σ

External load stress

Tension

−σ Compression

(c) Tension

Resultant stress

Compression

Resultant stress

(d) Stress profile in a round bar in the loaded state where residual stresses after induction surface hardening and loading stresses add up. See text for details. Source: Ref 34

Fig. 67

face must have the highest compressive stresses. ● If the total sum of stresses, namely, load tension plus residual stresses on the surface, are always compressive, then there is no chance for the occurrence of cracks and crack growth. ● To ensure good behavior of the surface and the hardened surface layer in the loaded condition, it is necessary to induce a suitable prestressing in the surface layer. This can be achieved by a carefully selected heat treatment method that would create the highest compressive residual stresses on the surface and desirable profile of the latter in the hardened subsurface layer. ● Induction surface hardening offers great opportunities to ensure considerable compressive stresses in the machine component surface and likewise to ensure restrained transformation of compressive surface stresses in the subsurface layer into tensile residual stresses. The endurance of machine components subjected to bending and torsion loads can be successfully increased by ensuring sufficiently high compressive residual stresses. To create a sufficient amount of compressive residual stresses that would have a favorable distribution is what any manufacturer wishes to achieve since only in this way is it possible to increase the reliability of components in operation. An early failure of a component in operation might cause catastrophic damage on a machine and thus a loss of profit. A decisive role in the occurrence of residual stresses is played by the synergistic effects among the heat treatment method, the kind of material, and shape of the workpiece. For this reason, heat treatment has to be treated from the point of view of heating, overheating, and cooling/quenching and from the point of view of created internal stresses at a certain point during the treatment. During heat treatment, internal stresses are created by the temperature differences and phase transformations between the core and the surface, which is a result of the volume differences between the core and the surface. The created volume differences between the core and the surface then give rise to internal stresses. During the process of heating and cooling, internal stresses may produce the following effects: ● In the case when in each moment lower in-

ternal stresses than that of the yield point are ensured, one can expect higher residual stresses induced by the heat treatment in the workpiece, but these would not cause distortions, cracks, or failure. ● In the case when during the heat treatment at a certain moment internal stresses exceed the yield point, distortions and usually lower residual stresses in the workpiece result. ● In an extreme case of very detrimental conditions during the heat treatment when internal stresses are higher than the tensile strength of the material, the workpiece would

crack, and larger distortions and usually also high residual stresses would occur. Numerous changes that take place in the hardened surface layer of the workpiece are always a result of the heating and quenching conditions. Therefore, it is necessary to study the events taking place in the workpiece directly after the hardening temperature is reached. In the workpiece heated to the hardening temperature one can distinguish three zones, shown in Fig. 67(a): the first where the outer layer is heated to the hardening temperature, the second zone layer heated below the hardening temperature between the temperatures TA1 and TA3 for rapid heating, and finally the third zone layer, which remains cold during the entire heat treatment process. Heating to the hardening temperature at a certain depth is followed by quenching. Quenching results in the occurrence of compressive residual stresses, as shown in Fig. 67(b), when the familiar transformations in the hardened layer take place. The second layer does not suffer the same distortions as the surface layer, though the heating there has been sufficient to improve the properties of the material. In the second layer, hardening is incomplete, which in comparison with the first layer results in lower hardness and strength of material. In cases when a machine component that has been surface induction hardened in this way is subjected to an external load, as shown in Fig. 67(c), then additional tensile residual stresses can be noted in the first layer and the second layer (Fig. 67d). Since fatigue of a machine component is a very delicate problem connected with accumulated tensile stresses in the second zone, there is a danger that, due to the size and shape and location of the hardened trace, the effects of fatigue are transferred to the surface. When a loaded layer is exposed to tensile external stress up to the surface, then the surface becomes very sensitive to the occurrence of cracks. This tendency to crack is further increased if defects are present in the surface of the workpiece material. A critical state in the second zone of the hardened surface layer also occurs on locally hardened workpieces where the surface was overheated or heated nonuniformly.

Fatigue Strength of Materials In professional literature, data on fatigue strength of materials are usually presented for a prescribed shape and size of specimens that have been adjusted to the testing device. Specimens for fatigue strength are usually cylindrical with a smaller diameter in the middle part and a rounded transition into the larger diameter part. The latter is then usually clamped for testing. Modes of loading the specimens vary but are usually either torsion, bending, and/or tension/ compression. The highest fatigue strength is displayed by a specimen subjected to bending loads (Ref 11, 32). For other modes of loading, the relation with bending fatigue strength rwb is ex-


● Surface hardening applied to specimens with

a smooth shape (curve 1) and specimens with a slot (curve 2) ● Quenching and tempering applied to smooth specimens (curve 4) and specimens with a slot (curve 6) The cementation steel is a chromium nickel steel with 0.15% C where the specimens were smoothly shaped (curve 3) and slotted (curve 5). The achieved hardness on the surface of the hardened specimens was 56 to 59 HRC and on the cemented specimens 58 to 59 HRC. In order to test the effects of the slot on fatigue strength on all the specimens, whether they were quenched and tempered, hardened, or cemented, a slot of equal size and shape was made. It was made in the middle of the cylindrical specimen to an equal depth of 0.4 mm. The depth of the surface hardening and cementation was the same—1.5 mm. The test results showed that there are significant differences in terms of different heat treatment methods and that the highest fatigue strength was found in surface hardened specimens. A comparison of the results of fatigue testing has shown that: ● In surface hardened specimens with a smooth

cylindrical shape and with a slot, the differ-

70

ence in the achieved fatigue strength is minimal. This can be attributed to a very desirable distribution and size of compressive residual stresses throughout the hardened layer. Since the depth of the slot reaches only one quarter of the hardened surface layer, the size of compressive residual stresses at the slot is still very high, so that the weakening due to the slot and stress concentration along the slot does not cause any essential drop in fatigue strength. ● In quenched-and-tempered specimens with no earlier prestressing of the surface layer ensured, the fatigue strength was considerably lower than in surface hardened specimens. Also remarkably lower was the fatigue strength of quenched-and-tempered specimens with a slot. The results in the graph show that the difference in fatigue strength in slotted surface hardened specimens and slotted quenched-and-tempered specimens is 5 to 1. ● Smooth cemented specimens displayed 25% lower fatigue strength than the surface hardened specimens of the same shape, whereas the cemented specimens with a slot displayed 50% lower fatigue strength than the same surface hardened specimens.

Tooth-root bending stress (σb), N/mm2

pressed empirically, that is, fatigue strength in torsion sw ⳱ 0.58 rwb, and fatigue strength in tension/compression rwz ⳱ 0.70 rwb. Figure 68 presents Wo¨hler curves for different modes of dynamically loaded specimens made from different steels that had been heat treated in different ways. From among six curves, four represent specimens made from heat treatable steel and two for cementation steel specimens (Ref 11). The heat treatable steel is Cr-Mo-Ni steel with 0.37% Ni, and the specimens were heat treated in two different ways:

1400 1200 1000 800

400 300 200

40

Surface-hardened (notched)

(a)

Carburized (smooth)

Tooth-root bending stress (σb), N/mm2

50 σwb, daN/mm2

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Number of load cycles, N

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Quenched and tempered (smooth)

30 Carburized (notched) 20 10 0

Residual Stresses after Induction Surface Hardening and Finish Grinding

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Confidence limit according to DIN 3990

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Fatigue strength of surface hardened and carburized specimens. Curves: 1, surface hardened (smooth); 2, surface hardened (notched); 3, carburized (smooth); 4, quenched and tempered (smooth); 5, carburized (notched); 6, quench and tempered (notched). Source: Ref 11

Fig. 68

1400 1200 1000

Confidence limit according to DIN 3990

800 600

Shot peened

400 300 200 103

Number of load cycles, N × 106

The question arises as to the fatigue strength in those specimens where the slot reaches deeper than the hardened layer. A regular problem occurring in these cases is crack occurrence and crack propagation starting from the slot. Due to the shape of the specimen and the slot, stresses start concentrating at these places, depending of course on the kind and size of external loads. Here it should not be forgotten that along the slot there are no compressive residual stresses, and that the size of tensile stresses along the slot plays a decisive role in crack occurrence. Figure 69 shows bending stress in the tooth root subjected to dynamical load versus the number of oscillations (Ref 32). Figure 69(a) shows the bending stress for the case of induction surface hardening of adjacent flanks of two teeth with a coil reaching into the tooth gap. In the process the tooth flank as well as the tooth root are hardened. This kind of heat treatment of gears from steels for induction surface hardening gives a fatigue bending strength in the range from 320 to 490 N/mm2. Figure 69(b) shows the same relationship for a case when the induction coil encircles an individual gear tooth. In this process, the tooth flank is hardened and the microstructure and hardness in the tooth root are preserved. A result of this method of hardening is that the fatigue strength is drastically lowered to values ranging from 200 to 300 N/mm2 for the entire range of steels suitable for induction surface hardening. This is a considerable drop in fatigue strength of the material in the root of the tooth (Ref 34, 35).

104

105

106

107

Number of load cycles, N (b) Bending fatigue strength of gear tooth at tooth gap hardening (a) and flank hardening (b) for various steels. Dashed lines denote confidence limit according to DIN 3990. Source: Ref 32

Fig. 69

For manufacturing crankshafts, a heat treatable 4140 AISI steel was used. This steel is very appropriate for statically and dynamically loaded parts of car engines and machines, especially because of its high hardness achieved after hardening (57 HRC). The steel is characterized by good hardenability and is thus suitable for manufacturing machine parts with large cross sections in which after refinement a very high strength can be obtained. After tempering the steel does not show a tendency to brittleness, and therefore no special heat treatment procedures are required. This steel is also suitable for surface hardening (flame hardening, induction surface hardening) and displays a very good resistance to wear. However, special attention has to be paid during product design, and great care should be given to the design of radius and transition areas to prevent notch effects under dynamical loads. The steel is adapted for the use in a wide range of temperatures and preserves high toughness even at low temperatures (Ref 17, 36). Figure 70 shows residual stress distribution after induction surface hardening in the central bearing location (A) and on the extreme left-side


Residual stresses (σRS), N/mm2

bearing location (C). For both bearing locations residual stresses were measured on two specimens. The distribution of residual stresses on the bearing location (A) is, as expected, very similar on both specimens, the highest compressive residual stresses ranging between ⳮ1020 and ⳮ1060 N/mm2 at a depth around 250 lm, then slowly dropping to a depth of 3.5 mm having the size of around ⳮ800 N/mm2, then experiencing a sharp fall to a depth around 5.5 mm. The residual stresses distribution after induction surface hardening on the bearing location (C) is very similar to that in the central bearing location (A), only its absolute values are slightly lower and a distinct fall in the residual stresses can be noted as early as around the depth of 3.5 mm, reaching its minimum value already at a depth around 5.5 mm. It can be seen that the residual stress distribution is just as favorable as in the central location except that its absolute values are slightly lower. The authors believe that the difference in the residual stress distribution can be related to the period of overheating on the austenitization temperature, which resulted in a thinner layer in austenitization and thus also a thinner hardened surface layer.

0 Bearing location A; Specimens A1, A2

−200 −400

A1

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C2

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A2 C1 1 2 3 4 5 6 Depth below the surface (z ), mm

7

Residual stress profiles after induction hardening on the specimens A1 and A2 of the mean bearing location in the middle of the crankshaft and on the specimens C1 and C2 on the extreme left-side bearing location. Source: Ref 37

Fig. 70

Residual stresses (σRS), N/mm2

0 Bearing location A: specimens A2: Normal grinding conditions

−200 −400

Bearing location C: specimens C2: Gentle grinding conditions

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Fig. 71

Variation of the residual stresses after induction surface hardening and grinding. Source: Ref 37

Under different machining conditions of grinding, different temperature cycles were obtained on the surface and in the depth of the heataffected zone, which has effected microstructural changes and changes in the microhardness and residual stresses (Ref 36–41). In the grinding process, the changes of temperature in the surface layer of the workpiece are very important. Temperature measurements provide data on temperature cycles, which, because of the relative movement of the workpiece and the grinder, indicate the variation of temperature both in heating and cooling of the given spot at the workpiece. The maximum temperatures achieved at the surface and in the surface layer are also very important. A distinction can be made among four characteristic cases of temperature cycles: ● The maximum temperatures at the surface

and in the surface layer are higher than the fusion temperature of the workpiece material, depending on the temperature cycles. Such conditions may occur due to very sharp grinding conditions or due to the selection of an inappropriate grinder with regard to the workpiece material. Both influences contribute to blunting of abrasive grains, which produces a larger contact zone between the abrasive grain and the workpiece, which, in turn, produces a stronger overheating of the workpiece. In such cases burns will occur at the workpiece surface and, consequently, softened spots that do not ensure the working life required of a component, that is a machine part. ● Thus, on the surface a maximum temperature higher than the melting temperature of the workpiece material was obtained. The depth of the remelted layer is only a few microns and makes a very fine ledeburite microstructure containing fine cementite spread in residual austenite. The newly formed microstructure has a slightly lower hardness than martensite. The residual stresses in the thin surface layer will be tensile due to plastic deformation of the surface layer in grinding caused by tensile forces in the contact zone of the workpiece material and the tensile stresses induced by the occurrence of residual austenite should be added to this. ● The maximum temperature in the contact zone is lower than the temperature required for the beginning of fusion of the given material and higher than the austenitizing temperature. The lower temperature, that is the austenitizing temperature, will shift because of a high rate of heating of the workpiece toward higher temperatures as known from transformation diagrams. In such cases, the surface layer is expected to heat up to such a temperature as to produce a change in the crystal structure so that an austenitic microstructure, through which the accompanying diffusion processes are going on, will form. Provided the previous microstructure of the surface layer was martensite-cementite-

carbide, after grinding a finer martensite microstructure with a higher carbon content obtained at the expense of cementite-carbide phases and with a possibility of a lower residual austenite content may be expected in the thin surface layer. The modified content of the cementite-carbide phase depends on the heating conditions, whereas the content of the residual austenite depends on the cooling conditions. Such a microstructure is still a typically quench microstructure, only in the very thin surface layer between 50 and 200 lm first austenization and then requenching occurred. The thickness of the requenched layer depends on the grinder, the grinding conditions, and the state of the grinder (sharp or used grains). Such a microstructure is still adequate and ensures the working life of the machine part. The only risk is too high a content of the residual austenite formed or various damages such as cracks, grooves, and galling to the surface and the surface layer. ● The maximum temperature in the contact zone is lower than the temperature required for the beginning of austenitization and higher than the lower temperature, which is limited by the temperature of steel tempering and amounts to approximately 200 C. In this case, the grinding conditions are very mild so that with the selection of the right kind of grinder neither major nor important changes are expected either at the surface or in the surface layer. In the surface layer only martensite tempering may occur if it was not performed already during the heat treatment of the workpiece. Such grinding conditions are very welcome in the cases that the distortion of the workpiece is relatively small, and the additions for final fine grinding of the surface are quite small. The volume changes that may occur in the surface layer after steel grinding are thus: ● Formation of the residual austenite contrib-

utes to the formation of tensile residual stresses due to grinding. ● The lower content of the cementite-carbide phase produces formation of ledeburite containing the residual austenite, which contributes to the formation of tensile residual stresses due to grinding. ● The tempering effects in the martensite structure also contribute to the formation of tensile residual stresses due to grinding. ● Material plastification due to grinding can produce compressive or tensile residual stresses depending on the type of grinding and the grinding conditions. Figure 71 shows residual stress changes resulting from induction hardening and grinding for main bearing spots A and C (Ref 37). The residual stresses were measured after grinding only to a depth of 200 lm. The variation of the residual stresses indicates that the favorable compressive residual stresses obtained with induction hardening were reduced only slightly so

246 / Residual Stress During Hardening Processes that in the thin surface layer, which is very critical, very high compressive residual stresses remained. Outer loads never exceeded the high compressive stresses, which means that there is no risk of crack initiation in strongly dynamically loaded universal-joint shafts. Figure 72 shows residual stress changes resulting from induction hardening and grinding for main bearing spots F and G (Ref 37). The same holds true for these two bearing spots, which means that the selected induction hardening and grinding conditions were favorable. Although grinding produced tensile stresses due to and characteristic mainly of grinding, the latter were almost negligible with regard to the total of the preceding residual stresses.

Summary Induction surface hardening of machine components and especially gears is a very complex process involving a whole range of possible heat treatment methods, which are all reflected in either good or bad serviceability of machine components. The heat treatment engineer has to be aware of the different effects of particular design shapes of induction coils, to be familiar with electromagnetic phenomena and eddy currents, and to have some experience in the right choice of energy inputs necessary for heating. The energy needed for heating can be provided by changing the generator power as well as by changing the frequency of the current. In progressive hardening, to achieve a suitable energy input, the workpiece feed rate or the rate at which the coil is moved has to be adjusted, whereas in single-shot hardening suitable energy input is achieved by adjusting the heating time with a high-frequency current. An essential advantage of induction surface hardening is that it is possible to achieve a sufficient repeatability of the hardened layer thickness on the workpiece as well as a desirable or even prescribed hardened layer profile, ensuring sufficient hardness and favorable distribution of residual stresses in the hardened layer. A variety of steels and a whole


0 −200 −400 Bearing location G Abusive conditions

−600 −800

Bearing location F Normal grinding conditions

−1000 −1200

Fig. 72

0

50 100 150 200 250 Depth below the surface (z ), µm

300

Variation of the residual stresses after induction surface hardening and grinding. Source: Ref 37

range of induction-hardening methods provide the possibilities for very accurate planning of the size and distribution of residual stresses. This is of growing importance since manufacturers are more and more often required to produce machine components, which, among other surface properties, will have to have quite specific residual stress distribution along the depth of the hardened layer. It has become a proven fact that high compressive stresses ensure high fatigue strength of machine components and reduce the danger of the occurrence and growth of cracks on the surface of components. As far as induction surface hardening is concerned, it is also quite important to choose the right quenching medium and quenching method. For this reason, engineers have to direct their attention not only to the method of heating and possible overheating of the surface layer, but also to the methods of quenching and the right choice of the medium for quenching. REFERENCES 1. P.A. Hassell and N.V. Ross, Induction Heat Treating of Steel, Heat Treating, Vol 4, ASM Handbook, 1991, p 164–202 2. S. Lampman, Introduction to Surface Hardening of Steels, Heat Treating, Vol 4, ASM Handbook, 1991, p 259–267 3. K.E. Thelning, Steel and Its Heat Treating, Chapter 6.6, Induction Hardening, Bofors Handbook, Butterworth, London and Boston, 1975, p 432–451 4. T. Ruglic, Flame Hardening, Heat Treating, Vol 4, ASM Handbook, 1991, p 268–285 5. K.E. Thelning, Steel and Its Heat Treatment, Chapter 6.7, Flame Hardening, Bofors Handbook, Butterworth, London and Boston, 1975, p 451–465 6. K. Sridhar and A.S Khanna, Laser Surface Heat Treatment, Chapter 3, Lasers in Surface Engineering, N.B. Dahotre, Ed., Surface Engineering Series, Volume 1, ASM International, 1998, p 69–70 7. O.A. Sandven, Laser Surface Hardening, Heat Treating, Vol 4, ASM Handbook, 1991, p 286–296 8. S. Schiller, S. Panzer, and B. Furchheim, Electron Beam Surface Hardening, Heat Treating, Vol 4, ASM Handbook, 1991, p 297–311 9. M. Field and J.F. Kahles, Review of Surface Integrity of Machined Components, Ann. CIRP, Vol 20 (No. 1), 1970, p 107–108 10. M. Field, J.F. Kahles, and J.T. Cammet, Review of Measuring Method for Surface Integrity, Ann. CIRP, Vol 21 (No. 2), 1971, p 219–237 11. M.G. Lozinski, Industrial Applications of Induction Heating, Pergamon Press, Oxford, 1969 12. V.I. Rudnev, R.L. Cook, D.L. Loveless, and M.R. Black, Introduction Heat Treatment, Basic Principles, Computation, Coil Construction and Design Considerations, Chap-

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ter 11A, Steel Heat Treatment Handbook, G.E. Totten and M.A.H. Howes, Ed., Marcel Dekker, 1997, p 765–767 D.L. Loveless, R.L. Cook, and V.I. Rudnev, Introduction Heat Treatment, Modern Power Supplies, Load Matching, Process Control, and Monitoring, Chapter 11B Steel Heat Treatment Handbook, G.E. Totten and M.A.H. Howes, Ed., Marcel Dekker, 1997, p 873–874 Electromagnetic Induction and Electric Conduction in Industry, Chapter 9, Heat Treatments by Induction, Centre Francais de IÉlectricite, 1997 G. Benkowsky, Induktionserwa¨rmung, VEB Verlag Technik, Berlin, 1985 W. Brunst, Die Inductive Wa¨rmebehandlung, Springer-Verlag, Berlin, 1957 S. Zinn and S.L. Semiatin, Elements of Induction Heating (Design, Control and Applications), Electric Power Research Institute and ASM International, 1988 S. Denis, M. Zandona, A. Mey, and S.A. Boufoussi, Calculation of Internal Stresses During Surface Heat Treatment of Steels, presented at the European Conference on Residual Stresses (Frankfurt, Germany), 1992, Residual Stresses, V. Hauk, H. P. Hougardy, E. Macherauch, and H.-D. Tietz, DEM Informationsgesselschaft mbH, Oberursel, 1993, p 1011–1020 U. Bru¨ckner, W. Schuler, and H. Walter, Untersuchungen zum Eigenspannungszustand beim inductiven Randschnitha¨rten, Eigenspannungen: Entstehung-MessungBewertung, Band 1, E. Macherauch and V. Hank, Ed., Deutsche Gesselschaft fu¨r Metallkunde E.V., Oberursel, 1983, p 293–308 M. Melander, Computer Calculations of Residual Stresses due to Induction Hardening, Eigenspannungen: Entstehung-MessungBewertung, Band 1, E. Macherauch and V. Hank, Ed., Deutsche Gesselschaft fu¨r Metallkunde E.V., Oberursel, 1983, p 309–328 A.J. Fletcher, Thermal Stress and Strain Generation in Heat Treatment, Chapter 9.2, Induction Hardening, Elsevier Applied Science, London and New York, 1989, p 182– 187 G.H. Ledl, Why Quenching Is Important in Induction Heating, Met. Prog., Dec 1967, p 200–204 O. Longeot and C. Delalean, Simulation numerique des procedes de traitment par induction, Trait. Therm., No. 280, 1995, p 33–47 T. Inoue, H. Inoue, F. Ikuda, and T. Horino, Simulation of Dual Frequency Induction Hardening Process of a Gear Wheel, Proc. Third International Conf. Quenching and Control of Distortion, G.E. Totten, B. Lisicic, and H.M. Tensi, Ed., ASM International, 24–26 March 1999, p 243–250 H. Fujio, T. Aida, Y. Masumoto, and T. Tsuruki, Paper No. 169–14, Distortion and Residual Stresses of Gears Caused by Hard-


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ening, Third Report, Induction Hardening of Gears Made of 535 C Carbon Steel, Bull. JSME, Vol 22 (No. 169), July 1979, p 1001–1008 D.J. Williams, “Quench Systems for Induction Hardening,” Reprint from Metal Heat Treat., July/August 1995 M. Melander, Proc. International Symposium on the Calculation of Internal Stresses in Heat Treatment of Metallic Materials, E. Attebo and T. Ericsson, Linkoping, Sweden, 1984, p 399–419 K. Fujita, A. Yoshida, and K. Nakase, Surface Durability of Induction Hardened 0.45% Carbon Steel and Its Optimum Case Depth, Bull. JSME, Vol 22 (No. 169), July, 1979, p 994–1000. G. Beck and A. Simon, Prediction of Residual Stresses, Advances in Surface Treatments: Technology, Application, Effects, Vol 4, International Guidebook on Residual Stresses, A. Niku Lari, Ed., Institute for Industrial Technology Transfer and Pergamon Press, 1987, p 303–326 G. Seulen and H. Voss, Oberfla¨chenha¨rtung mit Induktionserhitzung bei mittleren Frequenzen, Stahl Eisen, Vol 63 (No. 51), 1943, p 929–935 K. Kegel, Die Praxis der Induktiven Wa¨r-

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mebehandlung, Werkstatt Betr., Vol 85 (No. 5), 1952, p 183–188 G. Parrish, D.W. Ingham, and M. Chaney, The Submerged Induction Hardening of Gears, Part 2: Properties Imparted and Problems Solved, Heat Treat. Met., Vol 25, No. 2, 1998, p 43–50 G. Parrish, D.W. Ingham, and M. Chaney, The Submerged Induction Hardening of Gears, Part 1: Processing and Application Aspects, Heat Treat. Met., Vol 25 (No. 1), 1998, p 1–8 S.L. Semiatin and D.E. Stutz, Induction Heat Treatment of Steel, ASM International, 1987 P.K. Braisch, The Influence of Tempering and Surface Conditions on the Fatigue Behaviour of Surface Induction Hardened Parts, Mater. Sci. Forum, Vol 102–104, 1992, p 319–334 J. Grum and D. Ferlan, Residual Internal Stresses after Induction Hardening and Grinding, 17th ASM Heat Treating Society Conf. Proc., Including the First International Induction Heat Treating Symposium, D.L. Milan, D.A. Poteet Jr., G.D. Pfaffmann, V. Rudnev, A. Muehlbauer, and W.A. Albert, Ed., ASM International, 1998, p 629–639 J. Grum, How to Select Induction Surface

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Hardening and Finish Grinding Conditions in Order to Ensure High Compressive Residual Stresses on Machine Part Surface, The 12th International Federation of Heat Treatment and Surface Engineering Congress, Congress Proceedings, Vol 1, The Institution of Engineers, Australia, Melbourne, Oct 2000, p 133–138 E. Brinksmeier, A Model for the Development of Residual Stresses in Grinding, Advances in Surface Treatments: Technology, Application, Effects, Vol 5, International Guidebook on Residual Stresses, A. Niku Lari, Ed., Institute for Industrial Technology Transfer and Pergamon Press, 1987, p 173– 189 R. Snoeys, M. Maris, and J. Peters, Thermally Induced Damage in Grinding, KeyNote Papers, Ann. CIRP, Vol 27 (No. 2), 1978, p 571–581 P.G. Althaus, Residual Stresses in Internal Grinding, Ind. Diamond Rev., No. 3, 1985, p 124–127 M. Moris and R. Snoeys, Heat Affected Zone in Grinding Operations, Proc. 14th International Machine Tool Design and Research Conf., F. Koenigsberger and S.A. Tobias, Ed., Manchester, 1973, p 569– 669



Hardening by Reheating and Quenching M. Narazaki, Utsunomiya University G.E. Totten and G.M. Webster, G.E. Totten and Associates Inc.

OF THE VARIOUS STEEL PROCESSING METHODS, heat treating has the greatest overall impact on control of residual stress and on dimensional control. Among the various processes involved in heat treating, quenching is one of the most important. One author has estimated that approximately 20% of the problems in heat treating relate to heating and as much as 80% of the problems relate to cooling (Ref 1). This article provides an overview of the effects of various material- and quenchant-related parameters on residual stress, distortion control, and cracking. The subjects that are discussed include:

● Measurement and evaluation of quenching ● ● ● ● ●

power Effect of process variables on cooling behavior and heat transfer Effect of cooling characteristics on residual stress and distortion Methods of minimizing distortion Tempering Prediction of residual stress and distortion

Phase Transformation during Heat Treating

● Phase transformations during heat treating ● Metallurgical sources of stress and distortion

Steel Transformation

during reheating and quenching ● Effect of materials and quench process design on distortion ● Quenchant selection

Properties such as hardness, strength, ductility, and toughness are dependent on the microstructures that are present in steel. The first step

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Time-temperature-transformation (TTT) diagram of an unalloyed steel containing 0.45% C. Austenite temperature ⳱ 880 C. Courtesy of Verlag Stahlessen mbH Dusseldorf

in the transformation process is to heat steel to its austenitizing temperature. Steel is then cooled rapidly to avoid the formation of pearlite, which is a relatively soft transformation product, to maximize formation of martensite, a relatively hard transformation product, to achieve the desired as-quenched hardness. The most common transformation products that may be formed in quench-hardenable steels from austenite are in order of formation with decreasing cooling rate: martensite, bainite, pearlite, ferrite, and cementite. The formation of these products and the proportions of each are dependent on the time and temperature cooling history of the particular alloy and elemental composition of that alloy. The transformation products formed are typically illustrated with the use of transformation diagrams that show the temperature-time dependence of the microstructure formation process for the alloy being studied. Two of the most commonly used transformation diagrams are time-temperature-transformation (TTT) and continuous-cooling-transformation (CCT) diagrams. TTT diagrams, also called isothermal transformation (IT) diagrams are developed by heating small samples of steel to the temperature where austenite transformation structure is completely formed, that is, austenitizing temperature, then rapidly cooling to a temperature intermediate between the austenitizing and the martensite start (Ms) temperature, and then holding for a fixed period of time until the transformation is complete, at which point the transformation products are determined. This is done repeatedly until a TTT diagram is constructed such as that shown for an unalloyed steel (AISI 1045) in Fig. 1. TTT diagrams can only be read along the isotherms. CCT Diagrams. Alternatively, samples of a given steel may be continuously cooled at different specified rates, and the proportion of transformation products formed after cooling to various temperatures intermediate between the austenitizing temperature and the Ms are determined to construct a CCT diagram such as the one shown for an unalloyed carbon steel (AISI 1045) in Fig. 2. CCT curves provide data on the temperatures for each phase transformation, the amount of transformation product obtained for a

Hardening by Reheating and Quenching / 249 given cooling rate with time, and the cooling rate necessary to obtain martensite. The critical cooling rate is dictated by the time required to avoid formation of pearlite for the particular steel being quenched. As a general rule, a quenchant must produce a cooling rate equivalent to, or faster than, that indicated by the “nose” of the pearlite transformation curve to maximize martensite transformation product formation. CCT diagrams can only be read along the curves of different cooling rates. Caution: Although it is becoming increasingly common to see cooling curves (temperature-time profiles) for different cooling media (quenchants) such as oil, water, air, and others, superimposed on either TTT or CCT diagrams, this is not a rigorously correct practice and various errors are introduced into such analysis due to the inherently different kinetics of cooling used to obtain the TTT or CCT diagrams versus the quenchants being represented. A continuous cooling curve can only be superimposed on a CCT, but not on a TTT diagram. Metallurgical Crystal Structure. When steel is slowly cooled, it undergoes a crystal structure (size) change as it transforms from a less densely packed austenite (face-centered cubic, or fcc) to a more densely packed body-centered cubic (bcc) structure of ferrite. At faster cooling rates, the formation of ferrite is suppressed and martensite, which is an even less densely packed body-centered tetragonal (bct) structure than austenite, is formed. Illustrations of these crystal structures are provided in Fig. 3. This results in a volumetric expansion at the Ms temperature as shown in Fig. 4. Figure 5 shows that the crystal lattice of austenite expands with increasing carbon content

(Ref 2). Typically, when a carbide-ferrite mixture is converted to martensite, the resulting expansion due to increasing carbon content is approximately 0.002 in./in. at 0.25% C and 0.007 in./in. at 1.2% C (Ref 2). The fractional increase in size when austenite is converted to martensite is approximately 0.014 in./in. for eutectoid compositions. This illustrates the effect of carbon structure and steel transformation on residual stresses and distortion, which leads to dimensional changes. Estimation of Volumetric Change. In the previous discussion, it is shown that there are various microstructures possible upon quenching of steel and that the potential microstructural transformations that are possible for a given steel are shown by their CCT or TTT diagrams. Furthermore, dimensional changes are possible, depending on the carbon content and microstructural transformation product formed. Table 1 summarizes the atomic volumes of different microstructural components as a function of carbon content (Ref 3). Table 2 provides an estimate of volumetric changes as a function of carbon content for different metallurgical transformations (Ref 4). Thelning reported that volumetric expansion that occurs as a result of quenching could be estimated from (Ref 5):

and C equals the weight percentage of carbon dissolved in austenite and martensite. Berns reported that if the value of (DV/V) is known or can be computed, then internal stresses that are developed in a part due to temperature differences (DT) arising from either one-dimensional heating or cooling could be estimated from (Ref 6): r ⳱ E • e ⳱ E • 1⁄3 (DV/V) ⳱ E • ␣ • DT

where E (modulus of elasticity) ⳱ 2 ⳯ 105 N/ mm2 and ␣ (coefficient of thermal expansion) ⳱ 1.2 ⳯ 10ⳮ5. Relative volume changes due to phase transformation are shown in Fig. 6 (Ref 6). Figure 7 shows that stresses, such as an increase in hydrostatic pressure, accelerate phase transformations (Ref 7). This will occur whether the stresses are tensile or compressive and will result with accelerated austenite decomposition and increasing Ms temperature. The strain of this process is often estimated as being equal to the volumetric expansion divided by 3 (Ref 8). Transformation plasticity is a process whereby a stress will affect linear strain. This is shown in

DV/V ⳯ 100 ⳱ (100 ⳮ VC ⳮ Va) ⳯ 1.68C Ⳮ Va (ⳮ4.64 Ⳮ 2.21C)

where (DV/V) ⳯ 100 equals the percentage change in volume, VC equals the volume percentage of undissolved cementite, (100 ⳮ VC ⳮ Va) equals the volume percentage of martensite, Va equals the volume percentage of austenite, (a)

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A1

Temperature, °C

600 Pearlite start Pearlite end

500 Bainite start

400

(b)

Bainite end

Martensite

300 200 100 0 0.7

1

102

10 60

103

104

105

Seconds 1

2

4 Time

Fig. 2

8 15 Minutes

30

60 1

2

4 68 Hours

16 24

Continuous-cooling-transformation diagram of an unalloyed steel containing 0.45% C. Austenite temperature ⳱ 880 C. Courtesy of Verlag Stahlessen mbH Dusseldorf

(c)

Fig. 3

Crystal structures. (a) Austenite, fcc. (b) Ferrite, bcc. (c) Martensite, bct

250 / Residual Stress During Hardening Processes Fig. 8 where the effect of applied stress on martensitic transformation strain is shown (Ref 8). Generally, the Ms temperature is increased by tensile stress and decreased by hydrostatic pressure. Figure 9 shows that stress exhibits very

Temperature, °F 1.4

0

200

400 600 800 1000 1200 1400 1600

1.2 Austenite 1.0

Linear expansion, %

High-temperature transformation

Table 1 Atomic volume of different microstructure constituents of ferrous alloys

0.8 Very slow cooling

˚3 Apparent atomic volume, A

Phase

Ferrite Cementite Ferrite Ⳮ carbides Pearlite Austenite Martensite

0.6 Rapid quenching

Pearlite 0.4 Martensite forms

large effects on the start and stop times for pearlitic transformation (Ref 7). Cooling and Steel Metallurgical Transformation. The following paragraphs discuss cooling of steel both with and without metallurgical transformation. Cooling without Transformation (Ref 8, 9). If steel is cooled sufficiently fast, cooling will not be accompanied by microstructural transformation changes. Under these conditions, the surface of the component cooled much more quickly than the core at first, as illustrated in Fig. 10 (Ref 10). At this point, the specific volume in the core is greater than that of the surface, and the reduction in volume at the surface (due to lower temperature) is resisted by the greater volume in the core, resulting in the surface being in tension and the core in compression.

11.789 12.769 11.786 Ⳮ 0.163 C(a) 11.916 11.401 Ⳮ 0.329 C(a) 11.789 Ⳮ 0.370 C(a)

Austenite (a) C, % C

0.2 Ms

Table 2 Volumetric changes with different steel transformations

0 0

100 200 300 400 500 600 700 800 900 Temperature, °C

Fig. 4

Steel expansion and contraction upon heating and cooling

Steel transformation

Volumetric change (a)

Pearlite → austenite Austenite → martensite Austenite → acicular lower bainite Austenite → feathered upper bainite

ⳮ4.64 4.64 4.64 4.64

Ⳮ ⳮ ⳮ ⳮ

2.21 0.53 1.43 2.21

C C C C

(a) C, % C

1.080

°

Austenite, A

3.61 3.59

a 0.132

1.060

3.57

c/a 3.55

3.04

c 2.96

1.020

2.88 0 0

a 0.4

0.8

1.2

1.000 1.6

Specific volume, cm3/g

°

Martensite, A

1.040

c/a

0.130

Martensite Martensite Retained austenite Tempered martensite

0.128 Ferrite + carbide 0.126 Austenite 0.124

0.122

Carbon, wt% Carbon content versus lattice parameters of (retained) austenite and martensite at room temperature. a at the top of the graph is the lattice parameter of fcc austenite. a and c in the lower half of the graph are the two lattice parameters of tetragonal martensite. The ratio of c/a for martensite as a function of carbon content is also given.

Fig. 5

0.120 0

0.4

0.8

1.2

1.6

2.0

Carbon content, %

Fig. 6 200 C

Specific volume (DV/V) of carbon steels relative to room temperature. Tempered martensite,

At the point of maximum temperature difference between the surface and the core (point T), the core cools (shrinks) more quickly than the surface, leading to an elastic dimensional reduction of the surface until a point of stress conversion is obtained, at which point the surface is in compression relative to the core. After cooling has been completed, the residual stress distribution, between the surface and the core shown at the bottom right in Fig. 10 (Ref 10), will be obtained. If the surface stresses exceed the hot yield strength of the material, it will plastically deform, resulting in thermally induced dimensional changes. Cooling with Transformation (Ref 8, 9). When steels that may undergo transformational changes are quenched, the possibility of the formation of both thermal and transformational stresses must be considered. Figure 11 illustrates three different examples of this process (Ref 9). Example 1, illustrated in Fig. 11(a), occurs when phase transformation of both the surface and the core occurs before the thermal stresses change sign. Above the Ms transformation temperature, the stresses that are formed are thermal. Upon further cooling, the stresses in the core exceed the yield strength and plastic deformation (elongation) occurs. Subsequent martensitic transformation at the core provides a substantial stress component due to volumetric increases from martensitic phase transformation. This causes the core to be in compression and the surface to be in tension simultaneously. Example 2 (Fig. 11b) illustrates the case that begins after the thermal stresses change sign. The transformation-induced volume increase of the surface layer adds to the compressive stresses at the surface. Since the stresses are balanced, there is a corresponding increase in the tensile stresses in the core. Example 3 is a case where, although the transformation of the core starts later, it finishes before the surface (Fig. 11c). During cooling, the sign of the stresses changes three times. There are important consequences whether the core transforms before or after the stress reversal because thermal stresses may be counteracted, and tensile surface residual stresses may result (Ref 8). This is illustrated in Fig. 12(a) where it is shown that if the steel transformation occurs before the thermal stress maximum, the ferrite/ pearlite structure of a cylindrical test specimen will be distorted into a barrel-shape (Ref 6). If the transformation occurs after the thermal stress maximum, the austenite is pressed into a barrel shape followed by a volumetric increase due to martensitic transformation as shown in Fig. 12(b). This will result in high tensile residual stresses on the surface. If the steel transformation occurs simultaneously with the maximum thermal stresses, as shown in Fig. 12(c), transformation in the core will occur prior to surface transformation, and a barrel shape will appear with high compressive stresses on the surface. If the surface is transformed prior to the core, the transformational stresses will decrease, or pos-

Hardening by Reheating and Quenching / 251

Tempering The tempering process involves heating hardened steel to some temperature below the eutectoid temperature in order to decrease hardness and increase toughness. In general, tempering is divided into four stages, which are summarized in Table 4 (Ref 10). These include: ● Tempering of martensite structure ● Transformation of retained austenite to mar-

tensite ● Tempering of the decomposition products of martensite and at temperatures 900 F (480 C) ● Decomposition of retained austenite to martensite (Ref 11) Figure 13 illustrates the effect of microstructural variation during tempering on the volume

changes occurring during the tempering of hardened steel (Ref 10). Figure 14 (Ref 11) illustrates the effect of dimensional variation and retained austenite content of a bearing steel (100 Cr 6) as a function of tempering temperature. In addition to those effects discussed previously, tempering may also lead to dimensional variation due to relaxation of residual stresses and plastic deformation, which is due to the temperature dependence of yield strength (Ref 10).

Metallurgical Sources of Stress and Distortion during Reheating and Quenching

occur in the plastic zone and are permanent. Upon heating, the stresses are gradually relieved by changes in the shape of the part due to plastic flow. This is a continuous process, and as the temperature of the part is increased, the material yield stress decreases as shown in Fig. 16 (Ref 13). It is a function not only of temperature but also of time, since the material will creep under lower applied stresses. It is apparent that the stresses can never be reduced to zero, because the material will always possess some level of yield strength below which residual stresses cannot be reduced. Material Movement. When parts are heated during heat treatment, a thermal gradient exists across the cross section of the component. If a

Basic Distortion Mechanism. Shape and volume changes during heating and cooling can be attributed to three fundamental causes (Ref 12):

3 285 MPa

● Residual stresses that cause shape change

when they exceed material yield strength. This will occur on heating when the strength properties decline. ● Stresses caused by differential expansion due to thermal gradients. These stresses will increase with the thermal gradient and will cause plastic deformation as the yield strength is exceeded. ● Volume changes due to transformational phase change. These volume changes will be contained as residual stress systems until the yield strength is exceeded.

Strain (∆L/Lo), %

sibly even reverse the thermal stresses. If this occurs, a spool shape will be formed. These data show that the position of cooling curves for both the surface and the core for the quenching process must be considered with the appropriate TTT curve for the steel of interest and that there are numerous mixtures of thermal and transformational stresses possible. Table 3 provides a summary of these processes (Ref 6). In some steels, those with higher carbon content and alloy steels, the martensite finish (Mf) temperature is below 32 F (0 C), which means that it is likely that at the conclusion of heat treating there will be as much as 5 to 15% of austenite remaining (Ref 11). The amount of retained austenite will exhibit significant effects on the magnitude of compressive stresses formed and ultimately on dimensional changes to be expected. Some of the factors affecting retained austenite formation include: chemical composition (which dictates the Ms temperature), quenching temperature, quenching cooling rates, austenitizing temperature, grain size, and tempering.

Relief of Residual Stress. If a part has lockedin residual stresses, these stresses can be relieved by heating the part until the locked-in stresses exceed the strength of the material. A typical stress-strain curve obtained from a tension test is shown in Fig. 15 (Ref 12). Initial changes in shape are elastic, but under increased stress they

Fig. 8

2 209 MPa 107 MPa 1 18 MPa

0

0

100

200

300

Temperature (θ), °C Dilatometer curves for a 0.6% C (60NCD11) for different applied stresses

steel

200 1000 900

Tim e ( t ) , s

800 1 atm Temperature, °C

700 F.P. =(12 12kbar) kbar F.P. =(23 23kbar) kbar

600 500

B =(11atm) atm

tF

400 300 200 100 0 1

B =(12 12kbar) kbar

Mss =(11atm) atm

B =(23 23kbar) kbar

12kbar) kbar Mss =(12

tD 0

Mss =(23 23kbar) kbar

0

20

40

60

80

Tensile stress (σ), MPa 10

102

103

104

105

Time, s

Fig. 7

100

Effect of hydrostatic pressure on the transformation kinetics of 50CV4 steel. B, bainite; F.P., ferrite-pearlite transformation; Ms, martensitic start temperature. Source: Ref 7

Effect of tensile stress on pearlite transformation starting and ending times. Isothermal transformation at 673 C, eutectoid steel. The tD and tF times are transformation starting and ending times, respectively.

Fig. 9

252 / Residual Stress During Hardening Processes component design. Poor component design promotes distortion and cracking by accentuating nonuniform and nonsymmetrical heat transfer during quenching. Component design characteristics that are common to distortion and cracking problems include (Ref 19, 20):

There are various factors that can affect distortion and growth of steel heat treating. These include: component design, steel grade and condition, machining, component support and loading, surface condition, heating and atmosphere control, retained austenite, and the quenching process (Ref 18).

● Parts that are long (L) with thin (d) cross sec-

tions. Long and thin parts are defined as: greater than L ⳱ 5d for water quenching, L ⳱ 8d for oil quenching, and L ⳱ 10d for austempering where L is the length of the

Component Design One of the overwhelming causes of steel cracking and unacceptable distortion control is

1000 Center Temperature, °C

section is heated so that a portion of the component becomes hotter than the surrounding material, the hotter material expands and occupies a greater volume than the adjacent material and will thus be exposed to applied stresses that will cause a shape change when the material strength is exceeded. These movements can be related to heating rate and section thickness of the component. Volume Changes during Phase Transformation. When a steel part is heated, it transforms to austenite with an accompanying reduction in volume as shown in Fig. 4 (Ref 14). When it is quenched, the structure transforms from austenite to martensite and its volume increases. If these volume changes cause stresses that are constrained within the strength of material, a residual stress system is created. If the stresses cannot be contained, then material movement will occur, which will cause cracking under extreme conditions. The expansion is related to the composition of the steel. Fig. 17 shows the relative volume increase of two steels as a function of austenitizing temperature and specimen dimensions. While all of these phenomena are well-known physical changes, the situation is made more complex when all three events occur simultaneously. In addition, other events such as heating rate, quenching, and inconsistent material composition further complicate the process.

T

Surface 0

500

0

0

10

100

1000

A

Residual stress

Time, s Tension

Tension

B Center B Surface 0

0

Surface

C

Effect of Materials and Quench Process Design on Distortion Compression

Fig. 10

Development of thermal stress on cooling in steel specimen. T, time instant of maximum temperature difference; O, time instant of stress reversal; curve A, stress variation at the surface under elastic condition. B and C are actual thermal stress variations at the surface and the core under elastic-plastic conditions.

Temperature

TA

Core

TA

Core

Surface

Surface

Surface

Ms

Core

TA

Ms

Ms

RT

+ Stress, σz

Quenchant selection and quenching conditions are critically important parameters in quench system design. For example, one study compared the distortion obtained with quenching of a 0.4% medium-carbon plain steel bar of 200 mm diameter by 500 mm long in water or oil from 680 C (Ref 15, 16). The results, shown in Fig. 18(a) and (c), show that essentially equivalent variation in diameter and length with both cooling processes were obtained that were due to thermal strains within the steel. Interestingly, the well-known diameter variations at the end of the bar, known as the “end effect,” were observed; this is attributed to heat extraction from both the sides and ends of the bar. When the bars of the same type of steel and the same dimensions were heated to 850 C to austenitize the steel and then quenched in water or oil, the results shown in Fig. 18(b) and (d), respectively, were obtained (Ref 15, 16). Considerably greater dimensional variation and lengthening of the bar (for the oil quench) were obtained due to both thermal and transformational strains with the steel. Thuvander and Melander modeled the dimensional changes of a 70 mm steel (0.15% C, 1% Mn, 0.75% Cr, 0.85% Ni) cube after austenitizing and then quenching in water and oil (Ref 15, 17). The results of this work (Fig. 19) show that the edges and faces shrink (becoming concave), and the effect is greater when quenched in water than when quenched in oil.

Compression Surface

Center

−

tu

tu

(a)

(b) Surface

tu Time

Time

Time (c)

Core

Thermal stress Total stress

Fig. 11

Comparison of thermal and transformational stresses for three different quenching conditions. See text for details. tu, time instant of stress reversal

Hardening by Reheating and Quenching / 253 parts and d is the thickness or diameter. Long and thin parts may be quenched using a support mechanism such as that shown in Fig. 20. ● Parts that possess large cross-sectional area (A) and are thin (t), are defined as: A ⳱ 50t.

of alignment. A general rule for solving such quench distortion problems is that the “short side is the hot side,” which means that the inside of the bowed metal was quenched more slowly than the opposite side (Ref 20).

Parts that exceed these dimensions often must be straightened or press quenched to maintain dimensional stability (Ref 20). If possible, materials with sufficient hardenability should be oil or salt quenched. A schematic of a press quenching system is shown in Fig. 21. Design symmetry is also an important variable to minimize distortion. For example, the unsymmetrical gear design shown in Fig. 22(a) typically may undergo distortion as shown in Fig. 22(b) (Ref 19). (The load on a gear tooth increases as the 4.3 power of the taper, Ref 19.) Solution to the gear design problem shown in Fig. 23 is to provide greater symmetry as shown in Fig. 23. If this is not possible, press quenching or tooth-by-tooth induction hardening may be the only solutions (Ref 19, 20). Another common design problem is with parts having holes, deep keyways, and grooves. One illustration of this problem is hardening of a shaft over a lubrication cross hole as shown in Fig. 24 (Ref 19). Preferred alternative designs are also shown in Fig. 24. If a radial cross hole is mandatory, the use of a carburized steel with oil quenching would be preferred. Distortion that was encountered when quenching a notched part, such as a shaft with a milled slot, is shown in Fig. 25 (Ref 20). In this case, nonuniform heat transfer results. The metal within the notch is affected by the shrinkage of the metal around it due to slower cooling within the slot caused by vaporization of the quenchant. Therefore, upon cooling the metal on the side with the shaft is “too short,” pulling the shaft out

Steel Grade and Condition Although quench cracking is most often caused by nonuniform heating and cooling, material problems may be encountered. Some typical material problems include (Ref 19):

Table 3 Fig. 12)

● The compositional tolerances should be

checked to ensure that the alloy is within specification. ● However, some alloys are particularly problematic. For example, some steel grades must be water quenched when the alloy composition is on the low side of the specification limit. Conversely, if the alloy composition is on the high side, cracking is more common. Steel grades that exhibit this problem include: 1040, 1045, 1536, 1541, 1137, 1141, and 1144. As a rule, steels with carbon contents

Size change and residual stress caused by heat treatment of prismatic parts (see

(DT)2

(DV/V)3

Dimensional dependency

(De)

Change of microstructure

Small

⬆0

e1 ⳱ e11 ⳱ e111

0

0

Thermal stress

Big

e1 e11 e111

0

0

Thermal and transformation stress Transformation R Ⳮ K after thermal stress maximum Transformation R before K after thermal stress maximum Transformation K before R after thermal stress maximum Transformation R Ⳮ K before thermal stress maximum

0

(rE)

Small Big

0 »0

e1 e11 e111 e1 e11 e111

00

»0 »0

Big

0

e1 e11 e111

0

0

Big

ⱖ0

e1 « e11 « e111

»0

«0

Small Big

0 0

e1 e11 e111 e1 e11 e111

0 0

00

Example

Tempering, precip. Hardening, isotropic material Quenching of austenitic steels

In air Full hardness penetration In water Medium hardness penetration Shallow hardness penetration (shell hardening) Normalizing, quenching without hardening

R ⳱ surface; K ⳱ core; DT ⳱ (TK ⳮ TR); DV/V ⳱ relative volume change; Convexity De ⳱ ek ⳮ em; em and ek dimensional change in middle of the plane, respectively, at the edge; rE ⳱ residual stress at the surface (remaining stress)

Table 4 Metallurgical reactions occurring at various temperature ranges and related physical changes of steel during tempering Transformation for 2 Temperature range

K C

F

Metallurgical reaction

0–200 200–300 230–350 350–700

32–392 392–572 446–662 662–1292

Precipitation of e carbide. Loss of tetragonality Decomposition of retained austenite e carbides decompose to cementite Precipitation of alloy carbides. Grain coarsening

1 2 3 4

Expansion/contraction

Contraction Expansion Contraction Expansion

∆Tmax B M

1

2

3

4

log t, s 1 ∆Tmax

Barrel

Fig. 12

UR

UK

2

UR

∆Tmax

UK

3

UK

∆Tmax

UR

4

UR

UK

Decomposition of martensite to ferrite and cementite

Increase in volume

Temperature , °C

Stage

P

R

Retained austenite to martensite Retained austenite to bainite

Carbide precipitation

∆Tmax 0

Spool Size change due to thermal changes and phase transformation. K, core; R, surface

100

200

300

400

500

600

700

800

Tempering temperature, °C

Fig. 13

Effect of microstructural constitutional variation on volume changes during tempering

900

254 / Residual Stress During Hardening Processes and hardenability greater than that of 1037 are difficult to water quench (Ref 19). ● Some steel grades with high manganese are prone to microsegregation of manganese and gross segregation of chromium are prone to cracking. These include: 1340, 1345, 1536, 1541, 4140, and 4150. If possible, it is often a good choice to replace the 4100 series with the 8600 series of steels (Ref 21). ● “Dirty” steels, those containing greater than 0.05% S, are more prone to cracking such as 1141 and 1144. The reasons for this include: greater alloy segregation in dirty steels lead to alloy-rich and alloy-lean regions, there are

0.4

Dimensional alteration

0 −0.4 −0.8 −1.2

Austenitizing temperature 800 °C 850 °C 910 °C

−1.6

typically more surface seams that act as stress risers with dirty steels, and steels with higher sulfur levels are often manufactured to coarse grain practice for improved machinability, which also imparts greater brittleness and propensity for cracking. ● Decarburization of up to 0.0025 in. per 1⁄16 in. diameter may be present. It is well known that cracking propensity increases with carbon content. Therefore, carbon content of steel is one of the determining factors for quenchant selection. Table 5 summarizes some steel mean carbon content concentration limits for water, brine, or caustic quenching (Ref 21). It is well known that regions containing high concentrations of coarse carbide microstructure as a result of improper forging may become the initiation point for subsequent quench cracking, particularly with parts of complex shape (Ref 22). It is important to provide a sufficient forging reduction ratio to allow the carbide formation to become fine and uniform (Ref 23). Since part manufacture, such as gear production, often requires machining, the condition of the steel that is going to be machined is critically important. Some workers have recommended that normalized and subcritical annealed steel is

the ideal condition (Ref 18). Subcritical annealing is performed to relieve stresses incurred during normalization without softening or homogenizing the steel. The subcritical annealing process reduces the carbon content and alloy carbide content in the austenite allowing the production of more lath martensite in the microstructure, which provides higher fracture toughness and higher impact toughness (Ref 22).

Machining Material removal during machining can result in high residual stress levels and ultimately unacceptable distortion (Ref 18). When excessive machining stresses are imparted, the process may require modification to include a rough machining and stress relieving followed by fine machining. This subject is covered in the article in chapter 5 and is not discussed in detail here.

Component Support and Loading Toshioka (Ref 16) examined the bending behavior of a piston rod that is heated vertically while suspended from the top of a furnace. After austenitizing, the piston rods were then oil quenched while still hanging vertically and the

16

Temperature, °F 200

800

8 4 0 RT

180

220

240

Tempering temperature, °C Dimensional variation and retained austenite content of 100Cr6 steel as a function of tempering temperature

Fig. 14

400

600

800

1000

1200 50

Low-alloy steel

600

40 Creep-resistant austenitic steel

400

30 20

200 10

Carbon-managanese Carbon-manganese steel steel 0

0

100

200

300

400

500

600

0.2% proof stress, tsi

12 0.2% proof stress, MPa

Retained austenite

20

700

Temperature, °C

Fig. 16

P Stress, σ = −−−− Ao Elastic

Variation of yield strength with temperature for three generic classes of steel

Plastic

90MnV8

Ultimate tensile strength

760 °C 800 °C 145CrV6 870 °C 830 °C

Yield stress

Uniform elongation

Necking

Volume increase, %

0.6

Fracture

0.4

0.2

0 Offset

Fig. 15

50 × 50 × 10

L − Lo Strain, ε = −−−−−−− Lo

Various features of a typical stress-strain curve obtained from a tension test

50 × 50 × 20

50 × 50 × 50

50 × 50 × 250

Specimen dimension, mm

Fig. 17

Volume increase of steels 90MnV8 and 15CrV6 as a function of austenitizing temperature and specimen dimensions

Hardening by Reheating and Quenching / 255 amount of distortion obtained, shown in Fig. 26, is widely variable from nearly zero to as much as 20 mm (Ref 16). Many parts may sag and creep under their own weight when heat treated; this is an important cause of distortion. An example of a type of component that is susceptible to such distortion is a ring gear, the dimension limits by which ring gears are classified are provided in Fig. 27 (Ref 18). (A general dimensional classification of various distortion-sensitive shapes is provided in Fig. 28, Ref 18.) Proper support when heating is required to minimize out-of-flatness and ovality problems, which may result in long grinding times, excessive stock removal, high scrap losses, and loss of case depth (Ref 18). To achieve adequate distortion control, custom supports or press quenching may be required. Pinion shafts, as defined in Fig. 28, are susceptible to banding along their length if they are improperly loaded into the furnace as shown in Fig. 29 (Ref 18). When this occurs, the pinion shafts must then be straightened, which will add to production cost.

Surface Condition Quench cracking may be due to various steelrelated problems that are only observable after the quench, but the root cause is not the quenching process itself. Many of these have been reviewed earlier and include: prior steel structure, stress risers from prior machining, laps and

seams, alloy inclusion defects, grinding cracks, chemical segregation (bonding), and alloy depletion (Ref 24). In this section, three problems related to surface conditions that may contribute to poor distortion control and cracking are discussed: “tight” scale formation, decarburization, and the formation of surface seams or “nonmetallic stringers.” Tight scale problems are encountered with forgings hardened from direct-fired gas furnaces with high-pressure burners (Ref 20, 21). The effect of tight scale on the quenching properties of two steels, 1095 carbon steel and 18–8 stainless steel, is shown in Fig. 30 (Ref 14). These cooling curves were obtained by still quenching into fast oil. A scale of not more than 0.08 mm (0.003 in.) increased the cooling rate of 1095 steel compared with the rate obtained on a specimen without scale. However, a heavy scale (0.13 mm, or 0.005 in., deep) retarded the cooling rate. A very light scale (0.013 mm, or 0.0005 in., deep) also increased the cooling rate of the 18–8 steel over that obtained with the specimen without scale. In practice, the formation of tight scale will vary in depth over the surface of the part resulting in thermal gradients due to differences in cooling rates. This problem may yield soft spots and uncontrolled distortion and is particularly a problem with nickel-containing steels. Surface oxide formation can be minimized by the use of an appropriately protective atmosphere. The second surface-related condition is decarburization, which may lead to increased distortion or cracking (Ref 23). At a given depth

within the decarburized layer, the part does not harden as completely as it would at the same point below the surface if there were no decarburization. This leads to nonuniform hardness, which may contribute to increased distortion and cracking because (Ref 20): ● The decarburized surface transforms at a

higher temperature than the core (the Ms temperature decreases with carbon content). This leads to high residual tensile stresses at the decarburized surface or a condition of unbalanced stresses and distortion. ● Since the surface is decarburized, it will exhibit lower hardenability than the core. This will cause the upper transformation products to form early, nucleating additional undesirable products in the core. The decarburized side will be softer than the side that did not

A

Oil quench

A 0.1 mm A

+0.1

Diameter change, mm

Diameter change, mm

Water quench

0 Change in length: −0.17 mm −0.1

0

250

500

+0.1

A

0

0

Distance from end of bar first into quench, mm

250

500

Distance from end of bar first into quench, mm

Change across midsection (A-A)

Dimensional changes in a 70 mm steel (0.15% C, 1% Mn, 0.75% Cr, 0.85% Ni) bar after austenitizing and then quenching in water or oil

Fig. 19

(b)

(a) 680°C/water quench. No transformation. Thermal strain only.

850°C/quench. Thermal and transformation strain.

+0.1

Diameter change, mm

Diameter change, mm

Outer-face change

WQ − change in length: +0.17 mm −0.1

0.3 mm

0 Change in length: −0.15 mm −0.1

0

250

500

Distance from end of bar first into quench, mm (c)

+0.1 OQ − change in length: +0.8 mm 0 WQ − change in length: −2.45 mm −0.1

0

250

500

Distance from end of bar first into quench, mm (d)

Dimensional variation of a medium-carbon (0.4%) steel bar (200 mm diam by 500 mm) after the indicated heat treatments. These bars were quenched vertically with one end down (marked 0 in the figure). (a) and (c) show no transformation, thermal strain only after water quenching from 680 C. (b) and (d) show thermal and transformation strains after quenching from 850 C. OQ, oil quench; WQ, water quench

Fig. 18

Fig. 20

Die quench system. Courtesy of Gleason Tooling Products Group

256 / Residual Stress During Hardening Processes undergo decarburizing, which is harder. The greater amount of martensite leads to distortion. The solution to this problem is to restore carbon into the furnace atmosphere or machine off the decarburized layer. The third surface-related condition that may lead to cracking or material weakening is the formation of surface seams or nonmetallic inclusions, which may occur in hot-rolled or coldfinished material. The presence of these defects prevents the hot steel from welding to itself during forging, for example, creating a stress riser. To prevent this problem with hot-rolled bars, stock should be removed before heat treatment. Recommendations made earlier by Kern are provided in Table 6 (Ref 21). Although not a published standard, Kern has reported that a seam or

nonmetallic depth of 0.001 in./0.13 in. diameter maximum is usually acceptable for cold-finished bars (Ref 21). If the seam depth is excessive, it is recommended that the bars be magniflux inspected prior to heat treatment.

Before heat treatment

Heating and Atmosphere Control An important source of steel distortion and cracking is nonuniform heating and not using the appropriate protective atmosphere. For example, if steel is heated in a direct-gas-fired furnace with high moisture content the load being heated may adsorb hydrogen leading to hydrogen embrittlement and subsequent cracking that would not normally occur with a dry atmosphere (Ref 4, 19). Localized overheating is particularly a potential problem for inductively heated parts (Ref 4,

After heat treatment

Fig. 25

Distortion often encountered when quenching a notch

Table 5 Suggested carbon content limits for water, brine, and caustic quenching Hardening method/shapes

Fig. 21

Schematic of a press quench system. Courtesy of Gleason Tooling Products Group

Carbon, % max

Furnace hardening General usage Simple shapes Very simple shapes, for example, bars

0.30 0.35 0.40

Induction hardening Simple shapes Complex shapes

0.50 0.33

100 diam

80 diam 140 diam 385

1775 2260

5 Shallow round bottom groove

The problem: gear tapers or warps

Fig. 22

Bending, mm

Gear before heat treating

4 3 2 1 0

Schematic of a gear that is difficult to harden without the distortion shown

Distortion of JIS SCM 440 (0.4 C, 1.05 Cr, 0.22 Mo) steel piston rods after oil quenching while vertically suspended from 850 C and tempering at 600 C

Fig. 26

Harden this length

WT

ID

A satisfactory design if hub must be offset

L Usual design (poor)

Design solutions to the distortion problem shown in Fig. 22

OD

Design for hardening over holes

Solution: the ideal design

Fig. 23

Better

Design solutions to the quench-cracking problem often encountered in shaft hardening over a cross hole

Fig. 24

Dimensions of a ring gear shape. Shape limitation: length/wall thickness ⱕ1.5; ID/OD 0.4. Minimum wall thickness (WT) is defined by WT ⱖ 2.25 ⳯ module Ⳮ 0.4 ⳯ 5冪mod ⳯ L ⳯ OD3

Fig. 27

Hardening by Reheating and Quenching / 257 25). Subsequent quenching of the part leads to quench cracks at sharp corners and areas with sudden changes in cross-sectional area (stress risers). Cracking is caused by increases of residual stresses at the stress risers during quenching. The solution to the problem is to increase the heating speed by increasing the power density of the inductor. The temperature difference across the heated zone is decreased by continuous heating or scanning of several pistons together on a single bar (Ref 25). For heat treating problems related to furnace design and operation, it is usually suggested that (Ref 19): ● The vestibules of atmosphere-hardening fur-

naces should be loaded and unloaded with purging. Load transfer for belt and shaker hearth furnaces should only occur with thorough purging to minimize atmosphere contamination. ● Hardening furnaces typically contain excessive loads prior to quenching. If the steel at quenching temperature is greater than 20% of the distance from discharge to charge door, it is too much. Either the production rate can be increased or some of the burners can be turned off.

Retained Austenite Dimensional changes may occur slowly or quickly and are due to the volume composition of the transformation products formed upon quenching. One of the most important—with respect to residual stress variation, distortion, and cracking—is the formation and transformation of retained austenite. For example, the data in Table 7 illustrate the slow conversion of retained austenite to martensite, which was still occurring days after the original quenching process for the two steels shown (Ref 15, 16). This is particularly a problem when dimensional control and stability are the primary goals of heat treatment.

Therefore, microstructure determination is an essential component of any distortion-control process.

Quenching Process

ommendations for quench media selection for use with various steel alloys is provided by standards such as AMS 2770. Some additional general comments regarding quenchant selection include (Ref 4, 20): ● Most machined parts made from alloy steels

Other than component design, the quenching process itself is one of the most frequently encountered problems in heat treating. When designing a quenching process, it is important to consider quenchant selection and quench severity and uniformity. Quenchant Selection and Severity. A more detailed discussion on quenchant selection and the ranges of quench severity possible with these media are provided in a subsequent section. However, here the general issue of quench severity is addressed. Quench severity is defined as: “ability of a quenching medium to extract heat from a hot steel workpiece, expressed in terms of the Grossmann number (H)” (Ref 26). A typical range of Grossmann H values for commonly used quench media are provided in Table 8, and Fig. 31 provides a correlation between the H value and the ability to harden steel as indicated by the Jominy distance (J distance) (Ref 20). Although Table 8 is useful to obtain a relative measure of the quench severity offered by different quench media, it is difficult to apply in practice because the actual flow rates for “moderate,” “good,” “strong,” and “violent” agitation is unknown. Alternatively, the measurement of actual cooling rates or heat fluxes provided by a specific quenching medium does provide a quantitative meaning to the quench severity provided. Some illustrative values are provided in Table 9 (Ref 27). Typically, the greater the quench severity, the greater the propensity of a given quenching medium to cause increased distortion or cracking. This usually is the result of increased thermal stress not transformational stress. Specific rec-

are oil quenched to minimize distortion.

● Most small parts, or finish-ground larger parts

●

●

●

●

●

are “free” quenched. Larger gears, typically those larger than 205 mm (8 in.) are fixture (die) quenched to control distortion. Smaller gears and parts such as bushings are typically plug quenched on a splined plug typically constructed from carburized 8620 steel. Although a reduction of quench severity leads to reduced distortion, it may also be accompanied by undesirable microstructures such as the formation of upper bainite (quenched pearlite) with carburized parts. Quench speed may be reduced by quenching in hot (150–205 C, or 300–400 F) oil. When hot oil quenching is used for carburized steels, lower bainite, which exhibits properties similar to martensite, is formed. Excellent distortion is typically obtained with austempering, quenching into a medium just above the Ms temperature. The formation of retained austenite is a significant problem with austempering processes. Retained austenite is most pronounced where manganese and nickel are major components. The best steels for austempering are plain carbon, chromium, and molybdenum alloy steels (Ref 20). Aqueous polymer quenchants may often be used to replace quench oils, but quench severity is still of primary importance. Gas or air quenching will provide the least distortion and may be used if the steel has sufficient hardenability to provide the desired properties.

1.00

WT Thin-walled tube (annulus)

0.80

Boundary A Ratio ID/OD

ID

Example Outside diameter: 200 mm Length: 1500 mm

L

Typical distortions and growths

OD

0.60

Out-of-straightness: 1000-2000 µm

Ring

OD shrinkage at center: 300-500 µm

0.40 Tube Wheel

0.20

0

Fig. 28

Increase in length: 1000-1500 µm

Pinion

0

1

Classification of shapes

2

3 4 5 6 Ratio length/wall thickness, L/WT

7

8

9

Retort wall

Fig. 29

Center pole

Retort wall

Typical pinion shaft distortion due to furnace loading

258 / Residual Stress During Hardening Processes ● Low-hardenability steels are quenched in

brine or vigorously agitated oil. However, even with a severe quench, undesirable microstructures such as ferrite, pearlite, or bainite can form. Quenchant Uniformity. Quench nonuniformity is perhaps the greatest contributor to quench cracking. Quench nonuniformity can arise from nonuniform flow fields around the part surface during the quench or nonuniform wetting of the surface (Ref 1, 20, 28–30). Both lead to nonuniform heat transfer during quenching. Nonuniform quenching creates large thermal gradients between the core and the surface of the part. These two contributing factors, agitation and surface wetting, are discussed here. Poor agitation design is a major source of quench nonuniformity. The purpose of the agitation system is not only to take hot fluid away from the surface and to the heat exchanger, but it is also to provide uniform heat removal over the entire cooling surface of all of the parts throughout the load being quenched. The batch quench system in Fig. 32 illustrates a system where axial (vertical) quenchant flow occurs throughout a load of round bars lying horizontally in a basket (Ref 19). In this case, the bottom surfaces of the bars experience greater agitation than the top surfaces. Cracks form on the upper surfaces because of the nonuniform heat loss. Agitation produces greater heat loss at the bottom, creating a large thermal gradient between the top and the bottom surfaces. If a submerged spray manifold is used to facilitate more uniform heat removal, the following design guidelines are recommended: ● The total surface of the part should experi-

ence uniform quenchant impingement.

● The largest holes possible (2.3 mm, or 0.09

in., minimum) should be used.

● The manifold face should be at least 13 mm

(0.5 in.) from the surface of the parts being quenched.

● Repeated removal of hot quenchant and vapor

should be possible. Excessive distortion was also obtained with an agitation system shown in Fig. 33 when the quenchant flow was either in the same direction relative to the direction of part immersion or in the opposite direction (Ref 31). The solution to this problem was to minimize the quenchant flow to that required for adequate heat transfer during the quench and to provide agitation by mechanically moving the part up and down in the quenchant. Even though agitation is a critically important contributor to the performance of industrial quenching practice, relatively little is known about the quality and quantity of fluid flow encountered by the parts being quenched. Recently, agitation in various commercial quenching tanks has been studied by computational fluid dynamics (CFD), and in no case was optimal and uniform flow present without subsequent modification of the tank (Ref 28). Thus, identifying sources of nonuniform fluid flow during quenching continues to be an important tool for optimizing distortion control and minimizing quench cracking. The second source of nonuniform thermal gradients during quenching is related to interfacial wetting kinematics, which is of particular interest with vaporizable liquid quenchants including, water, oil, and aqueous polymer solutions. Most liquid vaporizable quenchants exhibit boiling temperatures between 100 and 300 C at atmospheric pressure. When parts are quenched in these fluids, surface wetting is usually time dependent, which influences the cooling process and the achievable hardness. Leidenfrost described the wetting process in the 1750s (Ref 32). The Leidenfrost Temperature is defined as the surface temperature where the vapor film is ruptured and the surface wetted by the liquid. Literature describes temperature values for this event for water at atmospheric pressure between 150 and 300 C (Ref 33–36).

1000

1400 1200

600 1000

No scale

800

400

600 400

200 Medium scale 0.08 mm (0.003 in.) 0

(a)

800 Temperature, °C

Temperature, °C

Heavy scale 0.13 mm (0.005 in.)

18-8 strainless 1B-B strainless steel steel

1600

Temperature, °F

1095 800

0

10

20 30 Time, s

1400 1200

No scale

600

1000 800

400

600 400

200 Light scale 0.013 mm (0.0005 in.)

200 40

0

50

1600

Temperature, °F

1000

0

10

20 30 Time, s

Table 6 Minimum recommended material removal from hot-rolled steel products to prevent surface seam and nonmetallic stringer problems during heat treatment Minimum material removal per side (a)

200 40

50

(b)

Centerline cooling curves showing the effect of scale on the cooling curves of steels quenched in fast oil without agitation. (a) 1095 steel, oil temperature ⳱ 50 C (125 F). (b) 18-8 stainless steel, oil temperature ⳱ 25 C (75 F); test specimens were 13 mm diam by 64 mm long (0.5 by 2.5 in.)

Fig. 30

For nonsteady-state cooling, the surface temperature is not equal to the Leidenfrost Temperature when the vapor blanket (or film boiling) collapses and wetting begins by nucleate boiling because of the influence of lateral heat conduction (relative to the surface) (Ref 37). This is due to the simultaneous presence of various heattransfer conditions during vapor blanket cooling—or film boiling (FB), nucleate boiling (NB), and convective heat transfer (CONV) with significantly varying heat-transfer coefficients ␣FB (100–250 W/m2 • K), ␣NB (10–20 kW/ m2 • K), and ␣CONV (700 W/m2 • K). Figure 34 shows the different cooling phases on a metal surface during immersion cooling (Fig. 34a) with the so-called wetting front w (separating the film-boiling phase and the nucleate-boiling phase) and the change of the heat-transfer coefficients, ␣, along the surface coordinate, z, (mantle line). In most cases, during immersion cooling (Fig. 34a) the wetting front ascends the cooling surface with a significant velocity, v, whereas during film cooling (Fig. 34b) the wetting front descends in the fluid direction (Ref 35, 38). An example of wetting heated cylindrical and prismatic probes that are submerged in water is shown in Fig. 35(a) and (b), respectively (Ref 35, 39). Because of the different wetting phases on the metal surface (and the enormous differences of their values of ␣FB, ␣NB, and ␣CONV), the time-dependent temperature distribution within the metal probes will also be influenced by the velocity of the wetting front as well as geometry. Figure 36 illustrates different types of wetting behavior under different conditions (Ref 40). By changing a quenching parameter, for example the chemical composition of the fluid, the period of wetting (tW) can be reduced over one magnitude. To quantitatively define the change of the wetting behavior, for example, to determine the cooling process or to develop or analyze quenching fluids, the measurement of the electrical conductance between the submerged sample and a counterelectrode is helpful (Ref 35). During the film-boiling phase, the hot metal is largely insulated by the vapor film surrounding the metal and conductance between the metal and the counterelectrode is low. When the vapor blanket

Condition

Nonresulfurized

Resulfurized

Turned on centers Centerless turned or ground

3% of diameter 2.6%

3.8 % of diameter 3.4%

(a) Based on bars purchased to special straightness, i.e., 3.3 mm in 152 cm (0.13 in. in 5 ft) maximum

259 / Hardening by Reheating and Quenching (film boiling) ruptures on the metal surface, localized wetting begins and conductance increases. The increase in conductance of the wetted metal is proportional to the amount of the metal surface wetted by the quenchant. When the metal surface is completely wetted, conductance is at its highest value. Figure 37(a) shows a normal electrical conductance, G, increase corresponding to the percentage of the wetted surface. Three other possibilities of wetting are also shown. Figure 37(b) shows a rapid rewetting process (or “explosive” wetting) similar to that shown in Fig. 35. Figure

Quench severity in terms of H value

x 5.0 2.0

H value

1.5 1.0 0.70 0.50 0.35 0.20 6

Fig. 31

9

12 15 18 J distance (1/16 in.)

21

24

Quench severity in terms of Grossmann (H) values. J, Jominy distance. Source: Ref 20

37(c) illustrates rapid wetting followed by insulation by bubbles adhering to the metal surface, and Fig. 37(d) illustrates rapid wetting with repeated new formation of film boiling, a process that occurs with many aqueous polymer quenchant solutions. In all four diagrams, the temperature, TC, is shown that is measured in the center of the probes. The TS point characterizes the temperature and the time when wetting begins. This shows that temperature measurements in the center of probes provide poor information about the real quenching process that is insufficient to adequately characterize the hardening process. This is also illustrated in Fig. 38 (Ref 30). The influence of the physical properties of the quenchant and the probe on the wetting process, and the heat-transfer coefficients (␣FB, ␣NB, and ␣CONV) and therefore on the quenching results is very strong. The wetting kinematics are identified as the starting time, tS, of wetting, the finishing time, tf, of wetting, and the difference between tf and tS is the wetting time tW. The effect of variation of these parameters on the quenching process is summarized in Table 10. The influence of a wetting process occurring over a long time (non-Newtonian wetting) on the temperature distribution in quenched parts is shown in Fig. 39 (Ref 23), where the temperatures measured near the surface of a submerged cylindrical probe at different distances z from its lower end are shown. The wetting front requires about 18 s to arrive at a height of 80 mm. If there is an explosionlike wetting of the probe (Newtonian wetting), the five temperature slopes are

congruent. If the temperature was measured (as usual) in the center of the probe, the large differences in wetting behavior would not be observed. The temperature distribution within the probe during quenching (indicated by isotherms), having a non-Newtonian wetting is shown in Fig. 40(a), where there is a great difference relative to that of the Newtonian wetting (Fig. 40b). In the case of Fig. 40(b), the main grad T is radial, whereas in the case of Fig. 40(a) it is axial. Of course the hardness distribution in the probes must be extremely different. Another major source of nonuniform quenching is foaming and contamination. Contaminants include sludge, carbon, and other insolubles. It includes water in oil and oil in water and aqueous polymer quenchants. Foaming and contamination leads to soft spotting, increased distortion, and possibly cracking. Quench Distortion and Cracking. In the previous discussion, two quenchant-related phenomenon have been discussed: quench cracking and quench distortion. Although quench cracking can be eliminated, quench distortion cannot. Instead, the issue is distortion control, not elimination. Both quenching-related distortion control and quench cracking are discussed in this section. Quench Distortion. One form of distortion that may occur upon quenching is defined as shape distortion, which is dimensional variation that occurs when the parts are hot and the stress

Quench cracks

Table 7 Dimensional variation in hardened high-carbon steel with time at ambient temperature Change in length, % ⴒ 103 Steel type

Tempering temperature, C

Hardness, HRC

After 7 days

After 30 days

After 90 days

After 365 days

None 120 205 260 None 120 205 260

66 65 63 61.5 64 65 62 60

ⳮ9.0 ⳮ0.2 0.0 0.0 ⳮ1.0 0.3 0.0 0.0

ⳮ18.0 ⳮ0.6 ⳮ0.2 ⳮ0.2 ⳮ4.2 0.5 ⳮ0.1 ⳮ0.1

ⳮ27.0 ⳮ1.1 ⳮ0.3 ⳮ0.3 ⳮ8.2 0.7 ⳮ0.1 ⳮ0.1

ⳮ40.0 ⳮ1.9 ⳮ0.7 ⳮ0.3 ⳮ11.0 0.6 ⳮ0.1 ⳮ0.1

1.1% C tool steel 790 C quench

1% C/Cr 840 C quench

Table 8 Typical quenching conditions and Grossmann H values Quenching medium

Poor (slow) oil quench—no agitation Good oil quench—moderate agitation Very good oil quench—good agitation Strong oil quench—violent agitation Poor water quench—no agitation Very good water quench—strong agitation Brine quench—no agitation Brine quench violent agitation Ideal quench

Grossmann H value

0.20 0.35 0.50 0.70 1.00 1.50 2.00 5.00

It is possible with high-pressure impingement to achieve H values greater than 5.00.

Tray

Quenchant flow

Fig. 32

Harmful effects of vertical quenchant flow through the load

Table 9 Comparison of typical heat transfer rates Quench medium

Still air Nitrogen (1 bar) Salt bath or fluidized bed Nitrogen (10 bar) Helium (10 bar) Helium (20 bar) Still oil Hydrogen (20 bar) Circulated oil Hydrogen (40 bar) Circulated water

Quenchant flow

Heat-transfer rate, W/m2 • K

50–80 100–150 350–500 400–500 550–600 900–1000 1000–1500 1250–1350 1800–2200 2100–2300 3000–3500

Quenchant flow

Fig. 33

Effect of quenchant flow direction on distortion

260 / Residual Stress During Hardening Processes of their own weight leads to changes such as bending, warpage, and twisting (Ref 1). Shape distortion is attributable to component support and loading as discussed previously. A second form of distortion is size distortion, which includes dimensional changes observable as elongation, shrinkage, thickening, and thinning. Size distortion is caused by the volumetric variation that accompanies each of the transformational phases formed upon quenching (Ref 1). Size distortion can be further classified as: onedimensional, two-dimensional, and three-dimensional. One-dimensional distortion is exemplified by the change in length when rod or wire is quenched and is primarily caused by transformational distortion. Two-dimensional distortion is also primarily caused by transformational distortion, and it is exemplified by size variation in two dimensions such as would occur with sheet or plate stock upon quenching. With bulk material that can undergo dimensional variation in three dimensions, the problem is due to both thermal and transformational distortion and is much more complicated (Ref 1). Owaku (Ref 1) has shown that one of the primary contributors to quench distortion is uneven (nonuniform) cooling. Quench Cracking. Stresses that lead to cracking are thermal, nonuniform cooling from TA and Ms and transformational stress formed between Ms and Mf. Nonuniform thermal stresses occur when nonuniform surface cooling occurs. In this case, there will be a deferred contraction in the slower cooling areas creating a “pull stress” re-

sulting in “pull cracking” (Ref 41). This is shown in Fig. 41(a) (Ref 41), where rapid, but nonuniform surface cooling to point A has occurred at which time it affects adjacent point B, which is cooling more slowly, causing a deferred contraction at point B⬘, both of which occur while the martensitic transformation occurs at the Ms point. As a result, point A, which cooled rapidly, undergoes compression, and point B⬘, which cooled more slowly, undergoes pulling. This means that pull stress is a tensile stress, and if this stress becomes large enough, cracking will occur and it will occur in areas where cooling is delayed. When there is nonuniform cooling within the part between the Ms and Mf, there will be a stretching or elongation in areas where the cooling is slow, which will act as a “push stress” leading to “push cracking” (Ref 41). This is shown in Fig. 41(b) (Ref 41) where point A, which cooled rapidly, stretches point B (which cooled more slowly) to point B⬘ below the Ms temperature, which is a state that will undergo expansion due to martensitic transformation. As a result, the rapidly cooled point A (exterior) will undergo pulling and the slowly cooled point B⬘ (interior) will undergo compression. This results in interior point B⬘ causing pushing and cracking at point A, which will occur in areas where quenching occurs rapidly. Therefore, pull cracking, which occurs with nonuniform surface cooling between TA and Ms, and push cracking, which occurs with nonuniform cooling within the part between Ms and Mf,

Steam

Film boiling

Nucleate boiling Fluid Convective heat transfer Heat transfer coefficient α

(a) Film of liquid Convection boiling

Sputtering

Mist cooling Fluid drops

z

(b)

Fig. 34

vorable if parts are immersed into the quenchant so the perimeter of the stress riser (PSC) simultaneously touches the liquid along the entire length. ● In the case where the perimeter of the stress riser touches the quenchant at the moment of immersion slowly in individual regions, quench cracking will be reduced substantially.

In addition to providing a uniform quench by optimizing agitation and surface cooling uniformity, the success of the quenching process is often dependent on the selection of a particular quenchant. However, there are typically many options to select from, and most quenching media are capable of providing a range of cooling rates. This section provides a brief overview of the various quench media that are available. Unfortunately, there is no uniform standard for reporting cooling rates available for a broad range of quenchant media. Therefore, various published comparisons are provided, and they will be sufficient for the reader to determine the relative quench severity offered by these quenchants.

Air

Gas

Wetting front w

● Conditions for quench cracking are most fa-

Quenchants

z Wetting front w

are the opposite of each other, although the cracking event takes place for both between the Ms and Mf. Figure 42 shows both push and pull cracking (Ref 41). For cracking to occur, the presence of a stress riser (points of stress concentration) is typically necessary. Two types of stress risers may be found. One is a geometric notch that includes cutting tool marks, sharp corner angles, and areas with rapid section thickness changes. The other type of stress riser commonly found is a notch in the material that may include intergranular effects, carbide segregation, and aggregates of impurities (Ref 41). Although it would be desirable to eliminate all stress risers to facilitate quenching without any potential for cracking, this simply is not possible in most cases. Instead, quenching methods that minimize potential cracking often must be developed. Polyakov (Ref 42) has provided immersion recommendations for parts with complex shapes where cracking potential is minimum and maximum (Fig. 43). The Polyakov rules for quenching such parts include (Ref 42):

Wetting behavior and change of heat-transfer coefficient ␣ along the surface. (a) Immersion cooling. (b) Film cooling. Source: Ref 14, 26

Perhaps the oldest, most common, and certainly least expensive quenching medium is air. Air, being a gas, cools the heated part by a filmboiling cooling mechanism. (See Fig. 34 for a schematic of different cooling mechanisms.) The relative quench severity offered by still air relative to other quench media is shown in Table 9. As with other quenching media, the heattransfer rates of air cooling are dependent on the

Hardening by Reheating and Quenching / 261 flow rate of air past the cooling metal surface. Figure 44 shows that the cooling rate, as measured by an instrumented 20 mm (0.8 in.) diam solid silver sphere, is significantly greater for cooling in compressed air (1 kg/cm2) relative to still air quenching (Ref 43). However, although air is inexpensive and commonly available, air quenching provides insufficient quench severity to adequately harden many steels.

Gas Quenching

Process of transition between the three cooling phases: film boiling (FB), nucleate boiling (NB), and convective cooling (CONV) during immersion cooling of CrNi-steel specimen with a cylindrical geometry 25 mm diam by 100 mm (a) wetting process of a cylindrical CrNi-steel specimen being quenched from 850 C into water at 30 C, an agitation rate of 0.3 m/s curves and (b) prismatic geometry (15 by 15 by 45 mm) in water of 60 C without forced convection; immersion temperature of 860 C. Source: Ref 14, 27

Fig. 35

Vacuum furnace heat treating technology, which includes gas quenching, is the fastest growing technology in heat treating. Gas quenching is typically performed by pressurizing a vacuum furnace after heating is completed. A broad range of quench severities, up to those achievable with water, are possible with some gas quenching media, as shown in Table 5 and in Fig. 45 (Ref 44). There are three main factors that affect the severity of gas quenching media: gas, flow velocity, and gas pressure. The most common gases used in gas quenching, in order of increasing quench severity, are argon, nitrogen, helium, and hydrogen (Ref 45). The high cost of argon precludes its use except for applications that demand chemical inertness. Hydrogen exhibits the best heat-transfer properties, as shown in Fig. 46 (Ref 45). Gas-quenching applications based on gas mixtures such as nitrogen/helium have also been studied (Ref 46). Gas blending allows the user to calibrate a particular system more cost effectively to the desired heat-transfer coefficient than can a single gas system. Quench severity is also dependent on gas pressure and flow rate, as shown in Fig. 47 (Ref 47). To avoid undesirable hot spots and corresponding thermal gradients, as shown in Fig. 48, an optimization of flow direction and flow rate is required to provide optimal distortion control and to prevent cracking (Ref 48).

Molten Metal One of the more common metals used in molten form as a quenchant is lead. Lead exhibits a melting point of 327 C (621 F) and is typically used at 343 to 927 C (650–1700 F). Below 343 C (650 F), the lead is too “mushy” (Ref 49). Molten lead is used for patenting of steel wire and for austempering. Due to the toxicity and disposal problems with lead, it is seldom used in the thermal processing of steel. However, because lead possesses a high thermal conductivity and no film-boiling stage, it provides relatively rapid cooling rates in a high-temperature range not easily achievable with other quenching media.

Salt-Bath Quenching Fig. 36 agitation.

Transition from film boiling (FB) to nucleate boiling (NB) during immersion of cylindrical silver specimen (15 mm diam by 45 mm) quenched from 850 C into a 10% aqueous polymer quenchant solution at 25 C without

Two quenching processes that require high temperatures are austempering and martempering (marquenching). Molten-salt baths have re-


● Highly alloyed steels, such as those shown in

Table 11, can be isothermally annealed.

● Scaling, cracking, and distortion of high-

speed tool steels are minimized.

● The risk of cracking during martensite for-

mation products is enhanced. Most quenching salts are either binary or ternary mixtures of potassium nitrate (KNO3), sodium nitrite (NaNO2), and sodium nitrate (NaNO3). The minimum quenching temperature depends on the melting point of the salt mixture. The ratio of the salt mixture may also affect the viscosity of the medium and therefore affect cooling rates. Quenching temperatures may

Conductance, G

G

Temperature, Tc

Conductance, G

mation, for example, spring wire, is reduced.

● The formation of high-temperature transfor-

Tc ts

G

Temperature, Tc

placed molten lead in most heat treating processes and are usually the medium of choice for high-temperature quenching. The advantages of salt quenching include:

Tc

range from 140 to 600 C (285–1110 F). However, melting points as low as 85 C (175 F) are attainable by the addition of up to 10% water. Salt-baths are susceptible to potential explosive degradation at temperatures greater than 600 C (1110 F). The selection of a martempering or austempering process depends on the steel being quenched. Salt-bath temperatures in the range of 195 to 350 C (385–660 F) exhibit only a minimal effect on the Grossmann H value (Ref 50). However, like all quenchants, heat-extraction capabilities depend on the agitation rate, as shown in Fig. 49 (Ref 50). The quench severity of a molten-salt bath may be substantially affected by the presence of water as shown in Fig. 50 (Ref 51). Variations in both agitation rate and water addition can profoundly affect the depth of hardening of AISI 4140 steel, as shown in Fig. 51 (Ref 51). Therefore, control of water content is important to achieve the maximum benefit of the increase in quench severity. However, automated monitoring equipment to

ts = tf

tf Time, t

Table 10 Effect of quenchant and material properties on quenching performance

Time, t (b)

(a)

Conductance, G

Tc

Temperature, Tc

G

G

Temperature, Tc

Conductance, G

Effect on property variation

Tc ts

ts = tf Time, t

tf

Fluid property

ts, tf

Dtw

␣

Fluid property Type of quenchant Addition of additives Increasing agitation (v) Increasing bath temperature (Tb)

I, D I, D D I

I, D I, D D I

I, D I, D I D

Metal property Increasing thermal diffusivity (a) Increasing cross-section size Increasing surface roughness Increasing surface oxidation

I I D D

I I D D

I D I D

Time, t

(c)

ts, starting time; tf, finishing time; tw, wetting time; ␣, heat-transfer coefficient; I, increasing; D, decreasing

(d)

Temperature decrease, TC, and increasing electrical conductance, G (proportional to the wetted surface) during quenching in different quenchants. (a) Slow wetting. (b) Rapid (explosive-type) wetting. (c) Rapid wetting followed by isolation of bubbles adhering to the metal surface. (d) Rapid wetting with repeated formation of film boiling after this process. See also Fig. 35 and 36. Source: Ref 14, 28

Fig. 37

1000

1000

C


Temperature, °C

750

800 3 2 1

Water 500 Polymer 250

1

z = 80 mm Wetting front


1000

2

500 3 250

60

R z

40 400 20 0 200

1-3 0

0 0

10

20

30

0

40

Time, s (a)

5

10

15

20

Time, s

0

5

10

15

20

25

30

35

Quenching time, s

(b)

Comparison of cooling curves measured at different positions in a cylindrical CrNi-steel probe (25 by 100 mm) during slow wetting (water) and sudden wetting (aqueous polymer solution) at (a) center (indicated by C) and (b) close to the probe surface at three indicated heights (1,2, and 3)

Fig. 38

0

Temperature drop on the surface of a cylindrical steel probe (25 mm diam by 100 mm) at various distances z from the lower end. Source: Ref 39

Fig. 39

Hardening by Reheating and Quenching / 263 control water content to within reasonably close tolerances is currently available. 700 °C 600 500 700 °C 600 400

800 °C 600 400 200 °C

200 °C

200 °C

t =5s

t = 10 s

t = 15 s

(a)

825 °C

725 °C

700 °C

250 °C

600

200

500

150 °C

750

800 775 °C

200 °C

775 °C

t =5s

t = 10 s

t = 11 s

t = 15 s

(b)

Fig. 40

Time-dependent temperature distribution during cooling of cylindrical steel probes (25 mm diam by 100 mm) in the case of slow non-Newtonian wetting and explosive Newtonian wetting

Pull stress

TA

Push stress

TA

B Disturbance A

A

B Interior M1

B

A

Fast

Exterior B

M1 B

Slow

Quench Oils

● Conventional (nonaccelerated) oils or cold

Stretch

A

Fluidized-bed quenching processes may be used as safer and more ecologically acceptable alternatives to molten-metal or molten-salt quenching systems. A fluidized bed is generated by blowing a gas (e.g., nitrogen, argon, carbon dioxide, helium, or hydrogen) through a solid support. Examples of solid supports include aluminum oxide, iron, copper, and molecular sieves (Ref 52). Generally, aluminum oxide provides the best heat-transfer capacity, thermal stability, and environmental compatibility. Particle size also contributes substantially to cooling properties. In general, cooling rates increase as alumina grain size increases. The lowest limit of particle size is 40 mesh (Ref 50). Fluidized-bed temperature can also affect heat-transfer rates. As expected, cooling rates decrease with increasing bed temperature, as shown in Fig. 52 (Ref 53). Traditionally, the most common gases for fluidized beds were nitrogen and air. However, other gases, such as hydrogen and helium, provide even greater potential for wider ranges of heat-transfer rates. The heat-transfer flow rates of hydrogen, helium, and nitrogen as a function of flow rate is shown in Fig. 53 (Ref 53). Reynoldson (Ref 54) has shown that it is possible to obtain cooling rates between those achievable by a mineral oil and by a low-pressure gas quenching system using air-fluidized beds.

Most quench oils are derived from petroleum oil basestocks, and the hydrocarbon fractions are classified as paraffinic, naphthenic, and aromatic. The ratio of these hydrocarbon components in the petroleum basestock used to formulate a quench oil determines the viscosity, viscosity-temperature, surface wetting, sludging, staining, and fire-resistant properties. Quench oils are selected on the basis of their ability to mediate heat transfer during quenching. Quench oils are usually classified on the basis of their quenching speed and application temperature as:

A1

Elongation

Elongation

A1

Fluidized Beds

oils

Temperature

B

C

Pull cracking

Push cracking Interior A

B

Stretch

Disturbance Pull

Exterior B

Uneven surface cooling (a)

Fig. 41

C

Ms

Ms

Fast A

Temperature

Push

Uneven body cooling (b)

Mechanisms that explain the generation of (a) pull stress and pull cracking and (b) push stress and push cracking

● Accelerated oils ● Marquenching oils or hot oils

Although there are other classifications such as fast, superfast, and water emulsifiable, the above three classifications are the most commonly encountered. Conventional quench oils are typically mineral oils, which may contain antioxidants to reduce the rates of oxidative and thermal degradation. Most of these oils have viscosities of up to 100 to 110 SUS (Saybolt Universal Seconds) at 40 C (100 F), although some have viscosities of up to 200 SUS at 40 C (100 F). Conventional quenching oils do not contain additives to increase cooling rate.

264 / Residual Stress During Hardening Processes Accelerated quenching oils are formulated from basestocks used for conventional quenching oils and are used at comparable temperatures. In addition to antioxidants, accelerated quench oils contain additives that enhance the wetting process during the quench, which results in reduced-film boiling as shown in Fig. 54. These oils are used with crack-sensitive, lower-hardenability steels. Martempering oils are used at temperatures between 95 and 230 C (200 and 450 F). They are usually formulated using solvent-refined oils with a very high paraffinic fraction to optimize oxidative and thermal stability, which is necessary in view of their high use temperatures. Stability is also enhanced by the addition of antioxidants. Because martempering oils are used at relatively high temperatures, a protective, nonoxidizing environment is often employed that allows them to be used much closer to the flash point than otherwise possible under open-air conditions. Nonaccelerated and accelerated martempering oils are available. The quench severity of accelerated and nonaccelerated quench oils is relatively insensitive to bath temperature as shown in Fig. 55 (Ref 55). However, agitation does significantly impact the performance of a quench oil as illustrated in Fig. 56 (Ref 54).

Aqueous Polymer Quenchants

Water Water is a relatively inexpensive and available quenchant that has been used for many years. The quenching properties of water are shown in Fig. 60, which shows (Ref 50):

quenching, higher cooling rates may increase the potential for distortion and cracking (Ref 50). The cooling power of brine solutions is not significantly affected by small variations in bath temperature. Although a brine can be used near the boiling temperature of water, maximum cooling rates are obtained at about 20 C (70 F).

Cracks are not formed

Cracks are formed

PSC φ

PSC

● Cooling times increase with increasing water

temperature. ● The maximum cooling rate decreases with increasing water temperature. ● The temperature where the maximum cooling rate occurs decreases with increasing bath temperature. Although the quenching properties of water are highly variable and very sensitive to thermal gradients in the water surrounding the cooling metal, particularly at areas of varying cross-section size and other stress risers, what is not seen in Fig. 60 is the fact that the film-boiling process is unstable and highly variable and that water does not rewet steel in a uniform manner during the quench. These variations produce high surface thermal gradients and often increasing distortion and cracking. It is interesting to note that the addition of 5 to 7% of an aqueous polymer quenchant will provide more uniform wetting properties without a significant decrease in cooling rates, which will result in great reductions in cracking and distortion (Ref 50).

A

A B

PSC

A

A−A B−B Rotate

B A−A View A

PSC A

PSC

PSC Immersion of cylindrical parts in a quenchant. The dashed horizontal lines indicate the level of the liquid; the vertical arrows indicate the direction of immersion of the part. PSC indicates the perimeter of the stress concentrator.

Fig. 43

Brine and Caustic Solutions The term “brine” refers to aqueous solutions containing various concentrations of salts such as sodium chloride. The cooling rates provided by brine are higher than that provided by water at the same temperature. Although the presence of salts will decrease the propensity for film boiling and soft spots often accompanying water

Compressed air

800

Temperature, °C

Aqueous polymer quenchants are aqueous solutions of a water-soluble polymer, the most common examples of which include: polyalkyleneglycol, polyvinylpyrrolidone, polyethyloxazoline, polysodium acrylate, and an additive to provide corrosion protection. Quenchant performance is due to polymer selection and solution viscosity. These quenchants are being used increasingly to replace conventional and accelerated oils because of their reduced cost, fire safety, and relatively low environmental impact. Typically, quench severity decreases with increasing quenchant concentration, increasing bath temperature, and decreasing agitation rates. This is shown in Fig. 57 for a polyalkylene glycol quenchant (Ref 56). As shown in this figure, it is possible to obtain quench severities analo-

gous to a slow oil to those faster than water by adjusting these variables. Of course, this also means that to minimize stresses from nonuniform quenching it is necessary to optimize agitation and control bath temperature and polymer concentration during use. The effect of bath temperature and agitation on the ability to through harden steel is shown, for one polymer quenchant, in Fig. 58 and 59, respectively.

600 Still air 400

(a) 200

0

0

10

20

30

40

Cooling rate, °C/s

Fig. 42

Comparison of cooling capacity of still and compressed air. Solid line, still air; dashed line, compressed air

Fig. 44

(b) Two forms of quench cracking: (a) pull cracking and (b) push cracking

Hardening by Reheating and Quenching / 265 fer coefficient. The Grossmann number (H) is defined as:

The most common alternative to NaCl brine solutions is aqueous solutions of NaOH (caustic). The addition of NaOH produces slower cooling rates than NaCl brines in the martensitic transformation temperatures for many steels (350 C, or 600 F) which would be expected to reduce cracking propensity as shown in Fig. 61 (Ref 50). Interestingly, the maximum cooling rate occurs at about 10% salt concentration for both NaCl and NaOH.

H ⳱ h/(2k)

where k is the conductivity of the metal. Thus, the H value is equal to the interfacial heat-transfer coefficient divided by twice the thermal conductivity of the metal. When the H value is multiplied by the dimensions of the body, their product corresponds to the well-known dimensionless Biot number (Bi) (Ref 57):

Measurement and Evaluation of Power of Quenching Media

Bi ⳱ HD ⳱ hD/(2k) ⳱ hR/k

When designing a quenching process, it is important to consider quenchant selection, quench severity, and quench uniformity. Quench severity is defined as: the ability of a quenching medium to extract heat from a hot steel workpiece. Heat removal from workpieces during quenching can be quantitatively described in terms of the interfacial heat-transfer coefficient. The heattransfer coefficient is defined as:

where D and R (⳱D/2) are the diameter and the radius of the cylindrical or spherical workpiece or, correspondingly, the thickness and halfthickness of the plate. The Biot number compares the relative magnitudes of surface heat transfer and internal conduction resistance to heat transfer. A very low value of the Biot number means that internalconduction resistance is negligible compared with surface heat-transfer resistance. This in turn implies that the temperature will be nearly uniform throughout the workpiece. Therefore, the magnitude of the Biot number shows the nonuniformity of temperature distribution throughout the body of the workpiece during quenching (Ref 57). The most significant deficiency of the H value is the incorrect assumption that cooling occurs at a constant rate during quenching. Even with the well-known limitation, the H value has been widely accepted by heat treaters. The Grossmann H values for commonly used quenching media are shown in Table 8.

h ⳱ Q/[A(Tp ⳮ T1)]

where h is the heat-transfer coefficient, Q is the heat flow from the workpiece to the quenchant, A is the surface area of the workpiece, Tp is the workpiece surface temperature, and Tl is the quenchant temperature.

Grossmann Number In steel quenching, the Grossmann number (Ref 26) is used more widely than the heat-trans-

Water

Cooling-Curve Analysis The cooling-curve tests with some metallic probes have been used as the most useful means of testing the cooling power of liquid quenchants such as oils, water, and polymer quenchants. The cooling curves are usually obtained by quenching a test specimen instrumented with thermocouples and measuring the temperature as a function of time at specific points within the specimen. The testpieces used are cylinders, plates, and spheres; the most common is a cylinder with a length three to four times its diameter and with a thermocouple located at its geometric center. There are several standard cylindrical specimens (standard probes). From the time-temperature curve of the standard probe, one can calculate the temperature/ cooling rate curve, the heat-transfer coefficient curve, and the heat flux curve. Several characteristic parameters that can be obtained from these curves are the maximum cooling rate, the cooling rate at 300 C (572 F), the characteristic temperature (the minimum temperature of film boiling), the temperature at the maximum cooling rate, cooling time from 800 to 400 C, and so forth. In order to harden steel, the maximum cooling rate and the temperature must be sufficiently high to minimize ferrite and pearlite transformation. The cooling rate at 300 C (572 F) can be used to indicate the probability of distortion and cracking because it is near the martensite temperature of most carbon and low-alloy steels.

Cooling-Curve Test Methods The most common method in use throughout the world to evaluate the cooling properties of quenching oils is cooling-curve analysis. Cooling-curve analysis provides a cooling time versus temperature pathway, which is directly pro-

Fluids

Polymer Oil Salt Nitrogen

Helium

40 bar 20 bar

Gases

3

10 6

1000

30 20

10

Single component

Nitrogen

Helium

6 bar 3 1

0

Temperature, °C

Load

10 bar 5

1

1200

Hydrogen

6 bar 3

2 1000

600

6 bar

Argon 400

3 2

2000

800

Helium 200 Hydrogen

Hydrogen 3000

4000

0

Heat-transfer coefficient, W/m2 • K

Fig. 45

Nitrogen

Comparison of the heat-transfer coefficients achievable with different gas quenching media for bulk-loading and single-component quenching

6

12 18 24 30 36 42 48 54 60 Time, min

Fig. 46

Comparison of cooling properties of common gases


Cross-section size Steel type

mm

in.

Hardness, HRC Martempering

Austempering

35–65 35–65 63

35–55 35–55 …

Low-alloy steel 13 0.5 Alloy steel 100 4.0 Cast iron 13 0.5

100

100

80

Cooling time, min

Cooling time, min

80

60

40

Diameter, in. (by 3 diameters long)

3 3000 rpm 2 2000 rpm 1000 rpm

1

400 400 °F F (205 °C) C) 0 0

1

2

3

4

5

6

7

8

9

10

Time, min 3 Diameter, in. (by 3 diameters long)

Table 11 Martempering (marquenching) versus austempering for various steels

or another preferred temperature (Ref 58). The temperature inside the probe and the cooling times are recorded at selected time intervals to establish a cooling curve (temperature-time curve). The cooling rate is derived from the temperature-time curve. JIS K 2242. The cylindrical silver probe (Fig. 63) was adopted and set in 1965 for the JIS method (Japanese industrial standard K 2242) (Ref 60), because silver does not exhibit phase transformations or surface-oxidation effects on the cooling curve and it also exhibits a high thermal sensitivity. However, the considerably different thermal conductivity from that of steel, the difficulty of preparing the delicate surface thermocouple assemblies, and the poor mechanical strength have been cited as disadvantages. Furthermore, the JIS silver probe is not appropriate for water and polymer quenchants, because water or polymer quenching of the JIS probe significantly decreases the lifetime of the silver-alumel thermocouple. Therefore, a modified silver probe (Fig. 64) is used for polymer quenchants

3000 rpm 2000 rpm

2

1000 rpm 1 500 500 °F F (260 °C) C) 0 0

1

2

3

4

5

6

7

8

9

10

Time, min 3 Diameter, in. (by 3 diameters long)

portional to physical properties, such as hardness of quenched steel parts. The results obtained by this test may be used as a guide in selecting heat treating oil or comparing the quench severities of different heat treating oils, new or used. ASTM D 6200 and ISO 9950. Cooling-curve analysis of quenching oils according to ASTM D 6200 (Ref 58) and ISO 9950 (Ref 59) is conducted using the Inconel 600 alloy probe (Fig. 62). The probe is heated to 850 C (1562 F) in an electric furnace and then immersed in at least 700 mL of the quenching oil, typically at 40 C,

3000 rpm 2000 rpm 2

1000 rpm

1 600 600 °F F (315 °C) C) 0 0

1

2

3

4

5

6

7

8

9

10

Time, min 60

Fig. 49

Effect of agitation on the quench severity of molten salt

40

20

20

50 0

0

4000

8000

12000

0

16000

Volumetric flow rate, ACFM

0

20

40

60

Cooling rate calculated from temperature curve measured in the center of a 25 mm diam steel specimen

80

Chamber pressure, PSIG (b)

(a)

(a) Effect of volumetric flow rate at constant density on cooling time. (b) Effect of chamber pressure at constant volumetric rate on cooling time

Areas of low heat transfer Cold spots formed

360° cooling

Maximum cooling rate, K/s

45

Fig. 47

1 vol% water added 40 Without water addition

35

30 (a)

(b)

Effect of gas flow pattern on quench uniformity. (a) Gas-injection nozzles with flow perpendicular to the workpiece. (b) Gas-injection nozzles with flow horizontal to the workpiece. (c) Combination of horizontal and vertical flow

Fig. 48

0

(c)

0.3

0.6

Agitation rate, m/s Maximum cooling rate of a hot-salt bath (Degussa AS-140) at 200 C (390 F) as a function of agitation and percentage of water added

Fig. 50

Hardening by Reheating and Quenching / 267 (Ref 61). It is the same shape as the JIS probe, and it is equipped with a metal-sheathed Chromel-Alumel (CA) thermocouple (K type) (1.0 mm outer diameter, 0.2 mm wire diameter) at these geometrical centers instead of the silveralumel thermocouple of the JIS probe.

Techniques for Estimation of HeatTransfer Coefficient To evaluate the cooling power of quenchants more qualitatively, the surface heat-transfer co-

55

55 With water addition

Without water addition

5 50

50

16 mm

efficient and/or the surface heat flux during quenching are estimated from the measured cooling-curve data of standard probes. The surface heat-transfer coefficient or the surface heat flux is necessary as the surface-boundary condition for computer simulation of the quenching process. Some practical techniques for estimation of the surface heat-transfer coefficient and surface heat flux have been proposed. The lumped-heatcapacity method (Ref 62) is a classical and simple method for the determination of the surface heat-transfer coefficient and the surface heat flux during quenching. This method provides accurate heat-transfer coefficients from quenching data obtained from silver probes that have high thermal conductivity (Ref 63–65). On the other hand, inverse methods are more suitable for estimating the heat-transfer coefficients from quenching data obtained using the Inconel 600

alloy probe, because of its low thermal conductivity (Ref 63–65). The lumped-heat-capacity method can be used if an assumption of uniform probe temperature during cooling can be justified (Ref 63– 65). If the probe temperature is uniform, the heat loss from the probe Q is equal to the decrease in the internal energy of the probe: Q ⳱ hA(Tp ⳮ T1) ⳱ ⳮcqV(dTp /dt)

where h is the heat-transfer coefficient on the probe surface, A is the surface area of the probe, Tp is the probe temperature, Tl is the quenchant temperature, c is the specific heat of the probe material, q is the specific density of the probe material, V is the volume of the probe, and t is time. So, dTp /dt is the cooling rate of the probe. If the quenchant temperature around the probe Tl is uniform, the next relationship is derived from Eq 1:

45

3

4

2 40

40

35

35 1

30

30 3/ 4 R 1/ 2 R 1/ 4 R

C

1/ 4 R 1/ 2 R 3/ 4 R

H2

Fig. 51 Influence of agitation rate and water addition on hardness distribution in 50 by 200 mm (2 by 8 in.) AISI 4140 steel bars quenched in a hot-salt bath (Degussa AS-140) at 200 C (390 F). Agitation rates and water additions: 1, 0 m/s, 0 vol%; 2, 0.3 m/s, 0 vol%; 3, 0.6 m/s, 0 vol%; 4, 0.6 m/s, 1 vol%; 5, 0.6 m/s, 2 vol%

(Eq 2)

where q is the heat flux on the probe surface. Here, probe weight qV is constant, but c and A change with temperature. If the change of the surface area of the probe A is ignored, only the temperature dependence of the specific heat c (Eq 2) need be considered, and then:

He

200

q ⳱ h(Tp ⳮ T1) ⳱ ⳮc(Tp)(qV/A)(dTp /dt) 100

0

2

4

6

8

10

12

14

16

Fluidizing flow Minimum fluidizing flow

Fig. 53

(Eq 3)

where c(Tp) is the specific heat as a function of probe temperature Tp. Thus, the heat flux q and/or the heat-transfer coefficient h can be directly calculated from the cooling rate dTp /dt (Ref 64, 65). Figure 65 shows heat-transfer coefficients calculated with the lumped-method and cooling-curve data of the JIS silver probe quenched in different quench media.

N2

0

50 mm diam

q ⳱ h(Tp ⳮ T1) ⳱ ⳮ(cqV/A)(dTp /dt)

300 Heat transfer (600 °C), Btu/h • ft2 • °F

47 HRC



4 mm 45

(Eq 1)

Effect of fluidized gas on heat transfer

1600

1400

7

1200

5 Cooling rate 800 500 °C

4

Temperature, °F

Cooling rate, °C/s

6

3 2

Cooling rate 800 300 °C

0

100

Fused salt 500 °F F

Martempering oil 500 °F F

1000

Molten metal 500 °F F

800

600

1 0 −100

Conventional quench oil 150 °F F

200

300

400

500

Fluidized bed temperature, °C Effect of fluidized-bed temperature on cooling rate between 800–500 C (1470–930 F) and 800–300 C (1470–570 F) measured with 75 by 100 mm (3 by 4 in.) 90MoCrV8 steel sample; temperatures measured at the center of the section

Accelerated quench oil 150 °F F

400

Fig. 52

200 0.7

1.0

1.5

2

3

4

5

7

10

15

20

30

40

Time, s

Fig. 54

Comparison of cooling-curve performance of accelerated versus a nonaccelerated quench oil

60

268 / Residual Stress During Hardening Processes The numerical inverse methods require techniques that decrease instabilities due to excessive sensitivity to measurement errors and noise. The accuracy of the solutions obtained by the numerical inverse methods may be questionable because of various conditions in the numerical calculation including: time step, spatial step size, magnitude of noise, error in measured data, and so forth. Furthermore, the accuracy is not achieved for all cooling stages in quenching, unless these conditions are appropriately set for each stage. One of the numerical inverse methods is the solution of the inverse heat conduction problem (Ref 66, 67). Another method is the iteration method, which utilizes both the lumped-heat-capacity method and a two-dimensional inverse method with the least residual procedure (Ref 64, 65). The calculation procedure is:

1. The initial values of heat-transfer coefficients are approximately calculated by a lumpedheat-capacity method from the cooling-curve data of the probe. 2. The total temperature region of the cooling process is divided into about 20 subregions and the initial heat-transfer coefficients are defined as stepwise continuous functions in each region. 3. The cooling curve is calculated by a two-dimensional finite difference method using these coefficients as the surface-boundary condition. 4. The residual sum of squares between the measured temperatures Texp and the corresponding calculated temperatures Tcal is given as R ⳱ (Texp ⳮ Tcal)2. 5. The cooling curve is calculated again after changing the heat-transfer coefficients. 6. The iteration of 3, 4, and 5 is performed until Tcrit {R/n}1 / 2 is satisfied.

16 Strong agitation Moderate agitation No agitation

15

Cooling rate at 550 °C, °C/s

14

where Tcrit is a critical value of the temperature difference between the measured temperatures and the corresponding calculated temperatures and n is the number of data Texp in the subregion. An iterative technique to minimize R is used. The same procedure is repeated in each subregion in the whole cooling process. Figure 66 (Ref 65) illustrates an example of heat-transfer coefficients calculated with the inverse method and cooling-curve data obtained using an ISO Inconel 600 alloy probe quenched in various quenchants. Heat-transfer coefficients that were calculated from the cooling-curve data of the JIS probe are also shown in Fig. 66. The lumped-heat-capacity method program “LUMPPROB” (Ref 63) was used for the JIS silver probe, and the inverse method program “InvProbe-2D” (Ref 64, 65) was used for the ISO

13 12 11 10 9 8 7 6 5

0

Fig. 55

4

8 12 16 20 24 Distance from surface, mm

28

Effect of agitation of a quench oil on the ability to through harden steel

probe. The values of the heat-transfer coefficients in the convection-cooling stage (the lower-temperature region) are almost the same for each quenchant, despite the differences of the sizes and the materials of these probes. However, the values in the higher-temperature region are very different for each probe. This is caused by the difference of the thermal properties between the JIS probe and the ISO probe.

Wetting Behavior and Nonuniform Quenching It is well known that the wetting process on the surface of hot metal affects cooling characteristics during water, polymer, and oil quenching (Ref 40). If the initial temperature of hot metal is sufficiently high, a vapor film is formed on the surface immediately upon immersion. After vapor blanket cooling stage (film boiling), a collapse of the vapor blanket (i.e., wetting) occurs progressively or explosively. The progressive wetting during quenching could increase nonuniform cooling because the heat-transfer coefficient on the nonwetted surface is significantly lower than that on the wetted surface. Hence, the wetting behavior is a major factor in cooling, and it affects quench distortion of steel parts. Cooling-curve analysis provides relatively little information about the wetting process. The temperature in the center of the probe at the transition point from lower to higher cooling velocity only describes the wetting of the nearest surface point and gives no information about the wetting process on the entire surface of the probe. The following techniques are employed for measuring the wetting process.

140

900

0.4

Predicted hardness for a quench oil (25 mm, or 1 in. bar)

0.6

135

800

0.4

700

Temperature, °C

600 15.7 HRC, 43 °C (110 °F), FPM = 0 31.5 HRC, 43 °C (110 °F), FPM = 100 16.6 HRC, 88 °C (190 °F), FPM = 0 32.1 HRC, 88 °C(190 °F), FPM = 100

500 400

Bath temperature, °F

130 0.6

125

0.8

120 0.6 115 0.8 1.0

110

300 Flow rate = 0 200

1.0 Flow rate = 100

100 15

100 0 1E − 2

1E − 1

1E + 0

1E + 1

1E + 2

1E + 3

1E + 4

1E + 5

1E + 6

1E + 7

Time, s

Fig. 56

0.8

105

Relative insensitivity of the ability of a quench oil to harden steel with respect to varying bath temperature. FPM, flow rate

Circ rate = 50 Circ rate = 75 Circ rate = 100

17 19 21 23 Polymer concentration, %

25

Effect of variation of quenchant concentration, agitation rate, and bath temperature on the Grossmann H value for one polyalkylene glycol quenchant. Circ rate in ft/min. Note: these curves vary greatly for each polymer quenchant; therefore, these data are for general illustrative purposes only.

Fig. 57

Hardening by Reheating and Quenching / 269 Measurement of Wetting Kinematics Direct Observation with Video or Photographs. For transparent quenchants, the surface wetting process may be observed by video or photographically. Images captured on videotape or sequential photographs provide detailed information about the wetting process. Figure 67 (Ref 68) shows examples of the wetting behavior and change of wetting distance Lf with time, during water, polymer, and oil quenching of the stainless steel disk specimen (30 mm diameter by 10 mm thick). A progressive collapse of the vapor blanket from the sharp edges was observed in water and oil quenching, while an instantaneous collapse occurred in polymer quenching. Wetting length Lf versus time t was estimated from the video images. The t-Lf curves provide wetting velocity, time when wetting starts (ts), and time when wetting is finished (tf). Temperature Measurement. The current method for examining the wetting process is to measure cooling curves by inserting thermocouples in near-surface positions along the specimen surface. Figure 68 (Ref 68) shows cooling curves during water, polymer, and oil quenching of the stainless steel disk specimen (30 mm diameter by 10 mm thick) without agitation. Temperatures were detected by metal-sheathed thermocouples attached to the specimen. Figure 69 shows the positions of metal-sheathed thermocouples for the measuring cooling curves. Thermocouples were inserted tightly into holes drilled to the geometrical center A and positions B, C, and D near the specimen surface. Basic information can be derived from the near-surface cooling curves. A period of slow cooling and a subsequent period of fast cooling are equivalent to a period of nonwetting cooling stage (vapor blanket stage) and nucleate-boiling stage. The transition point indicates the transition from film boiling to nucleate boiling at the thermocouple location. The onset and conclusion of wetting, and thus the velocity of wetting front, can be calculated by extrapolating the local transition times to the starting and finishing positions of the wetting.

Conductance Measurement. Another method for determining the wetting process is to measure the electrical conductance between the specimen and an electrode immersed in the quenchant (Ref 69) (Fig. 70). When a vapor blanket forms around the entire specimen surface, the conductance between the specimen and the electrode is low. When the vapor blanket collapses on the specimen surface, the conductance increases as shown in Fig. 71. The increase in the conductance is approximately proportional to the wetted portion of the specimen surface. The conductance is at its highest value when the entire sample surface is completely wetted. Conductance-time curves provide the time when wetting starts (ts) and the time when wetting is finished (tf).

Effect of Process Variables on Cooling Behavior and Heat Transfer The quenching of steel requires a wide variation and sufficient reproducibility of heat transfer in order to achieve the required cooling rate, which is dependent on the hardenability of the steel and the section size of the workpiece. Therefore, it is important to recognize the influence of the variables during quenching. Heat transfer during quenching is affected by many factors, such as the quenchant, bath temperature, agitation, and the dimensions and shape of the workpiece being quenched. Only a few of these factors can be realistically varied, including bath temperature, agitation rate, and the quantity and racking arrangement of the workpieces.

Effect of Quenchant Selection The selection of quenchant is the most basic factor that affects cooling behavior. When selecting a quenchant, it is important to consider quench severity and quench uniformity. The cooling curves in Fig. 72(a) were obtained using a 10 mm diam silver specimen

1000

1000 30 °C C

800 40 °C C

Temperature, °C

Temperature, °C

800

600 50 °C C 400 30 °C C 200

0

Fig. 58

5

50 °C C

600

40 °C C 400

750 0 m/s 500

0.3 m/s 0.6 m/s

250

200

20 °C C

0

C 20 °C Temperature (TC), °C

1000

quenched in various quenchants without agitation. Different cooling curves were obtained for each quenchant. A lumped-heat-capacity method was used to estimate heat-transfer coefficients from these cooling-curve data. These coefficients are shown in Fig. 72(b). In general, the cooling curve during water, polymer, and oil quenching has three stages (stage A: vapor blanket cooling (film-boiling) stage, stage B: nucleate-boiling stage, and stage C: convection-cooling stage). Heat-transfer coefficients in the high-temperature region (vapor blanket stage) are relatively low. Cooling curves of workpieces quenched into nonvolatile quenchants such as molten salt, liquid metal, and gas, do not exhibit vapor blanket cooling or nucleate boiling. The wetting behavior in the quenching of hot metal is affected by quenchant properties such as the type of quenchants, quenchant temperature, and so forth. As shown in Fig. 67, in water and oil quenching, the vapor blanket was formed around the entire surface of the specimen immediately after immersion and then ruptured progressively from the sharp edges to the center of the flat surface of the disk specimen. The progressive collapse of the vapor film begins immediately after immersion in water. The progressive collapse starts after the formation of a stable vapor blanket stage in oil quenching. The time of duration varies according to the oils used. The starting time of the wetting during polymer quenching depends on the type of polymer used, polymer concentration, and liquid temperature. Wetting starts immediately upon immersion for some aqueous polymer solutions and after the formation of a stable vapor blanket stage for other polymer quenchants. The wetting velocity (the propagation velocity of wetting front) during water or oil quenching is significantly slower than during polymer quenching. Such a slow wetting velocity could cause a nonuniform surface cooling in the specimen, because the heat-transfer coefficient on the nonwetting surface is significantly lower than that on the wetting surface. Figure 68(a) shows the cooling curves at representative positions

0 10 Time, s

15

20

0

0

Effect of bath temperature on the ability to through harden steel

50

100 150 Cooling rate, °C/s

0

200

Fig. 59

15

30 Time (t ), s

45

60

Effect of agitation rate on the ability to through harden steel


In the vapor blanket stage during water, polymer, and oil quenching, heat is transferred across

1000

1800

Temperature, °C

800

600

NaOH

14

NaCl

2.8

2.5

12

2.1

10

1.8

8

0

Fig. 61

5

10 15 20 Salt concentration, %

1.4 25

Effect of salt concentration on the heat-transfer coefficients of NaCl and NaOH brine solutions

1600 1400 1200 1000 800

400

16

Temperature, °F

Water temperature: 40 °C 50 °C 60 °C 70 °C 80 °C 90 °C

fer depends on the temperature difference between the quenchant and the surface of the workpiece. It also depends on quenchant viscosity, which governs the convection flow of the quenchant around the workpiece. The effect of water temperature on cooling curves of a 12.5 mm diam by 60 mm Inconel 600 probe is shown in Fig. 60. By decreasing

Heat transfer coefficient (α), (Btu/ft2 • h • °F) × 10−3

Effect of Quenchant Temperature

the surface through the vapor blanket by conduction, radiation, and convection. When the surface temperature of the workpiece decreases, the thickness of the vapor blanket is reduced until the liquid contacts the hot surface of the workpiece. This is the start of the wetting process. By direct contact with the surface, the vapor film begins to collapse, dramatically increasing the heat flux and the cooling rate. By increasing liquid temperature, the energy required for evaporation is reduced and the thickness of the vapor film increases. As a result, both the cooling rate and the heat-transfer rate decrease. In addition, by stabilizing the vapor blanket, the transition temperature from lower to higher cooling rate (the minimum temperature required for film boiling) decreases. Once wetting has begun, heat transfer by nucleate boiling controls the cooling rate. This stage is also dependent on quenchant temperature. In the convection-cooling stage, heat trans-

Heat transfer coefficient (α), mW/m2 • K

and the temperature differences between these positions during water quenching. Cooling immediately upon immersion is very rapid on the edges (position D), and the difference of the surface temperature, TB ⳮ TD, is very large (about 500 C at maximum). Instantaneous collapse of the vapor blanket occurs in polymer quenching. Wetting velocity after the start of the breakdown of the vapor film is very high. Such wetting behavior could reduce the nonuniformity of surface cooling of a specimen. Figures 68(b) and (c) show that the differences of the surface temperature (TB – TC and TB ⳮ TD) during polymer quenching is smaller than that in water quenching (Fig. 68a) or oil quenching (Fig. 68d).

Termination φ 12.5 φ 9.5

600 400

200

Support tube

200 0

0

10

20

30 Time, s

40

50

60 φ 1.5

(a)

1000

100

150

6

Cooling rate, °F/s 50

250

200

30°

1800

1000 800 Water temperature: 40 °C 50 °C 60 °C 70 °C 80 °C 90 °C

200

0

20

40

60

80 100 Cooling rate °C/s

120

140

≥200

r 0.75

600 400

30

400

φ 1.5 mm sheathed thermocouple ≥160

1200

Temperature, °F

Temperature, °C

1400

600

0

30

1600 800

Probe 200 160

(b)

Fig. 60

Effect of water bath temperature on heat removal using a 12.5 mm diam by 60 mm Inconel 600 probe with a flow velocity of 0.25 m/s (50 ft/min)

ISO Inconel 600 alloy probe. International standard, ISO 9950. r, radius; ␾, diameter. Dimensions given in mm. Source: Ref 59

Fig. 62


Insulating tube Supporting rod

Silver wire Silver pipe

30

Heatresistant insulator 10

M6 × 1 φ5

5

Almel wire φ3

15

Silver rod body

15 ± 0.1

Insulation tube

φ10 ± 0.1

Japanese industrial standard silver probe. JIS K 2242-1997. ␾, diameter. M6 ⳯ 1, metric fine screw thread. Dimensions given in mm. Source: Ref 63

Fig. 63

water temperature, the duration of film boiling decreases, which is indicated by the accelerated transition from slower cooling to faster cooling. In addition, cooling rates of the three different cooling stages are increased. Cooling curves during oil quenching are relatively insensitive to bath temperature as shown in Fig. 55. However, the temperature of an aqueous polymer solution does significantly impact on the cooling performance as shown in Fig. 58. Cooling curves of workpieces quenched by nonvolatile quenchants such as molten salt, liquid metal, and gas do not possess a vapor blanket and nucleate-boiling stage. Workpieces are cooled by radiation and convection of the quenchant. In this case, the heat-transfer coefficient depends on the temperature difference between the quenchant and the surface of the workpiece.

Effect of Agitation In addition to quenchant temperature, vaporfilm stability is greatly affected by quenchant agitation. A high flow velocity increases the heat transfer by convection and reduces the thickness of the vapor film. Furthermore, agitation of the liquid reduces the stability of the vapor/liquid interface by disturbing the liquid flow adjacent to the vapor film. Therefore, agitation reduces the duration of film boiling. Heat transfer in the convection-cooling stage directly depends on agitation. The effect of agitation on the heat transfer by nucleate boiling is not significant because nucleate boiling agitates the liquid adjacent to the boiling surface by itself (self-agitation effect). Figure 73 shows the effect of selected flow velocities (0–0.4 m/s) on cooling curves of a cylindrical silver probe (10 mm diameter by 30

mm, Fig. 64) quenched in 80 C oil. In the vapor blanket stage and convection stage, the temperature of the specimen decreases slowly and the cooling rates in these stages accelerate by the agitation. As the vapor film collapses, the temperature drops rapidly because of the transition from film boiling to nucleate boiling. This transition temperature from lower to higher cooling rates is almost unaffected by flow velocity. Figure 59 shows the effect of selected flow velocities (0, 0.3, and 0.6 m/s) on cooling curves in polymer quenching. In this case, the liquid flow around the workpiece reduces the stability of the vapor blanket. Therefore, the transition from lower to higher cooling rates may be strongly influenced by the liquid flow velocity, and the agitation reduces the duration of film boiling. The effect of agitation on the wetting process on a stainless steel disk (30 mm diameter by 10 mm thick) during water quenching is shown in Fig. 74 (Ref 68). Figure 75 shows the effect of agitation on the cooling curves of this stainless steel disk at the representative positions (shown in Fig. 69) and the temperature differences between these positions during water quenching. These results show that the agitation of water increases the wetting velocity and hence shortens the finishing time of wetting tf. However, the starting time of wetting ts in water quenching does not depend on the flow velocity because the wetting at the sharp edges always starts immediately after immersion (edge effect). As a result, the degree of nonuniformity of the surface cooling (see the values of TB – TD and TC – TD) during water quenching significantly is decreased by the agitation. Figures 76 and 77 (Ref 68) illustrate the effect of agitation on the wetting process and the cool-

Supporting rod 105

M6 5 φ5

5 15

Silver rod body

Water, 30 °C 10% polymer quenchant (PAG), 30 °C 10% brine, 30 °C Oil (JIS1-2), 80 °C Oil (JIS2-1), 120 °C Molten salt, 230 °C

105

Water (30 °C): JIS probe and LUMPPROB Water (30 °C): ISO probe and InvProbe-2D 10% PAG (30 °C): JIS probe and LUMPPROB 10% PAG (30 °C): ISO probe and InvProbe-2D Oil: JIS1-2 (80 °C): JIS probe and LUMPPROB Oil: JIS1-2 (80 °C): ISO probe and InvProbe-2D

5 × 104 Heat-transfer coefficient (h ), W/m2 • K

φ1.0 sheathed thermocouple


106

104

103

2 × 104 104 5000

2000 1000 500

200

15

100 0 102

0

61

Modified silver probe. M6, metric coarse screw thread. Dimensions given in mm. Source: Ref

400

600

800

1000

Surface temperature, °C

φ10

Fig. 64

200

Heat-transfer coefficients calculated with the lumped method and the cooling-curve data of the JIS silver probe quenched in representative quenchants

Fig. 65

200 400 600 800 Surface temperature (T ), °C

1000

Heat-transfer coefficients calculated with the lumped method and the cooling-curve data of the JIS silver probe or with the inverse method and the cooling-curve data of the ISO Inconel alloy probe. Source: Ref 65

Fig. 66


30 °C still water

TA − TB TB − TC TB − TD

TB (surface: B)

600

TC (surface: C) 400

TD (edge: D)

200

0

10

0

800

600

400

A B C D

15 7 7 1

200

800

0 30

20

TA (center)

TD (edge: D)

200

0

10

400

A B C D

15 7 7 1

200

0 30

20 Time (t ), s


TA (center) TB (surface: B)

600

TC (surface: C) TD (edge: D)

400

200

0

0

10

20

30

A B C D

40

800

600

400 15 7 7 1

50

200

80 °C still oil (JIS 1-2) T A − TB TA (center) T B − TC TB (surface: B) T B − TD TC (surface: C)


60 °C still 25% PAG

Temperature difference (∆T ), °C

(b)


600

TC (surface: C) 400

Time (t ), s

0 60

600

TD (edge: D) 400

A B C D

15 7 7 1

800

600

400

200

200

0

Time (t ), s

Fig. 68

800


TB (surface: B)

600

0

(a)

(c)

30 °C still 10% PAG

0

20

10 Time (t ), s

(d)

Cooling curves and variation of temperature difference during (a) water, (b) and (c) polymer, and (d) oil quenching of stainless steel disk

0 30



TA (center)


800


Change of wetting length with time on the surface of stainless steel disk specimen during water, polymer, and oil quenching. Quenchants: city water, PAG polymer aqueous solutions, and quenching oils. Source: Ref 68


Fig. 67

ing characteristics during polymer quenching where agitation of the polymer quenchant hardly affects the wetting velocity during quenching. Therefore, the degree of nonuniformity of the surface cooling during polymer quenching is not affected by the agitation. However, the starting time of wetting ts in still polymer quenching varies widely because the poor reproducibility of the formation and collapse of the vapor blanket without agitation. However, agitation of the polymer quenchant often prevents the formation of the vapor blanket and achieves the reproducible rapid cooling immediately after immersion. Figures 78 and 79 (Ref 68) show the effect of agitation on the wetting process and the cooling characteristics during oil quenching. Agitation of the quenching oil hardly affects the starting time of wetting ts, but increases the wetting velocity and shortens the finishing time of wetting tf. As a result, the degree of nonuniformity of the surface cooling during oil quenching is somewhat decreased by agitation. However, the effect of agitation on the cooling characteristics is insignificant, because the vapor blanket in oil quenching is stable in the high-temperature region where the temperature is greater than the transition temperature with or without agitation.

Hardening by Reheating and Quenching / 273 Furthermore, the transition temperature in oil quenching hardly depends on the flow velocity and the wetting at the sharp edges starts after vapor blanket cooling.

Effect of Surface Conditions In actual heat treating, the surface conditions of the parts vary due to oxidation, contamination, coating with other material, surface roughening, and so forth. Therefore, the effect of surface conditions on the cooling characteristics in quenching is very important. Surface Oxidation. As discussed in the section “Effect of Materials and Quench Process Design on Distortion” in this article, oxide scale affects cooling during oil quenching of steel parts, as shown in Fig. 30 (Ref 14). In general, light scale (thin oxide layers) increases the cooling rate in oil quenching, but heavy scale (thick oxide layers) retards the cooling rate. This phenomenon often occurs in water or polymer quenching.

10

1.5

Figures 80 and 81 (Ref 70, 71) illustrate the effect of surface oxidation of silver, nickel, stainless steel, and pure iron cylinders with hemispherical ends (without edge effect) on cooling curves during quenching in still water. These results show: ● Oxidation of a probe surface exhibits little ef-

fect on the cooling characteristics during vapor blanket cooling. ● Surface oxidation increases the lower-limit temperature of the vapor blanket stage. This tendency is more remarkable in the case of lower water temperature. ● The presence of a porous oxide layer on the surface results in a remarkable rise of the vapor blanket, the transition temperature from lower to higher cooling rate (the minimum temperature required for film boiling) because of the low thermal conductivity and large roughness of the oxide layer. A similar result was reported for spray cooling of a hot steel plate (Fig. 82) (Ref 72). It has been confirmed that this cooling acceleration effect with thin oxide layer is caused either by suppression of the vapor blanket formation or by acceleration of the collapse (destabilization of vapor blanket) by the existence of the oxide layer.

φ1.6 sheathed thermocouple

● Surface texture and roughness exhibit little

Specimen

effect on the cooling characteristics at the vapor blanket stage. ● Surface roughness causes the rise of the lower-limit temperature of the vapor blanket stage.

φ30 B 7

C

A

14 D 3

Unstable cooling phenomena due to surface oxidation were observed for water quenching of steel (Fig. 83). Unstable changes of the cooling rate during cooling were obtained due to flaking of the oxide layer (Ref 70, 71). Coating Effects. The presence of a low thermal conductivity layer such as oxides exhibits a remarkable influence on the cooling characteristics of hot metals, as described previously. Coatings of clay, glass, salt, and heat-resistant paint exhibit a similar effect. Figure 84 shows that a clay coating less than about 100 lm thick results in a cooling acceleration effect in water quenching of S45C steel cylinders. Such a phenomenon was observed at the full range of water temperatures (Ref 73). This effect is caused either by suppression of the vapor blanket formation or by acceleration of the collapse by the existence of the clay coating layer (Ref 71, 73). Kikuchi et al. (Ref 74) explained this phenomenon by considering the surface-temperature decrease during intermittent liquid-solid contact. Figure 85 illustrates a similar result for a clay coating on a silver probe (Ref 71, 73). In this case, the thicker the clay coating layer, the lower the cooling acceleration effect, because of the insulation effect of the clay layer. Surface Texture and Roughness. The effect of surface texture and roughness on the cooling characteristics in quenching is very important. Narazaki et al. confirmed the effect of the surface texture on the cooling curves of metallic specimen during quenching in still water (Ref 75). The results showed:

A similar result (Ref 72) has been reported for spray cooling of a hot copper plate (Fig. 86). It is presumed that these effects are caused by the destabilization of the vapor blanket, which results from microscopic liquid-solid contacts on the rough surface. Various effects of surface texture on cooling characteristics have been reported (Ref 71, 75, 76). Figure 87 shows the effect of surface finish on the cooling curves of a S45C steel specimen during polymer quenching (Ref 71, 76). In this case, the surface texture finished by lapping stabilizes film boiling. Sandblasted surfaces often cause a similar effect. These phenomena may be due to the stabilization of vapor film in liquidsolid contacts by recovering of vapor film, which is promoted by many homogeneous bubble nucleation cavities on the lapped sandblasted surfaces.

3

Steel disk specimen for measuring cooling curves. Dimensions in mm. Specimen: steel disk (30 mm diam by 10 mm thick). Thermocouple: metallic sheathed CA thermocouple (1.6 mm outer diameter). Measuring position: geometrical center (A) and 1.5 mm beneath surface (B, C, and D). Source: Ref 68

Fig. 69

Data scanning system: Temperature T Conductance G

Fluid Unwetted Wetted

Sample surface (a) Cooling curve of center of sample and variation of wetted surface area as a function of time during cooling of cylindrical chromium-nickel steel sample (15 mm diam by 45 mm long). (b) Photographs show the wetting behavior at times A, B, and C. TS and tS, respectively, are temperature and time of starting wetting; Tf and tf, respectively, are temperature and time of finishing wetting. Source: Ref 69

Fig. 71

Backplate electrode

Fig. 70 Measuring principle for determination of percentage of sample surface wetted during cooling of immersion-cooled samples. Source: Ref 69

Effects of Geometry Edge Effect. The shape of steel parts is a very important factor for water and aqueous polymer quenchants, but it is not as important for oils (see Fig. 88–90) (Ref 71). The initial rupture of the

274 / Residual Stress During Hardening Processes curve tests to avoid the influence of surface oxidation and phase transformation. The effect of specimen material on cooling characteristics in quenching has been reported (Ref 71, 76). Figure 91 illustrates surface heat-transfer coefficients obtained during oil quenching of cylindrical silver, nickel, and stainless steel specimens. The results show that the specimen material does not affect the heat-transfer coefficients in the vapor blanket stage and during the convection-cooling stage. However, the minimum temperature of the vapor blanket stage is affected by the specimen material. Similar results are confirmed in the case of water quenching of cylindrical silver, nickel, and stainless steel specimens with hemispherical ends (without edge effect) (Ref 71, 76). This phenomenon arises from instability of the vapor blanket on the surface of lower thermal

φ10 × 30 mm silver probe 80 °C quench oil (JIS 1−2)

800

600 500 400 300 200 100 0

0

2

1

3

Fig. 73



80 °C oil JIS 1-2

600

0

120 °C oil JIS 2-1

230 °C molten salt 30 °C water 30 °C, 10% polymer quenchant 30 °C 10% brine 0

1

2

3

4

Fig. 72

6

7

8

9

10

30 °C 10% brine 230 °C molten salt

30 °C water 104 120 °C oil JIS 2-1 103 30 °C, 10% polymer 102

5

0

200

80 °C oil JIS 1-2

400

600

800


Time (t ), s (a)

5

Effect of agitation on cooling curves in oil quenching. Probe: cylindrical silver probe (10 mm diam by 30 mm long). Quenchant: 80 C quench oil (JIS 1-2 type)

800

200

4

Time (t ), s

105

400

Still 0.1 m/s 0.2 m/s 0.3 m/s 0.4 m/s

700

Material Effects Heat-resistant materials such as silver, gold, platinum, stainless steel, nickel, Inconel alloy, and so forth are used as specimens for cooling-

conductivity of specimen. If the thermal conductivity of the specimen material is lower, destabilization and premature collapse of the vapor film occurs at a higher temperature because of the increase of the surface temperature drop by the intermittent liquid-metal contact during the vapor blanket stage. Steel chemical composition determines the thermodynamic parameters of the material, transformation behavior of austenite, and surface oxidation. Therefore, it affects cooling behavior during quenching. Latent heat of transformation from austenite into ferrite/pearlite bainite, or martensite also influences the cooling rate. The transformation temperature and the amount of latent heat depend on the chemical composition of the steel and the cooling rate. Thermodynamic properties of the material also have an effect on cooling behavior.

900


vapor blanket usually starts at sharp edges of steel parts, and wetting behavior is strongly influenced by the geometry of the edges (edge effect) (Ref 35, 40, 77). Figures 88(a) and 89(a) show that the edge shape of the ends of cylindrical specimens is very important in still water and polymer quenching. This arises from the instability and the premature collapse of the vapor blanket at the edges of both ends. However, cooling curves during oil quenching are not sensitive to the end or edge shapes of cylindrical specimens as shown in Fig. 90. This arises from the stability of the vapor blanket around the specimen during oil quenching. However, the effect of edge shape in water and polymer quenching can be eliminated by agitation as shown in Fig. 88(b) and 89(b), because agitation destabilizes the vapor blanket and eliminates the vapor blanket cooling stage independent of the edge shape. Effect of Size. Cooling becomes proportionately slower when the thickness of a workpiece is increased (mass effect). Therefore, rapid cooling of the core of a workpiece with large cross sections is impossible with any quenching media. In addition, cooling rates of the core are limited by the thermal diffusion in the workpiece. Size of a workpiece also affects the stability of vapor film on the surface of the workpiece and the wetting behavior. The velocity of wetting is reduced, and the time interval of wetting increases with increased section size. Vapor flow rate, vapor thickness, and quenchant temperature around the workpiece increases with the increasing workpiece size. As a result, surface heat transfer of a workpiece is influenced by the workpiece size.

(b)

Cooling curves of a silver probe and heat-transfer coefficients in quenching in representative quenchants. (a) Cooling curves of a 10 mm diam by 30 mm long silver probe. (b) Heat-transfer coefficients estimated with lumped-heat-capacity method


Effect of Cooling Characteristics on Residual Stress and Distortion from Quenching Steel quenching requires a wide variation in cooling rates to achieve the required hardness and strength, which is dependent on the hardenability of the steel and section size of the workpiece. At the same time, residual stresses, distortion, and crack formation must be minimized. However, these are often contradictory objectives. For example, although increasing cooling rates increases hardness, it often increases the potential for distortion, stress, and cracking. Similarly, distortion and stress during quenching are affected by many factors, such as the quenchant, the bath temperature, and agitation. The dimensions, shape, and material of the workpiece also influence the distortion, stress, and cracking.

Effect of Quenchant Selection The selection of quenchant is the most basic factor affecting the cooling characteristics of workpieces. Therefore, it is the basic factor to be considered for stress and distortion control during quenching. The selection of a particular quenchant depends on the quench severity desired. For example, water, brine, or lower concentrations of aqueous polymer solutions are used for plain carbon steels. Accelerated oils are used for lower-alloy steels. Conventional oils or higher concentrations of polymers are used for higher-alloy steels. Molten salts or liquid metals are often used for martempering (marquenching) and austempering. The dimensions and shape of the workpiece being quenched should also be considered in selecting a quenchant. Generally speaking, the thicker the workpiece, the more severe the quenchant. However, severe quenching often increases stress and distortion of the quenched

workpiece. For steel parts with thick and thin cross sections, the selection of a quenchant is more difficult. Many such shapes increase the nonuniformity of cooling and therefore increase the potential for stress, cracking, and distortion. Wetting during quenching in a volatile quenchant, such as water, oil, or aqueous polymer solutions, results in nonuniform (uneven) cooling of the workpieces producing high surface thermal gradients and often increasing distortion and stress. Many aqueous polymer quenchants will provide more uniform wetting properties, which will result in substantial reductions in cracking and distortion (Ref 68). Figures 92 and 93 show the distortion and residual stress of 30 mm diam, and 10 mm thick carbon steel disk specimens quenched in various quenchants without agitation. Different stress distributions and distortions were obtained for each quenchant. This is a result of the difference of the cooling power of each quenchant, which dominates the cooling path on the CCT curve and therefore the internal distribution of martensite and ferrite/pearlite. The wetting process on the surface of the specimen during water, polymer, and oil quenching also affects the stress and distortion. After vapor blanket cooling, a collapse of the vapor blanket (i.e., wetting) occurs progressively during water quenching. This results in a nonuniform cooling of a steel specimen and increases stress and distortion. However, if the vapor blanket collapses simultaneously or explosively, as in polymer quenching, the simultaneous collapse provides uniform quenching, which is effective for reducing stress and distortion. The results shown in Fig. 92 and 93 illustrate the effectiveness of uniform quenching using a polymer quenchant. Molten-salt and liquid-metal quenching also provide uniform quenching, decrease cooling rate, and nonuniformity of the temperature of a steel part because of the high quenchant temperature. These characteristics are effective for the reduction of stress, distortion, and cracking.

The cooling rate of a workpiece being quenched shows an inverse relationship with respect to the increasing thickness of the workpiece by mass effect. In addition, the cooling rates of the core are limited by the thermal diffusion in the workpiece. Therefore, stress and distortion during quenching are affected by the dimensions, shape, and material of the workpiece being quenched. Figure 94 (Ref 78) shows the axial stress development during water quenching of AISI 1045 steel cylinders. The 10 mm (0.4 in.) diam cylinder starts to transform to martensite at the surface, and the transformation front moves gradually inward, resulting in a typical tensile stress at the surface. The large-diameter cylinders first transform to ferrite/pearlite at intermediate radii and then to martensite at the surface. This causes two stress minima, seen in the dashed curves in Fig. 94(a) to (c). The final residual stress is compressive at the surface and tensile in the core. The relationship of stress to specimen diameter and quenching medium is summarized in Fig. 95 (Ref 78, 79). The difference between oil and water quenching decreases with increasing diameter.

Effect of Agitation As discussed in the section “Effect of Materials and Quench Process Design on Distortion” in this article, quench nonuniformity can arise from nonuniform flow fields around the part surface during the quench or nonuniform wetting of the surface. In addition, poor agitation design is a major source of quench nonuniformity. The purpose of the agitation is not only to increase cooling power of quenchant, but also to provide uniform cooling in order to suppress the excessive distortion and stress of quenched steel parts. Nonuniformity of the surface cooling during water quenching is decreased significantly by the

5

30 Still 0.3 m/s 0.7 m/s

Starting (t s ) and finishing (t f ) time of wetting, s

Wetting length (Lf ), mm

Workpiece Size Effects

20

10

Lf

t s : Starting time of wetting t f : Finishing time of wetting

4

3

2

tf 1

ts 0

0 0

1

2

3

0

Time (t ), s (a)

Fig. 74

0.3

0.7

Flow velocity (v ), m/s (b)

Effect of (a) agitation and (b) flow velocity on wetting process on the surface of stainless steel disk specimen (30 mm diam by 10 mm thick) during water quenching. Quenchant: 30 C city water. ␾, diameter. Source: Ref 68


0

0

10 Time (t ), s

20

600

TB (surface: B) 400

400


200

0

200

0

10 Time (t ), s

20


800

TA − T B TB − T C TB − T D



TA (center)

600

Lf

0

1

2

600

TB (surface: B) 400

400


200

0

200

0

10 Time (t ), s

20


TA (center)

800


TA (center)

600

0

800

T A − TB T B − TC T B − TD

600

TB (surface: B) 400

400


200

0

200

0

10 Time (t ), s

20

0

(b)


800

2

1

tf

0

TA (center)

600


800

600

TB (surface: B) TC (surface: C)

400

400

TD (edge: D) 200

200

ts

0

0

20

3

Time (t ), s

(a)



10

0

15 400 7 7 1 200

10 Time (t ), s

800

3

600

0

600

(a)

Still Still 0.3 m/s 0.7 m/s

20

0

(b) 800

200

30

(a) 800

400

0

0

TC (surface: C) TD (edge: D) A B C D


200

400 15 7 7 200 1

600

800


TD (edge: D) A B C D

400

TB (surface: B)


0.3 Flow velocity (v ), m/s

0

0.7

0

10 Time (t ), s

20


TC (surface: C)

TA (center)


600

Figures 100 and 101 show the effect of agitation of quenchants on the residual stresses on the side surface of 20 mm diam, 60 mm long carbon steel bars quenched in water and a polymer quenchant. Figure 100 shows that nonuniform surface cooling in still water quenching results in uneven residual stress distribution on the surface of the steel bar. Agitation of water results in even stress distributions except near the ends. In addition, the submerged and open spray cooling result in high compression stresses. Figure 101 shows the effect of agitation on stress distribution after polymer quenching. Agitation of polymer quenchant results in even stress distribution and high compression stresses except near the ends. However, still polymer quenching can also make even and high compression stress



TB (surface: B)

800 TA − TB TB − TC TB − TD 600

of the vapor blanket collapse on the surface. However, agitation of polymer quenchant does not decrease the quench distortion (Fig. 97) because the instantaneous and explosive collapse of the vapor blanket on the specimen surface occurs with and without the agitation. Figures 98 and 99 show the effect of agitation methods of quenchants on the quench distortion of 20 mm in diam, 60 mm long carbon steel bars quenched in water and a polymer quenchant. Figure 98(a) shows that nonuniform surface cooling in still water quenching results in uneven diameter of the steel bar. The increases of diameters near the ends of bars that were observed are attributable to heat extraction from the edges of the bar by edge effect. The upward flow of water decreases end effect, because the agitation reduces the nonuniformity of the surface cooling of the steel bar. The lateral submerged and open spray decrease the diameter and increase the length of steel bars, because the lateral flow causes the fast cooling of the side surface and the thermal shrinkage of diameter, which also results in the elongation in length of the steel bar (Fig. 98b). On the other hand, agitation of polymer quenchant hardly affects the quench distortion (Fig. 99) because the instantaneous and explosive collapse of the vapor blanket on the specimen surface definitely occurs with and without the agitation.


TA (center)

800


agitation (as shown in Fig. 75). Therefore, stress and distortion are largely affected by agitation. However, polymer quenchant agitation hardly affects the degree of nonuniformity of the surface cooling (as shown in Fig. 77) because of the explosive collapse of vapor blanket. Figures 96 and 97 show the effect of agitation of quenchants on the profile of the flat surface of the steel disk after quenching. Figure 96 shows that nonuniform surface cooling in still water quenching results in concaving of the steel disk specimen and the agitation of water significantly decreases the quench distortion in water quenching. This occurs because agitation reduces the nonuniformity of the surface cooling of the steel disk since agitation accelerates the propagation

0

(c)

(b)

(c)

Effect of agitation on cooling curves and temperature differences of stainless steel disk specimen during water quenching. Quenchant: 30 C city water. Flow velocity: (a) still, (b) 0.3 m/s, (c) 0.7 m/s. Source: Ref 68

Effect of (a) agitation and (b) flow velocity on wetting process on the surface of stainless steel disk specimen (30 mm diam by 10 mm thick) during polymer quenching. Quenchant: 30 C 10% PAG polymer aqueous solution

Effect of agitation on cooling curves and temperature differences of stainless steel disk specimen during polymer quenching. Quenchant: 30 C 10% PAG polymer aqueous solution. Flow velocity: (a) still, (b) 0.3 m/s, (c) 0.7 m/s

Fig. 75

Fig. 76

Fig. 77

A B C D

200

0

400

200

15 7 7 1

10 Time (t ), s

20

0

600

800

TB (surface: B) TC (surface: C) TD (edge: D)

400

600

400

200

0

200

0

10 Time (t ), s

20


400

600


TA (center)


800

TB (surface: B) TC (surface: C) TD (edge: D)

600

0


TA (center)


because the uniform cooling occurs with and without the agitation. Table 12 shows the effect of agitation on the frequency of quench cracking in water and polymer quenching of steel disks, the geometry and dimensions of which are shown in Fig. 102. The specimen in this case (30 mm in diameter by 10 mm thick) did not contain any notches; however, it contained an eccentrically located 10 mm diam hole. This specimen, used in the work of Owaku (Ref 1), was adopted by the Quench Cracking Working Group of the Japan Heat Treatment Society. Steel materials used were Japanese standard S45C, SK4, and SCM435. These results show that agitation of water largely suppresses the occurrence of quench cracking. On the other hand, quench cracking susceptibility to agitation of polymer quenchant is not clear because there is no crack on the polymer-quenched specimen with or without agitation.



0

(b)

(a)

Fig. 79

Effect of agitation on cooling curves and temperature differences of stainless steel disk specimen during oil quenching. Quenchant: 80 C quenching oil (JIS 1-2 oil). Flow velocity: (a) still, (b) 0.3 m/s

Effect of Surface Condition


30

800

Still 0.1 m/s 0.2 m/s 0.3 m/s

20

Stainless steel cylinder

Nickel cylinder Temperature (T ), °C

Effect of Surface Texture and Roughness. As already described in the section “Effect of Process Variables on Cooling Behavior and Heat Transfer” in this article, the surface texture and roughness affect the cooling characteristics of the steel workpiece in quenching. Therefore, these factors affect the stress and distortion of

600

400 Silver cylinder

3 2

200

2 1

3 0 0

2 1

3 20

10

1

30

40

50

60

70

Time (t ), s Effect of surface oxidization on cooling curves of cylindrical silver, nickel, and stainless steel specimens in water quenching. Quenchant: 30 C still water. Specimen shape: cylinder with hemispherical ends (10 mm diam by 30 mm long). Heating conditions: 1, 5 min up to 800 C in argon; 2, 5 min up to 800 C in air; 3, 8 h at 800 C in air. Source: Ref 70, 71

Fig. 80 10

Lf 0

0

1

2

3

4

5

Time (t ), s

(a)

800 50 °C

4

tf



5

3


2 1

ts

600

Water temperature = 95 °C 5 min in argon

400 10 min in air

200

5 min in argon

10 min in air

0 0

0.1 0.2 Flow velocity (v ), m/s

0.3 0 0

(b)

10

20

30

40

50

60

70

80

90

100

Time (t ), s Effect of (a) agitation and (b) flow velocity on wetting process on the surface of stainless steel disk specimen (30 mm diam by 10 mm thick) during oil quenching. Quenchant: 80 C quenching oil (JIS 1-2 oil)

Fig. 78

Effect of surface oxidization on cooling curves of cylindrical pure iron specimens in water quenching. Quenchant: 50 and 95 C still water. Specimen shape: cylinder with hemispherical ends (10 mm diam by 30 mm long). Source: Ref 70, 71

Fig. 81

Heat-transfer coefficient, W/m2 • K × 103

278 / Residual Stress During Hardening Processes the workpiece quenched. In addition, the surface texture and roughness are very important factors for quench cracking because the microscopic geometry and roughness of the surface affect the tendency to crack. Table 13 shows an example of such a case (Ref 80). The results are:

20 5 µm 10 µm

15

50 µm

10

● Surface roughness increases the tendency for

Water flux = 0.6 m3/m2 min

5

0 100

300

200

400

500

600

700

800


Fig. 82

Effect of surface scale on heat-transfer coefficient during spray cooling of a hot steel plate. Source: Ref 72

1000 Flaking of scale


800 Fall of scale flake 600 Fall of scale flake 400

Flaking of scale

Heavy scale

200 No oxide scale 0 0

1

2

3

4

5

6

7

8

9

10

Time (t ), s

Fig. 83

Unstable cooling phenomena due to surface oxidization during water quenching of steel specimen. Quenchant: 30 C still water. Specimen: JIS S45C cylinder (10 mm diam by 30 mm long)

quench cracking of steel if surface roughness (maximum height of irregularities Ry, or 10 points height of irregularities Rz) is larger than approximately 1 lm. ● Surface texture made by lapping tends to cause a higher occurrence of quench cracking than by grinding or emery polishing if each roughness is almost similar. This phenomenon is caused mainly by the stress concentration at the surface of the steel workpieces. Geometric shapes on the surface such as polishing marks, lapping marks, grinding marks, cutting tool marks, micronotches, and so forth act as a stress riser and a trigger for inducing quench cracking. Effect of Oxide or Coating Layer. The presence of a thin layer such as oxide scale and clay coating, for example, causes a cooling acceleration effect by suppression of vapor blanket formation or by acceleration of the collapse by the existence of a thin coating layer (as mentioned in the section “Effect of Process Variables on Cooling Behavior and Heat Transfer”). In addition, uniform cooling is caused by the existence of a thin layer. Therefore, quench cracking is suppressed by a thin scale or coating layer. Tables 14 and 15 show that the existence of oxide scale or clay coating largely suppresses the occurrence of quench cracking. However, a heavy oxide scale of the steel workpiece often causes unstable cooling and decarbonization.

Minimizing Distortion Distortion can be controlled by appropriate selection of component design, steel grade, quenchant, agitation, and quenching method. 800

1000

Without coating 800


Temperature, °C

Without coating 600 Clay coating 15 5 µm µmthick thick 400 15 µm

40 µm 200

25 µm

80 µm

Clay coating thickness δ 100 µm

400

1

2

3

4

5

6

7

8

9

10

Time, s

Fig. 84

200 µm

25 µm 50 µm

0 0 0 0

150 µm

10 µm 200

Effect of clay coating on cooling curves of steel specimen in water quenching. Quenchant: 30 C still water. Specimen: JIS S45C steel cylinder (10 mm diam by 30 mm long)

1

2 Time (t ), s

3

4

Effect of clay coating on cooling curves of silver specimen in water quenching. Quenchant: 30 C still water. Specimen: silver cylinder (10 mm diam by 30 mm long)

Fig. 85

Hardening by Reheating and Quenching / 279 Component Design

Heat-transfer coefficient, W/m2 • K × 103

20 Water flux = 0.6 m3/m2min 15

13.2 9.5 7.5 5.5 1.8 1.0

10

One of the causes of unacceptable distortion and cracking of steel parts is component design. Poor component design promotes distortion and cracking by accentuating nonuniform and nonsymmetrical heat transfer during quenching. Component designs that minimize distortion and cracking include the following. Design Symmetry. It is important to provide greater symmetry. One of techniques for design symmetry is to add dummy holes, key grooves, or other shapes to steel parts. Balance of Cross-Sectional Area. The difference between a large cross-sectional area and a thin one can be decreased by:

60 120 1000

5

0 100

Fig. 86

Surface roughness Rz, Paper µm No.

300 Surface temperature, °C

200

400

500

● Adding dummy holes to large cross-sectional

Effect of surface roughness on heat-transfer coefficient during spray cooling of a hot copper plate. Source: Ref 72

areas

● Changing from blind holes to through-type

holes

● Changing from thick solid shapes to thin hol-

low shapes

● Dividing a complicated shape into sectional

components Emery No. 800 Emery No. 320


800

Avoiding Sharp Corners and Edges. Distortion and cracking are encountered when quenching a part with sharp corners and edges, which increase cooling nonuniformity and act as stress risers. Therefore, it is effective to round corners and edges or to employ a tapered shape.

Emery No. 240 Lapping C No. 800

600

Lapping C No. 320 400

Steel Grade Selection 200

Although quench distortion and cracking are most often due to nonuniform cooling, material selection can be an important factor. Some attention should be paid to material selection:

0 0

1

2

3

4 5 Time (t ), s

6

7

8

9

10

● The compositional tolerances should be

1000

800

800


1000


Fig. 87

Effect of surface finish on the cooling curves of a S45C steel specimen during polymer quenching. Quenchant: 30 C 15% polymer (PAG ) quenchant. Specimen: JIS S45C steel cylinder (10 mm diam by 30 mm long)

600

400 R0

0.2 m/s

600

JIS 200

C1

200

R5 R3

0

1.0 m/s

R3 R0 JIS C1 R5

400

R3 C1 JIS

Cracking propensity increases as the Ms temperature and the carbon equivalent increase. Quench cracks were prevalent at carbon equivalent values above 0.525, as shown in Fig. 103.

R5 R0

Selection of Quenchant and Agitation

0 0

(a)

5

10 Time (t ), s

15

20

0

2

4

6

8 10 12 Time (t ), s

14 16 18

20

(b)

Effect of specimen shape on the cooling curves of cylindrical silver specimen cylinder (10 mm diam by 30 mm long) during quenching in 30 C water. Specimen shape: JIS, JIS silver probe type; R0, with flat ends and sharp edges; R3, with rounded edges of 3 mm radius; R5, with hemispherical ends of 5 mm radius; C1, with chamfered edges of 1 mm by 45

Fig. 88

checked to ensure that the alloy is within specification. ● It is often better to choose a lower carbon content, because the higher carbon content often causes the higher susceptibility for distortion and cracking (as mentioned in the section “Effect of Materials and Quench Process Design on Distortion”). ● If possible, it is better to choose a combination of a high-alloy steel and a very slow cooling rate. As a matter of course, the selection of high-alloy steels markedly raises the material cost.

Quenchants must be selected to provide cooling rates capable of producing acceptable microstructure in the section thickness of interest. However, it is not desirable to use quenchants with excessively high heat removal rates. Typically, the greater the quench severity, the greater


Quenching Methods Part design, material selection, quenchant selection, and so forth. are the most important factors to suppress the quench distortion and cracking of steel parts. In addition, several methods for minimizing distortion and eliminating cracking are employed, for example, interrupted

quenching, press quenching, plug quenching, and so forth. Interrupted quenching refers to the rapid cooling of the steel parts from the austenitizing temperature to a temperature where it is held for a specified time, followed by slow cooling. There are several different types of interrupted quenching: austempering, marquenching (martempering), time quenching, and so forth. The temperature at which the quenching is interrupted, the length of time the steel is held at temperature, and the cooling rate can vary, depending on the type of steel and workpiece thickness. Marquenching (martempering) is a term that describes an interrupted quenching from the austenitizing temperature of steels. The purpose is to delay the cooling just above the martensitic transformation temperature until temperature equalization is achieved throughout the steel part. This will minimize the distortion, cracking, and residual stress. The term martempering is somewhat misleading, and the process is better described as marquenching. Figures 104(a) and (b) (Ref 81) show the significant difference between conventional quenching and marquenching. The marquenching of steel consists of: 1. Quenching from the austenitizing temperature into a hot quenching medium (hot oil, molten salt, molten metal, or a fluidized particle bed) at a temperature usually above the martensite range (Ms point) 2. Submerging in the quenching medium until the temperature throughout the steel workpiece is substantially uniform 3. Cooling (usually in air) at a moderate rate to prevent large differences in temperature between the outside and the core of the workpiece The formation of martensite occurs fairly uniformly throughout the workpiece during the cooling to room temperature, thereby avoiding excessive amounts of residual stress. Straightening or forming is also easily accomplished

upon removal from the marquenching bath while the part is still hot. Marquenching can be accomplished in a variety of baths including hot oil, molten salt, molten metal, or a fluidized particle bed. Cooling from the marquenching bath to room temperature is usually conducted in still air. Deeper-hardening steels are susceptible to cracking while martensite forms if the cooling rate is too rapid. Marquenched parts are tempered in the same manner as conventionally quenched parts. The time lapse before tempering is not as critical because the stress is greatly reduced. The advantage of marquenching lies in the reduced thermal gradient between surface and core as the part is quenched to the isothermal temperature and then is air cooled to room temperature. Residual stresses developed during marquenching are lower than those developed during conventional quenching because the


the propensity to cause increased distortion or cracking. Although a reduction of quench severity leads to reduced distortion, it may also be accompanied by undesirable microstructures. Therefore, it is difficult to select an optimal quenchant and agitation. Cooling power of quenchant should be as low as possible while maintaining a sufficiently high cooling rate to ensure the required microstructure, hardness, and strength in critical sections of the steel parts. Specific recommendations for quench media selection for use with various steel alloys and general comments regarding quenchant selection were already shown in the section “Effect of Materials and Quench Process Design on Distortion.” Nonuniformity of cooling is perhaps the greatest contributor to quench distortion and cracking. Nonuniform cooling can arise from nonuniform flow fields around the part surface during quenching or nonuniform wetting of the surface. Nonuniform quenching creates large thermal gradients between the core and the surface of a steel part, or among the surfaces of the parts. These contributing factors, agitation, and surface wetting should be considered to select a quenchant and an agitation method. Good designs of agitation, racking, and support fixturing are major factors of uniform quenching. The purpose of the agitation system is not only to take hot fluid away from the surface of steel parts, but it is also to provide uniform heat removal over the entire cooling surface of all of the parts throughout the load being quenched.

600 R3 R5

JIS R0

400

C1 200

0 0

2

4

6 8 Time (t ), s

10

12

Effect of specimen shape on the cooling curves of cylindrical silver specimen cylinder (10 mm diam by 30 mm long) during quenching in 80 C still oil. Specimen shape: JIS, JIS silver probe type; R0, with flat ends and sharp edges; R3, with rounded edges of 3 mm radius; R5, with hemispherical ends of 5 mm radius; C1, with chamfered edges of 1 mm by 45

Fig. 90

Still

600 C1 400

R5 JIS

200

1.0 m/s

0.2 m/s



800

600 R0

C1 R5 R3 JIS R0

R0 0

R3

0 0

(a)

2

4

6

C1 R5 JIS

400

200

R3

Heat-transfer coefficient (h), W/m2 • K

104

8 10 12 Time (t ), s

14 16 18

0

20 (b)

2

4

6

8 10 12 Time (t ), s

Stainless steel cylinder Nickel cylinder Silver cylinder

2000 1000 500

200 100 50

14 16 18

20

Effect of specimen shape on the cooling curves of cylindrical silver specimen cylinder (10 mm diam by 30 mm long) during quenching in 30 C 15% polymer (PAG) quenchant. Specimen shape: JIS, JIS silver probe type; R0, with flat ends and sharp edges; R3, with rounded edges of 3 mm radius; R5, with hemispherical ends of 5 mm radius; C1, with chamfered edges of 1 mm by 45

Fig. 89

5000

0

200

400 600 ∆Tl = TW − Tl, (K)

800

Effect of specimen material on the heat-transfer coefficients during oil quenching. Quenchant: 80 C still quenching oil (JIS 1-1 type). Specimen: cylindrical silver, nickel, and stainless steel specimen with hemispherical ends (10 mm diam by 30 mm long)

Fig. 91


Change of thickness (∆t/2), mm

greatest thermal variations occur while the steel is in the relatively plastic austenitic condition and because the final transformation and thermal changes occur throughout the part at approximately the same time. Marquenching also reduces susceptibility to cracking. Modified marquenching differs from standard marquenching only in that the temperature of the quenching bath is below the Ms point (Fig. 104c) (Ref 81). The lower temperature increases the severity of quenching. This is important for steels of lower hardenability that require faster cooling in order to harden to sufficient depth. Therefore, modified marquenching is applicable to a greater range of steel compositions than is standard marquenching. Austempering consists of rapidly cooling the steel part from the austenitizing temperature to a temperature above that of martensite formation, holding at a constant temperature to allow isothermal transformation, followed by air cooling. The steel parts must be cooled fast enough so that no transformation of austenite occurs during cooling and then held at bath temperature long enough to ensure complete transformation of austenite to bainite. Molten-salt baths are usually the most practical for austempering applications. Parts can usually be produced with less dimensional change by austempering than by conventional quenching and tempering. In addition, austempering can decrease the likelihood of cracking and can improve ductility, notch

toughness, and wear resistance. However, austempering is applicable to a limited steel and parts size. Important consideration for the selection of steel parts for austempering are: ● The location for the nose of the TTT curve

and the speed of the quenching

● The time required for complete transforma-

tion of austenite to bainite at the austempering temperature ● The location of the Ms point ● Maximum thickness of section that can be austempered to a fully bainitic structure Carbon steels of lower carbon content will be restricted to a lesser thickness. For 1080 steel, the maximum section thickness is about 5 mm (0.2 in.). Low-alloy steels are usually restricted to about 10 mm (3⁄8 in.) or thinner sections, while more hardenable steels can be austempered in sections up to 25 mm (1 in.) thick. Nevertheless, sections of carbon steel thicker than 5 mm (0.2 in.) are regularly austempered in production when some pearlite is permissible in the microstructure (Ref 82). Time quenching is an interrupted quenching method and is used when the cooling rate of the part being quenched needs to be abruptly changed during the cooling cycle. The usual practice is to lower the temperature of the part by quenching in a medium with high heat removal characteristics (for example, water) until the part has cooled below the nose of the TTT

0.05 0.025 0 −0.025 −0.05

10

15

(Left side)

5

0

5

10

Radius horizontal (l s ), mm

15 (Right side)

Water (30 °C, still) 10% PAG polymer solution (30 °C), still) Oil (80 °C, still)

t = 10 mm

ds

ls

o o

2r = 30 mm dia.

ls

Distance from the center of thickness ds, mm

(a)

5 2.5 0 −2.5 −5 −0.1 −0.05 0 0.05 0.1 Change of radius (∆r), mm

(b)

Fig. 92 distortion

Effect of quenchants on quench distortion of JIS S45C carbon steel disk quenched in still quenchants. Specimen dimensions were 30 mm diam by 10 mm thick. (a) Distribution of axial distortion. (b) Distribution of radial

curve and then to transfer the part to a second medium (for example, oil, air, an inert gas), so that it cools more slowly through the martensiteformation range. Time quenching is most often used to minimize distortion, cracking, and dimensional changes. Restraint quenching refers to the quenching under restraint of distortion of steel, for example, quenching by using restraint fixtures, press quenching, cold-die quenching, plug quenching, and so forth. There are many round, flat, or cylindrical parts that distort to an unacceptable degree by conventional immersion quenching. Under such conditions, it is necessary to resort to special techniques. However, the equipment for those special techniques are expensive and production rates are slow. Consequently, the resulting cost of heat treatment is relatively high. Therefore, use of these techniques should be considered only when minimal distortion is mandatory. Restraint fixturing is costly and is used primarily for highly specialized applications. Representative examples are the quenching of rocket and missile casings or other large components with thin wall sections. Press Quenching and Plug Quenching. Probably the most widely used special technique is press quenching. To minimize distortion caused by the quenching cycle, press and plug quenching dies must be made to provide the proper quenchant flow and hold critical dimensions of the part being quenched. In quenching, the die or plug contacts the heated part, and the pressure of the press restrains the part mechanically. This occurs before quenching begins, while the part is hot and plastic. The machine and dies then force the quenching medium into contact with the part in a controlled manner. Cold-Die Quenching. Thin disks, long thin rods, and other delicate parts that distort excessively by conventional immersion quenching can often be quenched between cold dies with no distortion. Cold-die quenching is limited to parts with a large surface area and small mass, such as washers, rods of small diameter, thin blades, and so forth. Large, thin thrust washers have to be flat after quench hardening, but considerable distortions are developed as a result of blanking and machining stresses. To ensure the required flatness, the washers are squeezed between a pair of water-cooled dies immediately after they leave the furnace. Other quenching techniques that can be used to minimize cracking and distortion are discussed here. Selective quenching is used when it is desirable for certain areas of a part to be relatively unaffected by the quenching medium. This can be accomplished by insulating an area to be more slowly cooled so the quenchant contacts only those areas of the part that are to be rapidly cooled. The clay-coating method is employed for selective quenching, for example, water quenching of Japanese swords. The distortion and microstructure of Japanese swords is controlled by the thickness distribution of the clay layer. A thick clay layer (0.1 mm) suppresses the cool-

282 / Residual Stress During Hardening Processes ing rate by its insulating effect, and thin clay layer increases the cooling rate during water quenching by its cooling accelerating effect (Fig. 84 and 85). Selective quenching is often effective to suppress excessive distortion or cracking. Spray quenching involves directing high-pressure streams of liquid onto the surfaces of steel parts. Spray quenching is often useful for minimizing distortion and cracking, because it can realize a uniform quenching by selecting optimal spray conditions and can be used where higher cooling rates are desired. The cooling rate can be faster because the quenchant droplets formed by the high-intensity spray impact the part surface and remove heat very effectively. Fog quenching utilizes a fine fog or mist of liquid droplets in a gas carrier as the cooling agent. Although similar to spray quenching, fog quenching produces lower cooling rates because of the relatively low liquid content of the stream. Intensive quenching (Ref 83) involves forcedconvection heat exchange both during high-temperature cooling and also during the transformation of austenite into martensite. Intensive quenching promotes temperature uniformity during cooling through the cross section of the part. Cooling intensity should be sufficient to promote maximum surface compressive stresses. This occurs when the Biot number is ⱖ18. The second criterion of intensive quenching is that the intensive cooling be stopped at the moment that maximum surface compressive stresses are formed.

Tempering Steel parts are often tempered by reheating after quench hardening to obtain specific values of mechanical properties. Tempering of steel in-

Cylinder diameter, in.

Effect of quenchants on residual stresses on side surface of JIS S45C carbon steel disk quenched in still quenchants. Specimen dimensions were 30 mm diam by 10 mm thick. (a) Circumferential stress on end surface. (b) Radial stress on end surface

Fig. 93

800

0.4

1.2

2.0

4.0 115

Water quench, core 85

600 400

60

200

30

Oil quench, surface

Axial stress distribution during water quenching for various AISI 1045 steel cylinders diameter D, at selected times (in seconds) after the start of quenching from 850 C (1560 F) in 20 C (70 C) water. The final microstructure of the 10 mm (0.4 in.) diam cylinder is completely martensite, while the others have a ferritic-pearlitic core. Source: 78, 79

−30

−200

−60

−400 Water quench, surface −600

−85

−800

−115

−1000

Fig. 94

0

0

10

30 50 Cylinder diameter, mm

100

Axial residual stress, ksi

Axial residual stress, MPa

Oil quench, core

−145

Dependence of axial residual stresses on cylinder diameter. Same steel as in Fig. 94. The core is martensite for 10 mm (0.4 in.) diameter, but is ferrite-pearlite for larger diameters. Source: Ref 78, 79

Fig. 95


100 µm

(a)

(b)

Fig. 96

creases ductility and toughness of quench-hardened steel and also relieves quench stresses and ensures dimensional stability. As mentioned in the section “Phase Transformation during Heat Treating,” the tempering process is divided into four stages:

100 µm

100 µm

(c)

Effect of agitation of water on quench distortion of JIS S45C carbon steel disk. Specimen dimensions were 30 mm diam by 10 mm thick. Quenchant was 30 C city water. Flow velocity: (a) still water, (b) 0.3 m/s, and

(c) 0.7 m/s

100 µm

100 µm

(a)

100 µm

(b)

(c)

Effect of agitation of polymer quenchant on quench distortion of JIS S45C carbon steel disk. Specimen dimensions were 30 mm diam by 10 mm thick. Quenchant was 30 C 10% polymer (PAG) quenchant. Flow velocity: (a) still polymer solution, (b) 0.3 m/s, and (c) 0.7 m/s

Fig. 97

1. Tempering of martensite structure 2. Transformation of retained austenite to martensite 3. Tempering of the decomposition products of martensite 4. The decomposition of retained austenite to martensite. These microstructural variations during tempering result in volume changes during the tempering of hardened steel (Ref 84). Figure 105 shows an example of dimensional changes of tool steel plates by tempering with different soak times. Tempering up to 200 C (390 F) is accompanied by a slight contraction in all directions of the plate. At a higher tempering temperature, there is an increase in the dimensions, with a maximum increase at 300 C (570 F), after which dimensions again decrease. The increased vol-

Water, 30 °C Still Upward (0.3 m/s) Upward (0.7 m/s) Submerged spray Open spray

0.05

0

−0.05 0

0.4

0.2

0

−0.2 20

40

Rate of diameter change, %

Change of diameter, mm

0.1 Open spray (lateral) Submerged spary (lateral) Upward (0.7 m/s) Upward (0.3 m/s) Still

60

0

0.05

Distance from lower end, mm

0.15

0.20

0.25

0.30

0.35

Change of length, mm

(a)

Fig. 98

0.10

(b)

Effect of agitation methods on distortion in water quenching of JIS S45C steel rod (20 mm diam by 60 mm long). Quenchant was 30 city water. Agitation methods were still, 0.3 m/s upward flow, 0.7 m/s upward flow, and lateral submerge in immersion quenching, and lateral open spray quenching in air. (a) Change of diameter. (b) Change

of length

0.05

10% polymer quenchant, 30 °C Still Upward (0.3 m/s) Upward (0.7 m/s) Open spray (lateral)

0

−0.05 0

0.4

0.2

0

−0.2 20

40

Rate of diameter change, %

Change of diameter, mm

0.1 Submerged spray (lateral) Upward (0.7 m/s) Upward (0.3 m/s) Still

60

0

Distance from lower end, mm (a)

Fig. 99

0.05

0.10

0.15

0.20

0.25

0.30

Change of length, mm (b)

Effect of agitation methods on distortion in polymer quenching of JIS S45C steel rod (20 mm diam by 60 mm long). Quenchant was 30 C 10% polymer (PAG) quenchant. Agitation methods were still, 0.3 m/s upward flow, and 0.7 m/s upward flow in immersion quenching. (a) Change of diameter. (b) Change of length

284 / Residual Stress During Hardening Processes ume at 300 C (570 F) is attributed to the transformation of retained austenite to bainite. At 400 C (750 F), the dimensions revert to values closer to the original values, prior to quenching and tempering. In addition to dimensional change by microstructural variation, tempering may also lead to dimensional variation due to relaxation of residual stresses and plastic distortion caused by the temperature dependence of yield strength (Ref 85). Figure 105 shows the distortion of round steel bars (200 mm in diameter and 500 mm in length) by quenching and by stress relieving in tempering. A medium-carbon steel bar (Fig. 105a to c) and a hardenable steel bar (Fig. 105d to f) are used in this experiment. Figures 105a and d are the results of quenching from 650 C without phase transformation. The distortion in each case is almost the same, regardless of the different quenchants and the different chemical

compositions. These convex distortions are caused by nonuniform thermal contraction and resultant thermal stress during cooling. Figures 105(b) and (e) are the results of quenching from 850 C with phase transformation. The distortion in Fig. 105(e) (hardenable steel) shows a convex configuration, but the distortion in Fig. 105(b) (medium-carbon steel of poor hardenability) shows a configuration that combines convex and concave distortion. In addition, water quenching (WQ) has a greater effect on distortion than oil quenching (OQ). Figures 105(c) and (f) show the configurations after tempering. These results show that tempering after quenching results in not only volumetric changes but also in convex distortions. Such distortions seem to be related to relieving residual stresses by tempering. Figures 106 and 107 (Ref 86) show an example of stress relief by tempering. A solid cylinder 40 mm in diameter and 100 mm in length

60 4

6

10

10 A

σz

20

σθ B 600


400 200 0 −200 −400 −600 −800 −1000 0

Still water 0.3 m/s upward 0.7 m/s upward 10

Spray (submerged) lateral Spray (open) lateral

20

30

40

50

60

(a) 600


400 200 0 −200 −400

−800 −1000 0

Still water 0.3 m/s upward 0.7 m/s upward 10

The computer prediction of thermomechanical behavior in quenching is very useful for the determination of a quenching condition, because it is possible to predict the microstructure, hardness, distortion, and stress of steel parts after quenching. In order to predict thermomechanical behavior, residual stresses, and distortion in quenching of steel parts, a simulation method based on metallothermomechanical theory (Ref 87, 88) and finite-element analysis is often applied. The metallothermomechanical theory is coupled with temperature, phase transformation, and stress/strain fields. In quenching, the fields of metallic structures and stress/strain as well as temperature affect each other. The triangular diagram shown in Fig. 108 shows such coupling effect (Ref 88). In carburizing-quenching process, the effect of carbon content on the three fields is also represented by the dashed lines in the figure. A series of theoretical models with consideration of the effect of carbon diffusion and distribution is introduced.

An example of introducing the governing equations in the framework of thermomechanical behavior for describing temperature and stress/strain fields incorporating metallic structures in the quenching process is summarized in this section (Ref 88–91). Mixture Rule. When a material point undergoing heat treatment is assumed to be composed of a multiphase structure, an assumption is made that a material parameter is described by the mixture law: N

v⳱

Spray (submerged) lateral Spray (open) lateral 20

30

40

50

60

Distance from lower end, mm (b) Effect of agitation methods on residual stress after water quenching of JIS S45C steel rod (20 mm diam by 60 mm long). Quenchant was 30 C city water. Agitation methods were still, 0.3 m/s upward flow, 0.7 m/s upward flow and lateral submerge in immersion quenching, and lateral open spray quenching in air. (a) Axial stress on surface. (b) Tangential stress on surface

Fig. 100

Prediction of Distortion and Residual Stress after Quenching

Governing Equations


−600

was examined for analyses and experiments of tempering performed after water quenching. Calculated residual stress distributions after water quenching are shown in Fig. 106; open and solid circles correspond to measured stresses on the surface of the cylinder by x-ray diffraction. Residual stress distributions after tempering at 400 C are shown in Fig. 107(a) and (b) for typical elapsed times of 2 and 50 h with measured values on the surface. These results show that the stresses in all directions decrease with elapsed time in tempering.

N

兺 vI nI and I⳱1 兺 nI ⳱ 1 I⳱1

(Eq 4)

where nI denotes the volume fraction for the Ith phase. Heat-Conduction and Diffusion Equations. The temperature field is governed by a special heat-conduction equation coupling stress work and latent heat due to phase transformation during quenching:

Hardening by Reheating and Quenching / 285 T qCT˙ ⳮ k ⳮ rij e˙ ijp xi xi Ⳮ q l n˙ ⳱ 0

冢冣

60 4

6

10

10

兺

A

σz

(Eq 5)

I I I

where k and lI denote the coefficient of heat conduction and the latent heat produced by the progressive Ith constituent. The boundary conditions of heat transfer on the outer surface are assumed to be:

20

σθ B 600


400

Still polymer, 10% 0.3 m/s upward, 10%

Spray (open) 10% 0.7 m/s upward, 10%

ⳮk

200 0

T ni ⳱ h(T ⳮ Tw) xi

(Eq 6)

where h is a function dependent on temperature, h and Tw denote the heat-transfer coefficient and the temperature of coolant on heat-transfer boundary with unit normal ni, respectively. Carbon content during carburizing is solved by the diffusion equation:

−200 −400 −600 −800

−1000 0

10

20

30

40

50

60


˙ ⳱ ⳮD C C xi xi

冢

冣

(Eq 7)

(a)

where C is content in the position xi direction, D is the diffusion constant determined by the boundary condition being specified by the reaction across the surface layer:

600


400 200

Still polymer, 10% 0.3 m/s upward, 10%

Spray (open) 10% 0.7 m/s upward, 10%

0 −200

D

−400 −600 −800

−1000 0

10

20

30

40

50

60

Distance from lower end, mm (b) Effect of agitation methods on residual in polymer quenching of JIS S45C steel rod (20 mm diam by 60 mm long). Quenchant was 30 C 10% polymer (PAG) quenchant. Agitation methods were still, 0.3 m/s upward flow, and 0.7 m/s upward flow in immersion quenching. (a) Axial stress on surface. (b) Tangential stress on surface

Fig. 101

C ni ⳱ hc(Ce ⳮ Cs) xi

(Eq 8)

where hc and Ce are the surface reaction rate coefficient and the known content of the external environment, respectively. Constitutive Equation. Total strain rate e˙ ij is assumed to be divided into elastic, plastic, and thermal strain rates and those by structural dilatation due to phase transformation and transformation such that: e˙ ij ⳱ e˙ eij Ⳮ e˙ pij Ⳮ e˙ Tij Ⳮ e˙ m ˙ tp ij Ⳮ e ij

(Eq 9)

Here, the elastic strain: eeij ⳱

1 Ⳮ m m rij ⳮ (rkk)dij E E

(Eq 10)

Table 12 Effect of agitation on quench cracking in water and polymer quenching of steel disks shown in Fig. 100 Steel materials are Japanese standard S45C, SK4, and SCM435.

10

2

Frequency of occurrence of quench cracking, % Quenchants and its agitation

City water (30 C) Still (nonagitated) 0.3 m/s upward

S45C 0.45%C-0.67%Mn

SK4 0.98%C–0.77%Mn

SCM435 0.35%C-0.76%Mn–1.06%Cr-0.20%Mo

100 70

100 (flat surface) 30 (flat surface) 70 (hole surface) 0 (flat surface) 100 (hole surface) 10 (flat surface) 90 (hole surface)

100 100

0 … 0

0 … 0

0.7 m/s upward

0

5 m/s open spray

0

10% polymer quenchant (30 C, PAG) Still (nonagitated) 0% 0.3 m/s upward 0% 0.7 m/s upward 0%

7 φ10 φ30

60 0 Disk specimen for quench-cracking test. Specimen dimensions were 30 mm diam by 10 mm thick; specimen contains an eccentrically located 10 mm diam hole.

Fig. 102

286 / Residual Stress During Hardening Processes with Young’s modulus E and Poisson’s ratio m. In the simulation of carburizing-quenching process, (1 Ⳮ m)/E and m/E are expressed as the functions of carbon content and volume fraction of the structure:

1 Ⳮm ⳱ E

N

兺冤 l⳱1

m E⳱

n

In the simulation of carburizing-quenching process, ␣ is expressed as the function of carbon content and volume fraction of the structure:

m

Ⳮ (C ⳮ C1)

mI2 EI 2

冧冥

(Eq 12) N

␣⳱

冦

冧冥

(Eq 11)

eTij ⳱ ␣(T ⳮ T0)dij

(Eq 13)

Table 13 Effect of surface texture and roughness on quench cracking in water quenching of steel disks shown in Fig. 100 Steel materials are Japanese standard S45C and SK4. Quenchant: water (30 C) agitated by upward nozzle jet (1 m/s) S45C 0.45%C-0.67%Mn Surface finishing and roughness

Grinding (WA No. 46J) Ry ⳱ 1.0 lm, Rz ⳱ 0.75 lm Emery polishing (No. 800) Ry ⳱ 0.15 lm, Rz ⳱ 0.13 lm Emery polishing (No. 320) Ry ⳱ 1.1 lm, Rz ⳱ 1.0 lm Emery polishing (No. 240) Ry ⳱ 2.2 lm, Rz ⳱ 2.0 lm Lapping (WA No. 3000) Ry ⳱ 1.1 lm, Rz ⳱ 0.88 lm Lapping (C No. 800) Ry ⳱ 2.4 lm, Rz ⳱ 2.0 lm Lapping (C No. 500) Ry ⳱ 3.0 lm, Rz ⳱ 2.9 lm

兺冤 I {(C2 ⳮ C)␣I 1 I⳱1 C2 ⳮ C1 n

冥

The thermal strain is the function of initial temperature of material T0 and thermal expansion coefficient ␣:

nI (C2 ⳮ C) C2 ⳮ C1

1 Ⳮ mI 1 1 Ⳮ mI2 Ⳮ (C ⳮ C1) EI 1 EI 2

N

兺冤 I 冦(C2 ⳮ C) EII11 I⳱1 C2 ⳮ C1

SK4 0.98%C-0.77% Mn Frequency of occurrence of quench cracking, %

Surface finishing and roughness

Frequency of occurrence of quench cracking, %

Grinding (WA No. 46J) Ry ⳱ 0.90 lm, Rz ⳱ 0.75 lm Emery polishing (No. 800) Ry ⳱ 0.15 lm, Rz ⳱ 0.13 lm …

20 (flat surface) 80 (hole surface) 0 (flat surface) 100 (hole surface) …

20

Emery polishing (No. 240) Ry ⳱ 2.0 lm, Rz ⳱ 1.9 lm …

0 (flat surface) 100 (hole surface) …

20

…

…

80

Lapping (C No. 500) Ry ⳱ 2.8 lm, Rz ⳱ 2.6 lm

100 (flat surface) 0 (hole surface)

30 0 0 60

Ry, maximum height of irregularities; Rz, ten points height of irregularities

Ⳮ (C ⳮ C1)␣I 2}

(Eq 14)

The plastic strain rate is reduced to the form by employing temperature-dependent materials parameters: e˙ pij ⳱ k

F rij

(Eq 15)

ˆ F rkl Ⳮ F T˙ k⳱ G rkl T N F ˙ F ˙ Ⳮ nI Ⳮ C C I⳱1 nI

冦

冧

兺

1 F F F ˆ ⳱ ⳮ epmn Ⳮ j rmn rmn G

冢

冣

(Eq 16)

(Eq 17)

with a temperature-dependent yield function: F ⳱ F(T,C,rij ,ep,nI,j)

(Eq 18)

where j is the hardening parameter. Strain rates due to structural dilatation and transformation plasticity depend on the Ith constituent:

Table 14 Effect of surface oxidation on quench cracking in water quenching of steel disks shown in Fig. 100 Steel materials are Japanese standard S45C and SK4. Quenchant: water (30 C) agitated by upward nozzle jet (1 m/s) S45C 0.45%C-0.67%Mn Surface condition (heating condition)

SK4 0.98%C-0.77%Mn Frequency of occurrence of quench cracking, %

No-scale (heated in argon)

Surface condition

30

Light scale (heated in air, 3 min)

0

Heavy scale (heated in air, 20 min)

0

No-scale (heated in argon) Light scale (heated in air, 3 min) Heavy scale (heated in air, 20 min)

Frequency of occurrence of quench cracking, %

20 (flat surface) 80 (hole surface) 80 (flat surface) 20 (hole surface) 0

Table 15 Effect of clay coating on quench cracking in water quenching of steel disks shown in Fig. 100 Steel materials are Japanese standard S45C, SK4, and SCM435. Frequency of occurrence of quench cracking, % Surface condition (coating condition)

No coating (bare) Clay coating (0.3 mm thick)

S45C 0.45%C-0.67%Mn

SK4 0.98%C-0.77%Mn

SCM435 0.35%C-0.76%Mn–1.06%Cr-0.20%Mo

100 10

100 0

100 0

Fig. 103 steels

Effect of MS temperature and carbon equivalent on the quench cracking of selected


Fig. 104

Comparison of cooling curves as workpieces pass into and through martensite transformation range for a conventional quenching and tempering process and for interrupted quenching processes. (a) Conventional quenching and tempering. (b) Marquenching. (c) Modified marquenching

Deformation of medium-carbon and hardenable steel bars by quenching from below and above transformation temperature and by stress relieving. lC, change of length. (a) and (d) Quenched from 650 C. (b) and (e) Quenched from 850 C. (c) and (f) Tempered at 680 C (a) to (c) JIS S38C steel (0.38%C). (d) to (f) JIS SNCM 439 steel (0.39C-1.80Ni-0.80Cr-0.20Mo).

Fig. 105

150

150

150

T = 400 °C t =2h

100

T = 400 °C t =∞

100

50

0

−50 σ

Fig. 106

0

5


−50

0

−50 σz

σ

−100

σ

−100

σr

σr

−150

0

50

σz

σz −100

50

Stress (σ), kg/mm2

Stress (σ), kg/mm2

Stress (σ), kg/mm2

100

−150 20

Stress distribution in cylinder after quenching

0

5


σr

20

(a)

Fig. 107

−150

(b) Stress distribution in cylinder during tempering

0

5


20

288 / Residual Stress During Hardening Processes N

e˙ m ij ⳱

兺 bI n˙ I dij and I⳱1 e˙ tp ij ⳱

3 2

N

兺 KI h(nI )n˙ I sij I⳱1

(Eq 19)

where b and KI stand for the dilatation due to structural change and parameter due to transformation plasticity depending on the Ith constituent. Kinetics of the Quenching Process. In the case of quenching, two kinds of phase transformation are anticipated: one is governed by the diffusionless or martensite mechanism. From thermodynamic consideration, the formula for this type of reaction from austenite is often assumed to be governed by the modified Magee’s rule (Ref 92) as: nM ⳱ 1 ⳮ exp{w1T Ⳮ w2(C ⳮC0) Ⳮ w31rij Ⳮ

w32 J 21/2

Ⳮ w4

(Eq 20)

where nM is the volume fraction of martensite that is the function of carbon content, temperature, and stress. Here J2 is the second invariant of deviatoric stress. w1, w2, w3, w4 are all coefficients obtained from experiments. The other type of phase transformation is controlled by diffusion mechanism, and the volume fraction of developing phase such as pearlite may be expressed by modifying the JohnsonMehl relation (Ref 93) as:

冦冮

np ⳱ 1 ⳮ exp ⳮ

t 0

ft(T) fs(rij ) fc(C)(t ⳮ s)3ds

(Eq 21)

In this equation, ft(T), fs(rij), and fc(C) are the function of temperature T, stress rij, and carbon content C, respectively. Since the TTT diagram under the applied mean stress rm in logarithmic scale deviates from the one without stress, which is represented by the function f(T), the kinetic equation of diffusion type is often applied to the variations of pearlite or ferrite structure in quenching processes. Identification of the function f(T) can be made possible by the use of some experimental data of the structure change. Transformation plasticity is known as the phenomenon of accelerated plastic deformation

caused by a low level of applied stress during the phase transformation. In addition to the coupling effects between stress and phase transformation, this phenomenon is also expected to influence the stress and/or strain distribution during quenching. Following Desalos et al. (Ref 94), the transformation plastic strain rate e˙ tp ij is determined by: Nⳮ1

兺I

e˙ tp ij ⳱

3

I

I

(Eq 22)

Based on the metallothermomechanical theory (Ref 88, 89), the formulated finite-element equation system considering the coupling between increment of nodal displacement {Du} and temperature {T} as well as volume fraction of structure nI can be expressed as: [P]{T˙ } Ⳮ [H]{T} ⳱ {Q(nI ), rij }

(Eq 23)

and [K(ui)]{Dui} ⳱ {DF(T,nI)}

(Eq 24)

Here, matrices [P], [H], and [K] represent the matrices of heat capacity, heat conduction, and stiffness, respectively, and the vectors {Q} and {DF} are heat flux and increments of thermal load. These equations are strong nonlinear equations and are derived by the use of the expression of stress increment vector as:

冢

N

{␣}dT ¯ ⳮ

兺

(Eq 26)

I

and ¯ ⳱ ([De]ⳮ1{r}) Ⳮ b {1} {b} I nI

(Eq 27)

␣I and bI are the coefficients of thermal expansion and dilatation due to Ith phase transformation, respectively. [De] denotes the elastic matrix of materials. In order to treat unsteady coupled equations depending on time, a “step-by-step time-integration method” and “Newton-Raphson method” are introduced in numerical calculation, while an incremental method is used for deformation and stress analysis. Because heat-transfer coefficient depends on variation of the temperature on the boundary of heat transfer, one also uses the nonuniform time step to calculate temperature, phase transformation, and deformation fields (Ref 89).

Examples of Simulation Results Simulation of Quenching Processes of a Carbon Steel Disk and Cylinder (Ref 95). A finite-element method code HEARTS was used for simulating the quenching processes of steel disk and cylinder (Ref 95). Models of a 0.45%

N

兺 I⳱1

φ30

冣

¯ {b}dn I

I⳱1

兺I

3d e¯ c {s} ⳮ 2r¯

N

兺 I⳱1

␣I

I I

Coupling Algorithm in Simulation by Finite-Element Analysis

{dr} ⳱ [D] {de} ⳮ

([De]ⳮ1{r}) Ⳮ T

冢␣ n {1} Ⳮ T n dT{1}冣

I ij

Here, KI is the transformation plasticity coefficient for martensitic or pearlitic transformation, which may be identified by the experimental results dependent on dilatation-temperature diagrams.

ⳮ

{␣} ¯ ⳱

冦2 K h(n )n˙ s 冧 and

h(nI) ⳱ 2(1 ⳮ nI)

Nⳮ1

where e¯ c and {s} are equivalent creep strain and deviatoric stress vector. [D] denotes an elasticplastic matrix based on Mises-type yield function. Here, the functions depending on temperature and phase transformation ␣¯ and b¯ can be written as:

z

3 1 KI h(nI )dnI {s} Ⳮ 2 S0

r¯ 2 dT Ⳮ T

冢

N

兺

I⳱1

r¯ 2 dnI {s} nI

冣

5

o

(Eq 25)

r

10

Thermal stress Temperature

Stress/strain

z

Heat generation due to work

Carbon content Latent heat

Stress-induced transformation

o

Metallic structure Temperature-dependent phase transformation

Fig. 108

Elements: 136 Nodes: 162

Transformation stress and transformation plasticity

Coupling effects of temperature, stress/strain, and metallic structure in heat treatment

Fig. 109

r

Finite-difference mesh for steel disk specimen 30 mm diam by 10 mm thick)

Hardening by Reheating and Quenching / 289 5 × 104 2 × 104 Heat-transfer coefficient (h), W/m2 • K

C steel disk were employed to simulate the quenching process. The diameter and thickness of the disk are 30 and 10 mm, respectively. Then, the finite-element model shown in Fig. 109 pertained to an axisymmetrical problem. Figure 110 shows the heat-transfer coefficients used for the simulation. One of these coefficients was estimated using the lumped-heatcapacity method program “LUMPPROB” (Ref 63) and the cooling-curve data of the JIS silver probe. Another coefficient was estimated using the inverse method program “InvProbe-2D” (Ref 64, 65) and the cooling-curve data of the ISO Inconel 600 alloy probe. These coefficients were modified by a trial-and-error method repeating the calculation of cooling curve and the modification of the surface-boundary condition. Figure 111 shows the calculated volume fraction of martensite after water quenching of S45C steel disk. The calculated volume fraction of martensite depends largely on the accuracy of the heat-transfer coefficients. Figure 112 illustrates the distribution of the calculated and the measured distortion of steel disk These results show that the modified heat-transfer coefficient gave the most accurate simulation of the distortion after water quenching. Figure 113 shows the distribution of residual stress on the flat end surface of S45C steel disk after water quenching. The residual stresses measured by x-ray diffraction are compared with calculated results in Fig. 113. The calculated stresses of simulation have good agreement to measured results as shown in this figure. However, the modified heat-transfer coefficient gave the better result of the simulation than the other. Finite-difference mesh for steel cylinder specimen (1/4 model, 20 mm in diameter by 60 mm) is shown in Fig. 114. Figure 115 illustrates the distribution of residual stress on the side surface of the steel cylinder after polymer quenching. The calculated residual stresses have good agreement to measured results. Figures 116(a) and (b) are simulated shape changes of S45C steel cylinder during water and polymer quenching, respectively. These results clarify that nonuniform cooling in water quenching causes larger distortion near the end than in polymer quenching. Prediction of Warpage of Steel Shafts with Keyway (Ref 96). The finite-element method system DEFORM-HT (Ref 97) was used for simulating quenching of a JIS S45C (0.45% C) steel shaft with keyway. A cylinder, 10 mm in diameter and 100 mm long, was with a keyway, 2.5 mm deep and 4 mm wide. A tetrahedral mesh containing approximately 33,000 elements was applied to one-half of the specimen; symmetry conditions were applied to the center surface. The results were evaluated against the experimental data. The simulated quench distortion history was compared against its real counterpart. Excellent resemblance was found between them, as Fig. 118 is compared with Fig. 117. In both reality and simulation, the shaft bent toward the keyway side in the beginning 1.7 s and bent to the other direction after 1.7 s. This phenomenon was believed to be caused by the combi-

hside

104 5000 2000 1000

hend

hend

500 200 100 50

JIS probe + LUMPPROB ISO probe + InvProbe-2D Modified: Even

hside

20 10 0

(hside = hend) 200

400

600

800

Even

Temperature (T ), °C Heat-transfer coefficients used for the simulation. These coefficients were estimated by using the lumpedheat-capacity method program “LUMPPROB” and the cooling-curve data of the JIS silver probe, or by using the inverse method program “InvProbe-2D” and the cooling-curve data of the ISO Inconel 600 alloy probe, and modified by a trial-and-error method by repeating the calculation of cooling curve and the modification of the surface boundary condition.

Fig. 110

Fig. 111

Calculated volume fraction of martensite after water quenching of S45C steel disk used for surface boundary conditions in simulation of 1/4 F M model of disk specimen shown in Fig. 109


Radius (horizontal)(ls), mm

Change of thickness (∆t ), mm

(Left side) 0.075

15

10

23 mm diam cylindrical model of SAE 1055 steel under scanning induction hardening as shown in Fig. 124. Figure 125 shows measured hardness and simulated volume fraction of martensite for scanning velocity v ⳱ 10 mm/s. The simulated effective case depth (defined as the region with 50% of martensite fraction) almost corresponds to the measured effective case depth (defined as the region over 500 HV). Figure 126 shows the simulated residual stress distribution along the surface of the cylinder with the measured values by x-ray diffraction. Both data of simulation and experiment for scanning velocity v ⳱ 10 mm/s give higher values than for v ⳱ 5 mm/s.

cross section of the ring at final step. Experimental results of distortion are plotted as solid marks in the figure. Changes in the distortion with time with and without transformation plasticity are shown in Fig. 123. The most remarkable difference between the two lies in the mode of distortion. Transformation plasticity gives convex shape on all surfaces, but concave without the effect. Experimental data agree well with simulated distortion with the effect of transformation plasticity in both carburized and normal quenching. Computer Simulation of Residual Stresses/ Distortion in Scanning Induction Hardening (Ref 99). Ikuta et al. (Ref 99) carried out a coupled metallothermomechanical analysis using heat treatment simulation code “HEARTS” for a

nation of thermal stress, deformation, and transformation-induced volume changes. Prediction of Distortion during Carburized-Quenching of Chromium-Molybdenum Steel Ring (Ref 98). Yamanaka et al. (Ref 98) carried out a coupled metallothermomechanical analysis using heat treatment simulation code “HEARTS” for a ring-shaped model (see Fig. 119 and 120) of chromium-molybdenum steel under the carburized-quenching process shown in Fig. 121. Diffusion equation for carbon content was solved and coupled with metallothermomechanical analysis. The results were compared with the experimental data to verify and evaluate the influence of transformation plasticity on simulation results. Figure 122 shows the simulated distortion of 5

0

Summary

(Right side)

5

10

15

This article provides a detailed explanation of the contributing factors affecting residual stress and dimensional control during quenching. These factors include phase transformations during heat treating, metallurgical sources of stress

0.05 0.025 0 −0.025 −0.05 −0.075 −0.1

φ20

Measured Horizontal Vertical 15

z

z

10

5

0

5

10

Radius (vertical)(ls), mm

(Upper)

15 (Lower)

Calculated heat-transfer coefficients JIS probe + LUMPPROB ISO probe + InvProbe-2D Modified (even on all surfaces)

(a)

30

t

Distance from the center of thickness ( t), mm

ds

ls

10 mm

o

r

o

0 2.5

o

5 −0.1

0

Fig. 114

400

200

200 Residual stress, MPa


Calculated and measured distortion after water quenching of S45C steel disk. (a) Distribution of axial distortion. (b) Distribution of radial distortion

400

0 −200 −400 −600 −800 −1000 15

Measured Calculated Heat-transfer coefficients JIS probe + LUMPPROB ISO probe + InvProbe-2D Modified (even on all surfaces) 10

5

0

5

Finite difference mesh for steel cylinder specimen (20 mm diam by 60mm long)

0 −200 −400 −600 −800

10

−1000 15

15

Radius, mm (a)

r Elements: 300 Nodes: 341

0.1

Change of radius ( r ), mm

(b)

Fig. 113

60

2.5

30 mm diam

Fig. 112

r

5

10

5

0

5

10

15

Radius, mm (b)

Calculated and measured residual stress distribution after water quenching of S45C steel disk. (a) Radial stress distribution on end surface. (b) Tangential stress distribution on end surface

Hardening by Reheating and Quenching / 291 400

Measured Calculated Heat-transfer coefficients JIS probe + LUMPPROB ISO probe + InvProbe-2D Modified (even on all surfaces)


200 0 −200 −400 −600 −800 −1000

10

0

20

30

40

50

60

Distance from lower end, mm (a) 400 Residual stress, MPa

200 0 −200 −400 −600 −800 −1000

10

0

20

30

40

50

60

Distance from lower end, mm (b) Calculated and measured residual stress distribution after polymer quenching of S45C steel cylinder. (a) Axial stress distribution on side surface. (b) Tangential stress distribution on side surface

Fig. 115

Fig. 117

Boiling behavior and distortion during quenching in still city water at 30 C. Keyway is on left side of specimen. Source: Ref 97

z

z

After quenching Before quenching t=2s t=4s t=6s t=8s Before heating

o (a)

r

o

0.5 s

0.8 s

1.0 s

1.2 s

1.7 s

2.0 s

2.4 s

3.3 s

4.0 s

r

(b)

Simulated shape change history of a S45C steel cylinder (1/4 shape of cylinder, 20 mm diam by 60mm long) during water quenching (a) and polymer quenching (b). Quenchants were 30 C city water and 30 C 10% polymer (PAG) quenchant without agitation. Distortion is enlarged by 100 times.

Fig. 116

0.3 s

Fig. 118

Simulated quench distortion history during water quenching. Source: Ref 97

292 / Residual Stress During Hardening Processes and distortion during reheating and quenching, effect of materials and quench process design on distortion, quenchant selection, measurement and evaluation of quenching power, effect of process variables (bath temperature, agitation, and others) on cooling behavior and heat transfer, effect of cooling characteristics on residual stress and distortion, methods of minimizing distortion, and tempering. Although quenching is a complex process, and although it exhibits one of the largest contributing effects to overall residual stress generation and dimensional control problems, an understanding of these effects allows the engineer to bring and keep the heat treating process under control.

REFERENCES 1. S. Owaku, Quench Distortion of Steel Parts, Netsu Shori (J. Jpn. Soc. Heat Treat.), Vol 32 (No. 4), 1992, p 198–202 2. S. Mocarski, Carburizing and Its Control–I. Basic Considerations, Ind. Heat., Vol 41 (No. 5), 1974, p 58–70 3. A. Bavaro, Heat Treatments and Deformation, Trait. Therm., Vol 240, 1990, p 37–41 4. F. Legat, Why Does Steel Crack During

5. 6. 7. 8.

9.

10. (a)

φ75

11.

φ25

12.

10

13. (b)

Fig. 119

With transformation plasticity Without transformation plasticity Initial Experimental

Dimension of ring-shaped specimen of chromium-molybdenum steel

14.

Simulated distortion after quenching with measured data. Distortion is enlarged by 100 times. Central axis is the left side. (a) Carburized quenching. (b) Normal quenching. Source: Ref 98

Fig. 122

2

15.

Quenching, Kovine, Zlitine, Technologie, Vol 32 (No. 3–4), 1998, p 273–276 K.E. Thelning, Steel and Its Heat Treatment, Butterworths, London, 1985 H. Berns, Distortion and Crack Formation by Heat Treatment of Tools, Radex Rundsch., Vol 1, 1989, p. 40–57 G. Beck, Internal Stresses Associated with Heat Treatment of Alloy”, Me´m. Etud. Sci. Rev. Me´tall., June 1985, p 269–282 T. Ericsson and B. Hildenwall, Thermal and Transformational Stresses, 28th Sagamore Army Materials Research Conf., 1981, p 19–38 P. Mayr, Dimensional Alteration of Parts Due to Heat Treatment, Residual Stresses in Science and Technology, Vol 1, GarmischPartenkirschen, 1986, DGM Informationsgesellschaft mbH, Federal Republic of Germany, 1987, p 57–77 C. Jensen, Dimensional Changes During Heat Treatment of Hot Work Steel, Ind. Heat., March 1993, p 33–38 R.W. Edmonson, Dimensional Changes in Steel During Heat Treatment, Met. Treat., Vol 20 (No. 6), 1969, p 3–19 G.E. Totten and M.A.H. Howes, Distortion of Heat Treated Components, chapter 5, Steel Heat Treatment Handbook, G.E. Totten and M.A.H. Howes, Ed., 1997, Marcel Dekker, p 292 D.A. Canonico, Stress-Relief in Heat Treating of Steel, Heat Treating, Vol 4, ASM Handbook, 1991, ASM International, p 33– 34 C.E. Bates, G.E. Totten, and R.L. Brennan, Quenching of Steel, Heat Treating, Vol 4, ASM Handbook, 1991, ASM International, p 67–120 W.T. Cook, Review of Selected Steel-Related Factors Controlling Distortion in

1

1 2 Time 10 s 60 s 2400 s With transformation plasticity

Fig. 120

Mesh division near a edge of ring-shaped model

930 °C

4h

850 °C

1h

1 h 30 min

Without transformation plasticity (a)

Cp 1.2%

Fig. 121

With transformation plasticity

0.85%

OQ (130 °C)

Heat cycle of carburized-quenching process

Without transformation plasticity (b)

Comparison of simulated results depending on the effect of transformation plasticity in course of quenching. Distortion is enlarged by 100 times. Central axis is the left side. (a) Carburized quenching. (b) Normal quenching. Source: Ref 98

Fig. 123

Hardening by Reheating and Quenching / 293 Heat-Treatable Steels, Heat Treat. Met., Vol 26 (No. 2), 1999, p 27–36 16. Y. Toshioka, Heat Treatment Deformation of Steel Products, Mater. Sci. Tech., Vol 1, Oct 1985, p 883–892 17. A. Thuvander and A. Melander, Calculation of Distortion During Quenching of a Low Carbon Steel, First ASM Heat Treatment and Surface Engineering Conference in Europe, Part 2, Trans. Tech. Publications, 1992, p 767–782 18. P.C. Clarke, Close-Tolerance Heat Treat-

19. 20. 21. 22.

ment of Gears, Heat Treat. Met., Vol 25 (No. 3), 1998, p 61–64 R.F. Kern, Thinking Through to Successful Heat Treatment, Met. Eng. Q., Vol 11 (No. 1), 1971, p 1–4 R. Kern, Distortion and Cracking, II: Distortion from Quenching, Heat Treat., March 1985, p 41–45 R. Kern, Distortion and Cracking, III: How to Control Cracking, Heat Treat., April 1985, p 38–42 H.-J. Chen and Z.W. Jiang, Microstructure

23.

24.

Finite-element mesh Cooling zone

Heating zone

25.

r D A

B

26.

C

z 54

110

27.

54 55

70

300

100

70

440

Fig. 124

Finite-element mesh and boundary condition of scanning induction quenching system. Source: Ref 99

28.

100

Martensite fraction (ξM ), %

90 80

29.

70 60

30.

50 40

31.

30 20 10 0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

32.

Depth (d ), mm (a) 100

33.

90 Hardness (H ), HV

80 70

34.

60 50 40

35.

30 20 10 0

0

1

2

3

4

5

6

7

8

9

10

Depth (d ), mm (b)

Fig. 125

Simulated volume fraction of martensite (a) and measured hardness (b) for scanning velocity v ⳱ 10 mm/s

36.

Improvement and Low-Temperature Quenching of Dies Made of Cr12-Type Steel, Jinshu Rechuli, No. 8, 1992, p 39–41 H.-H. Shao, Analysis of the Causes of Cracking of a 12% Cr Steel Cold Die During Heat Treatment, Jinshu Rechuli, No. 11, 1995, p 43 R.R. Blackwood, L.M. Jarvis, D.G. Hoffman, and G.E. Totten, Conditions Leading to Quench Cracking Other Than Severity of Quench, Heat Treating Including the Liu Dai Memorial Symposium, Proc. 18th Conf., R.A. Wallis and H.W. Walton, Ed., 1998, ASM International, p 575–585 X. Cheng and S. He, Analysis of Quenching Cracks in Machine-Tool Pistons under Supersonic Frequency Induction Hardening, Heat Treat. Met. (China), No. 4, 1991, p 51–52 J.R. Davis, ASM Materials Engineering Dictionary, ASM International, 1992, p 407 P.F. Stratton, N. Saxena, and R. Jain, Requirements for Gas Quenching Systems, Heat Treat. Met., Vol 24 (No. 3), 1997, p 60–63 H.M. Tensi, G.E. Totten, and G.M. Webster, Proposal to Monitor Agitation of Production Quench Tanks, Heat Treating: Including the 1997 International Induction Heat Treating Symposium—Proceed. 17th Conf., D.L. Milam, D.A. Poteet, G.D. Pfaffmann, V. Rudnev, A. Muehlbauer, and W.B. Albert, Ed., ASM International, 1997, p 423–441 G.-F. Long, Control of Quenching Distortion in Gears, Jinshu Rechuli, No. 5, 1994, p 39–40 H.M. Tensi, A. Stich, and G.E. Totten, Fundamentals of Quenching, Metal Heat Treat., March/April 1995, p 20–28 R.T. Von Bergen, The Effects of Quenchant Media Selection on the Distortion of Engineered Steel Parts, Quenching and Distortion Control, G.E. Totten, Ed., ASM International, 1992, p 275–282 G.J. Leidenfrost, De Aqua Communis Nonnullis Tractus, 1756, translated from original; C. Waves, Int. J. Mass Transfer, Vol 9, 1966, p 1153–1166 A. Yamanouchi, Effect of Core Spray Cooling in Transient State after Loss of Cooling Accident, J. Nucl. Sci. Technol., Vol 5, 1968, p 547–558 R.B. Duffly and D.T.C. Porthouse, The Physics of Rewetting in Water Reactor Engineering Core Cooling, Nucl. Eng. Des., Vol 31, 1973, p 234–245 Th. Ku¨nzel, “Einfluss der Wiederbenetzung auf die Allotrope Modifikationsa¨nderung tauchgeku¨hlter Metallko¨rper,” Dr. Ing. Dissertation, Faculty for Mechanical Engineering of the Technical University of Munich, 1986, 138 pages D. Hein, “Modellvorstellung zur Wiederbenetzung durch Fluten,” Doctoral Thesis Technical University of Hannover, 1980, 182 pages

294 / Residual Stress During Hardening Processes 37. R. Ladish, “Untersuchung der Minimalen Filmsiedetemperaturen auf Keramischen und Metallischen Leitern,” Report of “Kernforschungsstelle Karlsruhe,” KfK-2970, 1980, 96 pages 38. P. Stitzelberger-Jakob, “Ha¨rtevorherbestimmung mit Hilfe des Benetzungsablaufes beim Tauchku¨hlen von Sta¨hlen,” Dr. Ing. Dissertation, Faculty for Mechanical Engineering of the Technical University Munich, 1991, 160 pages 39. H.M. Tensi and K. Lainer, Wiederbenetzung und Wa¨rmeu¨bergang beim Tauchku¨hlen in Hochleistungso¨len, Ha¨rt.-Tech. Mitt., Vol 52, 1997, p 298–303 40. H.M. Tensi, Wetting Kinematics, Theory and Technology of Quenching, B. Liscic, H.M. Tensi, and W. Luty, Ed., SpringerVerlag, Berlin, 1991, 484 pages 41. S. Owaku, Criterion of Quench Cracking: Its Sources and Prevention, Netsu Shori (J. Jpn. Soc. Heat Treat.), Vol 30 (No. 2), 1990, p 63–67 42. A.A. Polyakov, Quenching Properties of Parts Having Stress Concentrators, Met. Sci. Heat Treat., Vol 37 (No. 7–8), 1995, p 324– 325 43. A. Rose, Cooling Power of Quenching Agents for Steel, Arch. Eisenhu¨ttenwes., Vol 13, 1940, p 345–354 44. P.F. Stratton and D. Ho, Individual Component Gas-Quenching in Progress in Heat Treatment and Surface Engineering, Proc. 5th ASM Heat Treatment and Surface Engineering Conf., E.J. Mittemeijer and J. Grosch, Ed., 7–9 June 2000 (Gothenburg, Sweden), ASM International, p 367–375 45. T.W. Ruffle and E.R. Byrnes, Quenching in Vacuum Furnaces, Heat Treat. Met., Vol 4, 1979, p 81–87 46. B. Lhote and O. Delcourte, Gas Quenching with Helium in Vacuum Furnaces, Quenching and Carburizing, Third International Seminar, International Federation for Heat

47. 48. 49. 50.

51.

52. 53. 54.

55.

56.

57.

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300

0 −100

100

−200 −300 −400 −500 −600 −700 −800

61.

62. 63.

64.

65.

66.

0 −100 −200 −300 −400 −500 −600 −700 −800

0

50

100

150

200

250

300

350

−900 −1000

400

Distance (z ), mm (a)

60.

σz calculated σθ calculated σz measured σθ measured

200 Residual stresses (σz,σθ), MPa

Residual stresses (σz,σθ), MPa

100

Fig. 126

59.

300 σz calculated σθ calculated σz measured σθ measured

200

−900 −1000

58.

Graw-Hill Kogakusha, Ltd., Tokyo, p 114– 115 “Standard Test Method for Determination of Cooling Characteristics of Quench Oils by Cooling Curve Analysis,” Standard D6200– 97, ASTM “Industrial Quenching Oil—Determination of Cooling Characteristics—Nickel-Alloy Probe Test Method,” ISO 9950, International Standards Organization, 1995(E) “Heat Treating Oils,” JIS K 2242–1997, Japanese Standards Association, Tokyo, Japan M. Narazaki, M. Kogawara, A. Shirayori, S. Fuchizawa, and G.E. Totten, Experimental and Numerical Analysis of Cooling Curves During Quenching of Small Probes, Heat Treating: Proc. 20th Conf., K. Funatani and G.E. Totten, Ed., 9–12 Oct 2000, ASM International, p 423–441 J.P. Holman, Heat Transfer, McGraw-Hill Kogakusha, Ltd., Tokyo, 1976, p 97 M. Narazaki, M. Kogawara, A. Shirayori, and S. Fuchizawa, Analysis of Quenching Processes Using Lumped-Heat-Capacity Method, Sixth Int. Seminar, International Federation for Heat Treating and Surface Engineering, 1997 (Kyongju, Korea), p 428–435 M. Narazaki, H. Hiratsuka, A. Shirayori, and S. Fuchizawa, Examination of Methods for Obtaining Heat Transfer Coefficients by Quenching Small Probes, Proc. Asian Conf. Heat Treatment of Materials, 13–15 May 1998 (Beijing), p 269–274 M. Narazaki, K. Kogawara, A. Shirayori, and S. Fuchizawa, Accuracy of Evaluation Methods for Heat Transfer Coefficients, Heat Treating Including the Liu Dai Memorial Symposium, Proc. of the 18th Conf. R.A. Wallis and H.W. Walton, Ed., ASM International, 1998, p 509–517 J.V. Beck and A.M. Osman, Analysis of Quenching and Heat Treating Processes Using Inverse Heat Transfer Method, Proc.

0

50

100

150

200

250

Distance (z ), mm (b)

Residual stresses along the surface of SAE1055 steel cylindrical specimen. Scanning velocity v ⳱ (a) 10 mm/s and (b) 5 mm/s

300

350

400


67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

First Int. Conf. Quenching and Distortion Control, 22–25 Sept 1992 (Chicago, IL), p 147–153 B. Hernandez-Morales, J.K. Brimacombe, E.B. Hawbolt, and S.M. Gupta Determination of Quench Heat-Transfer Coefficients Using Inverse Techniques, Proc. First Int. Conf. Quenching and Distortion, Control, 22–25 Sept 1992 (Chicago, IL), p 155–164 M. Narazaki, M. Kogawara, A. Shirayoria, and S. Fuchizawa, Influence of Wetting Behaviour on Cooling Characteristics During Quenching of Hot Metal, Proc. Third Int. Conf. Quenching and Control of Distortion, 24–26 March 1999 (Prague), p 112–120 H.M. Tensi, Determination of Quenching Power of Various Fluids, Theory and Technology of Quenching, B. Liscic, H.M. Tensi, and W. Luty, Ed., Springer-Verlag, Berlin, 1991, p 208–219 M. Narazaki, S. Fuchizawa, M. Kogawara, and M. Inaba, Effects of Surface Oxidation on Cooling Characteristics During Quenching of Heated Metals in Subcooled Water, Tetsu-to-Hagane (J. Iron Steel Inst. Jpn.), Vol 79, 1993, p 583–589 M. Narazaki, A. Asada, and K. Fukuhara, Recent Research on Cooling Power of Liquid Quenchants in Japan, Proc. Second Int. Conf. Quenching and Distortion Control, 4–7 Nov 1996 (Cleveland, OH), p 37–46 T. Tamari and H. Yoshida, Effect of Surface conditions on Heat Transfer Coefficient During Spray Cooling on a Hot Stationary Plate, CAMP-ISIJ (Report of ISIJ Meeting), Vol 8, 1995, p 444 M. Narazaki, S. Fuchizawa, and N. Takeda, Effect of Surface Coatings on Cooling Characteristics During Water Quenching of Hot Metals, Netsu Shori (J. Jpn. Soc. Heat Treat.), Vol 28, 1988, p 279–285 Y. Kikuchi, T. Hori, H. Yanagawa, and I. Michiyoshi, The Effect of Thin Layer on Heat Transfer Characteristics During Quenching of Hot Metals in saturated Water, Int. Trans. ISIJ, Vol 26, 1986, p 576– 581 M. Narazaki, S. Fuchizawa, and M. Inaba, Effects of Surface Texture on Cooling Curve During Quenching of Heated Metals in Subcooled Water, Tetsu-to-Hagane (J. Iron Steel Inst. Jpn.), Vol 76, 1990, p 902– 909 M. Narazaki, Effects of Work Properties on Cooling Characteristics During Quenching, Netsu Shori (J. Jpn. Soc. Heat Treat.), Vol 35, 1995, p 221–226

77. M. Narazaki, S. Fuchizawa, and M. Usuba, Effects of Specimen Geometry on Characteristic Temperature During Quenching of Heated Metals in Subcooled Water, Tetsuto-Hagane (J. Iron Steel Inst. Jpn.), Vol 75, 1989, p 634–641 78. T. Ericsson, Principles of Heat Treating of Steels, Heat Treating, Vol 4, ASM Handbook, ASM International, 1991, p 16 79. H.J. Yu, U. Wolfstieg, and E. Macherauch, Zum durch messereinfluss auf die Eigenspannnngen in o¨l-und Wasserabgeschreckten Stahlzylindern, Arch. Eisenhu¨ttenwes., Vol 51, 1980, p 195 80. M. Narazaki, S. Fuchizawa, and M. Kogawara, Effect of Surface Roughness and Surface Texture on Quench Cracking of Steel, Netsu Shori (J. Jpn. Soc. Heat Treat.), Vol 33, 1993, p 56–63 81. H. Webster and W.J. Laird, Jr., Martempering of Steel, Heat Treating, Vol 4, ASM Handbook, ASM International, 1991, p 137 82. J.R. Keough, W.J. Laird, Jr., and A.D. Godding, Austempering of Steel, Heat Treating, Vol 4, ASM Handbook, ASM International, 1991, p 152–163 83. N.I. Kobasko, M.A. Arpnov, G.E. Totten, and A.V. Sverdlin, Method and Equipment for Implementation of Intensive Quenching, Heat Treating Including the Liu Dai Memorial Symposium, Proc. of the 18th Conf., R.A. Wallis and H.W. Walton, Ed., ASM International, 1998, p 616–621 84. M. Wisti and M. Hingwe, Tempering of Steel, Heat Treating, Vol 4, ASM Handbook, ASM International, 1991, p 121–136 85. Y. Toshioka, Heat Treatment Deformation of Steel Products, Mater. Sci. Technol., Vol 1, 1985, p 883–892 86. T. Inoue, K. Haraguchi, and S. Kimura, Analysis of Stresses Due to Quenching and Tempering of Steel, Trans. ISIJ, Vol 18, 1978, p 11–15 87. T. Inoue and B. Raniecki, Determination of Thermal-Hardening Stress in Steels by Use of Thermoplasticity, J. Mech. Phys. Solids, Vol 26, 1978, p 187–212 88. T. Inoue, D.Y. Ju, and Y. Arimoto, MetalloThermo-Mechanical Simulation of Quenching Process—Theory and Implementation of Computer Code HEARTS, Proc. First Int. Conf. Quenching and Distortion Control (Chicago), 1992, p 205–212 89. D.Y. Ju, M. Sahashi, T. Omori, and T. Inoue, Residual Stresses and Distortion of a Ring in Quenching-Tempering Process Based on Metallo-Thermo-Mechanics,

90.

91.

92. 93. 94.

95.

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97.

98.

99.

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Metallo-Thermo-Mechanics— Application to Quenching T. Inoue, Kyoto University, Japan

COMPUTER SIMULATION is indispensable for research, development, and design in various fields of industry. In particular, popularization of general-purpose programs based on the finiteelement method enables engineers to execute highly reliable analysis and design. However, many open problems still remain to which the general-purpose programs cannot be applied. Heat treatment process associated with phase transformation is one of the examples, and the development of a program specialized for heat treatment simulation is required from an engineering point of view. Owing to the fact that metallic structures, temperature, and stress/strain are strongly coupled in the process incorporating phase transformation, metallo-thermo-mechanics for taking the coupling effect into account was proposed and applied to some problems by the authors (Ref 1– 7). In this article, the summary of the metallothermo-mechanics is briefly introduced; governing equations identifying the fields of metallic structure, temperature, and stress/distortion are stated; and the correlation between the problems of phase transformation and the theory is briefly discussed. In the following sections, the developing strategy, methodology, and structure of the developed system “HEARTS (HEAt tReaTment Simulation system)” based on the theory for simulating the engineering process incorporating phase transformations are stated (Ref 8– 10). Some examples of simulated results are presented: infinitely long cylinder quenched by water (Ref 8), induction hardened and carburized quenched rings (Ref 11, 12), induction hardened gear wheel (Ref 13), and Japanese sword during quenching (Ref 14–16). The validity of the theory and the system are evaluated by comparing the simulated results with the experimental data.

phase changes, such as solid-solid transformation in quenching, tempering, and other heat treatments of steels, and also solid-liquid transformation in welding, casting, continuous casting, and so on. In such cases, three kinds of parameters are dominant: phases of metallic structures, temperature field, and elastic—or in many cases, inelastic—stress and strain. A variation in any of the three parameters will have an effect on the others, and the interaction is properly termed a metallo-thermo-mechanical coupling (Ref 1–7). Figure 1 depicts a schematic diagram for these parameters and the effect of their interaction (Ref 1–6). When the temperature distribution in a material (and in some cases the heating and cooling rate) is uniform, thermal stress: ● Is caused in the solid and the temperature-

dependent phase transformation

● Leads to alterations in metallic structure (i.e.,

austenite-pearlite and austenite-martensite transformation in the solid phase and the melting or solidification in solid-liquid transition); local dilation due to phase changes in the solid brings about transformation stress ● Interrupts the stress or strain field of the body. In addition, transformation plasticity effect is sometimes considered to be important (Ref 17– 21).

Metallo-Thermo-Mechanics Materials often behave in a complicated manner during engineering processes incorporating

Fig. 1

Metallo-thermo-mechanical coupling

Contrary to these effects, which are taken into account in ordinary stress analyses, arrows pointing the opposite direction indicate the coupling modes. Part of the mechanical work done by existing stress in the material converts into heat generation, thus disturbing the temperature. The acceleration of phase transformation by stress or strain, called stress- (or strain-)induced transformation (Ref 22–28), has been discussed and is sometimes applied to improve the mechanical properties of metallic materials. Arrow corresponds to the latent heat generation due to phase transformation, which affects the temperature distribution. When distribution of chemical composition occurs inside the material, say, in the case of carburized quenching, the effect of diffused carbon content also changes the property of such fields, as indicated by the dotted lines in the figure. Since mechanical and thermophysical properties appearing in the analysis of such fields depend on the material itself, the necessity of a database for the materials is strongly recognized, and some trials are ongoing. The aim of this section is to formulate the fundamental relationships governing these three interacting parameters relevant to some problems of heat treatment of steels, taking into account the effects of coupling, and to formulate some

Metallo-Thermo-Mechanics-Application to Quenching / 297

Kinetics of Phase Transformation A material undergoing structural change due to phase transformation is assumed to consist of a mixture of N constituents (Ref 29), such as pearlite, austenite, bainite, martensite, and liquid phase, as schematically shown in Fig. 2. Liquid phase is to be considered in welding, casting, or so on, but this is not necessary in the usual case of heat treatment. Denoting the volume fraction of the Ith constituent as nI, the mechanical and physical properties v of the material are assumed to be expressed by the mixture law as a linear combination of the properties vI of the constituents: N

v

兺 vI nI I⳱1

(Eq 1)

where N

兺

nI ⳱ 1

(Eq 2)

I⳱1

In the practice of heat treatment, mostly four kinds of volume fraction are chosen: pearlite nP, austenite nA, bainite nB, and martensite nM in the case of quenching. Diffusion-Type Transformation. Many rate equations for diffusion-type transformation have been proposed to depict pearlitic reaction from austenite, including the form by Johnson and Mehl (Ref 30): nP ⳱ 1 ⳮ exp(ⳮVe)

(Eq 3)

t0

where Ve ⳱ f (T) (t ⳮ s) ds, are employed as a basis. Here, Ve is the extended volume at time, t (0 ⱕ s ⱕ t). The existing stress, or sometimes strain, is known to accelerate the reaction, as experimentally observed by many authors (Ref 22–28). 3

Figures 3 (Ref 26) and 4 (Ref 25) show examples of pearlitic reaction accelerated by applied stress. So, the volume fraction of pearlite may be expressed as:

by use of the function w(rij) representing the effect of stress in the form:

nP ⳱ 1 ⳮ exp(ⳮVe)

J2 ⳱

Ve ⳱

t

冮

0

¯f (T, r ) (t ⳮ s)3ds ij

(Eq 4)

by modifying the Johnson-Mehl relation (Eq 3). For the function ¯f (T, rij), one uses: ¯ f (T, rij) ⳱ exp( prm) f (T)

(Eq 5)

since the time-temperature-transformation (TTT) diagram under the applied mean stress rm, with some extent p, on a logarithmic scale deviates from one without stress and since Eq. 5 expresses the normal TTT diagram by applying the function f (T). The same type of kinetic equation (Eq 4) might be adopted for the reaction of austenite from pearlite during heating process, when necessary. Diffusionless Transformation. The other type of phase transformation is the diffusionless one, or martensite reaction. In this reaction, volume fraction of martensite nM is just the function of temperature, but not of the history as seen in diffusion-type reaction, and the equation proposed by Magee (Ref 31).

w(rij) ⳱ Arm Ⳮ BJ 21/2 1 sij sij 2

Heat Conduction Equation and Diffusion Equation of Carbon The local energy balance or the first law of continuum thermodynamics is usually given in terms of internal energy U [⳱G Ⳮ Tg Ⳮ 1/qrij eeij] as (Ref 32): ˙ ⳮ rij e˙ eij Ⳮ qi ⳱ 0 qU xi

1.00

nM ⳱ 1 ⳮ exp[u(T ⳮ Ms)]

(Eq 6)

is widely used with the material parameter u, which means that martensite generates as the temperature changes from martensite start temperature Ms. Introducing thermodynamic considerations on the effect of stress based on the experimental evidence, the equation is modified to: nM ⳱ 1 ⳮ exp[u(T ⳮ Ms) ⳮ w(rij)]

(Eq 7)

0.75

0.25 0.00 10

Fig. 4

104

Growth of pearlite depending on stress

0.8 Fracture of martensite, ξM

•••

103

1.0

150

100

50

Tension 0.6

0.4 Compression 0.2

ξN

Concept of mixture. n1 to nN (N–end) denote the volume fractions of constituents.

102 Time (t ), s

Start time Finish time

ξ1

Fig. 2

σ, MPa ,0 , 72 , 144 , 226 , 316 , 412

0.50

250

Time (t), s

ξ3

(Eq 9)

with Gibbs free energy G, entropy g per unit mass with density q, stress rij, and elastic strain eeij. Applying the expressions for the specific heat c ⳱ (T g/T) and enthalpy H ⳱ (G Ⳮ Tg),

200

ξ2

(Eq 8)

The first term denotes the effect of mean stress rm (⳱rkk /3), and the second is that by deviatoric stress sij. The parameters A and B can be identified if one has the data of martensite transformation affected by stress as shown in Fig. 5 (Ref 26).

Fracture of pearlite, ξP

fundamental equations for the finite-element method.

0

Fig. 3

0

20

40 60 Stress (σ), MPa

80

100

Start and finish time of pearlite reaction depending on stress

0 0

500

1000

Stress (σ), MPa

Fig. 5

Martensite fraction depending on stress

1500

298 / Residual Stress During Hardening Processes Eq 9 is reduced to the general form of heat conduction equation: eeij H qcT˙ Ⳮ T r˙ ij ⳮ rij e˙ iji ⳮ q T eiij

冢

N

H e˙ iij ⳮ q j˙ Ⳮ q lI nI j I⳱1

冣

⳱ k

兺

2T xi x i

(Eq 10)

Here, Fourier’s heat conduction law: qi ⳱ ⳮk

T xi

(Eq 11)

with heat conductivity k is adopted, and the latent heat lI when producing the Ith constituent: H lI ⳱ nI

derive the constitutive equation. Readers are requested to refer to monographs on thermodynamics (Ref 32) for detailed discussion, but here the authors simply utilize some results for the application. The Gibbs free energy G in the thermodynamic state is assumed to be the function of stress rij, temperature T, and other internal variables related to inelastic deformation such as inelastic strain eiij, hardening parameter j, and back stress ␣ij as well as the volume fraction nI of each constituent or phase: G ⳱ G(rij , T, eiji , ␣ij, j, nI)

C C ⳱D t xixi

D ⳱ exp[a(C ⳮ b)]

兺 nI GI (rij, T, eiji , ␣ij, j) I⳱1

Ⳮ ␾I4(T ⳮ T0)dij Ⳮ ␾I1dij

(Eq 17)

GI(rij, T, eiji , ␣ij, j)

2␾I3 ⳱

1 Ⳮ mI EI

Now the restriction of the second law of thermodynamics, called Clausius-Duhem inequality is adopted, indicating that the internal dissipation is nonnegative, or that the inequality (Ref 32):

2␾I2 ⳱

mI EI

˙ Ⳮ gT) ˙ ⳮ r˙ ij eije Ⳮ rij e˙ iji ⳮq(G

when, EI, mI and ␣I are Young’s modulus, Poisson’s ratio, and thermal expansion coefficient of the constituent, respectively, and 3bI is volumetric dilation due to phase change in this case. Then, one has:

⳱ GIe(rij, T) Ⳮ GiI(T, eiji , ␣ij, j)

(Eq 18)

1 T ⳮ qi ⭌0 T xi

(Eq 19)

holds in every process. Applying Eq 16 to Eq 19 one obtains:

冣

冢

冣 (Eq 20)

When one focuses simply on the first term, the relation: eeij

Ge ⳱ rij

␾I4 ⳱ ␣I ␾I1 ⳱ bI

e eIij ⳱

G G r˙ ij ⳮ q g Ⳮ rij T

1 T T˙ Ⳮ • • • ⳮ qi ⭌0 T xi

(Eq 21)

is to be satisfied, otherwise the inequality is not satisfied for the change of stress rij. Substituting Eq 18 into Eq 21, one obtains:

(Eq 15)

Elastic Strain. In the case of a complicated coupling of mechanical field with temperature and phase change, continuum thermodynamics provides a tool for fundamental consideration to

(Eq 25)

Since the first two terms of Eq 25 mean the Hooke’s law, the third is thermal strain, and the fourth corresponds to isotropic strain of the Ith constituent provided that the parameters are constant, one can put:

N

eije ⳱ ⳮq

兺 nI I⳱1

GeI (rij, T) rij

(Eq 27)

with the Kronecher’s delta dij. Finally, elastic stress-strain relation of the mixture takes: eeij ⳱

1 Ⳮ m m rij ⳮ rkkdij E E Ⳮ ␣(T ⳮ T0)dij Ⳮ bdij

with global material parameters: E⳱

(Eq 22)

Expansion of Geij(rij, T) around the natural state rij ⳱ 0 and T ⳱ T0 (T0 is reference temperature),

(Eq 26)

1 Ⳮ mI mI rij ⳮ rkkdij EI EI Ⳮ ␣I(T ⳮ T0)dij Ⳮ bIdij

1 N

兺

nI EI

N

nImI EI

I⳱1

e˙ ij ⳱ e˙ eij Ⳮ e˙ iij

(Eq 24)

It is already confirmed in the framework of infinitesimal strain theory that the Gibbs free energy is divided into recoverable and inelastic parts:

冢

Stress/strain state in the process incorporating phase transformation is very complicated because inhomogeneous temperature and the gradient vary with time, thus inducing thermal stress and phase transformation stress. Such stress often exceeds the yield stress, and elasticplastic stress analysis considering the temperature-dependent material parameters is needed. Strain and the rate (or the increment) are generally assumed to be divided into recoverable elastic part e˙ eij and irrecoverable inelastic one e˙ iji .

N

兺 nIeIije I⳱1

eije ⳱

N

⳱

(Eq 23)

where uI0, uI1, uI2, uI3 and uI4 are the polynomial function of stress invariants and temperature and fI (T ⳮ T0) is the function of temperature rise. Then, Eq 22 reads:

eeIij ⳱ 2␾I3rij Ⳮ 2␾I2rkkdij

ⳮ eeij ⳮ q

Stress-Strain Constitutive Relation

ⳮ T0)rkk Ⳮ fI(T ⳮ T0)

G(rij, T, eiji , ␣ij, j, nI)

(Eq 13)

(Eq 14)

Ⳮ ␾I2(rkk)2 Ⳮ ␾I3rklrkl Ⳮ ␾I4(T

with

2

with diffusivity D as the form, for example:

GeI (rkl, T) ⳱ ⳮq[␾I0 Ⳮ ␾I1rkk

When the same hypothesis of mixture law for each phase is again applied to G, then:

(Eq 12)

is adopted. The third term on the left hand side of Eq 10 denotes the heat generated by inelastic dissipation, which is significant when compared with the elastic work represented by the second term, and the fourth term arises from the latent heat by phase change. Equation 10 is easily reduced to the original equation of heat conduction, provided these terms are neglected. As for the case of carburized quenching, one needs the distribution of carbon content diffused from the surface of the body. This process is generally performed before quenching, so the coupling with stress and structural change is not to be considered. Then, the normal type of diffusion equation for carbon content C takes:

(Eq 16)

based on the theory of isotropic function, leads to:

m ⳱

兺 I⳱1 N

n

兺 I I⳱1 EI

(Eq 28)

Metallo-Thermo-Mechanics-Application to Quenching / 299 N

␣⳱

兺 nI ␣I I⳱1

b⳱

兺 nIbI I⳱1

N

(Eq 29)

Yield Function and Plastic Strain Rate. Subsequent yielding as well as initial yielding of material with plastic strain epij, hardening parameter j at temperature T under multiaxial stresses is controlled by a criterion using the yield function expressed in stress space as: F⳱

F(rij, epij,

j, T, nI) ⳱ 0

(Eq 30)

with existing plastic strain epij, hardening parameter j, to be discussed later, temperature T, and volume fraction of phases nI. The yield function F necessitates a simple mathematical structure and is adequately capable to fit the experimentally observed yield condition. One of the most widely used yield functions in engineering practice is the von Mises type, taking the form: F⳱

1 1 sijsij ⳮ r¯ 2(j, T, nI) 2 3

(Eq 31)

where sij is the deviatoric stress such that: sij ⳱ rij ⳮ

1 dijrkk 3

(Eq 32)

and r(j, ¯ T, nI) stands for the flow stress of the material with hardened state j at temperature T, also depending on temperature T. The other type of yield function widely used for ductile metals is the Tresca type: F ⳱ (r1 ⳮ r3) ⳮ r(j, ¯ T, nI)

(Eq 33)

200 150

Torsional stress (τ), MPa

100 50

where r1 and r3 denote the maximum and minimum principal stresses. The hardening parameter j is identified depending on loading history, and the evolution is expressed either by plastic work as: j˙ ⳱ rije˙ ijp

(Eq 34)

or by equivalent plastic strain as: j˙ ⳱ e˙¯ p e˙¯ p ⳱

冪3 e˙ e˙ 2

p p ij ij

(Eq 35)

where epij is plastic (or inelastic) strain. The parameter defined by Eq 34 is sometimes called the work-hardening parameter, while the one by Eq 35 is the strain-hardening parameter. How the subsequent yield surface develops during the course of successive plastic loading is called the hardening rule. Experiments determining the surface show that the yield surface expands its diameter accompanying the shift of center position in stress space (see Fig. 6, Ref 33). For simplicity, however, two characteristic types of hardening rule are used. Isotropic-Hardening Hypothesis. The yield surface is assumed to expand isotropically in size, keeping the center by this hypothesis, which gives the yield function in the form: F ⳱ F(rij, j, T, nI) ⳱ f (rij) ⳮ r(j, ¯ T, nI)

(Eq 36)

This means that plastic strain epij does not affect the shape of the yield surface. The solid line in Fig. 7(a) illustrates the subsequent yield surface represented in p plane, while the circle indicated by a broken line is the initial surface. If the initial yield point is denoted by Y on the stress-strain curve in Fig. 7(b), unloaded stress AB from point A is the same as the compressive yield stress BC and is larger than initial yield stress. The concept of this hypothesis is too simple to express the generalized Bauschinger effect, but nevertheless it is widely used for many kinds of analyses when the direction of loading trajectory changes slightly. Original meaning of Bauschinger effect is such that yield stress with prior plastic strain

0 −50

−200

0 σ1 (a)

50

100

150

200

250

Tensile stress (σ), MPa

Fig. 6

How can one identify the back stress ␣ij in Eq 37? Two typical models can be used. The Prager model (Ref 34) asserts that the subsequent yield surface moves parallel to plastic strain rate e˙ pij and is expressed in the form: ␣˙ ij ⳱ C˙epij

(Eq 38)

with a parameter C. Since the plastic strain occurs perpendicular to the normal of the yield surface as is discussed later, the direction of ␣˙ ij by this model is parallel to the normal surface (see Fig. 9). The Ziegler model (Ref 35) to determine the back stress rate is expressed as: ␣˙ ij ⳱ l(r ˙ ij ⳮ ␣ij)

(Eq 39)

which follows that the center moves in the direction connecting the stress point and the back stress as seen in Fig. 9. Now, the normality of the plastic strain rate vector induced at the regular point of the yield surface leads to the flow rule for plastic strain rate: e˙ pij ⳱ K

F rij

(Eq 40)

σ

A 0

Experimentally determined yield surfaces

B

Y′

E

C

σ2

A Y

0

T °C 20 150 400 450 0

(Eq 37)

σ3 Y

−150

F ⳱ F(rij ⳮ ␣ij, T, nI)

σ

σ3

−100

(say, in compression) is lower than initial yield stress in the opposite direction (in tension). The concept is extended to the general case in multidimensional stress space, and the generalized Bauschinger effect is stated as the change in yield stress in the different direction from that in prestrained direction. Kinematic-Hardening Hypothesis. The model assumes that the yield surface with unchanging shape moves in stress space due to plastic deformation as illustrated in Fig. 8(a), and stressstrain diagram is given under the condition YY⬘ ⳱ AC in Fig. 8(b). Qualitative representation of Bauschinger effect is available by this model since OY BC. Provided the center of the yield surface in stress space, called back stress, is denoted by ␣ij, the mathematical description of the kinematichardening hypothesis is now derived by substituting rij ⳮ ␣ij instead of rij as the initial yield function in Eq 36 as:

(b)

B

0 σ1 (a)

Y′

E

C

σ2 (b)

300

Fig. 7 curve

Representation of yield hypothesis of isotropichardening type. (a) Yield surface. (b) Stress-strain

Fig. 8 curve

Representation of yield hypothesis of kinematichardening type. (a) Yield surface. (b) Stress-strain

300 / Residual Stress During Hardening Processes since the normal direction of the function F in stress space is represented by F/rij. The parameter K is a function that depends on stress, stress rate, and strain and its history. Since the equation implies that the plastic strain rates derived from a potential F, the theory is known as the plastic potential theory. The next problem is how to identify the parameter K in Eq 40. During plastic loading, the stress components always satisfy the yield condition F ⳱ 0 at any moment, which implies F˙ ⳱ 0. Then, one has the relation called the Prager’s consistency relation: F F F F˙ ⳱ r˙ ij Ⳮ p e˙ ijp Ⳮ j˙ rij eij j N

F ˙ nI ⳱ 0 nI

兺

I⳱1

(Eq 41)

Substituting the expression in Eq 40 into Eq 41 as well as the definition of hardening parameters in Eq 34 and 35, the parameter K is easily determined as:

冢

Ⳮ

冣

兺

冣

˙ ⳮ 1 F F T˙ (˙ekl ⳮ dkl␣T) S0 rij T (Eq 47)

where S0 ⳱

1 ˆ 2GG

Ⳮ

F F rmn rmn

(Eq 48)

(Eq 42)

1 F F ˙ T S0 r T

冦冧

{r}T ⳱ {rx ry rz sxy syz szx} (Eq 50)

0 0}

冢

兺

0 0 0

ε• ij

p

F ˙ F nI nI rij

冣

−1.0

Axial stress, σz (MPa) 50 0 −30 −50

−1.5

α• ij (Prager)

α• ij

−2.5

(Ziegler)

0

αij

1/2

冣

F j

(Eq 45)

for the strain-hardening parameter in Eq 35. Rate Form of the Stress-Strain Relation. The elastic strain rate e˙ eij is easily derived from Eq 28: e˙ eij ⳱

冢

冣

1 m r˙ ij ⳮ dijr˙ kk 2G 1 Ⳮ m Ⳮ dij␣T˙ Ⳮ dijb

(Eq 46)

where G, m, and ␣ stand for shear modulus, Poisson’s ratio, and linear expansion coefficient, respectively, in the global forms in the sense of Eq. 29. Substituting Eq 44 and 47 into Eq 46,

Fig. 9

− Equivalent stress, σ

mn

F rmn

800

0 169 MPa 137 92 55 0

0

1 F F ⳱ ⳮ p ˆ rmn emn G 2 F

600

0.5

σij − αij

for the work-hardening parameter in Eq 34, and:

冢3 r

400

(a)

σij

(Eq 44)

Direction of back stress evolution

Axial strain (εz), %

冣

200


P

1 F F F ⳱ ⳮ p Ⳮ rmn ˆ emn j rmn G

ⳮ

冥

1 ⁄2 0 1⁄2 0 0 1⁄2 (Eq 52)

0 0 0

(Eq 43)

ˆ is termed as the hardening function and Here, G takes the form:

冢

0 0 0

0

ˆ F r˙ kl Ⳮ F e˙ pij ⳱ G rkl T

I⳱1

冤

sym

(Eq 49)

{e}T ⳱ {ex ey ez cxy cyz cyx}

and finally:

T˙ Ⳮ

1 ⳮ m 1 ⳮ 2m m 1 ⳮm 1 ⳮ 2m 1 ⳮ 2m m m 1 ⳮ m [De] ⳱ 2G 1 ⳮ 2m 1 ⳮ 2m 1 ⳮ 2m

and (see Eq 53). As an example of yield functions, consider

˙ {r} ˙ ⳱ [Dep] ({˙e} ⳮ {␣}T)

{␣}T ⳱ {␣ ␣ ␣ 0

N

with

For further application of the constitutive equation in the finite-element method, it is useful to present the relation in the matrix form (Ref 36):

ⳮ

(51)

−0.5

F ˙ nI nI

I⳱1

冢

[Dep] ⳱ [De] ⳮ [Dp]

where the components in matrices of stress and strain in engineering notation and coefficient of linear expansion are, respectively:

ˆ F r˙ mn Ⳮ F T˙ K⳱G rmn T N

m 1 F F r˙ ij ⳱ 2G dikdjl Ⳮ dijdkl ⳮ 1 ⳮ 2m S0 rij rkl

Here, the matrix [Dep] is given as (Ref 36):

Axial dilation (Ez), %

F ˙ Ⳮ TⳭ T

one obtains the expression for the total strain rate:

−0.5

−1 −41 −82 −137 −164

−1.5

dσ− H ′ = −−−−− d− εp −2

0

200

400

600

800

Temperature (T ), °C 0 0

Fig. 10

Equivalent plastic strain, −εp Stress-plastic strain curve and definition of hardening coefficient

(b) Experimental data of the effect of applied stress on induced strain. (a) Pearlitic transformation. (b) Martensitic transformation

Fig. 11


2G [D ] ⳱ S0 p

                  

F

2

冢r 冣

sym

x

F F rx ry

冢r 冣

F

F F rx rz

F F ry rz

冢r 冣

1 F F 2 rx sxy

1 F F 2 ry sxy

1 F F 2 rz sxy

1 F 4 sxy

1 F F 2 rx syz

1 F F 2 ry syz

1 F F 2 rz syz

1 F F 4 sxy syz

1 F 4 syz

1 F F 2 rx szx

1 F F 2 ry szx

1 F F 2 rz szx

1 F F 4 sxy szx

1 F F 4 syz szx

2

y

F

2

z

the von Mises condition with isotropic hardening: F⳱

1 1 sijsij ⳮ r(¯ ¯ ep, nI)2 2 3

(Eq 54)

冢冣

2

2

冢冣

1 F 4 szx

2

冢冣

                  

冢

1 2 ⳱ ⳮ smnsmn ˆ 3 G

dr¯

p

(Eq 55)

Introducing Eq 55 into Eq 43 with T˙ ⳱ 0 leads to the so-called Prandtl-Reuss flow rule: (Eq 53) e˙ pij ⳱

3 e¯˙ p sij 2 r¯

(Eq 56)

The hardening coefficient H ⬘ is defined as the tangent modulus of the (equivalent) stress(equivalent) plastic strain diagram in Fig. 10. When employing H ⬘, Eq 56 becomes:

Here, temperature dependence on flow stress r¯ is ignored for simplicity. Bearing in mind that F/rij ⳱ sij, the hardening function in Eq 45 is easily expressed as:

e˙ pij ⳱

3 r¯˙ sij 2 rH ¯ ⬘

(Eq 57)

The matrix [Dp] in Eq 53 is simplified in this case (Ref 37) to the form:

2G S0

0.2 Transformation plastic strain (εtp), %

2

˙ 4 r¯ 2r¯ ¯ p 3 e˙

⳱

[Dp] ⳱ z

冤

s2x sxsy sxsz sxsxy sxsyz sxszx

s2z 2 szsxy sxy szsyz sxysyz s2yz szszx sxyszx syzszx s2zx

(Eq 58)

with

2

0

5

S0 ⳱

6

−0.1

1 3

2 1 r˙¯ r¯ 1 Ⳮ 3 3G e¯˙ p

冢

⳱

−0.2

7 8

Experimental −25

0

25

冥

sym s2y sysz sysxy sysyz syszx

0.1

−0.3 −50

冣

2 H⬘ r¯ 1 Ⳮ 3 3G

冢

冣

(Eq 59)

Creep Strain. When the quenching time is

4

50

y

Stress (σ), MPa (a)

(a)

z

0.5 Transformation plastic strain (εtp), %

1/2

冣冢ⳮ 3 r¯ d¯e 冣

Pre/postprocessor

2 18

10 0.4

9

6

3 19

Intermediate file

Intermediate file

14 13

0.3 7

21 11

0.2

12

1 17 5

Interface

15 4 0.1 Experimental 0

16

Post-treatment file

20

0

25

50

75

8

y

100

Stress (σ), MPa (b) Transformation plastic strain versus applied stress diagram. (a) Pearlitic transformation. (b) Martensitic transformation

Control/analytical condition file

List image data file Solver

x

Final results file

(b)

Fig. 12

Node/element file

Fig. 13

Finite elements available in the system. (a) Two-dimensional. (b) Three-dimensional

Fig. 14

Material database Structure of HEARTS


e˙ iij

⳱

e˙ pij

Ⳮ

e˙ cij

(Eq 60)

e˙ pij

Here, the plastic strain rate is given in Eq 43, and the creep strain rate e˙ cij is given in the similar form: e˙ cij ⳱ Kc

G rij

(Eq 61)

is normally expressed as a linear function of applied stress, and the rate is expressed by: e˙ tp ij ⳱

3 2

N

兺 KIh(nI)sij I⳱1

h(nI) ⳱ 2(1 ⳮ nI)

(Eq 66)

for N kinds of transformation in the form of Greenwood–Johnson (Ref 38). This component of strain is also superimposed to inelastic strain rate, if necessary.

0.8 Experimental Calculated Carbon content (C), %

long in the case of machine component with large dimension, effect of time on inelasticity is not negligible, especially at elevated temperature. This effect in metals and alloys is due to creep in most cases. Such time-dependent (or rate dependent) inelasticity, sometimes termed viscoplasticity, has been developed to formulate sophisticated constitutive equations, under plasticity-creep interaction condition. The most simple and practically used constitutive model is the so-called superposed type of plasticity and creep, while the unified model does not separate the inelastic strain into two parts. In the superposed model, the inelastic strain rate e˙ iij in Eq 15 is composed of plastic and creep strain rates:

by use of creep function, equivalent to the yield function:

0.6

0.4

0.2

Method of Numerical Simulation A series of equations governing the heat treatment process described previously are to be numerically solved, since the fundamental equations, Eq 4, 7, 10, and 15 are highly nonlinear. There are some techniques for numerical calculation, but the finite-element method (FEM) would be most promising for engineering practice. Based on the theory available to the heat treatment simulation, the authors developed some programs for simple case of two-dimensional and axisymmetric problems in their laboratory to simulate the quenching process of a solid and thick-walled cylinders, and gear wheels (Ref 39– 44). In 1992, modification of the program was carried out to develop the computer-aided engineering (CAE) system HEARTS (HEAt tReaTment Simulation code) by the cooperation with CRC Research Institute Company, Japan, to deliver a commercial code, and it has been used by many users. After the development of the HEARTS, some codes were independently released: DEFORM-

0 0

1.0

2.0

3.0

4.0

Distance from center (r ), mm

G ⳱ G(rij, ecij, jc, T, nI)

(Eq 62)

Fig. 15

Distribution of diffused carbon 900

with creep-hardening parameter j . Consistency relation held during creep loading:

(Eq 63)

leads to the final form for creep constitutive equation: G

冢r

r˙ kl Ⳮ

kl

N

Ⳮ

G

G ˙ T T G

兺 n˙ I冣 rij I⳱1 nI


400

200

Without transformation plasticity

0 0

1.0

3.0

2.0

von Mises or Tresca type is also employed when the creep function is similar to the yield function. Transformation Plastic Strain. Large inelastic deformation is induced under relatively low stress applied during phase transformation (Ref 17–21). As is observed in some alloys, such an inelastic strain is sometimes very large, thus called transformation superplastic strain. The strain induced during quenching is, however, mostly small since the operating time is relatively short; this phenomenon is simply called transformation plasticity. Figure 11(a) (Ref 21) and (b) (Ref 19) show examples of experimental data of the effect of applied stress on the induced strain during pearlite and martensite transformations, respectively. The transformation plastic strain is plotted against applied stress in Fig. 12 (Ref 21), which

Fig. 16

600 300 0 −300

4.0

5.0

σz σθ σr

−600 −900

0

6.0

Time (t ), s

(Eq 64)

Fig. 18

2 3 1 Distance from center (r ), mm

4

Residual stresses distribution

Temperature variation on the surface 900

Volume fraction of constituents, ξA, ξM, ξP

ˆc e˙ cij ⳱ G

600

1.0

Axial residual stresses (σz), MPa

兺

800


˙ ⳱ G rij Ⳮ G e˙ ijc Ⳮ G T˙ G rij eijc rT N G Ⳮ ⳱0 I⳱1 nI

Residual stresses (σr, σθ, σz), MPa

c

Pearlite

0.8 0.6 0.4

Martensite 0.2 Austenite 0

0

Fig. 17


4

Distribution of volume fraction of martensite, pearlite, and retained austenite

Experimental With transformation plasticity Without transformation plasticity

600 300 0 −300 −600 −900

0

Fig. 19


4

Effect of transformation plasticity on axial residual stresses



HT by SFTC Company, United States; SYSWELD by FRAMATOME Company, France; GRANTAS by Komatsu Company, Japan (see Ref 45). By introducing the optional code available to calculate phase change calculation into ABAQUS, some trials are also made. The strategy and the structure of the HEARTS are briefly introduced in this section. 1200 1000 800 600 400 200 0

S45C out-top S45C out-mid S45C in-mid SUS304 out-top SUS304 out-mid SUS304 in-mid

1

2

5

Volume fraction of austenite and martensite (ξA, ξM), %

(a)

10 20 Time (t ), s

50 100

250

The finite elements available for the HEARTS system are two- and three-dimensional type as illustrated in Fig. 13. The two-dimensional element in Fig. 13(a) is converted to a triangular element by overlapping three nodes, for example, No. 1, 2, and 5, and other threedimensional type elements are easily generated by joining the three nodes located on the corner in Fig. 13(b). The continuum elements are used in the analyses of heat conduction, stress/strain, and diffusion. The two-dimensional element in Fig. 13(a) is also applied to axisymmetrical problems. For stress/strain analysis, plane stress/strain problems and generalized plane

strain problems are also available. This procedure is proposed for developing a program for practical use that can analyze very large systems and add some different types of elements and kinds of functions without difficulty. In the case of the coupled analysis of timedependent metallic structure, temperature, and stress/strain, the step-by-step method with very short time step is employed to avoid the increase of necessary memory due to the nonsymmetric matrix and also to reduce execution time. The heat-conduction analysis is carried out by considering the latent heat generation calculated by microstructural evolution analysis followed

100 80

Martensite

60 40

Austenite

20 0

1

2

5

10 20 Time (t ), s

50 100

250

1

2

5

10 20 Time (t ), s

50 100

250

Radial displacement (Ur), mm

(b) 0.4 0.3 0.2 0.1 0.0 −0.1

(c) Axial displacement (Uz), mm

0.25 0.20 0.15 0.10 0.05 0.00 −0.05

1

2

5

10 20 Time (t ), s

50 100

Fig. 22

Mode of distortion of cross section (central axis on the left)

Fig. 23

Distributions of tangential and axial residual stresses on the top surface

250

(d) Variation of temperature, structures, and distortions, at typical locations of a ring for carbon steel and SUS304

ρ

Tangential plastic strain (εθ), %

Fig. 20

0.6 0.4 S45C 0.2

SNC815

0 SCM440 −0.2 −0.4 36

Fig. 21

SUS304 38

40 42 44 46 Radius (r ), mm

48

50

Tangential plastic strain distribution for four steels


Fig. 24

by the stress/strain analysis depending on the structural distribution based on the temperature distribution determined. When the stress/strain analysis ends, calculation in the next step is carried out. In the case when the coupling effect is negligible, independent analysis of three fields is also possible. The time integration in the heat conduction and diffusion analyses employ the hmethod, which is reduced to the trapezoid and Euler backward methods in the special cases. Nonlinear equations in each analysis are made by the Newton’s iteration method. CAE Environment. As shown in Fig. 14, the system HEARTS was developed under the prerequisite condition to be used in the CAE environment combined with a proper pre/post-processor. The system is designed for exchanging data between solver and pre/post-processor, such as PATRAN and I-DEAS. Data necessary for the simulation are created by a pre/post-processor. These data are output in the format of “intermediate file” and then converted into “control/analysis condition data file” and “nodal point/element data file” by an interface program. In addition, input data regarding the characteristics of the elements are made by users in the form of “characteristics data file.” The results of calculation by the solver are output in such forms as “post-processing file,” “list image file,” and “restart file.” The contents of the post-processing file are converted to the form of the intermediate file through the interface. The resulting data contained in the intermediate file can be displayed in various forms by using the pre/post-processor according to the instructions of the users.

Distributions of tangential and axial residual stresses on the outer face

Illustrative Examples of Simulation

Time-dependent distribution of diffused carbon content

5000 4000 3

2

1

3000 2

1 2000 4

3

1000 0

0

Fig. 26

200

400 600 800 Temperature (T ), °C

1000

Temperature-dependent heat transfer coefficient on each face (Ref 46)

0.4

Radial displacement (ur), mm

4 Radial displacement (ur), mm

Heat transfer coefficient (ht), W/(m2 • °C)

Fig. 25

Some examples of simulated results on temperature, structural change, and stress/strain as well as carbon content during the heat treatment process of engineering components in two- (or, axisymmetric) and three-dimensional shape and a Japanese sword are illustrated by use of the system HEARTS combined with an available pre/post-processor, and the validity of the system is evaluated by comparing with experimental data.

With TP Without TP Outer Inner

0.3 0.2 0.1 0 −0.1 1 (a)

Fig. 27

10

102 Time (t ), s

103

104

0.4 0.3 0.2 0.1 0 −0.1 1 (b)

10

102 Time (t ), s

103

104

Variation of radial distortion. TP, transformation plasticity. (a) Carburized quenching. (b) Normal quenching

Metallo-Thermo-Mechanics-Application to Quenching / 305 Carburized Quenching of Cylinder The first example is the carburized water quenching of a long cylinder of a case-hardening steel containing molybdenum (Ref 8). The cylinder of 8 mm diameter is treated. Since the cylinder is assumed to be long enough and no temperature gradient is imposed in axial direction, the calculations are made for a series of elements arrayed in the radial direction, and the generalized plane-strain condition for the stress/strain analysis is such that the resultant surface force acting in axial direction disappears, and that axial displacement of all nodes at any radial point is the same, or the axial cross section is kept inplane. Before quenching, the cylinder is kept in methane gas at 925 C for carburization for 9000 s and diffused for 9000 s in vacuum. Calculation of diffusion mode of carbon based on the diffusion equation (Eq 13) is made prior to quenching, and the result is shown by solid line in Fig. 15. Circles in the figure denote the experimentally measured data by x-ray diffraction, which gives good agreement with the simulation. The cylinder is heated to 800 C and quenched in water at 20 C. Calculated temperature variation on the surface is presented in Fig. 16. Here, the solid line is the data when considering the effect of transformation plasticity formulated by Eq 66, while the broken line is without the effect. At the beginning of cooling from 800 C, no difference is seen between both lines, but from the pearlite start temperature at 400 C, where the latent heat generation raises the temperature, the effect of transformation plasticity appears. Figure 17 represents distribution of volume fraction of metallic structures after quenching such as martensite, pearlite, and retained austenite. Calculated residual stress distribution in axial, tangential, and radial components are plotted by curves in Fig. 18 with the comparison of measured axial residual stress indicated by circles near the surface. The effect of transformation plasticity on the residual stress is also depicted in Fig. 19.

t=8s ξ M, % 100

80 70 60

t = 30 s

50 40 30

t = 600 s

20 10 0

t = 2400 s With TP

Fig. 28

Without TP

Successive change of cross section with martensite fraction (central axis on left). TP, transformation plasticity

(a)

(b) With transformation plasticity Without transformation plasticity Iinitial Experimental

Induction Hardening and Carburized Quenching of Ring A ring-shaped body is widely used as a typical example of fundamental quenching tests, since it is also considered as a model of a gear wheel with boss hole. From this viewpoint, two kinds of simulations are carried out: one is induction hardening (Ref 11), and the other is carburized quenching (Ref 12), discussed in next section. A ring with the dimension of 100 and 75 mm in outer and inner diameter, respectively, and 24 mm in height has the upper half modeled as the axisymmetric problem. Induction heating is made on the outer surface with expected hardening depth of 2 mm during 4.0 s heating period, followed by cooling (Ref 14). Materials employed are carbon steel (JIS-S45C), Cr-Mo steel (SCM440), and Ni-Cr steel (SNC815) with hardenability and stainless steel (SUS304) without hardenability for comparison.

90

t = 15 s

Fig. 29

Comparison of distorted cross section with experiment. (a) Carburized quenching. (b) Normal quenching

Fig. 30

Comparison of residual stresses with experiment. (a) Carburized quenching. (b) Normal quenching


Fig. 31

Additional magnetic field to metallo-thermomechanical coupling

The heat generation during induction heating is assumed to occur in the area of 2.0 mm depth from the outer surface. The heat-generation rate is determined by trial and error so that the maximum temperature at the surface reaches the measured value. All surfaces are regarded as adiabatic boundary during heating process, while in cooling process the outer surface is defined as the convection boundary with uniform and constant convection coefficient 20,000 W/(m2 • K). To know the effect of hardenability, or phase transformation, on some parameters, calculation of temperature, structures and distortion at typical locations of the ring are compared for typical two steels of plain carbon steel and SUS304 in Fig. 20, and the difference in plastic strain distributions for four steels is depicted in Fig. 21. Such effect is characterized for distortion for four steels as seen in Fig. 22 with triangles indicating measured data; volumetric dilation due to martensitic transformation is seen to give the expansion of radius (see Fig. 22a, b, and c), while contraction in diameter occurs for SUS304 (Fig. 22d). Figure 23 depicts the distributions of tangential and radial residual stresses on the top surface where a wavy pattern of stress is observed in SUS304 steel. Tangential and axial stresses on the outer surface are shown in Fig. 24.

Carburized Quenching of Ring To investigate the more detailed behavior of the influence of transformation plasticity on carburized quenching, a ring of chromium-molyb-

Fig. 32

denum steel (SCM420) with 25 and 75 mm inner and outer diameter, respectively, with 10 mm in height is employed for the simulation (Ref 12). Carburizing and diffusion were performed in the atmosphere of controlled butane gas keeping carbon potential Cp at 1.2% for 4 h and 0.85% for 1 h at 930 C, respectively, followed by intermediate period for 1 h and steady temperature stage of 850 C for 30 min with Cp ⳱ 0.85%. Consequently, quenching was carried out with a hot oil quenchant of 130 C and specimen was kept in oil bath for 10 min. Flat surface of the specimen was held horizontally in both carburizing and quenching. Figure 25 represents the calculated time-dependent distribution of diffused carbon content with the experimental data by means of electron probe microanalysis (EPMA) from flat surface to 2.5 mm in depth. Carbon seems to diffuse beneath the surface with carburizing time, and the gradient becomes lower with diffusion time. Experimental data measured by EPMA after the process of 23,400 s show good agreement with calculated results. Different values of heat transfer coefficient (Fig. 26) are applied to each surface according to the experimental data by Bodin and Segerberg (Ref 46). After 10 min elapsed, air cooling was executed until complete cooling with steady heat transfer coefficient of 200 W/(m2 • C). The simulated variation of radial distortion with respect to time at the middle point on outer and inner faces of quenched ring in both conditions with and without consideration of transformation plasticity is depicted in Fig. 27(a) for carburized and normal quenching, respectively.

Finite-element discretization of a gear and induction coil

1200 Simulated Measured Tip PCD Bottom


1000 Tip

PCD

800

Fig. 34

Generated heat pattern. t ⳱ (a) 0.0 s. (b) 1.8 s. (c) 2.7 s. (d) 2.88 s

tt=13,500 s

600 400 9,000 s

200 0

0

Fig. 33

1

2

3 Time (t ), s

4

5

6

Simulated and measured temperature variation

Fig. 35

Temperature pattern. t ⳱ (a) 1.8 s. (b) 2.88 s


Fig. 36

In the case of carburized quenching, radial displacement both at outer and inner faces is moderate when considering the effect in comparison with that without transformation plasticity. In the case of normal quenching, on the other hand, the effect on radial displacement is smaller, as shown in Fig. 27(b). Variations of the simulated cross-sectional distortion with and without the effect are shown in Fig. 28 with the volume fraction of martensite. Outer sides of ring in different conditions at ap-

Pattern of martensite fraction

Volume fraction of martensite, ξm

1.0

0.8 Tip

PCD PCD

0.6

0.4

0.2 0

9,000 s Tip 0

Fig. 37

Root

4 3 2 1 Distance from surface (d ), mm

5

Distribution of martensite fraction

proximately 8 s are similarly distorted to the bottom due to the difference of heat transfer coefficient among the surfaces. Since martensite transformation starts around at 15 s from the corner for normal quenching (see Fig. 28b), the concave shape of cross section takes place, while a similar shape is seen in the final stage for carburized quenching without transformation plasticity effect. The effect appears at 30 s in the case of carburized quenching to give a convex shape being kept until end of cooling at 2400 s. Figure 29 illustrates the simulated distortion of cross section at final step under both conditions. Solid lines in the figure represent the estimated pattern of distortion from initial shape shown in thin dotted line when considering the effect. Experimental results of distortion are plotted in solid marks in the figure to compare with simulated patterns. The most remarkable difference between surfaces with transformation plasticity and those without in carburized quenching lies in the mode of distortion as depicted in Fig. 28 and 29. The transformation plasticity gives a convex shape to all surfaces, but surfaces without transformation plasticity are concave. Experimental data agree well with simulated distortion with the effect in both carburized and normal quenching. Residual stress distribution for carburized and normal quenched ring are represented in Fig. 30. It is concluded that the transformation plastic strain contributes remarkable effects on distortion of ring-shaped models especially in the case of carburized quenching.

Dual-Frequency Induction Hardening of a Gear Wheel

Fig. 38

Distortion of a tooth. (a) Dual frequency. (b) Single frequency

Fig. 39

Heat transfer coefficient depending on clay thickness

Dual-frequency induction hardening is conducted for suitable appropriate preheating period by medium frequency (3–10 kHz) and a rapid subsequent heating by high frequency (100–250

Fig. 40

Pattern of pasted clay

Fig. 41

Finite-element meshes. (a) Global view. (b) Near the tip

308 / Residual Stress During Hardening Processes kHz) followed by spray quenching. This process makes it possible to achieve contour hardening, and the advantage of the process is to provide high hardness and residual compressive stresses on the surface compared to small distortion with enough toughness in the core part. The pattern of frequency used in the present experiments is 3 kHz for 1.8 s in preheating and 150 kHz for 0.18 s during subsequent heating (Ref 13).

Fig. 42

Effect of clay thickness on martensite distribution

Fig. 43

Successive mode of distortion with temperature variation

Combining two kinds of coupling analyses, metallo-thermo-mechanical and electromagnetic, to evaluate heat generation during heating and to introduce the result into the calculation of metallo-thermo-mechanical fields is performed by the HEARTS and MAGNA, for electromagnetic field analysis (see Fig. 31). The magnetic permeability generally depends on the magnetic field as well as on temperature. One assumes,

Fig. 44

however, in the first approximation of practical calculation, that permeability is constant in the workpiece during heating since the magnetic field is almost steady, but that the magnetic permeability and conductivity are functions of temperature. The workpiece treated throughout the study is a spur gear of 0.45% C steel (JIS-S45C). The dimensions are 126 mm outside diameter, 120

Successive mode of fraction of martensite (a) and pearlite (b)

Metallo-Thermo-Mechanics-Application to Quenching / 309 mm in the pitch circle diameter (PCD) (or module 3), 66 mm in boss hole diameter, and 20 mm in tooth width with 40 teeth. A one-turn coil with an inner diameter of 130 mm and a cross-sectional area of 22 by 35 mm2 is equipped outside of the gear wheel. Figure 32(a) shows finite-element division of a gear and coil. The workpiece is enlarged in Fig. 32(b). The simulated and experimental temperature variations at three typical locations such as the tooth tip, PCD, and the bottom in dual-frequency induction hardening are depicted in Fig. 33. The simulated distribution of heat generation at the beginning of heating t ⳱ 0.0 s and the end of heating at t ⳱ 1.8 s during preheating are shown in Fig. 34(a) and (b), respectively. Figures (c) and (d) represent the distributions at the beginning of heating t ⳱ 2.7 s and the end of heating t ⳱ 2.88 s in the subsequent heating process. The simulated temperature variation at the tooth bottom is delayed, as seen in Fig. 33, but the maximum temperature is higher compared to the measured one in preheating. In the subsequent heating stage, the temperature variations agree well with measured data except at the tooth bottom saturating to around 800 C. One of the reasons for this disagreement may come from rough mesh division in depth direction.

Fig. 45

Successive mode of longitudinal stress

Simulated results of temperature distribution at the end of the preheating and the subsequent heating in the dual-frequency process are shown in Fig. 35(a) and (b), respectively. Volume fraction of martensite after quenching is also presented in Fig. 36, and Fig. 37 shows the distribution of martensite fraction, the pattern of which is similar to measured values of Vickers hardness. Figures 38(a) and (b) represent the comparison of simulated distortion for induction hardening using dual frequency and conventional, single frequency. Actual distortion of 5 lm is expressed by 2.0 mm in the geometry scale. When comparing the two cases, the distortion of conventional induction hardening in the tooth width direction is about two times as much as that of dual-frequency induction hardening. The typical characteristic of dual-frequency induction hardening that less distortion and deformation occur due to hardening only in the contour zone is confirmed by these results.

Quenching of Japanese Sword Quenching of a Japanese sword is one of the typical examples of quenching processes. The

sword master controls the initial heating temperature and that of water as well as the heat transfer coefficient by pasting a kind of clay on the surface. The blade pattern with martensite structure, called hamon, and distortion or bent shape, termed sori, are evaluated from artistic viewpoint. Most Japanese swords with some exceptions are made of steel called tamahagane, or traditional Japanese steel, specially prepared by the tatara system using iron sand, not normal iron ore. The hammering process is repeated to obtain a block, where about 15 folds, called orikaeshi, are repeated to get laminated materials bonded by the mechanism of mechanical alloying. Before quenching, mixed clay with powders of charcoal and whetstone, yakibatsuchi, is pasted on the surface of the sword to control the heat transfer coefficient depending on the thickness (see Fig. 39). The thickness on the back is about 1 mm and 0.1 mm on the blade, as shown in Fig. 40. Then, the sword is heated up to about 800 C in the furnace and quenched in water of 40 C. During this process, the tip is severely cooled to be the blade made of martensite structure, while the other part is transformed into pearlite and troostite. Very complicated deformation, or sori, is observed during the process due to the time delay of cooling and phase transformation, and the stress changes to induce the residual stresses. Three-dimensional finite-element mesh division of the sword is represented in Fig. 41, which shows the sword cut in half in the width direction for symmetry. This model is supposed to consist of two regions to which different material data are applied and also two parts of the surface with heat transfer coefficients of different values. To investigate the effect of the clay thickness on the martensite formation corresponding to the width of blade, quenching simulations are made with different patterns of pasting the clay. Figure 42 shows the volume fractions of martensite after quenching under different conditions. When the sword is quenched without any clay, martensite hardly appears except for on the blade (Fig. 42a). However, almost the entire region becomes martensite when thin clay is pasted on the entire surface as shown in Fig. 42b. If the clay is pasted thin on the blade side, and thick on other part, an ideal pattern of martensite is obtained, where martensitic hardened blade and ductile, pearlitic main body are realized (Fig. 42c). The border of the martensite structure in white color is termed hamon. Figure 43 shows the temperature distribution of the sword with time variation from the beginning of the quenching, and the mode of enlarged deformation is also depicted in the figure. The thin part of the blade shrinks by thermal contraction due to severe cooling, which leads to downward bending, termed as gyaku-sori, or reverse bending. However, when martensitic transformation starts to occur in that part, normal bending, or sori, to the upper direction is observed due to the volumetric dilation by martensite formation. Gyaku-sori again appears, be-


3.

4.

5.

6.

7.

8. Distribution of residual stress along typical three portions. (a) Hasaki, edge (b) Shinogi, ridge (c) Mune, back surface

Fig. 46

cause of the pearlitic transformation in the back part. In the successive stages, the back side shrinks gradually because of thermal contraction, and finally normal bending can be obtained owing to the difference of the coefficient of dilation by martensite and pearlite transformation, as shown in Fig. 44. The change in the longitudinal stress distribution on the surface and the inside of the sword is represented in Fig. 45. The calculated residual stresses in the longitudinal direction on typical three locations of the sword being equivalent to the stress distribution at t ⳱ 30 s are depicted in Fig. 46, and the data are compared with experimental data denoted by solid circles by x-ray diffraction technique.

9.

10.

11.

REFERENCES 1. T. Inoue, S. Nagaki, T. Kishino, and M. Monkawa, Description of Transformation Kinetics, Heat Conduction and Elastic-Plastic Stresses in the Course of Quenching and Tempering of Some Steels, Ing.-Archiv., Vol 50 (No. 5), 1981, p 315–332 2. T. Inoue and Z.G. Wang, Coupling Phenomena between Stress, Temperature and Metallic Structures in the Process with Phase Transformation, Proc. of the Inter-

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national Symposium on Calculation of Internal Stresses in Heat Treatment of Metallic Materials, Linkoping Univ. Press, 1984, p 298–310 T. Inoue, Metallo-Thermo-Mechanical Coupling—Application to the Analysis of Quenching, Welding and Continuous Casting Processes, Berg Huttenmann. Monatsh., Vol 132 (No. 3), 1987, p 63–71 T. Inoue, Inelastic Constitutive Relationships and Applications to Some Thermomechanical Processes Involving Phase Transformation, Thermal Stresses V, R.B. Hetnarski, Ed., North Holland, 1988 T. Inoue, Metallo-Thermo-Mechanics— Application to Phase Transformation Incorporated Processes, Trans. JWRI, Special Issue on Theoretical Prediction in Joining and Welding, Vol 25 (No. 2), 1996, p 69–87 T. Inoue, Residual Stress and Distortion— Metallo-Thermo-Mechanics Simulation of Engineering Processes Incorporating Phase Transformation, Mathematical Modeling of Weld Phenomena, H. Cerjak, Ed., IOM Communications Ltd., Vol 4, 1998, p 547– 575 T. Inoue and B. Raniecki, Determination of Thermal-Hardening Stresses in Steels by Use of Thermoplasticity Theory, J. Mech. Phys. Solids, Vol 26 (No. 3), 1978, p 187– 212 T. Inoue, K. Arimoto, and D.Y. Ju, MetalloThermo-Mechanical Simulation of Quenching Process—Theory and Implementation of Computer Code “HEARTS,” Proc. First Int. Conf. Quenching and Control of Distortion (Chicago, IL), ASM International, 22–25 Sept 1992, p 205–212 T. Inoue, K. Arimoto, and D.Y. Ju, Theory and Implementation of Heat Treatment Simulation Program “HEARTS,” Proc. Eighth Int. Congress on Heat Treatment of Materials (Kyoto), 17–20 Nov 1992, Japan Heat Treating Society, p 569–572 T. Inoue and K. Arimoto, Development and Implementation of CAE System “HEARTS” for Heat Treatment Simulation Based on Metallo-Thermo-Mechanics, J. Mater. Eng. Perform., Vol 6 (No. 1), 1997, p 51–60 T. Inoue, H. Inoue, T. Uehara, F. Ikuta, K. Arimoto, and T. Igari, Simulation and Experimental Verification of Induction Hardening Process for Some Kinds of Steel, Proc. Second Int. Conf. Quenching and Control of Distortion (Cleveland), ASM International, 4–7 Nov 1996, p 55–62 S. Yamanaka, T. Sakanoue, S. Yosii, T. Kozuka, and T. Inoue, Influence of Transformation Plasticity on the Distortion of Carburized Quenching Process of Cr-Mo Steel Ring, Proc. 18th Conf. Heat Treating, 12– 15 Oct 1998, ASM International, p 657– 664 T. Inoue, H. Inoue, F. Ikuta, and T. Horino, Simulation of Dual Frequency Induction Hardening Process of a Gear Wheel,

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Proc. Third Int. Conf. Quenching and Control of Distortion (Prague), ASM International, 1999, p 243–250 T. Inoue, T. Uehara, H. Ikuta, and I. Miyata, The Japanese Sword—Heat Treatment Process Simulation Incorporating Phase Transformation, Proc. Int. Conf. Materials and Mechanics ’97 (Tokyo), Japanese Society of Mechanical Engineering, 1997, p 137–142 T. Inoue, The Japanese Sword—The Material, Manufacturing and Computer Simulation of Quenching Process, Mater. Sci. Res. Int., Vol 13 (No. 4), 1997, p 193–203 T. Inoue, The Japanese Sword in Comparison of Others, Proc. Eighth Int. Conf. Mechanical Behaviour of Materials (Victoria, Canada), 1999, p 458–463 F.G. Rammerstorfer, D.F. Fischer, W. Mitter, K.J. Bathe, and M.O. Snyder, On Thermo-Elastic-Plastic Analysis of Heat Treatment Processes Including Creep and Phase Changes, Comp. Struct., Vol 13, 1981, p 771–779 J.B. Leblond, G. Mottet, J. Devaux, and J.C. Devaux, Mathematical Models of Anisotropic Phase Transformation of Steels and Predicted Plastic Behaviour, Mater. Sci. Technol., Vol 1, 1985, p 815–822 G. Besserdich, B. Schoaltes, H. Muller, and E. Macherauch, Consequence of Transformation Plasticity on the Development of Residual Stresses and Distortion during Martensitic Hardening of ASE 4140 Steel Cylinder, Steel Research, Vol 65 (No. 1), 1994, p 41–46 P.H. Shipway and H.K.D.H. Bhadesia, The Effect of Small Stress on the Kinetics of the Bainite Transformation, Mater. Sci. Eng., Vol A201, 1995, p 143–149 T. Inoue, Z.G. Wang, and K. Miyao, Thermal and Phase Transformation Stresses in a Carburized Quenched Gear Wheel, Proc. 32nd Japan Cong. Materials Research, Society Materials Science, Japan, 1989, p 21– 26 E. Gautier, A. Simon, and G. Beck, Deformation of Eutectoid Steel during Pearlitic Transformation under Tensile Stress, Proc. Fifth Int. Conf. Strength of Metals and Alloys (ICSMAS), P. Haasen, V. Gerold, and G. Kostorz, Ed., 1980, Vol 2, p 867–873 S. Denis, A. Simon, and G. Beck, Estimation of the Effect of Stress/Phase Transformation Interaction when Calculating Internal Stress during Martensitic Quenching of Steel, Trans. ISIJ, Vol 22, 1982, p 504–513 M. Fujita and M. Suzuki, The Effect of High Pressure on the Isothermal Transformation in High Purity Fe-C Alloys and Commercial Steels, Trans. ISIJ, Vol 14, 1974, p 44–53 S. Bhattacharyya and G.L. Kehl, Isothermal Transformation of Austenite under Externally Applied Tensile Stress, Trans. ASM, Vol 47, 1955, p 351–379 H. Onodera, H. Gotoh, and I. Tamura, Effect of Volume Change on Martensitic Transformation Induced by Tensile or Compressive Stress in Polycrystalline Iron Alloys,


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Proc. First JIM Int. Symposium on New Aspects of Martensitic Transformation, Japan Inst. Metals, 1976, p 327–332 J.P. Patel and M. Cohen, Criterion for the Action of Applied Stress in the Martensitic Transformation, Acta Metall., Vol 1, 1953, p 531–538 S.V. Radcliffe and M. Schatz, The Effect of High Pressure on the Martensitic Reaction in Iron-Carbon Alloys, Acta Metall., Vol 10, 1962, p 201–207 R.M. Bowen, Theory of Mixture, Continuum Physics, Vol 3, A.C. Eringen, Ed., Academic Press, 1976, p 2–129 W.A. Johnson and R.F. Mehl, Reaction Kinetics in Processes of Nucleation and Growth, Trans. AIME, Vol 135, 1939, p 416–458 C.L. Magee, Chapter 3, The Nucleation of Martensite, American Society for Metals, 1968 G.A. Maugin, The Thermodynamics of Plasticity and Fracture, Cambridge University Press, 1992 T. Inoue and K. Tanaka, Subsequent Yield Conditions of Metal under Cyclic Loading at Elevated Temperature, Ing. Archiv., Vol 44, 1975, p 53–62 W. Prager, A New Method of Analyzing Stress and Strains in Work-Hardening Plastic Solids, J. Appl. Mech., Vol 23, 1956, p 493–496

35. H. Ziegler, A Modification of Prager’s Hardening Rule, Quart. Appl. Math., Vol 17, 1959, p 55–65 36. T. Inoue and K. Tanaka, An Elastic-Plastic Stress Analysis of Quenching when Considering a Transformation, Int. J. Mech. Sci., Vol 17, 1975, p 361–367 37. Y. Yamada, N. Yoshimura, and T. Sakurai, Plastic Stress-Strain Matrix and Its Application for the Solution of Elastic-Plastic Problems by the Finite Element Method, Int. J. Mech. Sci., Vol 10, 1968, p 343– 354 38. G.W. Greenwood and R.H. Johnson, The Deformation of Metals under Small Stresses During Phase Transformation, Proc. R. Soc. (London) A, Vol 283A, 1965, p 403–422 39. T. Inoue and Z.G. Wang, Coupling between Stresses, Temperature and Metallic Structural During Processes Involving Phase Transformation, Mater. Sci. Technol., Vol 1, 1985, p 845–850 40. T. Yamaguchi, Z.G. Wang, and T. Inoue, Analysis of Temperature, Metallic Structure and Stress During Carburized Quenching of a Gear with Consideration of Carbon Content, J. Soc. Mater. Sci. Jpn., Vol 33, 1984, p 1470–1476 (in Japanese) 41. T. Inoue, T. Yamaguchi, and Z.G. Wang, Stresses and Phase Transformations Occurring in Quenching of Carburized Steel Gear

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Wheel, Mater. Sci. Technol., Vol 1, 1985, p 872–876 K. Miyao, Z.G. Wang, and T. Inoue, Analysis of Temperature, Stress and Metallic Structures in Carburized-Quenching Gear Considering Transformation Plasticity, J. Soc. Mater. Sci. Jpn., Vol 35, 1986, p 1352– 1357 (in Japanese) T. Inoue, Z.G. Wang, and K. Miyao, Simulation of Quenching Process of Carburized Steel Gear under Metallo-Thermo-Mechanical Coupling, Proc. IUTAM Symposium on Thermomechanical Coupling in Solids (Paris), 1986, p 257–262 Z.G. Wang and T. Inoue, Analysis of Temperature and Elastic-Viscoplastic Stress during Continuous Casting Process, Proc. International Conference on Computational Mechanics (Tokyo), Vol VIII, Japan Soc. Computational Mechanics, 1986, p 103– 108 G. Besserdich, M. Ehlers, Th. Lubben, A. Majorek, G. Schmitt, and D. Wiedmann, Weniger Verzung beim Harten durch Computersimulation, Hart.-Tech. Mitt., Vol 54, 1999, p 201–208 J. Bodin and S. Segerberg, Further Investigations of Quenching Conditions and Heat Transfer in Hardening Steel Components, Proc. Ninth Int. Congress on Heat Treatment and Surface Engineering (Nice), Ivrysur-Seine, 22–28 Sept 1994



Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling N.I. Kobasko, V.S. Morganyuk, and V.V. Dobrivecher, Ukraine National Academy of Science, Kiev

THE ADVANTAGES OF INTENSIVE HEATING AND COOLING when quenching alloy and high-alloy steels are discussed in this article. Alloy steels are quenched in mineral oils or high-concentration aqueous polymer solutions, which can replace the oil. Mineral oils retard the cooling process in the area of the transformation of austenite into martensite. Proceeding from numerous experimental data, it has been considered a firmly established fact that intensive cooling in the field of martensite transformations results in the formation of quench cracks and, afterward, extensive deformation of parts after their quenching. In the late 1990s, many papers appeared based on experimental and calculating data that prove that starting with definite intensity of cooling, the heat-transfer intensification results in avoiding the formation of quench cracks and reduction of the deformation of quenched parts. This allows a change in the technology of alloy steel quenching in principle, because instead of expensive and fire-dangerous oils one can use water (Ref 1, 2). This article discusses the mathematical model and gives the analysis of results of computer simulation and physical grounds for the results obtained. This article considers in detail two steel-quenching methods: intensive and uniform cooling of alloy steel parts during the entire cooling interval and the influence of the growth of intensity of cooling on distortion and crack formation of quenched parts is studied. Two-step quenching is investigated. It has been shown that one can reach minimum distortion at the first stage, which can be preserved during intensive cooling at the second interval of the transformation of austenite into martensite. On the basis of the Pisarenko-Lebedev criterion, it has been shown that one can prevent the formation of quench cracks during intensive quenching at both the first and second stages of cooling (Ref 3). The criterion of Pisarenko-Lebedev establishes the conditions of the quench-

crack formation. If the strength factor is greater than one, quench cracks will not form. If it is less than or equal to one, quench cracks will form. It is emphasized that the reduction of distortion and prevention of the formation of quench cracks are due to the formation of hard martensite layer on the entire surface, which fixes the initial sizes of the part and forms high residual compressive stress on the surface quenched parts. Examples of the application of intensive steel-quenching methods for alloy steel parts are given in practice.

Mathematical Model for the Calculation of Thermal and StressStrain State The coupled equation of nonstationary thermal conductivity, as known, is given as: cq

T ⳮ div(k grad T) ⳮ rij e˙ ijp Ⳮ qI lI n˙ I ⳱ 0 s

with corresponding boundary conditions for film boiling: T ␣f Ⳮ (T ⳮ Ts)|r⳱R ⳱ 0 r k

T bm Ⳮ (T ⳮ Ts)m|r⳱R ⳱ 0 r k T(r, sf) ⳱ u(r)

Finally, at the area of convection heat transfer, the boundary conditions are analogous to those for film boiling, that is: T ␣cn Ⳮ (T ⳮ Tc) ⳱ 0 r k T(r, snb) ⳱ w(r)

The condition of transfer from nucleate boiling to one-phase convection is given by qnb ⳱ qconv. These equations determine boundary conditions of the third kind and describe conditions of the change of heat-transfer regimes. However, in practice, one often uses boundary conditions of the first kind, which can be obtained from experiments. In this case, the main differential equation of heat conductivity must be added with the aforementioned conditions, that is: T(ri, s)|ri⳱Ri ⳱ u(Ri, s)

where i is, in this case, the coordinate index, and u(Ri, s) is a value of temperature at different points of the surface, which is being cooled. Plasticity theory equations are presented in detail in Ref 4 and 5 and have the following form:

and initial conditions: T(r, 0) ⳱ T0

The transition from film boiling to nucleate boiling is made when the following is fulfilled: qcr2 ⳱ ␣ f(Treg ⳮ Ts)

where qcr2 ⳱ 0.2 qcr1. At the stage of the nucleate boiling, the boundary conditions appear as:

e˙ ij ⳱ e˙ pij Ⳮ e˙ eij Ⳮ e˙ Tij Ⳮ e˙ ijm Ⳮ e˙ tp ij

with relevant initial and boundary conditions, where T is temperature, rij is stress, e˙ ij is total strain rate, e˙ eij is elastic strain rate, e˙ pij is plastic strain rate, e˙ Tij is thermal strain rate, e˙ m ij is strain rate for structural dilation due to phase transformations, e˙ tp ij is strain rate for structural dilation due to transformation plasticity, k is thermal conductivity, and c is specific heat. These equations are described in detail in the article

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 313 “Metallo-Thermo-Mechanics: Application to Quenching” in this Handbook.

Crack formation probability, %

100 80

Computation of Stress-Strain State

60 40 20 0

0

200

400

600

800

Cooling rate, K/s Effect of cooling rate in the martensite range on the crack formation in cylinder-shaped samples of 6 mm diameter, of steel 40X (DIN 41 Cr4), which is equivalent to AISI 5135

Fig. 1

Input

Discretion of computation region into finite elements

Output listing of initial data

Time cycle start

Iterative solution of nonlinear problem of heat conduction

Construction and output of isometric fields and the material structural composition

On the basis of numerous experimental studies, it has been established that with the cooling rate increase within the martensite transformation range, the probability of quench-crack formation grows to a maximum value and then lowers to zero (Ref 1) (Fig. 1). Substantiation of regularity is of great practical and scientific importance. To that end, the calculation was performed for the thermal and stress-strain states of steel parts on the basis of finite-element methods (FEM) (Ref 6). For mathematical simulation of part quenching, a mathematical model was used that included a nonlinear equation of nonstationary heat conduction, equations of the theory of thermal, elastic, and plastic flow with kinematic strengthening under the appropriate boundary conditions of the first and third kinds (Ref 5). The calculation process is divided into time steps. At each time step, a heat-conductivity problem is solved. The resulting temperature field determines mechanical characteristics and temperature load for the thermal plasticity problem. The initial conditions for thermal conductivity and thermal plasticity problems are taken from results of solving the corresponding problems at previous steps. Besides, at each time step the calculation results are compared with the thermokinetic diagram of the supercooled austenite transformations, and new thermal, physical, and mechanical characteristics for the next step are chosen depending on the structural components (Ref 7). In every separate region of the diagram a specific transformation law is established, if necessary. The calculations are made

Iterative solving the problem of thermoelastoplasticity

800

600

Construction and output of fields of relocations, strains, and stresses

σz

400 σi σ, MPa

Evaluation of possibility of destruction and calculation of safety factor

200

Construction and output of the field of safety factor

σr 0 σe

Time cycle end

200 400 0

Output

Fig. 2

Chart describing the algorithm of the software package

0.005 0.01 0.015 0.02 0.025 0.03 0.035 Radius of the specimen, R, m

Fig. 3 stress

Stresses at the end of the specimen heating. rr, radial stress; rh, circumferential stress; rz, axial

until the part is cooled. These regularities are described in detail in Ref 8. Joint consideration of these issues (the selection of calculation methods, scheme of the phase-transformation diagram, boundary conditions, and physical and mechanical properties of the material) is of great practical and scientific interest. The principal block diagram of the computing complex developed at the Institute for Strength Problems with the participation of Engineering Thermophysics Institute, both part of the National Academy of Sciences of Ukraine, is shown in Fig. 2. The calculation results are: temperature field, material phase composition, migration of points in the volume which is calculated, components of stress and strain tensors, intensities of stress and strain, and the field of the safety factor, that is, a relation of stresses at which the material is destroyed. These values are presented in the form of tables and isometric lines that allow observation of the kinetics of phase changes in the process of heating and cooling (Ref 8–10). Using the potentialities of the computing complex, the current and residual stresses were determined, depending on the cooling capacity of quenchants. Calculations were also fulfilled for quenching parts of complex configuration. With the purpose of testing these computation methods, a problem has been solved allowing comparison of the computational data with experimental ones. A specimen for this purpose was cylinder-shaped, made out of steel 45 (0.44% C), diameter of 65 mm, length of 130 mm. Quenching was made by induction, and cooling was under intensive water shower. The thermal plasticity problem at heating was solved based on the assumption that the temperature distribution is the same at time heat ends and cooling starts and is known (in Fig. 6, this is a curve at time ⳱ 0 s). For this purpose, the properties from handbooks for this grade of steel have been used. Figure 3 shows results of solving the heating problem. The cooling conditions have been set in the form of boundary conditions of the first kind (Fig. 4, curve 1). The initial conditions are determined by results of solving the heating problem. The temperature and time dependencies of density q and linear expansion coefficient ␣ have been calculated with the use of Yuriev formulas (Ref 11) and thermokinetic diagram (Fig. 4). The other dependencies have been built on the basis of experimental data for dependencies of material properties on the temperatures with corrections on the basis of continuous cooling transformation (CCT) diagrams. Figure 5 shows isochronous curves of dependencies of mechanical properties on temperature at time, s ⳱ 1 s. Results of solutions of problems of thermal conductivity and thermal plasticity for cooling process give the full picture of functions of temperature field, structure, and stress-strain state for part quenching. Figure 6 shows the change in temperature field for cooling of the specimen. The comparison of cooling data and CCT diagram established that the depth of the layer con-


1100 25%

2

0%

1000 3

100% 75% 50%

900

ments have been made in the search for intensively cooling quenchants, such as aqueous solutions of salts with special admixtures preventing surface corrosion of quenched parts. Optimal concentrations of aqueous polymer solutions have been found, which exhibit the inverse solubility. Such solutions provide intensive and uniform cooling of parts to be quenched. Circular residual stresses on the surface of cylindrical bodies versus generalized Biot number are presented in Fig. 9. Intensive quenching methods suppose that after quenching on the sur-

400 200 0 200 400

700 0% 600

600

1300

10%

0.2 s

800 400

0s

30%

500

50%

1100 1s

70%

400

90%

2s

900 102

10

1

103

104

τ, s

T, K

1 300 10−1

200 σz, MPa

T, K

800

axial stresses to become negative and remain compressive until cooling was complete. Figure 8 shows calculated residual stresses compared with experimental data. One can consider that the results of calculations agree well with experimental data. The most important results used for developing the intensive methods of quenching are discussed next. It has been stated that with the quench-intensity increase, the residual stresses grow at first, then lower, with further increase in Biot number and change over to compression stresses. Intensive quenching can be reached through the application of jet cooling, directed streams of water, and aqueous solutions providing high critical heat flux densities. In the aforementioned conditions, the boiling film is reduced to the minimum or eliminated. The basic processes are nucleate boiling and one-phase convection heat transfer. In this case, it is important to know conditions of the transfer from nucleate boiling to one-phase convection heat transfer. On the basis of this approach, a lot of experi-

σe, MPa

taining more than 50% martensite was 5 mm; the total depth of the hard layer was 7.5 mm. Figure 4 shows curves (1) of the change in temperature on the surface of a specimen, (2) at a depth of 5 mm, and (3) at a depth of 7.5 mm. Figure 7 shows circumferential stresses at characteristic points versus time. At the beginning of cooling, the stresses on the surface were tensile because of the thermal reduction of the material. From 0.15 s on the surface martensite transformation started, and an abrupt extension of the steel resulted, causing circumferential and

3s

0 200

700 400

Continuous cooling transformation diagram of cooling austenite transformation for steel 45

Fig. 4

4s 600

500

300 0 1000

0 0

iment.

T, 106/K

0.2

400

400 3 200

400

4 2

200

300

2

200 400 300

Residual stress (σ ), MPa

0

σ, MPa

0 0

200 1 400 600

500

700

900

Residual stresses in the specimen. Solid lines relate to calculations; dotted lines relate to exper-

Fig. 8

0.3 y

1100

T, K Isochronous curves exhibiting dependencies of mechanical properties on temperature. Dashed lines relate to handbook data; solid lines relate to data used in experiments. ru, ultimate strength; ry, yield strength; ␣T, coefficient of linear expansion

0.005 0.01 0.015 0.02 0.025 0.03 0.035 R, m

Temperature field at the time of cooling of the specimen

Fig. 6

u 600

200

Radius of the specimen, R, m

0.4

800

u, y, MPa

0.005 0.01 0.015 0.02 0.025 0.03 0.035

0.5

σr, MPa

400 1200

800 10−2

10−1

1

10

102

103

τ, s

Fig. 5

Circumferential stresses for cooling of the specimen. 1, on the surface; 2, at 5 mm depth; 3, at 7.5 mm depth; 4, at the axis

Fig. 7

200 100 0 100 200 300 400

Fig. 9

0

2.5

5 7.5 Biot number

10

12.5

Circular residual stresses versus generalized Biot number

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 315 face residual compressive stresses always appear (when Biv ⱖ 4.5). Working within the range where Biv 4.5, one can avoid cracking. Note that between the generalized Biot number and usual Biot number there is a link, which follows: Biv ⳱

␣ S K k V

where Biv is generalized Biot number, ␣ is heattransfer coefficient, k is heat conductivity, K is Kondratiev form coefficient, S is surface, and V is volume. Some results of calculation of current surface stresses of parts to be quenched are shown in Fig. 10. During quenching, great compressive stresses appear on the surface, and then they disappear. Maximum compressive surface stresses correspond to the optimal depth of hard layer. The technology to fix these stresses has been developed. Figure 10 shows current surface stresses and inside the part at slow and intensive cooling. As one can see from Fig. 10, the higher the cooling intensity, the greater the value of maximum compression stresses on the surface of hard parts.

Possibility of Predicting Hardening Cracks It is well known that intensification of quenching processes improves the hardening characteristics and strength of steel articles, but in this way it is possible for quench cracks to form. In order to avoid damage to articles during hardening, in practice one often uses oil cooling together with alloy steels. Small stresses arise during oil cooling, and alloying promotes sufficient tempering capacity under these conditions.

However, economically it is more suitable to use simple carbon steels and water or an aqueous solution as cooling agent. It is necessary to achieve cooling methods that would provide sufficient strength and the absence of quench cracks. For example, this is possible with water quenching under pressure and in aqueous solutions of polymers, and so forth. Before starting the manufacture of industrial equipment for realizing such procedures, it is useful to carry out numerical analysis of different cooling schedules and to select the most effective of them. This analysis is possible on the basis of calculating the thermal and stress-strain state during hardening. Now consider developing a procedure of strength calculation for engineering components during hardening, taking account of phenomena accompanying steel structural transformations (Ref 7). On the basis of building a mathematical model for the hardening process, a suggestion is made about the dependence of steel thermal, physical, and mechanical properties on temperature and cooling time, since temperature and time govern the structural state of steel during cooling. A complete set of equations for calculating the thermal stress state during hardening includes a nonlinear thermal conductivity equation and equations for plastic flow theory; these are given in Ref 8 to 10 and 12. All computational works have been made as follows: 1. Computation of thermal and stress-strain state during heating to the austenite formation temperature. 2. Final results of heating to the austenite formation temperature (distortions and changes in sizes of parts) were initial data for cooling process.

1200

1200

T0

T0

TS 800

800

TS 400

400 σ

0

σ0

0

0 σS

Fig. 10

(Eq 1)

where v ⳱ rf /rc, rf is ultimate tensile strength, rc is ultimate compressive strength, r1 is greatest principal stress, and ri is stress intensity. For an ideal plastic material v ⳱ 1, and for an ideal elastic material v ⳱ 0. The use of the general criterion (Eq 1) applied to hardening requires the existence of experimental dependencies of ultimate tensile strength and ultimate compressive strength on temperature and time rf ⳱ rf(T,s) and rc ⳱ rc(T,s) in accordance with the thermokinetic diagram of supercooled austenite transformation. Equation 1, confirmed by numerous experiments of different workers, is one of the most widely used criteria in strength calculations for machine and structural components since its use requires the minimum experimental data (only rf and rc). In order to prove the selected mathematical model, the hardening process of an inner bearing ring 7515/02 made of steel ShKh15 (AISI 52100) (Fig. 11) with water cooling was studied. The points on the surface indicated in Fig. 11 show places where the boundary conditions of the first kind have been set. Thermocouples were

φ102 10

31

400

800 10−1

vri Ⳮ (1 – v)r1 ⱕ rf

Temperature, (T ), K

Stress (σ ), MPa

Ms

The results of computations after final heating and cooling to the temperature of the environment are considered in this article. Considering the dependence of physical and mechanical properties on temperature and time and in accordance with plastic flow theory with kinematic strengthening, temperature fields and stress distribution have been calculated. Solution of the thermal conductivity and thermoplasticity problems gives a complete picture of the change in temperature field. The thermokinetic diagram for the transformation of supercooled austenite (Ref 7) allows one to follow the kinetics of phase transformation and to determine the depth of hard layer. By evaluating the stress-strain state of an article during hardening using some failure criterion, it is possible to assess the probability of hardening crack formation. A generalized Pisarenko-Lebedev criterion (Ref 3) was selected as a failure criterion during hardening:

11 12 13

φ75

σS

9

6 5 4 3 2 1

14 15

8 7

16 1

10 Time (t ), s

Current stresses versus time

102 10−2

10−1 1 Time (t ), s

φ87

10

Fig. 11

Drawing of bearing ring 7515/02. Thermocouple location is indicated by dots.

316 / Residual Stress During Hardening Processes melted to the surface of the ring, which allowed boundary conditions of the first kind to be fixed at many points. The temperature values at intermediary points between thermocouples were found through the extrapolation of temperature values obtained through experiment. The experimental and extrapolated values of temperatures are given in Table 1. However, methods of calculating temperature fields and stresses in relation to intensive steelquenching methods with regard to their specifics need to be developed. As known, the bearing industry generally uses slowly cooling oils as quenchants. These oils are very expensive and can cause fire, but reduce distortion and prevent the formation of quench cracks. However, there is an alternative way: intensive cooling, which must gain acceptance in the bearing industry. Numerous experiments confirm this idea. The al-

ternative method has great prospects, since water and aqueous solutions of polymers of optimal concentration exhibit inverse solubility, are inexpensive, do not cause or support fire, and allow the required values of Biot numbers to be reached, so that high compression stresses always form on the surface to be quenched. In turn, the compression stresses on the surface of quenched parts make their service life longer. Therefore, the control and determination of the residual stresses on quenched metal surfaces is of great practical value.

(a)

(d)

(b)

A record of changes in temperature at different points on the surface and the moment of failure was made for hardening an actual model. Ten specimens were tested, and all of them were heated to 1100 K, then cooled in water at 300 K. As a result of this quenching, cracks of the upper flange occurred in the radial direction (Fig. 12). Average time from the start of cooling to the moment of failure was 4.3. s. Experimental data (see Table 1) were used as boundary conditions in calculating the first-kind thermal conductivity problem. Since it is known that for the selected brand of steel through-hardening is specified over the entire cross section of the bearing ring—that is, only martensitic transformation occurs—then the dependence of material characteristics on time may be ignored and only the dependence of thermal, physical, and mechanical properties of steel ShKh15 on temperature is used in the calculation. In view of the absence of an experimental temperature dependence of ultimate compressive strength for steel ShKh15 during hardening, some simplification was used. It was assumed that in the austenitic condition and partly in the region of martensite transformation (510–480 K) the material is ideally plastic (v ⳱ 1). Below 440 K, when more than 50% of martensite forms in supercooled austenite, the material becomes ideally brittle (v ⳱ 0). In the range of 480 to 440 K it was assumed that the dependence of value v on temperature is linear. Consequently:

冦

1 with T ⱖ 480 K v ⳱ (T ⳮ 440)/40 with 480 K T 440 K 0 with T ⱕ 440 K (Eq 2)

(e)

In the course of the calculation at each time step, in addition to solving the thermal conductivity and thermoplasticity problems, the cooling path was compared with the thermokinetic diagram in order to determine the structural composition of the material, and a field for the save factor was plotted: k(xi,s) (c)

冦

rf with re 0, re ⳱ vri Ⳮ (1 ⳮ v)r1 ⳱ re

with re ⱕ 0

(f)

Structural composition and shape of the bearing ring profile during hardening. (a) Initial (cold and heated) states. (b) After 0.8 s. (c) 1.6 s. (d) 2.2 s. (e) 3.2 s. (f) 4 s. The unshaded area is austenite, single hatching indicates the area up to 50% martensite, and cross hatching indicates the area of failure

Fig. 13

Fig. 12

Table 1

Bearing ring failure in the case of water quenching. Sizes of ring are given in Fig. 11.

In addition to Fig. 13, it should be noted that in the case of very intensive quenching, a thin martensite layer is formed simultaneously on the

Results of thermometry during water quenching for a bearing ring 7515/02 Temperature for thermocouple No., K

s, s

0.1 0.2 0.3 0.5 1.0 2.0 5.0 10.0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

1023 773 623 498 413 393 378 348

1048 856 714 573 446 399 380 350

1098 1008 874 699 508 415 385 354

1100 1010 819 644 497 422 390 365

1100 1000 773 598 488 418 395 375

1120 993 848 673 503 428 393 373

1100 1026 898 723 513 413 388 361

1098 1020 897 727 515 415 383 350

1090 1025 902 748 518 417 384 352

1088 1038 925 769 543 428 389 363

1080 1044 937 794 619 447 393 369

1090 1051 951 791 700 469 397 376

1100 1053 953 775 674 664 394 371

1097 1050 949 723 385 445 387 355

1074 1022 898 694 513 413 382 352

1055 880 740 585 455 401 380 350

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 317 entire surface independently of the thickness of the bearing ring, which is the main cause of the reduction of bearing ring distortion. Thus, very slow and very intensive cooling reduced the distortion of bearing rings. The advantages of intensive cooling are as follows: the increase in the hardenability of steel parts and improvement of mechanical properties of the material. Thus, as a result of this calculation a complete picture was obtained for the change in thermal, structural, stress-strain, and strength states of the bearing ring during hardening. In order to build up the shape of the profile from the original cross section (cold condition), values of calculated displacements for points on the contour were plotted for capacity at a magnification of 30 times. Figure 13(a) shows the profile of the bearing ring cut section in the cold condition and heated to the austenitization temperature (1130 K); Fig. 13(b) shows the bearing ring profile after the start of cooling. This instant corresponds to the set of phase transformation in the coldest part of the bearing ring (lower flange). In the time interval of 0 to 0.8 s, there is only thermal contraction of supercooled austenite. Nonuniformity of temperature field connected with more rapid cooling of thin parts of the bearing ring leads to very large thermal stresses exceeding even the yield point and to a change in cross-section configuration, in particular to the occurrence of bearing ring tapering at the inner surface. Mainly tension stresses act over the entire surface of the bearing ring. Starting from 0.8 s in the most highly cooled parts of the bearing ring, martensite forms which, having a greater specific volume, leads to material expansion. This involves an increase in diameter

of the lower part of bearing ring, whereas the central and upper parts are essentially austenite, which continues to contract (Fig. 13c). Martensite formation in the most highly cooled layers at first causes a reduction in tensile stresses and then a transition to compressive stresses. As long as cooling continues, martensite transformation proceeds within the cross section, which increases the diameter of both the lower and central part of the bearing ring. This is the reason for the change in taper to an opposite sign (Fig. 13d). There is some concavity of the inner surface adjacent to the hottest part of the bearing ring, which is explained by further contraction of austenite predominant in the area. In the most highly cooled areas, martensite formation is essentially finished, and therefore with a reduction in temperature martensite starts to contract, whereas in the inner layers there is expansion due to rapid formation of martensite. This leads to a reduction in compressive stresses in the cold parts of the bearing ring and to the appearance of tensile stresses. The bearing ring profile at 3.2 s is shown in Fig. 13(e) when the martensite transformation covers the whole area. With further cooling, the

400 K 100 100

0

100

440

0 420

200

400

100 MPa 400

σf

0

300 (a)

(b) 200

200

1.5

σi

σe

100

1

σ, MPa

100 0

200 100 100

0

1.5

σl

Predicting the Deformation of Bearing Rings during Hardening

100 0 200

1.5

100 200 MPa

300

0

1

2

3

4

(c)

1.5 (d)

τ, s Nature of change in principal stress rl, stress intensity rI, equivalent stress re, and ultimate tensile strength rf with passage of time

Fig. 14

diameter of the lower part increases slightly since the main mass of austenite has been converted to martensite. In the inner layers of the upper part of the bearing ring there is rapid formation of martensite, which leads to a site that predominantly tends to contract thermally. This leads to a marked increase in circumferential tensile stresses. At 4 s in the area denoted in Fig. 13(f) by cross hatching circumferential tensile stresses reach values exceeding the ultimate strength. Typical changes in values of rl, ri, re, and rf with the elapse of time in the center of this region are shown in Fig. 14. In the time interval of 0 to 1.8 s according to Eq 2, the equivalent stress re coincides with stress intensity of ri, and starting from 3.2 s the value of re coincides with the principal stress rl, which is the circumferential stress (according to Eq 1, the latter stress at 4 s leads to material failure, that is, the cross-hatched area in Fig. 13f). Fields for isotherms, axial and circumferential stresses, and also the reserve strength factor (only the most critical zones are shown in Fig. 13d) at 4 s are shown in Fig. 15. At this point the calculation was stopped since the reason, location, and instant of failure have been revealed. By comparing experimental and calculated data it is possible to note that cracks form in the bearing ring due to tensile circumferential stresses since they spread into planes of meridianal cross sections. The location and time of crack development coincide satisfactorily. It should be noted that chipping at the upper surface of the flange in the region of a crack (see Fig. 12) indicates that the crack propagates from within (from the area shown in Fig. 13f), branching at the surface. Thus, the method proposed can be used to predict hardening cracks. This is very important for intensive steel-quenching methods. As known, in the case of intensive steel-quenching methods, quenched compression stresses appear on the surface of parts. Therefore, during intensive quenching, quench cracks can appear inside the part, which are invisible but can result in disruptions. The above-mentioned forecast is especially important for quenching of bearing rings, which are hardened thoroughly through intensive cooling. On the other hand, in the work process quenchants change their quenching properties. In this condition it is important to predict the formation of quench cracks by criterion of Pisarenko-Lebedev discussed previously.

Fields of isolines for temperature (a), axial (b), and circumferential (c) stresses, and also the reserve strength factor (d) at the instant for the start of failure of a bearing ring 7515/02

Fig. 15

Machining allowances should be made with consideration of the real deformation of components during heat treatment. In plant practice, the change in the dimensions of components during hardening is evaluated on the basis of experimental-statistical data. Theoretical computation of the change in dimensions makes it possible to predict machining allowances and to ascertain basic factors having the most signifi-

318 / Residual Stress During Hardening Processes the basis of the computation of its temperature and stress-strain states during heating and cooling carried out in conformity with the method cited in Ref 3 and 6 (Fig. 18, 19). After the bearing ring had been immersed in oil for 30 s, its temperature in the most cooled section had been lowered to 510 K; this corresponded to the outset of the austenite-to-martensite transformation (curve 3 in Fig. 19). From the start of cooling to this moment, the specific volume of the steel decreased, and the generatrix was displaced to the right owing to the temperature drop. The position of the generatrix after 39 s of immersion in the oil corresponded to curve 4 (Fig. 19). At this moment, the basic mass of the austenite had already been transformed into martensite in the lower section of the bearing ring, as a result of which the specific volume of the steel, and, correspondingly, even the diameter of the lower section of the bearing ring increased. In the upper portion of the bearing ring, however, the

martensitic transformation had just begun. According to computations, the final position of the generatrix corresponded to curve 5 (Fig. 19). The transformation of austenite into martensite in the upper portion of the bearing ring effected a change in the slope of the generatrix. The mean-statistical values of the displacements of the generatrix of the inner surface in the case of broad and narrow bearing ring ends, which were determined experimentally, are given by the points in Fig. 19. It is apparent that the computed and experimental displacement values are very close: the maximum deviation of the computed from the experimental data was 3 lm (1%). This suggests the correct selection of the mathematical model of the process. In addition to the comparison of numerical and experimental data relating to distortions, the comparison has been also made for values of residual stresses in cylinder-shaped samples treated by induction heating and cooled in water. Reference

2500

100

2000

50

E 1500

Ultimate strength ,σu Yield strength ,σy

1000

E′

50 100

500 0

0

αT, 106/K

E(×102), E ′(×101), σu, σy, MPa

cant effect on the deformation of components. Determination of the character of the effect of these factors on current and residual strains is a very critical and complex problem. The method used for these investigations is inadequately developed. Below are some results of the computation of the strain state during the hardening of an internal bearing ring made of steel ShKh15 (AISI 52100). The heating temperature of the bearing ring for quenching was 1130 K, while cooling was carried out in MZM-16 quenching oil with a temperature of 330 K. Reference data on the thermal and physical properties of steel ShKh15 as a function of temperature and boundary conditions of the third kind were used to solve the heat-conductivity problem. The dependence of the heat-transfer coefficient in the MZM-16 oil on the surface temperature of the specimen is shown in Fig. 16 (Ref 13). Heat-transfer coefficients presented in Fig. 16 have been determined through solving inverse problems using selection of electric models (Ref 13), which is one of many possible methods of solving inverse problems (regularization method and others). It is known that the stress-strain state of a solid subjected to hardening is dependent to a significant degree not only on the temperature gradient in this solid, but also on the variation of the specific volume of structural components during phase transformations, as well as on the kinetics of the variation in mechanical properties, for example, the tendency to exhibit superplasticity (Ref 14). The temperature dependence of the mechanical properties of steel ShKh15 with allowance for the effect of superplasticity, which arises during cooling at the time of the most vigorous formation of martensite, was used to compute the thermoelastoplastic stress-strain state (Fig. 17a). The change in the specific volume during the transformation of austenite into martensite was accounted for by the temperature dependence of the coefficient of linear expansion (Fig. 17b). Values of the physical and mechanical properties of steel ShKh15 were taken from Ref 15. The complete picture of the shape variation of a bearing ring during hardening was obtained on

0

400

600

800

T, K

(a)

0

1000 1200

0

400

600

800

1000 1200

T, K

(b)

Variation in strength properties, elastic modulus E, hardening modulus E⬘ (a), and coefficient of linear expansion ␣T of steel ShKh15 (AISI 52100) with allowance for increase in specific volume as austenite transforms into martensite (b), as functions of temperature

Fig. 17

260 140

120

420

460 220

100 180

160

6000

380

α, W/m2 • K

5000

140 180

4000

100

80 3000

340

200

2000

60

220 1000 0

0

1000

500

T sf,K

Fig. 16 men

60

1500

Dependence of heat-transfer coefficient in MZM-16 oil on surface temperature of speci-

(a)

240 260 (b)

280 300

20 (c)

(d)

Lines of equal displacements (indicated near curves in lm) in section of bearing ring. (a) and (b) Current radial displacements after 30 and 39 s, respectively, of immersion in oil. (c) and (d) Residual radial and axial displacements, respectively

Fig. 18

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 319 5 presents this comparison, which shows that there is good agreement between such numerical calculations and experimental data. For mathematical modeling of the quenching process, different intensities of cooling within the martensite range were set by giving different values of coefficients of heat transfer ␣, selected with regard to water flow rate, sprayer, mixing, vibration, and so forth. There are formulas allowing determination of heat-transfer coefficients (Ref 14) for all these cases. It appears that at very intensive cooling within the martensite range, the conicity of the rings being quenched is the least, while at moderate intensity of cooling it is higher (Table 2). Bearing rings are cooled in two steps. The first step is mineral-oil cooling until the minimum conicity is achieved. At the second step, different cooling rates determined by the technology are applied. A hard shell is formed over the entire surface almost simultaneously at the maximum cooling rate, and therefore the conicity is at the minimum, since this shell hampers further deformation of the part through phase changes inside the rings. Maximum compression and tensile residual stresses observed over the ring cross section are given in Table 2. While quenching in circulating water and in a shower, the residual stresses are low since the condition BiV → 4.5 is satisfied (Fig. 9). The decrease in conicity at intensive shower cooling can be explained by simultaneous formation, over the whole surface, of the martensite layer that fixes the ring initial form. Under moderate cooling rates, a thin cross section of the ring is cooled at first in which martensite transformations begin that cause displacements and coning formation. By adjusting the intensity of cooling, one can control the

value of residual stresses and reduce the distortion to the minimum. This is true for both one-step and two-step quenching. In the first case, the martensite shell is formed uniformly on the whole surface at the time of immersion of the part into the quenchant. In the second case, a more uniform martensite shell is formed at the second stage of two-step cooling. Figure 20 shows that at slow cooling (a) the phase transformation starts in the thin section of the part and due to change in specific volume of martensite results in the increase in distortion. In the case of intensive cooling Fig. 20(b), a thin shell of the martensite phase forms uniformly on the whole surface, it fixes the shape of the part, and thus the distortion is lower. Thus, the method of numerical modeling of the hardening process can be used to predict hardening distortions and to designate machining allowances for bearing rings, as well as to define the laws governing deformation as a func-

tion of the methods adopted for the heating and cooling of rings of different steels with different sectional configurations, diameter, and so forth. The above-stated problem is especially important for the bearing industry because in the case of big distortions of bearing rings, workers have to perform a lot of turning and polishing. Upon removal of the thin surface layer from the surface of the quenched bearing rings, residual stresses in the bearing rings are redistributed, which can have negative results; that is, it can reduce the service life of finished bearing rings. Moreover, the surface layer of bearing rings is the hardest. The removal of this surface layer also reduces the quality of a bearing, to say nothing of the extremely high costs for the turning treatment of bearing rings. Therefore, the idea regarding the reduction of distortions of bearing rings by the intensification of quench cooling is very appealing. It should be also added that instead of mineral oils, at the first stage of cooling one can use

Table 2 Residual stresses and bearing ring conicity depending on the cooling conditions within the martensite range at the second stage of cooling Stresses, MPa Method of cooling

In air In oil In circulating water Under intensive shower

r22

r33

rI

Conicity

ⳮ90Ⳮ130 ⳮ110Ⳮ130 ⳮ75Ⳮ200 ⳮ70Ⳮ130

ⳮ130Ⳮ165 ⳮ150Ⳮ180 ⳮ180Ⳮ230 ⳮ100Ⳮ180

70 180 240 170

0.044 0.045 0.051 0.005

35

30

1

3

4

5

2

Height of ring, Z, mm

25

20

15 10

5

0

0

0.1

0.2

0.3

0.4

0.5

Displacement, U, mm Displacements of generatrix of inner surface of bearing ring during hardening (lines denote computed data, and points experimental data). 1, after turning on lathe; 2, after heating to quenching temperature; 3 and 4, after 30 and 39 s, respectively, of immersion in oil; 5, after quenching

Fig. 19

(a)

Fig. 20

(b)

Phases distribution at slow and intensive cooling. 1, austenite; 2 and 5, martensite


5

φ190

1 700

Carburized layer φ225 φ203.8

88.2

Tsurface

3 500 2

1

2

3

300

100 φ342.4 (a)

0

2

4 τ, min

6

8

(b)

Fig. 21

(a) Sizes of the carburized bushing. (b) Surface temperature in the carburized bushing during oil quenching at 137 C

aqueous polymer solutions exhibiting properties of inverse solubility. At the second cooling stage, rings are simultaneously washed and intensively cooled in accordance with results presented in Table 2. Thus, two-stage quenching of bearing rings with the use of intensive cooling at the second stage results in the reduction of distortion. It is very important to solve the problem of the optimization of steel part heat treatment processes for two-stage quenching.

Study of Thermal Stresses Formed in Carburized Steel Products due to High-Rate Quenching Quenching of a carburized bushing with twostep cooling was studied as a thermoplasticity problem using FEM. Instantaneous and residual stresses were analyzed in the component at various cooling rates. It was shown that an increase 0

100 0 MPa

0 MPa

200 100 0

0

200 100 0

100 (a)

(b)

Distribution of axial (a) and circumferential (b) stresses in the carburized bushing at the end of the first cooling stage. Deformation is enlarged by 25⳯.

Fig. 22

of cooling rate through the phase-transformation range improves the distribution and lowers the level of residual stresses in the as-quenched components (Ref 16). The carburized bushing (Fig. 21) made of steel 14KhGSN2MA was heated in an electric furnace to 850 C and cooled initially for 20 s in air and then in hot MS-20 oil at an optimal temperature of 100 to 140 C. On reaching a mean temperature of 220 C in the carburized part, the first-stage cooling process was interrupted and the part was transferred to another cooling medium for cold treatment. Use of the optimal MS20 oil temperature led to better bushing roundness (Ref 16). The second stage of multistage quenching (when the carburized layer undergoes martensite transformations) can be carried out at a slow cooling rate (in air) or using higher-rate cooling, for example, in a circulating fluid. It was noted in Ref 16 that high-rate cooling through the martensitic range raises mechanical properties and reduces the risk of quenching cracks. For this reason, it was of practical and theoretical interest to reveal the effect of second-stage high-rate cooling on the strain and stress patterns in the hardened part. The simulation study of the quenching process was based on a set of equations describing the distribution of temperatures, stresses, and strains, including a nonlinear unsteady-state heat-conduction equation and plastic flow equations, as well as initial and boundary conditions. It is assumed in the CCT diagram of supercooled austenite that all thermal and mechanical characteristics of material are functions of temperature and time. The iterative approach to solving such heat-conduction and high-temperature plasticity problems on the basis of the FEM was reported elsewhere (Ref 9, 15). Solution of heat-conduction and thermoplasticity problems gives a good picture of the variations of temperature, stress, and strain distributions in the product during quenching. The variations of the temperature field in combination with a known CCT diagram of supercooled austenite can be used to follow the kinetics of phase transformations and to describe the quenched layer depth (Ref 15).

To test the computer package, the authors solved a problem for which theoretical results could be compared to experimental data (Ref 17). In addition, FEM was used to solve the nonlinear unsteady-state heat-conduction problem and thermoplasticity problem, both of which have an analytical solution. The comparison demonstrated a good agreement of analytical and numeric data (Ref 6). To analyze the first cooling stage, the authors selected first-kind boundary conditions that were determined experimentally (see Fig. 21), and for the second cooling stage they prescribed thirdkind boundary conditions. During cooling in MS-20 oil, temperature gradient over the bushing section was insignificant. This was due to high thermal conductivity of steel. The upper and lower bushing flanges cool down slightly faster than the wall, and, in addition, the coefficient of thermal contraction for carburized steel (a) is higher than for noncarburized. These two factors result in appreciable distortions. During the first cooling stage, the bushing is barrel-shaped. The distribution of axial and circumferential stresses at the end of stage one is illustrated in Fig. 22. In the second stage, the carburized layer begins to undergo martensitic transformations. During further cooling, the carburized layer expands because of the greater specific volume of martensite compared to austenite, and the bushing crown sags in. The difference of the maximum and the minimum radii of the bushing inner diameter of cylinder generatrix, Dr, as a function of secondstage heat-transfer coefficient is shown in Table 3. Increase in the second-stage cooling rate reduces residual strain, which is in agreement with earlier research (Ref 15). The minimum value of Dr versus maximum cooling rate at the second stage can be interpreted as follows. During high-rate cooling, the martensitic transformations are completed almost simultaneously over the entire carburized layer surface. The compliance of the surface material in noncarburized steel also drops sharply due to reduced temperature. Thus the surface layers of the part form a rigid skin that resists any further deformation of the bushing which could result from cooling of the core section. The difference Dr can be diminished by increasing heat transfer at the first cooling stage. An increase of the first-stage cooling rate will raise the temperature gradient and enhance bushing deformation. Since deformation at stage two is opposite to stage one, the increase in the first-

Table 3 Difference of the radii with respect to heat-transfer coefficient at the second stage Heat transfer coefficient ␣, W/(m2 • K)

30 1000 5000

Difference of radius Dr, m

0.165 0.162 0.155

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 321

0

0

Generalization of Computational and Experimental Results for Heating and Cooling of Bodies of Various Configurations For bodies of a simple shape (plate, ball, cylinder, parallelepiped), solving the heating problem for the medium with constant temperature (boundary condition of third kind) one can state:

Stage I

ε=0

ln(Tc T1)

ε=R

ψ

180 φ

ln(Tc T2) τ1

0

Fig. 24

180 φ τ2

350 MPa

50 100 550 850 950

50

1000

50 400

1050 350

350 350 100 900 1050 1150 1200 1250 1300 1350 1400 1450

TC ⳮ T ⳱ TC ⳮ TO

300

250 200 150 100

300

1050

400

1400

50

1000 950 850 550

150 200

1350

250

1300 1250

150

1200 1150

100

1050 50

900

0

100

0 (a)

Fig. 23

(Eq 3)

l1,i l2,i l3,i … ln,i …

FoV ⳱ (␣s/R2V) is the Fourier number, where the determining size of the part is taken as a generalized size. According to the above inequality, each following term of Eq 3, when FoV grows, will be negligibly small in comparison with the previous term, and the sum of all roots will have very little difference from the value of the first term. Therefore, beginning from a definite value of Fourier number Fo1, the use of the first term of Eq 3, can be restricted, that is: TC ⳮ T ⳱ TC ⳮ TO

3

兿 An,iU冢ln,i Rii冣 i⳱1 x

冤冢

冣冥

2 RV FoV R2i when FoV Fo1

2 • exp ⳮ ln,i

(Eq 4)

Beginning from this value of Fo1, the time function of (TC ⳮ T) is described by a simple exponent. Applying the logarithm to Eq 4, one obtains:

200

1100

冣冥

2 RV FoV R2i

where TC is the temperature of medium, TO is the initial temperature of the body, and T is the temperature of the body at a point (x, y, z) and at time s. An,i ⳱ (An,1, An,2, An,3), which are initial thermal amplitudes depending on the initial temperature distribution and shape of the part. U[ln,i (xi /Ri)] is a function regarding the change in temperature on coordinates (x ⳱ x1, y ⳱ x2, z ⳱ x3); R1, R2, and R3 are the sizes of the part; RV is a generalized size of the part equal to the part volume (V) divided by the surface area (S); that is, RV ⳱ V/S (for infinite plate RV ⳱ R, for infinite cylinder RV ⳱ 1⁄2R, for ball RV ⳱ 1⁄3R); ln,i are roots of characteristic equations, ordered as:

1n

1450

x

冤冢

100

350

3

50

1150

1150

兺兿 An,iU冢ln,i Rii冣 n⳱1 i⳱1 2 • exp ⳮ ln,i

ψ

Function ln(TC ⳮ T) versus time in the cooling process

0 MPa

1100

Stage II

ln[Tc T(ξ,τ)]

stage deformation can reduce residual strain. As can be seen in Fig. 22, the first cooling stage results in low bushing stresses. This suggests that high-rate cooling at this stage does not lead to material failure. Note that the distribution of residual stresses in the part is the same for second-stage heattransfer coefficient of 5000 and 300 W/(m2 • K) as for ␣ ⳱ 1000 W/(m2 • K). Figure 23 shows that the highest compressive stresses occur in the carburized layer. A comparison of results obtained at various second-stage heat-transfer coefficients demonstrates that high-rate heat transfer at this cooling stage does not increase residual tensile stresses and even slightly reduces them. A similar favorable distribution of residual stresses during high-rate cooling was observed in multistage quenching of ShKh15 steel bearing rings (Ref 17). Thus it is possible to improve the efficiency of carburized bushing cooling process (compared to oil quenching) by raising the cooling rate without risk of a quenching crack. Similar computations can be done for heat treatment of rolled steel and tubing. More information about intensive quenching is given in Ref 14, 18, and 19.

(b) Distribution of axial (a) and circumferential (b) residual stresses in the carburized bushing at the end of the second cooling stage at ␣ ⳱ 1000 W/m2 • K. Deformation is enlarged by 25⳯.

TC ⳮ T ⳱ TC ⳮ TO

冤

冢

3

兺 i⳱1

• 1n A1,iU ln,i

冣冢

2

␣s

冣 R冥

xi RV ⳮ ln,i Ri Ri

2 V

(Eq 5)

Thus, the time function of 1n(TC ⳮ T) on the graph is a straight line (see Fig. 24). In the case of lengthy cooling, the temperature at all points will be the same and equal to TC (stationary state). Therefore, the entire cooling process can be divided into three stages. The first stage of irregular conditions is characterized by the fact that the biggest role is played by the initial temperature distribution. Any irregularity in the initial distribution is reflected in the temperature distribution at next moments of time. The dependence between (TC ⳮ T) and s is described by Eq 4. The second stage is called regular conditions.

322 / Residual Stress During Hardening Processes The dependence between (TC ⳮ T) and s is described by simple exponent (Fig. 24). The temperature distribution inside the body is described by function U and does not depend on the initial temperature distribution, because the value of A1,i is a factor; that is, it determines the scale and not the essence of the phenomenon. The third stage corresponds to the stationary state (FoV ⳱

), when the temperature in all points of the body equals the temperature of environment. Figure 24 shows graphs of 1n(TC ⳮ T) as a function of s for the surface and core of the body. As is seen from Fig. 24, at the stage of regular conditions these graphs are in the form of straight lines. If the temperature at the initial time is equal in all the points and equal to TO, then the curves must originate from one point. Since the surface layers are cooled more quickly than central ones, the curve 1n(TC ⳮ T) ⳱ f(s) at the first stage for the central layer has the convexity facing the ordinate and for the surface layers facing the abscissa (Fig. 24). The above-mentioned analysis is correct for bodies of any shape. It has been shown (Ref 20) that any heating (cooling) problem for bodies of any shape can be reduced to heating (cooling) problem for a body of simple shape (plate, cylinder, ball) using the criterion of approximate similarity. The tangent of the angle of the line inclination (for the stage of regular conditions) will be: tg(180 ⳮ w) ⳱ ⳮtgw 1n(TC ⳮ T1) ⳮ 1n(TC ⳮ T2) ⳱ ⳱ m ⳱ const s2 ⳮ s1

The constant m is the rate of the time function of the logarithm of the superfluous temperature, that is: [1n(TC ⳮ T)] ⳱m s

ⳮ

(Eq 6)

It is the same for every point of the body and also for volume average temperature T¯ and is

3

m⳱

兺冢l1,t i⳱1

2

冣

RV Ri

a R2V

(Eq 7)

Therefore, the value of m is determined by thermal and physical factors, size, and shape of the body. On the basis of Eq 6 and boundary condition of the third kind, for body of any shape one can state the following equation, which is true at the stage of regular conditions of cooling (heating): ccV

dT¯ ¯ ⳱ ␣S(TC ⳮ Tp) ⳱ ccV(TC ⳮ T)m ds

(Eq 8)

m⳱

␣S TC ⳮ TP ␣a ␣ • ⳱ W ⳱ 2 Kn ccV TC ⳮ T¯ kRV RV

(Eq 9)

0.8 2

Kn ⳱ BiVW ⳱

t⳱

␣ RVW k

冣

mR2V ⳱ a

3

兺冢l1,i i⳱1

2

冣

RV Ri

0.6

0.2 0

Fig. 25

4

8 12 Biot number, BiV

16

Universal approximate function Kn ⳱ f(BiV). 1, for plate; 2, for ball; 3, for cylinder

冤2.095 Ⳮ 3.867Bi kBiV

V

is a Kondratiev number, W ⳱ (TC ⳮ TP)/(TC ⳮ T) is a parametrical criterion characterizing the unevenness of the temperature field, since it is equal to the superfluous temperature of the part surface divided by the volume-averaged superfluous temperature. If the temperature distribution in the body is even (BiV → 0), then W ⳱ 1. The greater the temperature unevenness, the lesser W. When W ⳱ 0, the unevenness of the temperature distribution is the greatest (BiV →

, and TP → TC). Thus, the Kondratiev number characterizes not only the unevenness of the temperature field, but also the intensity of interaction of the part surface with the environment. The theory of regular conditions is based mainly on Eq 6; that is, the ratio of the local cooling (heating) rate and superfluous temperature is a constant value:

Kn ⳱ WBiV ⳱

0.4

kBiV

Therefore, the Kn criterion is determined by the shape of the part and characteristic numbers, l1,1, l1,2, l1,3, and therefore also by Biot criterion, since the characteristic numbers are functions of Biot criteria. It has been proved that curves Kn ⳱ f(BiV) for geometrically absolutely different bodies—a ball, parallelepiped, cylinder, and so on—are so close to each other that all of them can be replaced by one averaged curve (see Fig. 25). The aforementioned formulas are true for the steel

冥

Ⳮ 1nh

or

where:

With regard to Eq 9, the important function of the theory of regular conditions is determined:

1

冤2.095 Ⳮ 3.867Bi

V

冢

3

heating. They can be used for calculation of the cooling process. In this case, one should use dimensionless formula: H ⳱ (T1 ⳮ TC)/(TO ⳮ TC) instead of H ⳱ (TC ⳮ T1)/(TC ⳮ TO). The results of theoretical and experimental investigations for determination of the heating and cooling time for bodies of various configuration have been generalized by author of Ref 10 and presented in the form of Eq 10 convenient for calculations. Theory of the regular heat conditions describes the process of cooling for bodies of different shapes. The cooling time of such bodies can be evaluated on the basis of the dimensionless dependence: FoVKn ⳱

From this it follows that:

dT 1 ⳱ m ⳱ const ds TC ⳮ T

1.0

Kondratiev number, Kn

called heating factor or cooling factor. Equation 5 is followed by equality:

Ⳮ 1n

TO ⳮ TC K T ⳮ TC aKn (Eq 10)

冥

where t is cooling time, FoV is generalized Fourier number, BiV is generalized Biot number, k ⳱ 1, 2, 3—corresponding to bodies of plate, cylindrical, and spherical shape, K is Kondratiev form factor, Kn is Kondratiev number, a is thermal diffusivity coefficient, TO is initial temperature of heated part, TC is temperature of the medium, and T is current temperature. According to patented technology, the process of intensive cooling should be performed in such a way that the martensite transformations begin uniformly at the entire surface simultaneously, forming high compressive stresses which, as was noted, achieve the maximum at a definite moment of time. This moment of time can be determined by Eq 10. For bodies with different configurations, temperatures are found at points the furthest from the surface that correspond to the maximum compressive stresses at the surface. Using these data and Eq 10, one can easily calculate time of achieving maximum compressive stresses without making expensive and complicated calculations. The proposed approach is also correct for bodies of complex configurations. The results of the above-stated generalization have served as a base for the creation of new technology of steel part heat treatment. The essence of the new technology is that alloy steel parts are quenched in conditions of intensive heat transfer until the moment when the maximum compressive stresses on the surface of the part to be cooled are reached, and then intensive cooling is interrupted and the part is kept at constant temperature of martensite start until full transformation of the overcooled austenite in central layers of the part (Ref 21). The moment when maximum compressive stresses on the surface to be quenched are reached is determined

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 323 by generalized Eq 10. There is a database for the determination of Kondratiev form coefficient K and Kondratiev number Kn, which are present in Eq 10. The values of Kondratiev number Kn for simple bodies can be calculated by formulas presented in Table 4. The Kondratiev form coefficient characterizes the shape and size of parts to be quenched, and Kn characterizes the cooling capacity of the quenchant. There is an average thermal conductivity a¯ in the formula, which characterizes thermal and physical properties of the material. Thermal conductivity a¯ of the material is a linear function of temperature. For this reason, one can use the average value of the thermal conductivity and it will not add big errors to calculations. Knowing the temperature in the core of the part when the compressive stresses are optimal on the surface, one can calculate the time of intensive cooling by the generalized Eq 10. The generalized data given previously can be used for the computerization of industrial processes. Link between Usual and Generalized Biot Criteria. In analytical solutions, a usual Biot number generally is used, which is, as known, dimensionless (Ref 22): Bi ⳱

␣ R k

where ␣ is the heat-transfer coefficient, c is the heat conductivity of the material, and R is the radius of a cylinder, ball, or half thickness of a plate. It is noted in Ref 22 that the characteristic size can be also determined as the volume of the body divided by its surface area, that is: RV ⳱

V S

where V is the volume of the body (m3) and S is the surface area (m2).

In the theory of regular heat conditions (Ref 23) the characteristic size is determined as value L that includes three parameters S, V, and K, that is: L⳱

Kn ⳱ WBiV

This universal relation remains true for bodies of arbitrary shape and when the range of the generalized Biot number BiV is from 0 to , the Kondratiev number Kn changes from 0 to 1, and the criterion of temperature field nonsmoothness W changes from 1 down to 0 (see Table 5). The physical sense of the criterion of temperature field nonsmoothness W follows from the formula:

Table 4 Functions for the analytical calculation of Kondratiev form factor Kondratiev form factor, K

Body shape

4R2 p2

Infinite plate, thickness of 2R

R2 5.783

Infinite cylinder

R2 p2

Ball Finite plate, dimensions of sizes: L1, L2, L3

Cube Finite cylinder, height: Z

1 1 1 1 p 2 Ⳮ 2 Ⳮ 2 L1 L2 L3

冢

冣

2

L2 3p2 1 5.783 p2 Ⳮ 2 R2 Z

(Eq 11)

where T¯sf is the average temperature on the surface of the body, Tm is the temperature of quenchant, and T¯V is the volume-average temperature. On the other side, the criterion of temperature field nonsmoothness W for bodies of arbitrary shape can be expressed through the generalized Biot number (BiV) as follows (Ref 22, 23): 1 (Bi 2V Ⳮ 1.437BiV Ⳮ 1)0.5

(Eq 12)

The analysis of Eq 11 and 12 shows that when BiV → 0, then W → 1 and T¯sf T¯V that is, the temperature field on the section of a body to be cooled is even. If BiV → , then W → 0 and T¯sf T¯m, that is, the temperature of the body to be cooled becomes equal to the temperature of environment at the time of its immersing into the quenchant. Since the above-stated dimensionless number is very important in practice, let us find the link between the generalized Biot number [Bi ⳱ (␣/ k)R] and generalized Biot number [BiV ⳱ (␣/ k)K(S/V)]. For an infinite plate it is as follows: BiV ⳱

␣ S ␣ 4R2 1 4 K ⳱ ⳱ 2 Bi k V k p2 R p

since K ⳱ (4R2 /p2), where in this case R is the half thickness of the plate.

R2 S 2 and ⳱ 5.783 V R

For a ball: BiV ⳱

This approach allowed establishment of the universal link between the Kondratiev number Kn, criterion of temperature field nonsmoothness W, and generalized Biot number BiV:

W⳱

␣ R2 2 2 • ⳱ Bi k 5.783 R 5.783

K⳱

␣ ␣ S L K k k V

T¯ sf ⳮ Tm W⳱ ¯ TV ⳮ Tm

BiV ⳱

since

S K V

where K is the Kondratiev form coefficient and in this case the generalized Biot criterion is: BiV ⳱

For an infinite cylinder:

␣ R2 4pR2 3 • ⳱ 2 Bi k p2 4/3pR2 p

Since for the ball: K⳱

R2 V 3 and ⳱ p2 S R

Thus, there are the following links for bodies that are plate-shaped, cylinder-shaped, and ballshaped correspondingly: BiV ⳱ 0.405Bi BiV ⳱ 0.346Bi BiV ⳱ 0.304Bi

Discussion of Results The studies made have shown that the values of the current and residual stresses can be controlled by many methods. Making intensive and uniform quenching, one can reach high compression stresses on the surface (see Fig. 9). It is very important that selecting heat-transfer coefficient, one can reach even null residual stresses on the surface, if necessary. Thus, increasing the heat-transfer coefficient beginning from BiV ⳱ 4.5, one can obtain high residual compression stresses on the surface. These residual compression stresses are compensated by tensile stresses in the core. It should be noted that residual compression stresses increase the service life of the steel parts quenched. It should be noted that intensive cooling has the effect of not only the formation of high compression stresses on the surface of parts quenched, but also the simultaneous reduction of distortion of quenched parts. The reduction of distortions and prevention of the formation of the quench cracks are due to the formation of hard martensite layer on all the surface, which fixes the initial sizes of parts and forms high compressive residual stresses on the surface of quenched parts. In addition, intensive heat transfer in the area of martensite transformations results in the improvement of mechanical properties of the material and makes the service life of the parts longer. The generalization of the abovementioned is given in Ref 24. It is especially important to discuss the process of two-stage quenching. This article considers the two-stage cooling process. During the first stage, one arranges slow cooling in oils or aqueous polymer solutions until the time of minimum distortions is reached, and then, at the second stage, one arranges intensive cooling and washing of the parts. Intensive cooling at the second stage fixes the attained minimum distortion

324 / Residual Stress During Hardening Processes Table 5

Links between generalized Biot number (BiV), criterion of temperature field nonsmoothness (W), and Kondratiev number (Kn)

BiV

W

Kn

BiV

W

Kn

0.00 0.01 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35

1.00000 0.99284 0.98574 0.97171 0.95791 0.94434 0.93101 0.91792 0.90507 0.89246 0.88009 0.86796 0.85607 0.84441 0.83298 0.82178 0.81081 0.80007 0.78954 0.77923 0.76913 0.75923 0.74954 0.74005 0.73076 0.72166 0.71274 0.70401 0.69545 0.68708 0.67887 0.67082 0.66294 0.65522 0.64766 0.16109 0.15981 0.15855 0.15732 0.15609 0.15489 0.15371 0.15254 0.15140 0.15026 0.14915 0.14805 0.14590 0.14382 0.14179 0.54484 0.53940 0.52622 0.51362 0.50157 0.49003 0.47898 0.46839 0.45823 0.44848 0.43911 0.43011 0.42146 0.41312 0.40510 0.39737 0.38992 0.38273 0.37580 0.36910 0.36263 0.35637 0.35032 0.34447 0.33880 0.33331 0.32799 0.32283 0.31783

0.00000 0.00993 0.01971 0.03887 0.05747 0.07555 0.09310 0.11015 0.12671 0.14279 0.15842 0.17359 0.18833 0.20266 0.21657 0.23010 0.24324 0.25602 0.26844 0.28052 0.29227 0.30369 0.31481 0.32562 0.33615 0.34640 0.35637 0.36608 0.37555 0.38476 0.39374 0.40249 0.41103 0.41934 0.42745 0.87796 0.87898 0.87998 0.88096 0.88193 0.88289 0.88383 0.88475 0.88566 0.88656 0.88744 0.88831 0.89001 0.89165 0.89325 0.53395 0.53940 0.55253 0.56498 0.57680 0.58804 0.59873 0.60891 0.61861 0.62787 0.63672 0.64517 0.65326 0.66100 0.66842 0.67553 0.68236 0.68892 0.69523 0.70129 0.70712 0.71274 0.71816 0.72338 0.72841 0.73328 0.73797 0.74251 0.74690

2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.10 6.20 6.30 6.40 6.50 6.60

0.31298 0.30827 0.30369 0.29925 0.29493 0.29074 0.28665 0.28268 0.27882 0.27505 0.27139 0.26782 0.26434 0.26095 0.25764 0.25442 0.25127 0.24820 0.24520 0.24228 0.23942 0.23662 0.23389 0.23122 0.22862 0.22606 0.22357 0.22113 0.21874 0.21640 0.21411 0.21186 0.20967 0.20751 0.20540 0.20334 0.20131 0.19932 0.19738 0.19547 0.19359 0.19175 0.18995 0.18817 0.18644 0.18473 0.18305 0.18140 0.17979 0.17820 0.17664 0.17510 0.17359 0.17211 0.17065 0.16922 0.16781 0.16642 0.16506 0.16371 0.16239 0.16109 0.15981 0.15855 0.15732 0.15609 0.15489 0.15371 0.15254 0.15140 0.15026 0.14915 0.14805 0.14590 0.14382 0.14179 0.13981 0.13789 0.13603

0.75115 0.75525 0.75923 0.76309 0.76682 0.77045 0.77396 0.77737 0.78069 0.78390 0.78703 0.79007 0.79302 0.79590 0.79870 0.80142 0.80407 0.80665 0.80917 0.81162 0.81402 0.81635 0.81863 0.82085 0.82302 0.82513 0.82720 0.82922 0.83120 0.83313 0.83501 0.83686 0.83866 0.84043 0.84216 0.84385 0.84551 0.84713 0.84872 0.85027 0.85180 0.85329 0.85476 0.85619 0.85760 0.85898 0.86034 0.86167 0.86297 0.86426 0.86551 0.86675 0.86796 0.86915 0.87032 0.87147 0.87260 0.87371 0.87480 0.87587 0.87692 0.87796 0.87898 0.87998 0.88096 0.88193 0.88289 0.88383 0.88475 0.88566 0.88656 0.88744 0.88831 0.89001 0.89165 0.89325 0.89480 0.89631 0.89778

BiV

6.70 6.80 6.90 7.00 7.20 7.40 7.60 7.80 8.00 8.50 9.00 9.50 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 35.0 40.0 45.0 50.0 60.0 70.0 80.0 100.0

W

Kn

0.13421 0.13244 0.13072 0.12904 0.12580 0.12273 0.11980 0.11700 0.11434 0.10817 0.10263 0.09764 0.09310 0.08897 0.08519 0.08171 0.07851 0.07555 0.07280 0.07025 0.06787 0.06564 0.06356 0.06160 0.05976 0.05803 0.05639 0.05485 0.05339 0.05200 0.05068 0.04943 0.04824 0.04602 0.04400 0.04214 0.04044 0.03887 0.03741 0.03607 0.03481 0.03364 0.03255 0.02799 0.02456 0.02187 0.01971 0.01647 0.01414 0.01239 0.00993 0.00000

0.89920 0.90059 0.90194 0.90325 0.90578 0.90817 0.91045 0.91262 0.91468 0.91945 0.92371 0.92754 0.93101 0.93416 0.93704 0.93967 0.94210 0.94434 0.94641 0.94833 0.95012 0.95179 0.95336 0.95482 0.95620 0.95749 0.95871 0.95986 0.96095 0.96198 0.96296 0.96389 0.96478 0.96642 0.96792 0.96929 0.97055 0.97171 0.97278 0.97377 0.97470 0.97556 0.97636 0.97970 0.98221 0.98417 0.98574 0.98810 0.98979 0.99106 0.99284 1.00000

of parts to be quenched, since the formation of martensite shell is observed on the entire surface, which fixes the shape of the part to be quenched. In addition to the method considered for the first stage, one can also arrange very intensive cooling until nucleate boiling finishes or maximum compression stresses are reached on the surface to be quenched. The latest technology is being patented in the Ukraine and is the subject of a separate discussion. It should also be noted that the technology developed is furnished with good mathematical support and corresponding software, allowing simulation of complicated technological processes and selection of optimal ways of quench cooling. The software package developed during 1975 through 1982 won good reputation with regard

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 325 to the agreement between results of computations and results of experiments. The good agreement between results of computations and results of experiments is explained by physically grounded selection of all parameters included in the mathematical models and describing the quenching process. Thus, intensive steel-quenching methods have great prospects; therefore the approach and calculation methods developed can be used for the implementation of intensive steel-quenching methods in practice. In practice it is important to select proper boundary conditions. In practice cooling properties of quenchants are determined by tests of specimens, and on this basis heattransfer coefficients are determined. Unfortunately, one cannot always use these results when the shapes and sizes of steel parts are changed, that is, at the transition from specimen to real parts (Ref 14). The authors have suggested another approach to the selection of boundary conditions based on the conception of self-regulated thermal process. The new approach lies in that it is possible to forecast the character of changes in the temperature of parts that are to be quenched, in the process of nucleate boiling, and also to determine the time of this process (Ref 1, 14, 25). Previous sections of this article discuss ways to reduce distortion and eliminate cracking during intensive heating and cooling of parts to be quenched. This is highly important for technological processes, since the intensive heating followed by intensive cooling results in the improvement of mechanical properties of steels and improvement of the material plasticity. The main regularities of intensive steel heating are presented in extensive work (Ref 26), and they can be briefly described: ● When the heating rate increases, the critical

steel points Ac1 and Ac3 grow continuously proportionally to V 1/3 H , and the growth rate for steel is significantly higher than for the iron. ● The higher the heating rate the lower the size of the austenite grain. By further quenching the austenite of such structure, one can reach fine-grain martensite or high-dispersion products of intermediary dissociation. ● In the intensive heating the austenite grain is less susceptible to the growth when the temperature increases and during tempering at such temperature. The problem of obtaining the fine grain at heating has been usually solved by the selection of steel alloying elements. As a rule, natural finegrain steels are those deoxidized by aluminum. Adding aluminum, which forms aluminum nitride (AlN) and does not bind the carbon, does not reduce the steel-strengthening capacity at quenching. Heat treatment of steel deoxidized by aluminum affects the dispersion values, distribution, and the amount of AlN, and through this, it affects the susceptibility of the austenite grain to growth. The temperature above which heating results in the growth of austenite grain is called the rough-condition temperature (Ref 26). The

rough-condition temperature for steel with AlN depends on temperature of its dissolution. Heating to 1000 C (1830 F) considerably reduces the amount of AlN, and heating to 1150 C (2100 F) results in its full dissolution. Maintaining the temperature below that of full dissolution for a long time causes the coagulation of isolations resulting in the growth of austenite grain. There exists a critical amount of AlN isolation; when this amount is exceeded, the effect of stopping is reduced. The presence of AlN particles affects mainly the rough-condition temperature for austenite and in no other way is a factor contributing to getting a fine grain of the austenite at phase transformation ␣ → c. The optimal amount of aluminum added to steel, in the case of deoxidizing not reducing the rough-condition temperature below 975 C (1790 F), should not exceed 0.03 to 0.04% (Ref 27, 28). Making steel alloys with carbide-forming elements allows an increase in the rough-condition temperature when carbides formed have sufficiently high dissolution temperature in the austenite. Compounds sufficiently resistant to dissolution are vanadium carbides (VC, in particular, V4C2) and vanadium nitride (VN). Its effect on the susceptibility of steel to austenite grain growth is considered in Ref 26 and 29 to 31. The temperature of full dissolution for VC in 30X2 steel is 1000 C (1832 F); for vanadium nitride it is approximately 1100 C (2010 F). The addition of vanadium allows slowing of austenite grain growth of the steel in the case of heating to 980 C (1800 F) (Ref 31). Besides, its critical amount is about 0.06%. The effect of zirconium on the susceptibility to austenite grain growth has been studied in Ref 32 to 36. The effect of slowing down due to adding titanium and zirconium to steel is connected with producing carbides, nitrides, and carbonitrides. The critical amounts of titanium and zirconium, which have great effect on the growth of austenite grains, can be varied from 0.03 to 0.08%, depending on the dispersion value of producing phases containing titanium in steels with various chemical composition. Adding titanium and zirconium to steel allows increase of the rough-condition temperature to 1150 to 1200 C (2100– 2200 F) (Ref 26). In practice, great interest is paid to steels alloyed by niobium (Ref 33, 36–39), which is connected with not only great resistance to overheating in comparison with steel alloyed with titanium, zirconium, or aluminum (Ref 30), but also with their good strengthening as a result of dispersion hardening and their high resistance to tempering (Ref 31). Since the carbides and nitrides of niobium dissolve worse in austenite than vanadium carbides and nitrides, steels with niobium have higher rough-condition temperatures. Their high resistance to overheating is due to the fact that niobium, in contrast to vanadium, slows down the process of recrystallization and increases its energy of activation by two times (Ref 40). The

critical amount of niobium in steel is approximately 0.02%. Thus, one of the advantages of microalloying is the possibility of preserving fine-grain austenite in cases when steel, for some reason (great weight of parts, danger of distortion, and so on), undergoes slow heating, and the strict requirements for the preservation of the shape or geometry of the part do not allow use of other methods of influence on the austenite structure. The other advantage of this method is that it allows regulation of the initial sizes of the austenite grain with the use of the selection of the complex of alloy elements of the compound, which can serve as barriers for the growth of austenite grain in steel heating at a wide range of temperatures. The determinative role of austenite grain size on the formation of steel properties in intensive thermal hardening is well known. One of the most systematic studies has been described in Ref 41 and 42. This study considers the role of the kinetic factor in the formation of the austenite grain. The experimental data received by this approach are very convenient for the selection of optimal temperature-time parameters of steel austenite formation in the case of intensive heat treatment, since they describe the dependence of the size of austenite grain on the temperature and heating rate. Figure 26 shows medium diameter of the austenite grain in steels 40 (Ref 42) and 40Kh2NGSM versus temperature and heating rate. Each of these steels exhibits different susceptibility of the austenite grain to the growth while the heating rate increases. In the case of the same percentage of carbon, they are also characterized by different susceptibility to austenite grain growth, which is connected with not only the degree of alloying, but also initial structure states before heating. The initial sizes of austenite grains for both carbon steel 40 (Ref 42) and complex-alloy construction steel 40Kh2NGSM are the same in the case of ferritepearlite structure when heating to ␣ → c phase transformation temperatures. However, as long as the heating temperature increases, the difference in the susceptibility to austenite grain growth is observed in these steels, and it is greater when the heating rate is lower, which is connected with not only kinetic characteristics of the austenite formation process for steels with different alloy composition in the case of intensive heating, but also with barrier effect of barely soluble carbides with the movement of the leading edge of the austenite grain in the alloy steel. Figure 27 shows various techniques of steel quenching, at which it is possible to prevent quench-crack formation (Ref 43); intensive heating has the effect of finer austenite grain, which improves the mechanical properties of the material. Intensive cooling in the martensite range is connected with additional strengthening of the material, which can be explained as follows. Martensite plates form in supercooled austenite, which is in an extremely high compressive stress state. The martensite has a larger specific volume than the austenite. As a result, the austenite undergoes extensive plastic deformation due to

326 / Residual Stress During Hardening Processes 0.03

0.06

0.08 2

3

1

1 2

0.04

3 0.01

Size (d), mm

0.02

Size (d), mm

Size (d), mm

0.06

1

0.02

4

0.04 2 3

0.02

4

4 0 800

900

0 750

1000

Temperature (T ), C (a)

850

950

1050

0 750

1250

1150

Temperature (T ), C

900

1000

1100

1200

Temperature (T ), C

(b)

(c)

Size of austenite grain versus temperature and heating rate. (a) Steel 40, the initial state is condition after burning (Ref 42). 1, 2, 3, and 4 are heating rates 0.03, 8, 200, and 1000 /s correspondingly. (b) Steel 40Kh2NgSM, the initial state is condition after burning at 650 C (1200 F) for 3 h and distortion of 50%. 1, without distortion, heating rate of 2 /s; 2, 3, and 4 are 2, 25, 200 /s correspondingly. (c) Steel 35Kh2NgSM, the initial state is condition after intensive tempering and distortion of 50%, 1, 2, 3, and 4 are at heating rates of 0.01, 2, 5, and 200 /s correspondingly.

Fig. 26

Slow (or fast or intensive) + slow Slow + intensive Fast + fast

Intensive + intensive

A1

Temperature

Austenite temperature range

Ms Martensite temperature range Mf Quench cracking prevented

Susceptible to quench cracking

Fig. 27

Scheme of several steel quench methods and their effect on the steel’s susceptibility to quench cracking

φ95 φ55 0.3

R60

15

8.5 45

∆1:15 Punch made of the molybdenum high-speed steel R6M5 AISI M20. Punch length, 126 mm; maximum diameter, 15.3 mm

Fig. 28

Fig. 29

0.3 Die made out of high-speed steel quenched intensively

“microhammering” by the martensite (this process can be compared to low-temperature thermomechanical processing, which also strengthens the material being processed) (Ref 44, 45). A high dislocation density is produced, and, because of the very rapid cooling, the dislocations are uniformly “frozen” in the quenched surface layer. This is what is believed to produce the additional strengthening or superstrengthening. Very rapid quenching (intensive quenching) in the martensite range and the formation of very high surface compressive stresses are prerequisites. The superstrengthening effect produced by intensive quenching has been used to enhance the performance of punches and dies made of high-speed steel (Fig. 28, 29) and of small dies made of bearing steel. The R6M5 punches are used at high loads in automatic forming machines. Conventionally quenched tools have relatively short lives, and productivity suffers when machines are shut down for tool changes. Punch life increased 2.5 times when tools were intensively quenched in water solutions of chlorides. Special additives were used to prevent corrosion. Performance data for the punches are given in Table 6. Dies for growing artificial diamonds must survive repeated cycles of high pressure and high temperature. Intensive quenching of high-speed steel dies increased their service life by 1.5 times. These dies are intended for growing artificial diamonds and work with heavy cyclical temperature and pressure loads. Despite this, the service life of these dies under such loads became greater by 1.5 to 2 times. It should be noted that these dies were quenched in water solutions of CaCl2 with special admixtures preventing the corrosion on the surface. The intensification took place due to the destruction of the steam film. Instead of aqueous solutions of salts, one can use aqueous solutions

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 327 Table 6 Tool life of punches in automatic forming machine (machine capacity: 175 strokes/min) Durability(a), No. of strokes Test No.

1 2 3 4 5 6 7

Existing technology

Intensive technology

Increase in tool life(b)

6,460 6,670 3,200 4,000 6,620 2,890 2,340

15,600 16,500 5,300 12,075 8,110 10,500 7,300

2.4⳯ 2.5⳯ 1.65⳯ 3.0⳯ 1.2⳯ 3.6⳯ 3.1⳯

(a) Number of strokes until a tool wore out. (b) Increase in tool life is due to intensive quenching

of polymers of optimal concentration exhibiting inverse solubility (Ref 19). During cooling in aqueous solutions of polymers exhibiting inverse solubility, a polymer film forms on the surface of parts, and thus the duration of the fullfilm boiling is reduced to the minimum. The mechanism of the heat transfer in these conditions has been studied insufficiently and requires the further experimental studies. In still another application (Fig. 30), the service life of dies made of ShKh15 (AISI 52100) bearing steel doubled when the tools were intensively quenched. Intensive heating and cooling have been widely used in practice. Some benefits of this technology are given in Ref 42 and 45 to 55 and in Table 7. This technique, on the whole, produces good results at numerical experiments and design of technological conditions.

φ15

φ50

50

Fig. 30

Table 7

Die made out of AISI 52100 steel quenched intensively

Thermal and Physical Fundamentals of Making High-Strength Materials In 1967, it was established that a high cooling rate within the martensite range results in not only the creation of high compressive surface stresses, but also the additional strengthening of material (Ref 56). These investigations are discussed in more detail in Ref 14, 18, 57, and 58. A rapid induction heating and intensive cooling of steel parts where the depth of the quenched surface layer is controlled, which increases the service life, is described in (Ref 2). Steel quenched using this method generally has low depth of hardened layer and fine grain with arrested growth of austenite grains at high temperatures. Due to limited hardenability, compressive stresses appear on the surface of such steel parts and the fine grain provides high strength. In addition to providing an increase in the service life of such heat treated steel parts, there is an opportunity to replace relatively expensive high-alloy steels with less expensive lower-alloy steels and replace fire and environmentally dangerous quench oils with water and water-based quenching solutions. However, the depth of hardness in steel parts hardened using this method is controlled by the chemical composition of the steel parts being hardened. Steel quenching where the depth of the hardened surface layer is controlled in accordance with this method is made in water jets. The service life of such heat treated steel parts where the depth of the hardened surface layer is controlled generally increases when compared to oil quenching. However, it is often necessary to select or create an appropriate steel alloy for use in steel parts having different configurations and sizes to obtain the effect of high surface compressive stresses. In addition, with this quenching method no criteria exist for calculating the rate of water flow for steel parts having different configurations and/or sizes. Thus, a relatively high water flow rate is normally chosen for all steel parts that is not always justified, results in unnecessary energy expenses, and makes the industrial process more complicated than necessary. While the high service life of steel parts where the depth of the hardened surface layer is controlled is considered an advantage for certain steel grades, other steel grades can also achieve the effect of increased strength (as compared with steel quenching methods known before) and high residual compressive surface stresses if the heat treating parameters are properly controlled. The heat treating method described previously is en-

tirely dependent on the composition of the steel alloys available. As a practical matter, it may be difficult to obtain steel alloys having a suitable composition. Accordingly, in practice, the hardening method should be adapted to those steel alloys that are available. Another known steel-quenching method is described in Ref 59. This steel-quenching method involves “shell hardening,” which results in uniform quenching of the entire surface to a certain depth until reaching high hardness using intensive jet cooling. In this method, examples of the application of medium carbon 1045 steel are given. One advantage of this method is the opportunity to increase the service life of steel parts using standard carbon steels, rather than alloy steels where the depth of the hardened surface layer is controlled by the composition of the steel. As discussed in publications (Ref 60), no consideration in this method is given to the parameters necessary to optimize the depth of the hardened surface layer, and the following correlation that the depth of the hardened surface layer should be changed for steel parts having different configurations and sizes should be added: Dd ⳱ constant D

(Eq 13)

where Dd is the optimal hardened depth, and D is the cross-sectional thickness. This correlation was developed in Ref 60 and is considered to provide a foundation for the quenching apparatus and method for hardening steel parts. In addition, this method does not have any criteria allowing the calculation of the optimal cooling solution quench flow, and the technological process is not optimized. Another steel-quenching method is described in Ref 61. In this method, alloy steel parts are quenched in such a manner that a hard surface layer of a given depth and an arbitrarily hard matrix are obtained. For given steel grades, ranges for hardening regimes are found by experimentation to increase the service life of such steel parts. One example of this method involves an alloy steel specimen containing 0.65 to 0.85% C, 0.23 to 0.32% Si, 0.4 to 0.9% Mn, approximately 2% Ni, 0.5 to 1.5% Cr, and 0.1to 0.2% Mo that is heated to 800 to 850 C and spray quenched with water fed under a 0.4 to 0.6 MPa pressure for 0.2 to 0.8 s. The steel specimen is then isothermally heated at 150 to 250 C for 10 to 50 min. This method considers only high-carbon alloy steels. In this method, the depth of the hard surface layer is not optimal for steel parts

Production applications of intensive-quenched limited-hardenability steels

Applications

Gears, modulus, m ⳱ 5 to 8 mm Large-modulus gears, m ⳱ 10 to 14 mm Truck leaf springs Rings and races of bearings thicker than 12 mm

Former steel and process

18 KhGT 12 KhN3A 60 C2KhG ShKh15CG and 20Kh2N4A

New steel and process

58 (55PP) ShKh4 45C ShKh4

Advantages

No carburizing; steel and part costs decrease; durability increases No carburizing, durability increases by 2⳯; steel cost decreases by 1.5⳯ Weight decreases by 15–20%; durability increases by 3⳯ No sudden brittle fracture in service; durability increases by 2⳯; high production rate

328 / Residual Stress During Hardening Processes having different configurations and/or sizes and, because of this, steel strengthening is not consistently achieved in all parts. In addition, this method does not consider the optimization of the quenchant solution circulation rate. Reference 62 describes a method of intensive quenching steel parts using intensive jet cooling. The author points out that the method of intensive cooling is applied to superficial hardening of small parts (shafts, axles, pins, etc.) made of alloy steels. The author underlines that under the condition of very intensive cooling, the deformation reduction is observed. Other authors (Ref 63) came to the conclusion that it is possible to provide a method for producing high-strength steel by heat treatment within a short time. Steel having the composition (wt%) 0.60 to 0.70% C, 0.35% Si, 0.60 to 0.80% Mn, 12.50 to 13.50% Cr and the rest Fe with inevitable impurities is heated to a quenching temperature by induction heating, and this heated steel is rapidly cooled (Ref 63). The authors have considered only induction heating and rapid cooling for alloy steel having 0.60 to 0.70% C. The intensive steel-quenching method described in Ukraine Patent (Ref 21) deals with heating, cooling until the appearance of maximum compressive surface stresses, and then isothermal heating (tempering). This method is based on cooling in the range of 0.8 ⱕ Kn ⱕ 1, where Kn is the Kondratiev number, until reaching maximum compressive surface stresses, then isothermally heating at martensite start (Ms) temperature until the complete transformation of the overcooled austenite of the matrix occurs, and then tempering. At the time of the end of intensive cooling, the optimal depth of the hard layer is automatically reached, which meets the condition in Eq 13. The time of reaching maximum compressive stresses on the surface can be calculated by Eq 12. In most cases, the time of the end of intensive cooling can be tied with the end of nucleate boiling. In this case the quenching process can be controlled, since the noises connected with the nucleate boiling are controlled with special devices (Ref 64). More detailed information on regularities of nonstationary nucleate boiling for steel part quenching is given in Ref 65 and 66. These works consider the so-called “self-regulated” thermal process, which is based on the fact that the surface temperature for the body to be quenched during nucleate boiling is supported at the level of the quenchant boiling temperature and differs very little from this value. The regularities of the nonstationary nucleate boiling, which have been discovered, have been used as a foundation of the new intensive steelquenching method, which provides the additional hardening (“superhardening”) of the material and reduces the deformation; it guarantees the absence of quench cracks during intensive quenching (Ref 49). The intensive cooling in accordance with the specified method should be terminated at the time of the end of the self-regulated thermal process, and then, after the tem-

perature field becomes equal at the cross sections of steel parts, intensive cooling should be continued to room temperature or below (Ref 49). That is why it is very important to elaborate a quenching apparatus for hardening a multitude of alloy steel parts used in, for example, metallurgy, machine construction, bearing and tool industry, quenching of carburized parts, and parts heated by induction, salt bath, the usual oven heating, and vacuum furnaces. At the end of the quench, some steel parts will benefit from isothermal cooling in the air (self-tempering). This process method results in additional strengthening of steel parts, and maximum compressive surface stresses are achieved, resulting in increased service life of the steel parts. Relatively expensive alloy and high-alloy steels can be replaced with less expensive low-alloy or standard carbon steels and instead of an oil-based quenching material, water or a water-based solution is used (Ref 49). The developed intensive methods of steel part heating and cooling have great prospects, since because of them it is possible to save materials and finances as well as increase the labor productivity considerably. These technologies are also ecologically clean.

Summary ● It has been established that one can control ●

●

●

●

●

● ●

the value of residual stresses on the surface of quenched parts. It has been shown that one can forecast the time and place of the formation of quench cracks on the basis of criterion of PisarenkoLebedev. It has been established that for quenching of wedge-shaped bearing rings there is a definite time at which the distortion becomes zero. It is suggested that this state can be fixed by the intensification of heat transfer at the second stage within the range of martensite transformations. The intensive and uniform cooling within the range of martensite transformations reduces the distortion of quenched parts in connection with the formation of a thin martensite layer on the entire surface of a quenched part. Two-step quenching of carburized parts, which lies in the moderate cooling at the first stage and intensive cooling at the second stage within the range of martensite transformations, also results in the reduction of distortion of quenched parts. A new approach has been developed for the reduction of distortion and elimination of crack formation by intensification of heat transfer at the phase transformations. Basic results of the calculations of intensive cooling have been proved by numerous experiments made in recent years. The intensive heating of steel parts has the effect of finer austenite grains and transition to higher temperatures of critical points on the iron-carbon diagram.

● In many cases, intensive heating to the aus-

tenite temperature is equivalent to slow growth of austenite grains, which is reached due to optimal addition of alloys such as titanium, zirconium, and vanadium. ● Intensive heating and intensive cooling improve mechanical properties of the material and reduce the distortion of quenched parts, which is unexpected and explained by the formation of the uniform martensite shell on the entire surface of the part. ● The history of the development of intensive heat steel treatment methods has been discussed, and the recent achievements in this field, which have been patented in many countries, have been considered. REFERENCES 1. N.I. Kobasko, Basics of Intensive Quenching, Adv. Mater. Proc./Heat Treat. Prog., Part I, Vol 148 (No. 3), Sept 1995, p 42W– 42Y; Part II, Vol 150 (No. 2), Aug 1996, p 40CC–40EE; Part III, Vol 153 (No. 2), Feb 1998, p 36FF–36HH 2. K.Z. Shepelyakovskii and F.V. Bezmenov, New Induction Hardening Technology, Adv. Mater. Proc., Oct 1998, p 225–227 3. G.S. Pisarenko and A.A. Lebedev, Deformation and Strength for Complex Stress State, Naukova Dumka, Kiev, 1976 (in Russian) 4. T. Inoue and K. Arimoto, Development and Implementation of CAE System “Hearts” for Heat Treatment Simulation Based on Metallo-Thermo-Mechanics, J. Mater. Eng. Perform., Vol 6 (No. 1), Feb 1997, p 51–60 5. V.S. Morganyuk, Method for Calculating the Thermal and Stress-Strain State During Hardening, Prob. Prochn., No. 6, 1982, p 80–85 6. O.C. Zienkiewiez, The Finite Element Method in Engineering Science, Mir, Moscow, 1975, 542 pages 7. A.A. Popov and L.E. Popova, Isothermal and Thermokinetic Transformation Diagrams for Supercooled Austenite, Mashgiz, Moscow, 1961, 430 pages (in Russian) 8. T. Reti, L. Horvath, and I. Felde, A Comparative Study of Methods Used for the Prediction of Nonisothermal Austenite Decomposition, J. Mater. Eng. Perform., Vol 6 (No. 4) Aug 1997, p 433–441 9. N.I. Kobasko, V.S. Morganyuk, and Yu.B. Gnuchiy, Study of Machine Part Manufacturing Processes in Machine Industries, Znanie, Kiev, 1979, 18 pages (in Russian) 10. N.I. Kobasko and V.S. Morganyuk, Investigation of Thermal and Stress State in the Process of Heat Treatment, Znanie, Kiev, 1981, 18 pages (in Russian) 11. S.F. Yuriev, Specific Volumes of Phases in Martensite Transformation of Austenite, Metallurgizdat, Moscow, 1950, 45 pages 12. V.S. Morganyuk, N.I. Kobasko, and V.K. Kharchenko, Strength Problems, No. 6, 1982, p 63–68 (in Russian)

Control of Residual Stress Formation and Steel Deformation during Rapid Heating and Cooling / 329 13. N.I. Kobasko, L.A. Kozdoba, and A.F. Moshnyanskii, Solution of Inverse Nonlinear Problems of Non-Steady Thermal Conductivity on Electric Models, Teplofiz. Teplotekh., No. 31, 1976, p 256 14. N.I. Kobasko, Steel Quenching in Liquid Media under Pressure, Naukova Dumka, Kiev, 1980, 206 pages (in Russian) 15. V.S. Morganyuk, N.I. Kobasko, and A.N. Kulakov, Predicting the Deformation of Bearing Rings During Hardening, Metalloved. Term. Obrab. Metal. (MiTOM), No. 9, 1982, p 22–24 (in Russian) 16. N.I. Kobasko, V.S. Morganyuk, and L.V. Lushchik, Study of Thermal Stresses Formed in Steel Products Due to High-Rate Quenching, Sov. Mater. Sci. Rev., No. 1, 1987, p 27–32 17. G.F. Golovin, Residual Stresses, Strength and Deformation During High-Frequency Surface Quenching, Mashinostroenie, Leningrad, 1973 (in Russian) 18. N.I. Kobasko, Intensive Steel Quenching Methods, Handbook: Theory and Technology of Quenching, B. Liscic, H.M. Tensi, and W. Luty, Ed., Springer-Verlag, Berlin, 1992, p 367–389 19. G.E. Totten and M.A.H. Howes, Steel Heat Treatment Handbook, Marcel Dekker, 1997, 1192 pages 20. G.A. Temkin, Analytical Theory of NonStationary Heat and Mass Transfer in the Process of Drying and Inverse Problems of Analytical Theory of Drying, Naukai Tekhnika, 1964 21. N.I. Kobasko, No. 4448, Ukrainian Patent, Bulletin 6-I, 1994 22. V.A. Lykov, Heat Conductivity Theory, Vysshaya Shkola, Moscow, 1967 23. G.M. Kondratiev, Heat Measurements, Mashgiz, Moscow, 1957, 244 pages (in Russian) 24. M.A. Aronov, N.I. Kobasko, J.F. Wallace, D. Schwam, and J.A. Powell, Practical Application of Intensive Quenching Technology for Steel Parts, Ind. Heat., April 1999, p 59–63 25. N.I. Kobasko, Intensive Steel Quenching Methods on the Way of Automation, Proc. First Int. Automotive Heat Treating Conf., R. Colas, K. Funatani, and C.A. Stickels, Ed., ASM International, 1998 26. V.N. Gridnev, Yu.Ya. Meshkov, S.P. Oshkaderov, and N.F. Chernenko, Technological Fundamentals of Electrical Heat Treatment of Steel, Naukova Dumka, Kiev, 1977, 204 pages 27. L. Bezdek, Castice AlN a mezni rozmer austenitickeho rzna, Kovove Mater., Vol 5 (No. 4), 1967, p 335–344 (in Russian) 28. C. Dasarathy and R.C. Hudd, An Example of Secondary Recrystallization Induced by Aluminum Nitride Precipitation, Acta Metall., Vol 15 (No. 10), 1967, p 1665–1671 29. V.I. Psarev and Yu.I. Makovichuk, Coagulation of Dispersion Phases at Tempering of Steel Quenched, Izv. Vuzov, Ferrous Met-

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330 / Residual Stress During Hardening Processes Macherauch, The Influence of Heat Transfer on the Development of Stresses, Residual Stresses, and Distortions in Martensitically Hardened SAE 1045 and SAE 4140, Proc. First Int. Conf. Quenching and Control of Distortion, 22–25 Sept 1992 (Chicago), ASM International, p 171–179 56. N.I. Kobasko, Effect of Structural and Thermal Stresses on Crack Formation at Steel Quenching, All-Union Conference on Increasing Output and Economical Efficiency of Heating Furnaces, Dnepropetrovsk, Dec 1967, Abstracts of papers, p 26–27 57. R.F. Ganiev, N.I. Kobasko, V.V. Kulik, et al., Vibration Phenomena in Multiphase Media and Their Application in Technology, Tekhnika, Kiev, 1980, 144 pages 58. R.F. Ganiev, N.I. Kobasko, and K.V. Fro-

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lov, On Principally New Ways of Increasing Metal Part Service Life, Doklady Akademii Nauk USSR, Vol 194 (No. 6), 1987, p 1364– 1473 R.F. Kern, Intense Quenching, Heat Treat., No. 9, 1986, p 19–23 N.I. Kobasko and V.S. Morganyuk, Study of Thermal and Stress-Strained State at Heat Treatment of Power Plant Industry Parts, Znanie Ukr. SSR, Kiev, 1983, 16 pages T. Naito, “Method of Steel Quenching,” No. 59–170039, Japanese Patent, Application 61–48514, 16 Aug 1984 Sh. Owaku, Intensive Cooling, Kindzoku Met. Technol., Vol 57 (No. 3), 1987, p 48– 49 K. Kawasaki, H. Koga, H. Yokota, and T. Nishikawa, “Production of High Strength

Steel,” No. 11293336 A, Japanese Patent, 26 Oct 1999, Filed: 14 April 1998 64. S.G. Povsten, N.I. Kobasko, A.A. Moskalenko, and A.A. Tyltin, On Application of Noise Control in New Methods of Steel Quenching, Proc. Seventh Int. Congress on Heat Treatment of Materials, 11–14 Dec 1990, Vol 3, Vneshtorgizdat, Moscow, p 53–57 65. N.I. Kobasko, Intensive Steel Quenching Methods on the Way of Automation, Proc. First Int. Automotive Heat Treating Conf., 13–15 July 1998 (Puerto Vallarta, Mexico), ASM International, 1998, p 430–438 66. N.I. Kobasko, Self-Regulated Thermal Process at the Hardening of Steel Parts, Promteplotekhnika, Vol 20 (No. 5), 1998, p 10– 14



Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure Ioan Alexandru and Vasile Bulancea, Technical University of Iasi, Romania

CRYOGENIC COOLING represents a useful and efficient means that, if correctly applied within the secondary heat treatment technologic flow, may cause marked increases in the service properties of steel parts and tools. The main purpose of cryogenic cooling is the continuation of the transformation to martensite of as much undercooled retained austenite as possible. After applying the cryogenic cooling to some steels with martensite finish (Mf) critical temperature below 273 K, such as plain-carbon steel with more than 0.6% C as well as alloy and high-alloy steels, important improvements were noticed in some of the service properties, including durability, wear resistance, fatigue life, hardness, and so on. To ascribe these marked improvements exclusively to the increase of martensite and the corresponding decrease of retained austenite would be rather simplistic and nonscientific. Recent research carried out at the “Gh. Asachi” Technical University of Jassy, Romania (Ref 1–3) and the Technologic Institute of Louisiana has emphasized that besides the continuation of the transformation of austenite to martensite, cryogenic cooling also provides: ● A favorable respreading of alloying elements

between martensite and the carbide phases

● The precipitation of a large amount of alloy-

ing carbide elements of very small size (under 1 lm) ● A favorable redistribution of residual stresses As shown in Fig. 1, the transformation of austenite to martensite takes place at cryogenic temperatures both during cooling and during subsequent heating back to the ambient temperature. The larger the cooling rate (curve B), the more intense the transformation of austenite to martensite, both during isothermal transformation and during heating back to ambient temperature, due to the thermal stresses induced during cooling. Cryogenic cooling proved to be effective only in those cases where the retained amount of austenite is larger than 10%, at room temperature, after classical (ordinary) quenching. Moreover,

cryogenic cooling has been especially effective for some parts (gear wheels, ball bearings, elements of injection pumps) and tools (for plastic deformation, for measuring and verifying) that require high values for certain service properties such as hardness, wear resistance, fatigue life, and durability, as well as dimensional and shape stability. For most of the alloy and plain-carbon steels, cryogenic cooling must be immediately applied after classical quenching, while for highspeed steels (HSS) it may be applied also after a previous tempering, particularly in the case of complex shape tools. The typical thermal range for cryogenic cooling lies between 203 and 153 K. It should be noted that cryogenic cooling cannot represent a final heat treatment since subsequent tempering heat treatment is absolutely necessary to achieve thermal stress relieving, fine carbide precipitation, and more favorable respreading of alloying elements between martensite and austenite. The possible heat treatment variants both with and without cryogenic cooling applied to highspeed steels are shown in Fig. 2, where the heating temperatures range between 1493 and 1563 K, the specific cryogenic temperatures are 203, 153, and 77 K, and the tempering temperatures are from 813 to 853. The variants designated by B and E are classical for high-speed steels and for plain-carbon and low-alloy steels, respectively. The variants A, C, and F are not practically applicable, being important only for research purposes, while the variants E and D are also applicable for plain-carbon and alloy steels, after a suitable adjustment of the temperature. Finally, the variants B, G, H, I, K, and M are applied mostly to HSS.

Residual Stresses Induced by Cryogenic Cooling and Their Measuring Methods Role of Internal Stresses within Martensitic Transformation at Cryogenic Temperatures The accurate determination of residual stresses within the cryogenically cooled metallic

materials constitutes a major factor for the proper design, building, and operating of the machine parts and tools since these stresses strongly influence the aforementioned service properties. The residual stresses are those stresses that persist in a solid body as a consequence of the treatment and mechanical manufacturing in the absence of any external or internal loads (forces, momenta, or accelerations). These stresses make up a force system that in normal conditions reaches local and global balance, which is thus hardly detectable, unless this balance is altered. According to the volume size at which they manifest themselves, three types of residual stresses are noticeable: first-order stress (macroscopic), second-order stresses (microscopic), and third-order stresses (ultramicroscopic), as illustrated in Fig. 3. Quantitatively, the cumulated residual stress in any point can be expressed as: rR ⳱ r1ⳭrIIⳭrII

(Eq 1)

The residual stress state is typically determined by the first-, second-, and third-order stresses overlapping, as shown in Fig. 4. In a biphase material (␣ Ⳮ b) the residual stress state is also the result of overlapping stresses, but Fig. 5 shows an even more complex stress distribution compared to Fig. 4. The residual stresses induced by cryogenic quenching heat treatments are especially of the second order, being the effect of both shape and volume accommodation of martensite within the austenite matrix. Consequently, as compared to classical quenching, it follows that cryogenic cooling causes a decrease of structural residual stresses, since it reduces the amount of retained austenite. In order to trigger the martensitic transformation it is necessary not only that martensite becomes more stable than austenite, but also that a certain critical value is reached for the difference between their corresponding free-energy levels. This critical free-energy difference requires austenite to be considerably undercooled, below its thermodynamic equilibrium temperature. Thus, for an austenite undercooling of 200 K, the above difference reaches 350 cal/at. gr.


Etot ⳱ Esurf Ⳮ Estrain Ⳮ Echem

(Eq 2)

where Esurf is the surface energy at the austenite/ martensite interface, Estrain is the coherent deformation energy caused by the misfit between the two lattices (that accompanies an elastic deformation), and Echem is the free-energy difference that occurs at the formation of the martensite volume (corresponding to a plastic deformation). Calculations have emphasized that martensite develops as a result of heterogeneous nucleation and that this nucleation is enabled by a favorable reaction between two stress fields: one caused by the Bain distortion and the other clustered around one or more dislocations from the undercooled austenite. Therefore, the dislocations are the preferred loci for martensite nucleation, which occurs between the critical martensite start (Ms) and Mf temperatures. Considering the stress state in a polycrystalline body, it is obvious that thermal variation is accompanied by the occurrence of an internal stress field (Ref 9). Such a stress field can be generated by several sources such as: the temperature gradient on the cross section, the anisotropy of mechanical properties, the different state of atoms on the grain boundary and inside the grains, the nonhomogeneity of chemical composition, the structural imperfections, the different space orientation of crystals, the differ-

ent specific volumes, and thermal expansion coefficients of austenite and martensite below the critical Ms temperature. All of the theories given in literature agree that martensitic transformation occurs in certain thermodynamic conditions by means of the nucleation and instant growth of martensite nuclei. These theories, however, have different points of view regarding the role of the thermal agitation of atoms or of the stress fields within the martensitic transformation (thermal theory—G.V. Kurdjumov, G. Fisher, et al. [Ref 10–13]; stress theory—A. Guleav, S. Crussard, et al. [Ref 4, 14, 15]; mixed theory, Bain distortion assisted by dislocations—K.E. Easterling, A.R. Tho¨leń et al. [Ref 16]). Consequently, it is important to settle whether it is the thermal agitation (oscillations) or the stress field that plays the major role within the martensitic transformation in the cryogenic field. As previously mentioned, martensitic transformation also proceeds when the thermal oscillations are prevented in the highest degree, such

1453–1563

A

Temperature, K

Besides the large free-energy difference, the martensitic transformation also requires an additional energy source to be available in austenite in order to overcome the energy barrier that separates the parent and product phases. Such an additional energy source for the initiation of the martensitic transformation may be supplied by two sources: nonuniform thermal gradients and mechanical stresses. Since in steels with carbon amounts higher than 0.6% the martensitic transformation also occurs in the proximity of 0 K, the first of the additional energy sources must be excluded. Therefore, only the second one becomes available. Easterling and Tho¨leń (Ref 8) have determined the total energy exchange, associated with the martensitic transformation, under the form:

B

C

E

803–843 Air 203 153 77

C1 C2 C3

F

F1 F2

G1 G2

F3

D3 H

203

203

G3

K

203

D1 D2

G

I

203

D

Oil

Time, h

Fig. 2

as in the proximity of 0 K. Moreover, as illustrated in Fig. 6, which refers to an alloy steel with Ms ⳱ 220 K cooled to 4 K, the lower the cooling rate the larger the amount of transformed martensite. A more comprehensive illustration of the effects of stress on martensitic transformation is obtained by comparing the transformation kinetics for two identical parts, with and without residual stresses, respectively. Such an example is given in Fig. 7, for an AISI H12 steel quenched from 1423 K, with Ms lower than 273 K. Thus, the transformation curve 1 was obtained for an ordinary polycrystalline specimen (with firstand second-order residual stresses), while curve 2 corresponds to a single-crystal powder specimen (with negligible stresses). It is noticeable that martensitic transformation occurred only within the polycrystalline specimen (curve 1). Therefore, it is the stresses and not the thermal agitation that represent the driving force for martensitic transformation at cryogenic temperatures.

M

203

203

Possible heat treatment variants for high-speed steels. Source: Ref 5

40 Martensite, %

B 30 A

20

A

σR

10 B 0 313

σR

σR 273

233

193

153

113

73

Temperature, K

Fig. 1 Transformation of austenite to martensite at cryogenic temperatures. Curve A, low cooling rate; curve B, high cooling rate. Source: Ref 4

First-order stresses (macrostresses)

Second-order stresses

Third-order stresses

(microstresses and microstrains)

Fig. 3

Different observation levels of residual stresses. Source: Ref 6

Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure / 333 Evaluation of Residual Stresses after Cryogenic Cooling

Based on these observations, it appears that the lower the temperature within the cryogenic field the weaker the residual stresses that actuate the martensitic transformation, since martensitic transformation develops with more and more difficulty as the temperature drops closer to Mf.

There are a multitude of methods for determining residual stresses, yet x-ray diffractometry is the only one that allows an estimation of the

σx

● The formation of crystallites and subgrains

σIII σII σR

with dimensions within the range of 10ⳮ2 to 10ⳮ1 lm ● The elastic distortion of relatively large crystals (1 lm) ● The formation of stacking faults

σIII

σR

σI

σmG

x

σII

Evaluation of First-Order Residual Stresses. In face-centered cubic (fcc) materials, residual-stress-induced faults cause both displacements and asymmetries of the diffraction maxima distribution; this effect is less intense in body-centered cubic (bcc) materials, while in hexagonal close-packed (hcp) materials, only a symmetrical enlargement of the above distribution is observed. In order to evaluate the residual stress that has caused a certain strain, the interplanar spacings must be determined both for the undeformed and the deformed material (dohkl and dhkl, respectively), and the elastic constants (Young’s modulus, or E, and Poisson’s ratio, or t) must be known. According to Bragg’s law, a relationship exists between the interplanar spacing (d) and the diffraction angle (h) for the same wavelength (k). If the spacing is expressed as a function of the diffraction angle and the relationship is differentiated, it follows that:

σIII

y

x

Fig. 4

Retained stress, σR

First-, second-, and third-order residual stresses overlapping in a single-phase material. Source: Ref 6

σII

Dd/d ⳱ [cot h]Dh

<σIl>α

α

<σIl>β

σI

β

<σ>α <σ>β

x

r ⳱ E(Dd/d) ⳱ E[cot h]Dh

80

Martensite, %

Martensite, %

1 20

10

40

r⳱ ⳮ 20 2

250

200

150

100

50

0

0 313

Temperature, K Martensitic transformation curves of an alloy steel 0.85% C, 14.8% Ni, 2.1% Mn, cooled down to 4 K. Curve 1, slow cooling; curve 2, fast cooling. Source: Ref 4

Fig. 6

1

2

293 0 300

60

273

233

193

153

113

E p [cot h0] • 2(1 Ⳮ t) 180 (2h) (2h) • ⳱ K (sin2w) (sin2w)

(Eq 5)

73

Temperature, K Martensitic transformation in AISI H12 steel, quenched from 1423 K. Curve 1, ordinary polycrystalline specimen; curve 2, single-crystal powder. Source: Ref 4

Fig. 7

(Eq 4)

where Dh is the angular displacement, caused by stress on the diffractogram, of the diffraction line corresponding to the h angle, as compared to the same line obtained with a standard unstressed specimen. Surface stresses in the direction OX can be determined with the relationship:

First-, second-, and third-order residual stresses overlapping in a biphase material. Source: Ref 7

30

(Eq 3)

where the left terms (Dd/d) represents the strain. Therefore, the stress (r), expressed by the Hooke’s law, becomes:

σIll

Fig. 5

“dynamics” of stresses up to atomic group level. The quantitative determination of residual stresses is based on Hooke’s law, which connects stresses to strains, the latter being, in fact, the very parameters that are actually measured. Considering that every type of stress induces a certain structural change, this change will be accompanied by an alteration of the diffraction pattern, namely an enlargement of the diffraction lines. This enlargement can be determined by:

where w is, according to Fig. 8(a), the angle between the normal of the reflecting planes and the normal at the surface of the specimen, and h0 is the diffraction angle for the unstressed specimen. Equation 5 can also be written under the form:

334 / Residual Stress During Hardening Processes r ⳱ ⳭK • B

(Eq 6)

where K⳱ ⳮ B⳱

E cot h0 p • 2(1 Ⳮ t) 180

(2h) (sin2w)

(Eq 7)

The value of the coefficient K depends on the specimen material and on the characteristic wavelength corresponding to h0. For several materials, the calculated K values are given in Ref 17. The value of the coefficient B from Eq 7 is determined, according to Fig. 8(b), as the slope of the straight line 2hw ⳱ f(sin2 w). In fact, the values of the h angle are measure for o group of planes (with the same Miller indices), and a plot similar to Fig. 8(b) is drawn from which the slope B is determined. The group of planes is chosen to maximize the measuring accuracy of h. Table 1 lists both the coefficient K and other parameters requested for the evaluation of the first-order residual stresses for several technical metallic materials. Evaluation of Second-Order Residual Stresses. Second-order residual stresses are located at microscopic scale at the level of mosaic blocks or crystalline grains and cause an enlargement of the diffraction maxima. Since the enlargement of the diffraction line can be correlated with the average grain size, provided it is less than 10ⳮ4 cm, it is expected that both heat and mechanical treatments cause crystallite breaking. If such a process occurs, then the enlargement of the diffraction line should be proportional to the ratio k/cos h in accordance with the relationship: ehkl ⳱

0.94k b1 cos h

(Eq 8)

in which ehkl is the average size of the crystallite (mosaic block) along the normal direction on the (hkl) plane, k is the wavelength of the applied xray, b1 is the physical width of the diffraction line on the diffractogram, and h is the corresponding diffraction angle for the analyzed (hkl) line.

However, experimental results have emphasized that the above enlargements are proportional to tan h and are independent of k. This disagreement could be explained if larger average crystallite sizes are taken into consideration (about 10ⳮ4 cm) in order to avoid the enlargement of the diffraction lines and the deformation of each crystallite due to the presence of secondorder stresses. Assuming the existence of second-order residual stresses within the lattice of a stressed mosaic block, then certain close-packed planes should exist with altered interplanar spacing, under the form dhkl ⳱ a Ⳳ Da. The nonhomogeneity degree of the interplanar spacing, designated by g(g⳱Dd/d), can be determined by three methods known as direct method, approximation method, and harmonic analysis method. The direct method allows evaluation of second-order residual stresses (rII) by means of the nonhomogeneity degree of the interplanar spacing expressed as: g ⳱ 冪B 2 ⳮ B 20 /4␣R tan h

(Eq 9)

where B0 is the experimental width of the diffraction line of the standard specimen, B is the experimental width of the diffraction line of the analyzed specimen, ␣ is the photometer “parameter,” namely the ratio between the paper speed and the counter speed, R is the radius of the cylindrical chamber, and h is the diffraction angle corresponding to the diffraction line under study. The approximation method considers that both the second-order internal microstrains and the breaking of mosaic blocks with dimension Dhkl 10 lm cause a supplementary enlargement of the diffraction lines. When the physical width b1, corresponding to dimensions Dhkl 0.1 lm, is influenced only by the microstresses or only by the mosaic blocks, then one of the following conditions must be true: b2 /b1 ⳱ tan h2 /tan h1 or b2 /b1 ⳱ cos h1 /cos h2, respectively, where h1 and h2 are angles and b1 and b2 the widths corresponding to the diffraction lines originating from the same reflecting plane but obviously with different reflection orders, that is, the planes (hkl) and (nh, nk, nl), respectively. When the actual width of the diffraction line is influenced both by the small size of mosaic

blocks and the presence of second-order residual microstresses, then the influences may take a Gauss (G), a Cauchy (C), or a Lorentz (L) form. For any combination under the form G-G, C-C, L-L, G-C, G-L, C-L, the physical width of the diffraction line becomes: b⳱

mn

冮M(x)N(x)dx

where M and N are any of the distribution functions associated with the widths m and n (m is the physical width of the line caused by the influence of mosaic blocks; n is the physical width affected by second-order residual microstress). Considering a combination of the type L-C, the size of the mosaic blocks may be expressed according to Eq 8, and the nonhomogeneity degree of the interplanar spacing becomes g ⳱ Dd/ d ⳱ n2 /(4 tan h2), where h2 is the diffraction angle corresponding to the large indices line (nh nk nl). The determination of n2 is graphically performed according to the constructive diagram in Fig. 9, by means of the curves N ⳱ f (b2 /b1). Second-order residual stresses are evaluated according to Hooke’s law with the relationship: rII ⳱ g • E (in MPa)

ψ1

ψ=0

ψ2

d1 d2

ψ = 90° σ

σ

dmin (a)

Fig. 8 Ref 5

d1

d2

σ1

d3

dmax

1 σ2 σ3

d4 (b)

2 3 sin2ψ

(a) Variation of interplanar spacing, d, and the w angle according to the orientation of the reflecting closepacked planes with respect to the stress direction. (b) Dependence of 2hw diffraction angle on sin2 w. Source:

(Eq 11)

where E is the longitudinal electricity modulus of the material under study. The harmonic analysis method consists of both the decomposition of the diffraction line profile into Fourier series and the consideration of the width influenced by microstrains. When the mosaic blocks are large, the enlargement of the diffraction line may represent a direct microstress evaluation. If besides the microstresses small mosaic blocks also exist, then the Fourier coefficient An corresponding to the physical width of the diffraction line, b, will be: g An ⳱ AD n An

(Eq 12)

g where AD n and An are the Fourier coefficients revealing the influence of the presence of mosaic blocks and the second-order microstresses, respectively, on the diffraction-line enlargement. By the logarithmation of Eq 12, under the condition Agn ⳱ exp(ⳮ2nⳮ212Z n2), it follows that:

lnAn ⳱ lnAnD ⳮ 2p212Z 2n θψ

(Eq 10)

(Eq 13)

Knowing An for several lines that differ from one another by the interference order, the relationship ln An ⳱ f (H2 Ⳮ K 2 Ⳮ L2) can be obtained for n ⳱ 1, 2, …, which leads to the fact that the slope of both obtained straight lines equals Z 2n and their intersection with the coordinate axes is ln AD n . In the above relationship Z 2n represents the average component of the deformation vector on the direction a3, from the space a1a2a3 (Ref 19). If the indices (nh nk nl) designate a line of the type (001), (002), (003), …, then the relationship ln An ⳱ f (l 20) represents a straight line, as shown in Fig. 10. It should be noted that the dependen-

Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure / 335 M ⳱ 8p2U 2d sin2 h/k2

cies in Fig. 10 have the tendency to curve toward low or toward high values of n, revealing the fact that the shape of the diffraction line undergoes a more intense influence of the mosaic blocks or the second-order microstrains, respectively. Evaluation of Third-Order Residual Stresses. Heat and/or mechanical treatments can cause a third stressing mode consisting of the displacement of a restricted group of atoms from their ideal positions. The change of the diffraction image due to the presence of third-order stresses seems to be analogous to that determined by the thermal agitation of atoms within crystals. For this mode of motion, a temperature factor, eⳮ2M, can be introduced as:

U 2d

⳱ ⁄3U , U 2

1

2

where U is the average of the square displacements of atoms on a given direction and U 2d is the average of the square dynamic displacements of atoms from their ideal positions at the temperature T, determined as: 2

冬U 冭 ⳱ 4p h•m•h 冤u冢T冣 Ⳮ 冢4T冣冥 9h2T

2 d

2

h

h

2

(Eq 14)

where u(⍜/T) is the Debye function and ⍜ is the Debye temperature. The first type of imperfection, caused by ther2

1.0

M1 = m110/β110 1

0.6

(111)

10−1

0.4

k ⳱

L = 60Å

AL

M1, N2

0.8

0.2

(333)

N2 = n220/β220 1.3

1.5

1.7

1.9

2.1

2.3

10−2

2.5

0

10

β2/β1 Dependence of the distribution functions M(x) and N(x) on the ratio of the physical widths of diffraction lines (110) and (220), recorded for high-speed steel by means of Mo K␣ characteristic x-ray radiation (constructive diagram). Source: Ref 18

Table 1

20

30

(Eq 15)

50

Family of linear dependencies [ln An – (nh nk nl ); (h2 Ⳮ k2 Ⳮ l 2); n ⳱ 1, 2, 3, …] for a brass with 30% Zn that underwent three deformation degrees, corresponding to the values of L, determined by means of other methods. Source: Ref 19

Fig. 10

The evaluation of the microstrain U 23, in solid solutions, is accomplished by eliminating the influence of thermal oscillations, since a standard pure annealed steel specimen is used. Using recorded diffraction spectra, the intensities of the diffraction peaks can be measured both for the analyzed and the standard specimens, Isp and Ist, respectively. It follows that: ln(Ist /Isp) ⳱ 2(M⬘ ⳮ M Ⳮ k)

(Eq 16)

Values of the parameters requested for the evaluation of the first-order residual stresses in several technical metallic materials

Sample material (the matrix)

Lattice type

Lattice parameter, 10 mm

Young’s modulus (E), GPa

Poisson’s ratio m

Characteristic x-ray radiation

Miller indices of the diffraction planes hkl

Diffraction angle, 2h,

Coefficient K(a) (Eq 7)

Cr K␣ Co K␣ Cr Kb Mn K␣ Cr K␣ Co K␣ Co K␣ Co K␣ Cr Kb Co K␣ Cu K␣ Co K␣ Co Kb Co K␣ Co K␣ Co K␣ Co K␣ Co K␣

(211) (310) (311) (311) (222) (420) (331) (333) (311) (400) (420) (400) (331) (321) (400) (331) (400) (121)

156.08 161.35 149.6 154.8 156.7 162.1 148.7 164.0 146.5 163.5 144.7 150.0 145.0 155.5 151.0 146.0 15.84 162.5

ⳮ30.33 ⳮ23.51 ⳮ36.26 ⳮ29.87 ⳮ9.40 ⳮ7.18 ⳮ12.78 ⳮ6.41 ⳮ25.00 ⳮ12.04 ⳮ26.42 ⳮ15.62 ⳮ18.38 ⳮ8.30 ⳮ15.08 ⳮ17.83 ⳮ16.55 ⳮ58.84

Co K␣ Co K␣ Cr Kb Cu K␣ Cr K␣ Co K␣ Co K␣ Cr K␣ Co K␣ Co K␣

(114) (222) (311) (420) (222) (331) (420) (211) (310) (531)

154.2 142.2 157.7 155.6 152.1 145.1 156.4 153.0 157.5 154.1

ⳮ17.51 ⳮ26.17 ⳮ27.88 ⳮ29.53 ⳮ13.11 ⳮ16.60 ⳮ11.03 … … …

␣Fe (ferrite-martensite)

bcc

2.8664

20.6–21.6

0.28–0.3

cFe (austenitic)

fcc

3.656

19.22

0.28

Brass or aluminum

fcc

4.049

6.90

0.345

Copper

fcc

3.6153

12.73

0.364

Brass 4-6

bcc fcc

… …

9.04–5.45

0.38–0.27

Brass 7-3

fcc

…

9.04

0.38

Copper-nickel Tungsten carbide

fcc fcc hcp

13.00 52.42

0.333 0.22

Titanium

11.35

0.321

Nickel

hcp bcc fcc

3.595 a ⳱ 2.91 b ⳱ 2.84 c ⳱ 0.976 2.9504 3.5238

20.80

0.31

Silver

fcc

4.0856

8.11

0.367

Chromium

bcc

2.8845

…

…

Diamond

5.4282

…

…

Silicon

40

h2 + k2 + l 2

Fig. 9

8p sin 2h U 23 3 k2

L = 90Å

(222)

L = 120Å 0 1.1

mal oscillations of atoms within the crystals and/ or by the displacement of atoms from their ideal positions, has dynamic character, having been designated as dynamic deformation, characterized by U 2d. Another kind of imperfection is caused by the static displacements of atoms, Us, from their ideal position (due to the difference between the atomic sizes or to the instability induced by the heat and/or mechanical treatments). According to Hooke’s law, the above displacements (considered microstrains) are associated with the residual microstresses, also called third-order residual stresses. Both the third-order microstrains, U3, and the dynamic displacements, Ud, lead to an intensity decrease of the diffracted beams, by means of a factor designated by eⳮ2k and analogous to the thermal displacement, where:

(a) K ⳱ [ⳮE/2(1 Ⳮ m)] • cot h0 • p/180. Source: Ref 17

336 / Residual Stress During Hardening Processes Thus, the microstrain U 23 becomes: U 23 ⳱

4p2 2kk2 3a2 sin2h

fect of the diffraction lines, caused by the simultaneous existence of both compression and tension in either the crystalline lattice or in mosaic blocks. As mentioned in the section “Evaluation of Residual Stresses after Cryogenic Cooling,” the temperature drop within the cryogenic range is expected to reduce the residual stresses. This effect has been emphasized in the research performed on high-speed steel SEW 320 S 3.3.2 (Fe-3Mo-2V-0.98C, wt%) (Ref 18), heat treated according to the variants A to G shown in Fig. 2. Figure 11 shows the variation of second-order residual stresses as a function of the cooling temperature in the case of S 3.3.2 high-speed steel. It is obvious that second-order residual stresses decrease from about 300 to almost 100 MPa, while the temperature drops deeper within the cryogenic field. Therefore, cryogenic cooling reduces these residual stresses to less than one-half of their initial value. In fact, cryogenic cooling has the same effect on the level of residual stresses as does tempering when applied after classical quenching. The number of tempering treatments significantly reduces the magnitude of residual stresses (compare, for instance, the variant B to the variants E or A), and if the effect of cryogenic cooling is also added, then the steel is almost completely stress relieved. The final stress value of 100 MPa is close to the usual value of the elastic stresses within the equilibrium crystalline lattice. The experimental values of the residual stresses, evaluated in the steel that has been cryogenically cooled at 153 and 77 K, are not significantly different; therefore a cooling performed at a temperature close to the industrial heat treatment temperature (203 K) appears to be sufficient. Thus, after a treatment performed at 203 K the stress decreased from 1.33⳯ (in the case of variant D1) to 1.62⳯ (variant G1). These decreases range from 1.40⳯ (variant D2) to 1.82⳯ (variant G2) after a cooling performed at 153 K and from 2.03⳯ (variant D3) to 2.47⳯ (variant G3) after cooling to 77 K. It is obvious that the heat treatment G variants, due to their

(Eq 17)

where M⬘ and M from Eq 16 are thermal coefficients previously determined by means of the evaluation of Debye temperature. A cryogenically cooled steel would certainly contain third- and second-order residual stresses, and first-order stresses might also exist. In this case, for the evaluation of third-order residual stresses, a rather large number of diffraction lines will be chosen, corresponding to the values of the sin2 h/k2 parameter that are less than 0.36 ˚ ⳮ2 in such a way that second-order residual A stresses are neglected.

Influence of Cryogenic Cooling on Residual Stresses and Dimensional Stability of Steels As emphasized in the previous section of this article, heat and/or mechanical treatments cause “anomalies” within the fine structure of metallic materials that are diffractometrically noticeable by both an enlargement and a displacement of the maxima of the diffraction lines. These “anomalies,” which are directly correlated with the substructure elements, are usually located either on the crystallite level or within the slip planes that occur in the crystallite structure. However, not all of the substructure elements are pragmatically interesting from both technical and scientific points of view. In practice, mostly the density of dislocations, the size of the mosaic groups, and the second-order strains (stresses) are of particular interest.

Influence of Cryogenic Cooling on the Residual Stresses The quantitative evaluation of second-order residual stresses is based on the enlargement ef-

Second-order stress, MPa

350 A

C1

E 250

C2

F1 B

F3

D2

150

G1 50 313

C3

F2

D1

D3

G2

G3 273

233

193

153

113

73

Temperature, K

Fig. 11

Dynamics of second-order residual stresses as a function of the cooling temperature, for the heat treatment experimental variants from Fig. 2 applied to SEW 320 S 3.3.2 steel. Source: Ref 20

multiple tempering, have always caused a more significant decrease with 18 to 23% of the stress state, as compared to the D variants. Since the stress-temperature dependence shown in Fig. 11 is linear, the crystalline lattice of the cryogenically treated steel undergoes elastic relaxation with the decrease in cooling temperature. In fact, it appears that the actual values of the second-order residual stresses are a little higher at 77 K than at the ambient temperature (where the measurements have been performed because in situ measurements were impossible) because during the heating back up to the ambient temperature the martensite amount slightly increases, as shown in Fig. 7.

Influence of Cryogenic Cooling on the Dimensional Stability of Steels The achievement and use of both high-precision mechanical equipment and tools for measuring and verifying require obtaining parts and tools with geometries that have extremely accurate tolerance and that must be preserved unchanged in time. Therefore, both parts and tools require dimensional and shape stability; that is, their structure must be as stable and as stress relieved as possible. The most common heat treatment applied to the majority of parts and tools consists of quenching and one or several subsequent tempering treatments. The resulting structures contain tempered martensite and, according to the tempering conditions, a lower or higher amount of retained austenite. However, both these phases are metastable and, when held within a thermal range close to ambient temperature, they slowly evolve toward more stable conditions. This natural evolution is accompanied by contraction and expansions that are the main causes of dimensional and shape variations. Cryogenic cooling affects dimensional stability by acting on those deformation sources that have the largest contribution on the dimensional variations, namely the continuation of the transformation of the retained austenite to martensite. When compared with classical quenching, performed to ambient temperature, cryogenic cooling has more effect on the steels with larger amounts of carbon or alloying elements. Within the negative temperature range that represents only 1⁄7 to 1⁄8 of the total temperature drop during ordinary quenching, just a small amount of austenite transforms to martensite. The largest amount of martensite was formed after ordinary quenching. After extensive research, G. Murry (Ref 21) introduced several heat treatment schemes in order to ensure a fair dimensional stability, according to two steel categories. Steels for which Retained Austenite Decomposes at 473 to 673 K. In this case, the retained austenite can be reduced by cryogenic cooling, by tempering at 523 K, or by a combi-

Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure / 337 nation of these treatments. The following procedures can be applied: ● Procedure A: Austenitizing and quenching to ambient temperature, immediate cooling to 163 K, maintaining this temperature, and then slow heating back to room temperature followed by a stress-relieving tempering at 423 to 473 K ● Procedure B: Austenitizing and quenching to ambient temperature, immediate cooling to 163 K, maintaining this temperature, slow heating back to room temperature, and tempering at 523 to 573 K, which achieves the total decomposition of retained austenite. ● Procedure C: Austenitizing and quenching to ambient temperature and tempering at 523 to 573 K with the same effects as above Procedure A obtains the maximum values for hardness and wear resistance in steels, because the very low retained austenite amount, which has been observed within the microstructure, can be neglected as long as the treated parts work at ambient temperature or at temperatures lower than 473 to 523 K. Procedures B and C cause the complete disappearance of both retained aus-

tenite and residual stresses. Consequently, a high dimensional stability is achieved; however, both hardness and wear resistance are reduced. It should be noted that Procedure C is more economical and productive compared with the other two. Steels for which Retained Austenite Decomposes at 823 to 973 K. This category includes alloy steels with elements that form stable carbides such as tungsten, molybdenum, and vanadium. They belong to the class of high-speed steels for which high amounts of retained austenite (18–60% Aret) are obtained after classical quenching. It should be noted that this retained austenite is highly stable from a thermal point of view. The cryogenic treatment applied to this category of steels has a high efficiency. It is usually accompanied by one or two tempers meant to achieve both the prescribed hardness and the improvement of steels properties. The following procedures are applicable: ● Procedure A: Austenitizing and quenching to ambient temperature, immediate cooling to 163 K, maintaining this temperature, slow heating back to room temperature followed by tempering at 823 to 848 K, cooling to ambient temperature, immediate cryogenic cooling to 163 K, maintaining this temperature, and subsequent slow heating back to room temperature with final tempering to 823 K ● Procedure B: Austenitizing and quenching to ambient temperature, immediate cooling to 163 K, maintaining this temperature, slow heating back to room temperature, tempering to 873 to 923 K, cooling to room temperature, cryogenic cooling to 163 K, maintaining this temperature, and subsequent slow heating back to room temperature with a final tempering to 823 K ● Procedure C: Austenitizing and quenching to ambient temperature, tempering to 873 to 923 K, cooling to room temperature followed by immediate cooling to 163 K, maintaining this

Expannsion ∆l/l, µm/mm

+20 A +10

0

1% 1% C–1.5% C-1.5% Cr Cr steel steel

−10 B −20

0

400

800

1260

1600

2000

Time, h Dimensional variation of an alloy steel, with 1% C and 1.5% Cr, during a long period at 348 K, of a classically (A) and a cryogenically (B) heat treated specimen. (The Mikus diagram). Source: Ref 21

Fig. 12

Table 2 Applied heat treatment variants and the resulting Vickers hardness, in the case of several low-alloy steels Steel

Heat treatment variant

Austenitizing

Quenching

Cryogenic cooling

Tempering

Vickers hardness

A B C A B C D

1098 K for 30 min 1098 K for 30 min 1098 K for 30 min 1123 K for 15 min 1123 K for 15 min 1123 K for 15 min 1123 K for 15 min

Oil Oil Oil Oil Oil Oil Oil

Yes Yes No Yes Yes No No

448 K for 1 h 523 K for 1 h 523 K for 1 h 448 K for 1 h 523 K for 1 h 523 K for 1.5 h 448 K for 1 h

861 712 969 826 715 696 802

02 SAE

L2 AISI

Source: Ref 21

Table 3 Applied heat treatment, with the aim of improving dimensional stability, in the case of several supercarburized high-speed steels Austenitizing

1523 K for 10 min 1523 K for 10 min 1523 K for 10 min 1523 K for 10 min Source: Ref 21

Quenching

Cryogenic cooling

Tempering, K

Cryogenic cooling

Tempering, K

Vickers hardness

Oil Oil Oil Oil

Yes Yes No No

823 873 873 873

Yes Yes Yes No

823 823 823 823

888 897 914 905

temperature, slow heating back to room temperature, and tempering to 823 K ● Procedure D: Austenitizing and quenching to ambient temperature, tempering at 873 to 923 K, and subsequent tempering to 823 K Procedure A can leave a very small amount of retained austenite that does not exist during Procedures B, C, and D due to their high tempering temperatures. These tempers are performed at 873 to 923 K, which is the maximum temperature range applicable when fair hardness values are required. The service temperature for this category of steels can reach 673 to 723 K without causing dimensional stability problems, providing two successive tempers have been applied. The cryogenic treatment followed by tempering represents an additional guarantee for obtaining high dimensional stability. In order to prove the effectiveness of cryogenic treatment on dimensional and shape stability, Murry (Ref 22) analyzed several steels to which both ordinary and cryogenic treatments were applied. The applied treatments and the resulting Vickers hardnesses are reviewed in Table 2 for low-alloy steels and in Table 3 for supercarburized high-speed steels. After a dilatometric study performed on an AISI L2 low-alloy steel part heat treated according to the variants listed in Table 2, the following conclusions can be reached: ● Dimensional stability increases with increasing tempering temperature applied after quenching. ● The large amount of retained austenite, detected after the classical treatment D, significantly decreases after the cryogenic treatment A; however, it does not disappear completely unless tempering is applied at 523 K as in variants B and C. Thus, the above heat treatments can be classified according to their influence on the dimensional stability: D, the lowest stability; A and C, average stability; B, the highest stability. ● It should be noted that treatment B induces a marked increase of both hardness and wear resistance over treatment C. The same aspects are also revealed in the case of the supercarburized high-speed steels under study. In general, the results offered by Murry have proved that by using cryogenic cooling it is possible to obtain a high dimensional stability with out decreasing the hardness and wear resistance of steels. Figure 12 shows the dimensional evaluation, during a long period at 348 K, of two specimens made from alloy steel (1% C, 1.5% Cr)—one classically treated (A) and the other cryogenically treated (B). In this way, the transformations occurring in both austenite and martensite can be analyzed and understood, especially during the service regime of the parts. Specimen A, subjected to a classical treatment, continuously expands in time due to the presence of a high-retained austenite amount at ambient temperature. This expansion is caused by the decomposition of the retained austenite

338 / Residual Stress During Hardening Processes that is accompanied by an important volume increase. Specimen B underwent a cryogenic heat treatment immediately applied after quenching and consequently contains an extremely low amount of retained austenite. During the long period at 348 K, the quenching martensite undergoes the first stage of tempering, namely the decrease of the tetragonality degree that causes a continuous contraction. This contraction continues to occur after 10 tempers at 348 K, since there is still tetragonal martensite that did not transform to cubic martensite. However, if specimen b was subjected to the same tempering (10 h at 348 K) as specimen a, tempered martensite

Hardness, HV5

1000 900 860 820 780

0

200

400

600

800

1000

Relative shrinkage, µm/m

Fig. 13

would occur and any contraction would no longer be observed. In conclusion, two phenomena were found responsible for the variation of dimensional stability of quenched steel parts: the transformation to martensite of the retained austenite left after quenching, which is accompanied by an increase of volume, and the evolution of metastable tetragonal quenching martensite toward more stable cubic tempered martensite, which is accompanied by a contraction. In order to avoid both the subsequent expansions and contractions, the most effective procedure would be to eliminate both the retained austenite by means of cryogenic cooling and the tetragonal martensite, respectively, using low tempering. However, particular care is to be taken when choosing both the temperature and the maintenance period for tempering since the contraction, occurring during the formation of tempered martensite in either oil or cryogenically quenched steels, is always accompanied by a sensible decrease of hardness. Such an effect is shown in Fig. 13, which shows the Vickers hardness decreasing as the relative shrinkage increases during the tempering heat treatment applied to a full martensitic steel part. Table 4 lists several variants of heat treatment, including cryogenic cooling, applied for the di-

mensional stabilization over time of AISI D2 steel. A high-speed steel, grade AISI M1, was either classically or cryogenically heat treated (Ref 10) according to the same variants shown in Fig. 2 for high-speed steels (SEW 320) S 3.3.2. The dimensional variation of heat treated AISI M1 steel, after five different storage periods (i.e., 10, 20, 50, 80, and 110 days) proved to be proportional to the retained austenite amount (Aret) and therefore also to the residual stress decrease, as listed in Table 5. The dimensional variations as a function of the storage periods described for AISI M1 steel heat treated according to several variants (illustrated in Fig. 2) are shown in Fig. 14. After about three months of storage, the relative dimensional variations of the cryogenically treated specimens are extremely low—less than 0.1 lm/mm, in particular, 0.074 lm/mm for variant D3 and 0.085 lm/mm in the case of variant G1, as shown in Fig. 14. The usual procedure used for analyzing the dimensional stability of different heat treated steel grades is based on the so-called French specimens. The typical geometry of a French specimen is shown in Fig. 15. In order to point out the superiority of the heat treatments applied below room temperature compared with classi-

Dependence of hardness on the relative shrinkage observed during tempering. Source: Ref 5 B

M1 Expansion (∆l / l ), µm/mm

Table 4 Heat treatment variants applied for the dimensional stabilization in time of AISI D2 steel Dimensional variation after 3 months


1. Austenitizing 1283 K, water quenching 2. Cooling at 77 K 3. Stress relieving for 1 h at 593 K, oil quenching (63 HRC)

ⳮ0.012 lm/mm

1. Austenitizing 1283 K, water quenching 2. Cooling at 77 K 3. Stress relieving for 1 h at 763 K, oil quenching (63 HRC) 4. Resuming three times operations 2 and 3 5. Stress relieving for 1 h at 503 K, air cooling (59.5 HRC)

ⳮ0.002 lm/mm

5 4 3 D1

2 1 0 −1

10

20

50

Time, days

Dimensional variation in time, of AISI M1 steel, heat treated according to several variants. Source: Ref 23

1

h

d

Table 5 Variation of the h typical dimension of French specimens, made from AISI M1 heat treated steel Heat treatment variant (Fig. 2)

B D1 D2 D3 G1 G2 G3

D3

−2 −3

Fig. 14

80

D2 G1 110 G2 G3

Retained austenite (Aret), %

(Dh/h)0(a), lm/mm

(Dh/h)1(a), lm/mm

(Dh/h)2(a), lm/mm

(Dh/h)3(a), lm/mm

(Dh/h)4(a), lm/mm

(Dh/h)5(a), lm/mm

51 (Dh/h)i(b), lm/mm

14.6 7.5 6.8 3.9 5.1 4.6 3.82

52 77 81 90 81 109 120

3.9 1.9 1.05 0.27 0.36 ⳮ0.25 ⳮ1.7

1.1 0.54 0.25 0 0.26 ⳮ0.18 0

0.76 0.28 ⳮ0.28 ⳮ0.25 0.12 ⳮ0.2 ⳮ0.18

0.52 0 ⳮ0.16 ⳮ0.11 ⳮ0.1 0 ⳮ0.08

0.38 ⳮ0.16 ⳮ0.1 ⳮ0.074 ⳮ0.085 ⳮ0.16 ⳮ0.082

Ⳮ6.66 Ⳮ2.56 ⳮ0.836 ⳮ0.164 0.555 ⳮ0.75 ⳮ1.878

(a) The relative expansions are measured: during the heat treatment [(Dh/h)0]; after 10 days [(Dh/h)1]; after 20 days [(Dh/h)2]; after 50 days [(Dh/ h)3]; after 80 days [(Dh/h)4]; and after 110 days [(Dh/h)5]. (b) Cumulative relative expansion, 110 days after the heat treatment

D

6 mm thick Schematic of a French specimen, with standard dimensions: D ⳱ 50 mm, d ⳱ 25 mm, h ⳱ 6 mm. Source: Ref 5

Fig. 15

Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure / 339

Temperature, K

cal treatments, the French specimens made from UNS K19667 ball-bearing steel (Fe-1.1Mn0.55Si-1.6Cr-0.98C) were heat treated according to the specific variants illustrated in Fig. 16. The typical dimensions of the heat treated French specimens—namely, D, d, and h—have been measured after 20 days and after 30 days of storage at room temperature as well as after a short exposure at 373 K (in boiling water). The results have been designated by the subscripts 2, 3, and 4, respectively, while subscript 1 corresponds to the dimensions of heat treated specimens. Therefore, the dimensional differences have been designated as D2ⳮ1 ⳱ (D2 –D1); (d2 – d1); (h2 –h1), D3 – 1 ⳱ (D3 –D1); (d3 –d1); (h3 –h1), D4ⳮ1 ⳱ (D4 –D1); (d4 –d1); (h4 –h1) and are illustrated in Fig. 17(a), (b), and (c), corresponding to the 20 days storage, the 30 days storage, and the 373 K exposure, respectively. The data in Fig. 17 show that the narrowest spreading of the dimensional differences occurs in the case of specific heat treatment variant V, which comprises cooling to 203 K followed by tempering to 503 K. The largest variations are noticed in the case of typical dimension h and occurred in the French specimens tempered at 373 and 423 K (heat treatment variants III and IV, respectively) both after 20 days of storage (Fig. 17a) and after 30 days of storage (Fig. 17b). The other variants are less significant, with the lowest values shown in Fig. 17(c), corresponding to a short 373 K heating. In the case of the heat treatment variation II, which includes no tempering after the cooling performed at 203 K, it is noticeable that residual stresses largely influence the dimensional stability due to the stress-relieving phenomenon. As the tempering temperature—applied after quenching at 203 K—reaches the upper admissible limit, the dimensional variation increases during heat treatment. However, the dimensional stability improves in time due to the stress relieving that occurs in the ball-bearing heat treated steel. From this viewpoint, the heat treatment variants designated by IV and V led to the best results in the case of UNS K19667 ballbearing steel. If these phenomena are considered with respect to residual stresses, which represent the only driving force for direct martensitic transformation, since the transformation becomes more and more difficult as the temperature decreases, it follows that the stresses also diminish with decreasing cooling temperature. A slight in-

1073 873 673 473 293

Influence of Cryogenic Cooling on the Structure and Substructure of Steels The structure, or in other words the phase composition, represents an important feature of the quality of metallic materials. The phase amounts and mostly the phase ratio are responsible for the values of several important properties of metallic materials, such as hardness, toughness, dimensional and thermal stability, durability, fatigue life, wear resistance, and so on. Thus, it is well known that retained austenite deteriorates the service properties of the tools and machine parts manufactured from quenched steel, due to its specific characteristics and mostly to its high instability. As previously pointed out, applying one or more tempers might not always be the most effective way to reduce the amount of retained austenite, because of the marked decrease of hardness, mechanical strength, and wear resistance that partially cancels the positive effect of retained austenite transformation. For this reason, a more effective method could be cryogenic cooling. However, because of the rather low amount of retained austenite (less than 15%) left by classical quenching in the microstructure of plain-carbon and alloy steels it appeared that cryogenic cooling would not cause marked additional microstructure improvements compared to ordinary quenching. However, the structure of cryogenically cooled metallic materials proved to be much more uniform and dense. In addition, cryogenic cooling has induced the occurrence of very fine carbides, with dimensions less than 1

1123

473

373 203

I

Fig. 16

crease is noticed, however, during the heating from cryogenic temperature back to ambient temperature due to the small amount of retained austenite that partially transforms to martensite. These results and discussion have proved that cryogenic cooling followed by low tempering (in order to maintain a high hardness value) represents a safe and effective procedure for the increase of dimensional and shape stability of precision parts and tools. Since cryogenic cooling achieves both an increase of quenched martensite and a considerable quantitative decrease of residual stresses, all international research carried out to date has emphasized its opportunity and advantages as an effective, practical heat treatment.

II

203 III Time, min

503

423 203 IV

203 V

Specific heat treatment variants applied to French specimens made from UNS K19667 steel. Source: Ref 5

lm, which occupy the microvoids and contribute to the increase of both density and coherence within the metallic material. The microcarbides that have been identified and counted by quantitative electronic microscopy are mostly responsible for the increase of wear resistance as well as other properties of cryogenically treated steels. Unlike surface treatments, the structural change induced by cryogenic cooling is uniform and takes place within the entire volume. Consequently, a cryogenically treated tool will undergo no sudden changes of structure until it is completely worn out, no matter which mechanical manufacturing operations (such as finishing, sharpening, and so on) it subsequently undergoes. Therefore, the cryogenic treatment causes a permanent irreversible molecular change (Ref 24). Two micrographs (Fig. 18) emphasize the microstructural effects caused by cryogenic cooling on the phase structure of classically quenched SEW 320 S 3.3.2 steel. Figure 18(a) is a micrograph of S 3.3.2 steel after a classical heat treatment (oil hardening followed by 2 to 3 tempers) corresponding to the variant B in Fig. 2. It is a usual microstructure comprising primary and secondary carbides embedded into a matrix composed by tempered martensite and retained austenite representing 10% of the phase amount. The microstructure in Fig. 18(b) is the same steel, but it underwent a cryogenic cooling and a subsequent stress-relieving tempering, in accordance with the variant D3, illustrated in Fig. 2. Besides stress relieving, the tempering heat treatment enables both microcarbide precipitation and alloying element respreading. For this reason, the observed structure has become more uniform, revealing a regular distribution of fine microcarbides with sizes less than 1 lm within a matrix formed mostly of tempered austenite, since the retained austenite amount is about 1.1%, detectable only by x-ray diffraction. In addition, the lower both cooling and maintaining temperature within the cryogenic range (203–77 K), the more uniform and refined the structure, compared to Fig. 18(a). For those tools made of high-speed steel that exhibit complex configurations as well as abrupt passes of the cross section, cryogenic cooling can be applied between two tempers, according to the heat treatment variant designated by G in Fig. 2. The final tempering has a special part consisting on one hand of the distribution of alloying elements among matrix and carbides and on the other hand of the carbide refinement that mostly improves the service properties of highspeed steels. By twice repeating the cryogenic cooling-tempering sequence, according to the variants designated by H and I in Fig. 2, as well as by increasing the number of tempers, according to the variants K and M, the precipitated carbides during the first tempering would coagulate, thus causing a structural nonuniformity, as depicted in Fig. 19. In fact, among the heat treatment variants for high-speed steels shown in Fig. 2, the

340 / Residual Stress During Hardening Processes 30

30

30

25

25

25

20

20

20

15

15

15

10

D

5

∆3-1, µm

∆2-1, µm

10

0 −5 −10

d

−15 −20 −25 −30

II

III 373

IV V 473

Temperature, K

Fig. 17

Fig. 18

d

0 −10

−15

−15

−20

−20 II

III 373

IV V 473

−25 573

Temperature, K

h

−5

−10

−30

D

5

−30

d

II

III 373

IV V 473

573

Temperature, K

Variation tendency of the differences of typical dimensions of French specimens as a function of the tempering within the specific heat treatment variants (Fig. 16) applied to UNS K19667 steel. (a) After 20 days storage. (b) After 30 days storage. (c) After a short exposure at 373 K. Source: Ref 5

Microstructure of SEW 320 S 3.3.2 rapid steel. (a) Classically heat treated. (b) Cryogenically heat treated. Micron bars ⳱ 10 lm. Source: Ref 20

Microstructure of T1 heat treated high-speed steel after a double cryogenic cooling tempering sequence according to the variant H from Fig. 2. Micron bars ⳱ 10 lm. Source: Ref 25

Fig. 19

0 −5

−25 573

10

h

D

5

∆4-1, µm

h

variants designated by D, and under certain circumstances also the variants G, proved to have the most homogeneous and uniform microstructures. Similar microstructural aspects have been observed after the cryogenic cooling of plastic deformation tools manufactured from chromium steels, plain-carbon tool steels, carburized or carbonitrided steels, or from ball-bearing steels. For these steels, only the variants designated by D, I, and K in Fig. 2 are applicable, for which cryogenic cooling is a continuation of ordinary quenching. The influence of cryogenic cooling on the amount of retained austenite, after several heat treatment variants (Fig. 2) applied to some tool steel grades, such as SEW 320 S 3.3.2, AISI T1, M1, M2, D2 is described in Table 6. Tempering at 813 to 853 K, after cryogenic cooling, causes martensite stress relieving as well as a slight increase of the martensite to the detriment of aus-

tenite. Thus, the retained austenite amount can reach 3.9% for M1 steel and 1.1% for S 3.3.2 steel. As previously pointed out, for those tools and machine parts that exhibit abrupt cross-section passes, the most suitable proved to be the heat treatment variant G, in order to avoid the occurrence of first-order stresses that could induce cracking. However, in the case of S 3.3.2 and M1 steels the variant G did not cause spectacular decreases of the retained austenite, since this heat treatment is especially meant to reduce the general stress state. Besides martensite and retained austenite, the structure of high-alloy steels also contains a carbide phase. The carbide precipitates are particularly influenced by cryogenic cooling regarding their development, quantity, dimensions, and distribution. A diffractometric study (Ref 23) performed on several high-speed steels as well as on the carbide powders that precipitate after the electrolytic decomposition of the metallic matrix (the carbide extract) obtained after different cryogenic heat treatment variants reveals an increase of the amount of carbide in alloying elements. At the same time, it was noticed that the sum of the carbide-forming elements that take part in carbide formation decreases after cryogenic cooling. This means that the martensitic matrix grows rich in alloying elements after cryogenic cooling, and this might explain the observed improvements of hardness and cutting performances at the tools made from cryogenically cooled high-speed steels. Chemical analysis of the carbide extracts, obtained from several heat treated high-speed steels, revealed much different structures and redistribution of alloying elements among the matrix and the carbide phase, at the variants that include cryogenic cooling compared with the classic heat treatment variant. This fact is emphasized in Fig. 20, which shows the repartition of the most important carbide-forming alloying elements (Cr, Mo, W, and V) among the matrix

Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure / 341 and the carbide phase as a function of the cryogenic cooling temperature in the case of M2 steel. The curves illustrated in Fig. 20 delineate the two domains among which the carbide-forming alloying elements are distributed: the matrix (the upper field) and the carbide phase (the lower field, under the curves). From Fig. 20 it is obvious that the lower the cryogenic cooling temperature the richer the matrix, in carbide-forming elements, and therefore the higher the hardness and the cutting characteristics of high-speed steel. Other researchers (Ref 21, 23) have emphasized that the increase in the iron amount within the carbides might be an argument for the formation of the (MFe)6C-type complex carbide with high iron content and eventually for the de-

composition of (MFe)2C-type complex carbide with low iron content (where M is metal). This fact is expressed by the increase of the ratio of those carbides that contain high iron amounts, and this increase leads to a quantitative augmentation of the carbide phase within the steel. The qualitative and quantitative determination of carbides has been accomplished using diffractometric analyses performed on carbide powders, extracted by electrolytic decomposition of the high-speed steel matrix. The diagram illustrated in Fig. 21 presents a decrease of the total chromium carbide amount, as much as 30%. Chromium can form carbides of the Cr23C6-type that are primary, coarse, with cubic lattice and very stable. Their amount decreases with the cryogenic cooling temperature.

Table 6 Influence of the heat treatment variant on the retained austenite in several highalloy tool steels Percentage of retained austenite (Aret), after: Heat treatment variant

Quenching

AISI T1 steel B G H I K M AISI M2 steel B D H G SEW 320 S 3.3.2 steel B D G AISI M1 steel B D G AISI D2 steel E D I

Cryogenic cooling to 203 K

First tempering


Second tempering


Third tempering

… … 5 … … 8

10 … 3 … … 0

… … 1.65 3.6

8 … 0 …

27 27 27 27 27 27

… … … 12 12 …

24 23 24 9 9 24

… 19 18 7 … …

16 9 10 0 5 16

21 21 21 21

… 7.5 … …

17 2.25 17 17

… … 13 13

11 … 3.64 3.6

29 29 29

… 8.2–3.3(a) …

23 6.25–1.1(a) 23

… … 8.3–3.5(a)

17 … 5.2–1.9(a)

… … …

10 … …

20.1 20.1 20.1

… 7.2–5.4(a) …

16.7 7–3.9(a) 16.7

… … 8.5–4.8(a)

15 … 5.1–3.8(a)

… … …

14.6 … …

… … 3.9

… … 3.3

… … …

… … …

10.1 10.1 00.1

… 6 6

7.2 4.2 4.2

(a) Values determined after cryogenic cooling to 77 K.

12.44

40

11

Carbides contents, %

Alloying elements sum, %

12

Matrix

10 9 8 7 6 273

Carbides

223 203 173 153 123 Temperature, K

30

Cr W Mo

20 V

77 73

Fig. 20 Dynamics of the repartition of the most important carbide-forming alloying elements among matrix and carbides as a function of the cryogenic cooling temperature, in the case of M2 steel, heat treated according to the variants D (open circles) and G (X data points). Source: Ref 20

10 273

223 203 173 153 123 Temperature, K

73

Variation tendency of the amount of chromium, tungsten, vanadium, and molybdenum carbides as a function of the cryogenic cooling temperature, in the case of SEW 320 S 3.3.2 steel. Source: Ref 20

Fig. 21

The other carbides, such as trigonal Cr7C3 and orthorhombic Cr3C2, are slightly increasing, which compensates for the decrease of the Cr23C6 amount. All chromium carbides have a rather low iron content (Ref 20). In the case of S 3.3.2 steel, the decrease in the cryogenic cooling temperature also determines a reduction in the total amount of vanadium carbides (VC and V2C), which usually undergo secondary precipitation due to the decrease in the number of tempers. It can be seen in Fig. 21 that the decrease of cryogenic cooling temperature induces an increase of tungsten carbide. Tungsten carbide can be cubic WC, hexagonal W2C, and complex cubic Fe3W3C. Disregarding the evolution of the amount of WC and W2C carbides, cryogenic cooling determines an increase in the amount of Fe3W3C carbide with high iron content. With regard to hexagonal Mo2C carbide, Fig. 21 shows that after cryogenic cooling at 77 K its amount becomes at least double compared with S 3.3.2 steel heat treated at room temperature. Besides the increase in both martensite and carbide, the improvement of cutting characteristics of the tools made from high-alloy steel, after cryogenic cooling, can be also ascribed to the changes produced in the size and distribution of the carbide phase. The values of the qualitative and quantitative parameters of the carbide phase are listed in Table 7 for some high-alloy steels. The measurements were performed by means of a Quantimet 720 quantitative microscope equipped with a computer interface. The determined parameters are: A, the total surface occupied by the carbide phase (%); I, the total sum of carbide dimensions on surface unit (mm/mm2); Im, the average size of carbides (mm); Nc, the total average number (density) of carbides on square millimeter (mmⳮ2), and the carbide density is distributed according to the dimensional ranges: 0 to 0.5 lm, 0.5 to 1 lm, 1 to 2 lm, 2 to 4 lm, 4 to 8 lm, 8 to 16 lm, 16 to 32 lm, and above 32 lm. Table 7 reveals the net superiority of cryogenic heat treatment variants compared with the classical treatment (B), with respect to both the size and distribution of carbides. Thus, the carbide surface (A) is larger for the cryogenic variants (except M1 steel for which three cryogenic variants, D2, G2, and G3 induce smaller surfaces) compared with the classical heat treatment variant. Considering that the average size of carbides (Im) has the same or lower magnitude order and that the total sum of carbides average dimensions on surface unit (I) is always larger, it follows that cryogenic cooling should cause an increase in the average number of carbides observed on square millimeter (Nc) compared with the classical heat treatment variant (B). This assumption is confirmed in Fig. 22, particularly in the case of smaller-dimensional carbides. It is obvious from these results that cryogenic cooling causes the occurrence of a large number of small-size carbides, coherent with the matrix, and that this could explain the improvement of

342 / Residual Stress During Hardening Processes the cutting characteristics of the tools made from high-alloy steel. In addition, due to cryogenic cooling a refinement of the carbide phase occurs by means of the increase of carbide density with sizes less than 1 lm. For instance, this increase reached 151% (for variant G1) in the case of S 3.3.2 steel and 146% (variant D2) in the case of M1 steel. The improvement of the quality of high-precision tools made from AISI D2 steel (for die forging, thread rolling, and so on) can also probably be ascribed to—besides the increase of small-size carbide density—the precipitation of

fine g carbides instead of e carbides (Ref 26). This fine carbide contributes to the increase of hardness within the martensite matrix that finally causes an improvement of both the durability and wear resistance of the tool. Another essential element for determining the quality of a steel is the substructure that can be defined as a detail of the structure, observable within the crystalline grains. The study, control, and evaluation by x-ray diffraction of the substructure parameters (dislocation density, second-order stresses, average size of the mosaic blocks, texture, short-range

0.14

30

D2 F3

D3 G3 D1 G1

20 15

0.12

F2 10–7ε, m

103 carbides, mm−2

25

G2 B

10

0.10

C2 E A

0.08 5

C1 D1

B

G1 0.06 313

0 0

0.5

1

2 4 8 16 Dimensional range, µm

32

64

Variation tendency of the average number of carbides on square millimeter (Nc) as a function of the dimensional range, in the case of M1 steel. Source: Ref 20

Fig. 22

Table 7

C3

F1

273

D3

order, etc.) also enable, among other prognoses, the optimization of heat treatment procedures. For the evaluation of the substructure elements, a special part is played by the real physical width of the diffraction line (b). As pointed out by Eq 10, the real physical width b of the diffraction line depends both on the mosaic blocks and on the second-order residual stresses. The “boundaries” of the mosaic blocks, with the dimensions determined using Eq 14, are formed by dislocation walls. At the beginning of the transformations, these walls are grouped in such a way as to create bidimensional dislocation networks (monolayer). As the transformation or the plastic deformation develops further, the boundaries of the mosaic blocks acquire an aspect of dense network with a rather large thickness. In this way, the dislocation density increases up to 1012 cmⳮ2. If both the real size erhkl of the mosaic blocks and the second-order residual stresses are known, the dislocation density can be determined according to the relationship introduced by Williamson and Smallman (Ref 19):

D2 G3

G2

233 193 153 Temperature, K

113

73

Variation tendency of the average size of the mosaic blocks as a function of the final cooling temperature in the case of SEW 320 S 3.3.2 steel subjected to several heat treatment variants. Souce: Ref 3

Fig. 23

q ⳱ 3n/(erhkl)2

(Eq 18)

where n is the number of dislocations located on the boundary of the mosaic blocks. Considering a chaotic distribution of dislocations along the mosaic blocks boundary (n ⳱ 1), it follows that q ⳱ 3/(erhkl)2. In order to emphasize the influence of the cryogenic cooling on two substructure elements (namely, dislocation

Qualitative and quantitative parameters of the carbide phase in some high-alloy tool steels Carbide number distributed according to the dimensional range, mmⴑ2


AISI T1 steel B D G H AISI M2 steel B D G H SEW 320 S 3.3.2 steel B D1 D2 D3 G1 G2 G3 AISI M1 steel B D1 D2 D3 G1 G2 G3 AISI D2 steel A E D I

A, %

l, mm/mm2

lm, mm

Nc, mmⴑ2

0–0.5

0.5–1

1–2

2–4

4.48 8.10 7.52 9.39

55.12 71.26 74.48 83.35

0.0013 0.0010 0.0009 0.0010

49,215 72,520 83,619 85,601

8,003 12,032 17,100 16,822

29,004 41,639 47,036 46,719

6,609 13,358 14,280 15,945

4,418 4,806 4,717 5,361

2.9 5.14 4.90 5.19

30.16 35.59 46.28 60.86

0.0009 0.0007 0.0009 0.0011

31,358 40,898 56,466 83,530

15,136 19,372 29,322 58,101

8,274 11,556 13,548 11,545

5,707 6,858 9,692 10,247

2.35 3.07 3.08 2.59 4.41 3.35 2.98

20.13 26.87 29.35 21.97 39.02 27.07 23.07

0.0009 0.0009 0.0008 0.0009 0.0008 0.0009 0.0009

22,080 30,885 36,600 23,350 48,935 28,901 24,585

11,450 15,541 20,456 11,457 24,871 14,174 11,718

5,554 6,985 7,852 4,951 11,472 6,407 5,593

8.10 9.70 8.21 7.34 9.32 7.39 7.31

52.13 59.14 68.08 58.16 53.29 46.97 61.14

0.0022 0.0018 0.0012 0.0012 0.0013 0.0012 0.0013

23,797 32,773 55,071 47,068 42,032 38,506 45,448

13,014 19,870 28,537 25,042 18,032 13,860 21,776

6.02 4.88 5.72 5.97

11.45 10.25 9.98 11.41

0.0081 0.0072 0.0068 0.0068

1,405 1,424 1,470 1,678

58 66 72 81

8–16

16–32

32

924 575 367 545

238 110 101 188

19 0 18 21

0 0 0 0

2,002 2,943 3,627 3,359

199 138 218 238

40 31 59 13

0 0 0 0

0 0 0 0

3,387 5,465 5,664 4,544 8,370 5,122 4,401

1,253 2,177 2,038 1,852 3,298 2,395 2,220

407 692 575 935 860 746 632

29 25 14 11 64 57 21

0 0 0 0 0 0 0

0 0 0 0 0 0 0

4,365 6,746 14,231 11,439 11,429 12,026 12,189

3,487 3,498 8,706 6,614 6,992 7,049 8,006

1,499 1,335 2,381 2,302 3,659 4,140 2,384

985 735 907 1,278 1,417 1,178 810

417 543 296 389 471 246 261

28 46 13 0 32 0 14

0 0 0 0 0 0 0

110 126 170 203

270 274 292 283

378 401 400 454

293 284 250 317

202 193 185 244

83 72 89 85

9 7 10 80

4–8

Effect of Cryogenic Cooling of Residual Stresses, Structure, and Substructure / 343 density and average size of the mosaic blocks) two high-speed steels, S 3.3.2 and M1, were subjected to the heat treatment variants illustrated in Fig. 2. For S 3.3.2 steel, Fig. 23 shows that the average size of the mosaic blocks increases with

7

B

1016 ρ, m−2

G1 G2

5

D1 C1

A E

G3

D2

D3

C2

3

F1

C3 F2 F3

1 313

273

233 193 153 Temperature, K

113

73

Variation tendency of the dislocation density as a function of the final cooling temperature in the case of SEW 320 S 3.3.2 steel subjected to the same heat treatment variants as in Fig. 23. Source: Ref 3

Fig. 24

Expansion ∆l /l, µm/mm

12

B

10

D1

8 6

G1

D2

4

the decrease in the cryogenic cooling temperature, as in the case of the variants F, C, D, and G. Figure 23 also shows that the largest values of the average sizes of the mosaic blocks have been obtained in the case of the variants E and F, which include tempering heat treatments after ordinary quenching. The increase in the number of tempers causes the decrease in the mosaic block size due to the martensite refinement. Actually, the blocks are broken and their crystalline lattice becomes stress relieved, as illustrated in Fig. 23 for the variants B, D, and G, causing the smallest sizes of the mosaic blocks. The deep cooling of steel enables the coagulation of the mosaic blocks, which therefore increase in size. The linear aspect of the variation shown in Fig. 23 proves that the coagulation phenomenon is of elastic type. The last aspect of the cryogenic cooling effects on the substructure of the S 3.3.2 heat treated steel is emphasized in Fig. 24, which shows the variation tendency of the dislocation density as a function of the final cooling temperature. After the first temper, a decrease of the dislocation density is noticed, and this decrease becomes more important after the subsequent tempering due to the breaking of the mosaic blocks. After cryogenic cooling, a marked decrease is noticed in the dislocation density, which proves that the crystalline lattice becomes more relaxed and the stress field diminishes, thus coming closer to the normal state. Since a linear variation is also noticeable in this figure, it is obvious that the dislocation density decrease can be related to the elastic phenomena produced within the crystalline lattice.

G2

2

G3 0

D3

−2 0

100

120 140

160

180

200 220 240

Second-order stress, MPa Dynamics of the dimensional stability as a function of the stress state, in the case of SEW 320 S 3.3.2 steel, heat treated according to the variants D (solid line) and G (dashed line). Source: Ref 20

Fig. 25

Properties—Residual Stresses— Structure and Substructure Correlation for Cryogenically Cooled Steels The increase in the transformation degree of retained austenite to martensite causes the de-

crease of second-order stresses that become favorably redistributed among the two phases. Moreover, the structure becomes harder and more uniform and finally durability increases. The influence of cryogenic cooling on the formation, the amount, and the distribution of the carbide phase is first revealed by the emergence of the fine carbides, which usually have smaller sizes compared with those occurring after classical heat treatments. The large number of extremely fine carbides, which has been experimentally determined after the cryogenic treatment, represents an argument for the conclusions discussed previously. The increase in both the surface occupied by the carbides and the carbide density as well as the large number of fine carbides measured after the cryogenic cooling lead to the development of a hard, uniform, homogeneous structure that induces a marked improvement of the properties of heat treated steels. As previously mentioned, cryogenic cooling contributes as well to the decrease in the stress state that largely assists the improvement in properties. Thus, in the case of the tools and parts made from S 3.3.2 steel, the decrease in the stress state leads to a fair dimensional stability, as shown in Fig. 25, where three heat treatment variants (B, D, and G in Fig. 2) are considered. Another effect of decreasing the stress state due to the cryogenic cooling is shown in Fig. 26, which shows the variation of the amount of retained austenite with the value of the secondorder stresses, for the same heat treatment variants. It is obvious that the lower the value of the stress state the more reduced the amount of retained austenite. It is well known that durability, which is the basic criterion for the effectiveness assessment of any heat treatment, is conditioned by the connection between the strength intrinsic characteristic of the material and the actual service conditions of the tools. Besides hardness and wear resistance, the most important characteristic that determines the durability is the structure quality.

100

G3

8 6

D1

G1

D2

4

G2

90 80

G2 D3

100

D3

D2 G3

G1

G2

D2 G1

70 60

D1

S 332 steel

D1 M1 steel

2

G3 0 0

B

D3 100

120

50 40 140

160

180

200

220

B

Variation tendency of the retained austenite amount as a function of the second-order residual stresses, in the case of SEW 320 S 3.3.2 steel. Source: Ref 20

G3

G2 D2

80

D1

70

G1

G1

D2 D3 G2

D1

M1 steel 60

B

B

50

SS3.3.2 332 steel steel

60 80 100 120 140 160 180 200 220 240 Second-order stress, MPa

Second-order stress, MPa

Fig. 26

G D3 3

90 Durability (T), min

B Durability (T), min

Retained austenite, %

10

Fig. 27 Dependence of durability on the relaxation of the elastic stress field in the case of two highspeed steels subjected to intensive service regimes (cutting speed: 32.67 m/min; cutting advance: 0.25 mm/rotation; cutting depth: 2.5 mm). Source: Ref 20

40 3

4

5 6 7 8 Alloying elements sum, %

9

10

Dependence of durability on the total amount of alloying elements dissolved in martensite in the case of two high-speed steels. Source: Ref 20

Fig. 28

344 / Residual Stress During Hardening Processes Thus, the phase composition (namely, the retained austenite amount), the phase distribution, the uniformity and refinement degrees of the phases, the distribution of the alloying elements among the martensite matrix and the carbides, the repartition of the carbides on dimensional ranges, the average size of the mosaic blocks, the dislocation density, and the second-order stress state represent the influencing elements of the durability of cutting tools made from highalloy tool steels. For instance, a low stress state, namely a relaxation of the elastic stress field, involves an increase in the martensitic transformation degree that causes an augmentation of the durability of cutting tools made from several high-speed steels, such as S 3.3.2 and M1, according to Fig. 27. On the other hand, Fig. 28 shows the influence of the matrix alloying degree on the durability of cutting tools. The figure illustrates an increase in durability of the tools made from two highspeed steels with the increase of the total amount of the alloying elements dissolved in the martensite matrix. In conclusion, the discussion in this article has brought evidence that the residual stresses play a very important part both during and after the cryogenic cooling. These stresses constitute the main cause for the continuation of the transformation of the retained austenite to martensite, within the cryogenic field. Surprising but true is the fact that after cryogenic cooling the value of the residual stresses becomes even lower compared with classical quenching, either in water or in oil, to the ambient temperature.

4. 5.

6.

7.

8. 9.

10. 11.

REFERENCES 1. I. Alexandru, Gh. Ailincai, and C. Baciu, Influence de traitements thermique a´ basse tempe´rature sur la dureé de vie des aciers a` outils a` coupe rapide tre`s allie´s, Rev. Me´tall., Vol 6, 1990, p 383–388 2. V. Bulancea, I. Alexandru, and D. Bulancea, Carburic Phase in Cryogenically Treated Tools Steels, MATEHN 94, First Int. Conf. Materials and Manufacturing Technology, 18–20 May 1994 (Cluj-Napoca, Romania), p 377–380 3. V. Bulancea, I. Alexandru, and D. Bulancea, The Substructure Elements Modification by

12. 13. 14. 15.

16.

Cryogenically Treated Fe-3W-3Mo-2V-C Highly Alloyed Steel Tools, Bull. Polytech. Inst. Jassy, Romania, Vol XLII (No. XLVI), 1996, p 167–174; ASM International Second Int. Congress Mater. Sci. Eng., (Jassy, Romania), 1997 A.P. Guleaev, Heat Treatment of Steel, MASHGIZ, Moscow, 1960, 438 pages V. Bulancea, I. Alexandru, D. Bulancea, and D.G. Galusca, Advanced Heat Treatment Technologies. Cryogenic Cooling of Steels, Cermi, Jassy, Romania, 1998, 196 pages N. Skalli and J.F. Flavenot, Prise en compte des contraintes re´siduelles dans un calcul pre´visionnel de tenue en fatigue, CETIMInformations, No. 90, 1985, p 35–47 V. Hauk, Micro Residual Stresses, Evaluation by X-Rays, Results, Assessment, Proc. of the Ninth Int. Conf. on Experimental Mechanics, 20–24 Aug 1990 (Copenhagen, Denmark), Technical University of Denmark, Vol 3, p 1227–1236 K.E. Easterling and A.R. Tho¨leń, The Nucleation of Martensite in Steel, Acta Metall., Vol 28 (No. 4), 1976, p 333–342 I. Alexandru, Gh. Ailincai, C. Picos, A. Dima, and V. Bulancea, Aspects of the Influence of Cryogenic Thermal Treatments on the Redistribution of Alloying Constituents between the Matrix and Carbides, Bull. Polytech. Inst. Jassy, Romania, Vol XXIX, 1983, p 7–12 G.V. Kurdjumov, Non-Diffusion (martensitic) Transformation in Alloys, J. Technol. Phys., Vol XVIII (No. 8), 1948 (in Russian) G.V. Kurdjumov and O.P. Maksimova, Low Temperature Martensitic Transition, Metallurgical and Metal Physics Problems, Tome 2, Metalurgizdat, 1951 (in Russian) G. Fisher and D. Turnbull, J. Appl. Phys., Vol 19, 1948 G. Fisher and D. Turnbull, Austenite-Martensite Transition Kinetics, J. Met., Vol 19, 1949 S. Crussard, Comptes Rendues de l’Academie des Sciences, Vol 24, 1955 F.L. Lokshyne, Dynamical Theory of Martensitic Transformation, Bull. of Polytech. of Novotcherkask, Vol 71 (No. 85), 1957 (in Russian) K.E. Easterling and A.R. Tho¨leń, On the

17.

18.

19. 20.

21.

22. 23.

24. 25.

26.

Growth of Martensite in Steel, Acta Metall., G.B., Vol 28 (No. 9), 1980, p 1229–1234 I. Alexandru, V. Bulancea, D. Pop, F. Pop, and A. Alexandru, Phase Analyses of Metallic Alloys, Cermi, Jassy, Romania, 1998, 233 pages V. Bulancea, I. Alexandru, and D. Bulancea, The Stress State Modification by Cryogenically Treated Fe-3W-3Mo-2V-C High Alloyed Steel Tools, Bull. Polytech. Inst. Jassy, Romania, Vol XLII (No. XLVI), 1996) p 161–166; ASM Int. Second Int. Congress Materials Science and Engineering, 1997 (Jassy, Romania) C. Gheorghies, The Fine Structure Control with X Radiation, Tehnica, Bucharest, Romania, 1990, 272 pages V. Bulancea, “The Influence of the Cryogenic Treatments on the Aspects Connected with the Substructure of the Highly Alloyed Steels and the Functional Characteristics of the Cutting Tools,” Ph.D. thesis, “Gh. Asachi” Technical University of Jassy, Jassy, Romania, 1992 G. Murry, La stabilite´ dimensionnelle des aciers apre´s traitements thermique. Aspects me´tallurgiques, Trait. Therm., France, No. 128, Oct 1978, p 43–50 G. Murry, Decomposition of Retained Austenite, Trait. Therm., No. 81, France, 1974, p 40–42 V. Bulancea, I. Alexandru, and D. Bulancea, The Dimensional Stability of the Frozen HSS Cutting Tools, Bull. Polytech. Inst. Jassy, Romania, Vol XL (No. XLIV), p 499–502; ASM Int. First Int. Congress Materials Science and Engineering, 15–17 Nov 1994 (Jassy, Romania) P. Paulin, Frozen Gears, Gear Technol., March–April 1993, p 26–29 I. Alexandru, “Contributions on the Influence of Thermal Treatments at Temperatures below 273 K of High-Alloyed Steels on their Cutting Properties,” Ph.D. thesis, “Gh. Asachi” Polytech. Institute of Jassy, Jassy, Romania, 1980 F. Meng, K. Tagashira, R. Azuma, and H. Sohma, Role of Eta-Carbide Precipitations in the Wear Resistance Improvements of Fe12Cr-Mo-V-1.4C Tool Steel by Cryogenic Treatment, ISIJ Int., Vol 34 (No. 2), 1994, p 205–210



Inducing Compressive Stresses through Controlled Shot Peening J. Kritzler and W. Wu¨bbenhorst, Metal Improvement Company, Inc., Germany

WITH MOST VEHICLES—whether for land or air transport—the level of stress increases during the production cycle. The increased starting weights of planes, the higher load on the axles of trucks, and the mounting of stronger and heavier engines in cars can be named as examples. In other cases, extreme forms of reduced weight construction must be attempted, for example, in aircraft construction or when unexpected damage occurs during trials. If the increased stress, as in the case of most components, is oscillating, the fatigue resistance must be increased. This is possible—apart from the trivial solution of increasing cross sections with their disadvantage of increasing weight— by measures relating to the materials, to the construction, or to the manufacturing process. The use of a so-called “better” material does less than generally expected, especially if one considers that increases of the tensile strength of the material is subject to strict limits due to manufacturing as well as cost considerations. An improvement of the construction in detail is in many cases the most elegant solution; however, especially in mass production such as car manufacture or high-cost light engineering, for example, aircraft construction, such possibilities are often already exhausted. Notches, and sharp notches at that, are frequently needed for functional reasons if one considers the threading of bolts or the radii of slots for fittings keys. In such cases and lately in increasing volumes, shot peening is used (Fig. 1). Apart from im-

Fig. 1

Shot peening process. Courtesy of Metal Improvement Company, Inc.

proving fatigue strength, shot peening is also used: ● In cases of corrosive fatigue, stress corrosion,

hydrogen embrittlement, friction corrosion, and wear by cavitation ● In surface texturing ● To close off porosity ● To test adherence of layers as well as peen forming

Historic Development of Shot Peening Sandblasting as an example for cleaning castings can be regarded as a predecessor of shot peening. Literature on this dates from the 1800s (Ref 1, 2). Shot peening was introduced by Zimmerli (Ref 3, 4) and Almen (Ref 5–9) in their respective companies Associated Spring Company and General Motors prior to 1930. In 1934, patents were granted for the shot peening machines (Ref 10), and during the years 1935 to 1945 Almen carried out the fundamental work (Ref 11–14), for example, development of the “Almen” strip. Shot peening was also investigated in Germany prior to World War II at the Technical Universities of Darmstadt and Braunschweig (Ref 15–18). Opel used shot peened valve springs from 1935. In about 1940 it was clear that shot peening increases the fatigue strength primarily by improved residual compressive stress and not by increasing the hardness of the material surface. World War II precipitated the industrial application on a large scale in the United States (Ref 19–21). An American Society for Metals conference about peening was held in 1944 (Ref 22, 23). One gets the impression that in contrast, the industrial application in Germany was lagging behind. All the same, a report (Ref 24) appeared about the optimizing peening depending on the type of machine, impact time, and shot size. In 1946, the measurement of the residual compressive stress of peened torsion springs was de-

scribed for the first time (Ref 25). In 1949, a report appeared on “stress peening” (Ref 26) in which leaf springs were peened under prestress to achieve a particularly high level of fatigue strength. The Society for Automotive Engineers (SAE) published its Manual on Shot Peening in 1952 (Ref 27). During the years 1951 to 1954, there were two conferences in the Soviet Union in which broad attention was dedicated to shot peening (Ref 28–38). Since 1954 (Ref 39) peen forming has been used for the manufacture of complex curved surfaces. The first norm, the MIL specification MIL-S-13165 (Ref 40), came into existence in 1956 and still applies today in a developed form (Ref 41, 42). Soon after, practically all aircraft (Ref 43–48) and automobile companies, and so forth, joined with their own regulations and norms. The norms named in the references represent merely a selection of the total available (Ref 49–58). A general industrial application of shot peening in the Federal Republic of Germany can be recorded from approximately 1955, and in this context especially the automobile industry should be named in which all springs (valve and suspension) are peened since this time. A report by W. Schu¨tz (Ref 59), stemming from the same period, reports about shot peening for improving the vibratory fatigue properties of components for tracked and road vehicles. The same author later covered the special requirements of drive technology (Ref 60).

Elementary Shot Peening Processes The elementary procedure in shot peening is an elastic-plastic impact process between the peening material and the workpiece. In this process, a transformation of the kinetic energy to work aimed at the elastic and plastic deformation of the work material depending on the mass of the peening material and the shot velocity takes place. The residual compressive stresses in the wake of shot peening are a result of the locally occurring plastic deformation on the surface of the workpiece and are caused by the impact of

346 / Residual Stress During Hardening Processes pact of the peening material passes, this leads to residual compressive stresses at the surface and internal tensile stresses. Hertz’s Compression. In the process of the Hertz’s compression, the maximal plastic deformations occur below the place of impact of the spherical peening material and the flat workpiece (Fig. 4b). Here, a residual compressive state is formed that has its maximal values below the workpiece surface. Both elementary processes occur always, as already stated, side by side and are influenced by both the workpiece material properties and the parameter of shot peening. The characterization and the key data of a compressive stress process caused by shot peening can be seen in Fig. 5 (taken from Ref 63). Detailed examples relating to this are shown in Ref 64.

the individual peening material particles. The distribution of the residual compressive stresses varies widely due to the variety of the working and peening materials and possesses significant differences (see Fig. 2, 3). The deformation processes or the generation of residual compressive stresses may be fundamentally explained according to Wohlfahrt (Ref 61, 62) in terms of two elementary processes: plastic stretching of the immediate workpiece surface and Hertz’s compression. Plastic Stretching of the Immediate Workpiece Surface. In Fig. 4(a) the stretching process of the area near the surface and its plastification is recognizable, declining with increasing distance to the edge layer. The only plastically deformed edge layer is impaired by the only elastically deformed layers below. After the im-

AL 2014 T6 (Z 400/0.020"A/100%)

AZ 31 (MI 330/0.016"A/100%)

0

Workpiece Material and Process Parameters

⫺100


Workpiece material and process parameters exert different effects on the residual compressive stresses generated by shot peening (Ref 65). The key parameters are shown in Fig. 7. Changing the parameters shifts the distribution of the generated residual compressive stresses into the respective direction shown. It is important to note that nearly all changes of the parameters lead on one hand to changes in the residual compressive stresses on the surface and on the other hand influence to a much greater extent the depth of the maximal residual stress below the surface. The hardness of the shot peening material influences the extent and the depth of the compressive stresses. For this reason, the peening

SF-Cu F20 (Z850/0.012"A/200%) (Z8500/0.012"A/100%)

⫺200 ⫺300 ⫺400

50 CrV 4 (MI 780/0.010"C/100%)

⫺500 ⫺600 ⫺700 0.0

0.2

0.1

0.3

0.4

0.5

0.6

Depth, mm

Fig. 2

The advantages of the residual stress caused by shot peening in a workpiece are shown in Fig. 6. The fatigue failure in most components is caused by tensile stresses on the surface. These tensile stresses probably arise when the components are newly installed. As each bending cycle or rotation puts the workload on the component and removes it, the component becomes increasingly susceptible to fatigue cracking until finally it cracks or a crack from stress corrosion becomes manifest, and the component fails. Including shot peening in the original design of the critical components prolongs its life span under fatigue. Figure 6(a) shows a component that has not been shot peened and has tensile stresses on the surface. The second component (Fig. 6b) has been shot peened and has compressive stresses on the surface. Figure 6(c) is a theoretical diagram of the shot peened component under load.

Typical stress profiles of “soft” metallic material. Courtesy of Metal Improvement Company, Inc.

0


15 CrNi 6 (MI 230H/0.014"A/200%) εr(z)

⫺500

σx(z) = σy(z)

τmax

εr(z)

σz(z) σES(z)

σES(z)

⫺1000 18 CrNiMo 5 (MI 230H/0.020"A/200%) ⫺1500 0.00

0.05

0.10

0.15

0.20

z

0.25 (a)

Depth, mm

Fig. 3

Typical stress profiles of “hard” metallic material. Courtesy of Metal Improvement Company, Inc.

Fig. 4

z (b)

Residual stress formation. (a) Stretching surface layer. (b) Hertzian pressure. Courtesy of Metal Improvement Company, Inc.

Inducing Compressive Stresses through Controlled Shot Peening / 347

SS

d

TS(MAX)

⫺100 0 2

CS(MAX)

4 6 8

12

Example of residual stress profile created by shot peening. Ss, surface stress, which is the stress measured at the surface. CS(max), maximum compressive stress, which is the maximum value of the compressive stress is induced, which normally is highest just below the surface. d, depth of the compressive stress is the point at which the compressive stress crosses over the neutral axis and becomes tensile. TS(max), maximum tensile stress, which is the maximum value of the tensile stress induced. The offsetting tensile stress in the core of the material balances the surface layer of compressive stress so that the part remains in equilibrium; TS(max) must not be allowed to become large enough to create early internal failures. Courtesy of Metal Improvement Company, Inc.

Fig. 5

Tension

0

Compression

Tension

Compression

HS HM

Tension

0

Compression stress

Residual stress

v, d, HS, HM


Shot peening parameters versus residual stress distribution. v, velocity of shot, m/s; d, shot size, mm; C, coverage, %; HS, hardness of shot, HRC, Hm, hardness of material, HRC. Courtesy of Metal Improvement Company, Inc.

Fig. 7

Depth, in. 0

0.004

0.008

0.012

0

0 ⫺50

46 HRC shot

⫺500

⫺100 ⫺1000

61 HRC shot 0

Tension stress

Compression stress

Tension stress

0

v , d , C, HS

HM

0.1

0.2 Depth, mm

⫺150

Residual stress, ksi

⫺50

0

0.3

Peening 1045 steel at 48 HRC with 330 shot. Courtesy of Metal Improvement Company, Inc.

Fig. 8

Peened surface

Surface metal (a) Unloaded beam

Depth, in.

(b) Shot peened beam 0 0

Compression Residual stress

M Applied load

M

Resultant stress

Peened surface (c) Shot peened beam under load


Tension

0.008

0.012

0 46 HRC shot ⫺500

⫺150 61 HRC shot

⫺1500

Fig. 6

Fig. 9

0 ⫺50 ⫺100

⫺1000

⫺200 ⫺250

0 Comparison of stress distributions. (a) Typical stress distribution in surface of metal beam, unloaded by exhibiting residual tensile stress from normal fabricating procedures. (b) Same beam after shot peening, still without external load. Surface stress is now compressive. (c) Beam, when subjected to design loading, still shows some residual compressive stress at surface. Courtesy of Metal Improvement Company, Inc.

0.004

0.1


+50

0


+100

(⫺) Compression

Depth below surface, %

(+) Tension

terial (see Fig. 10). Coverage at less than 100% is only admissible in the case of peen forming. Despite the fact that compressive stress layers are formed—in an incomplete and uneven distribution—with shot peening at less than 100% coverage the danger of a potential crack in an unpeened area remains. Especially in conjunction with high-tensile gear-wheel materials, it is

Compression

Ultimate tensile strength, %

shown in Fig. 8 and 9 confirm the advantages of using hard peening material on high-tensile steel. Similar reports about the results of shot peening using specially hard peening materials are contained in Ref 66 and 67. A change in shot size influences the distribution of residual compressive stresses and the roughness. In the case of high-tensile working materials, an increase in the shot size leads to a substantial increase in the size of the compressive layer. The surface tension remains nearly identical; however, the maximum residual compressive stress, as well as the positioning of the maximum in depth, increases. In “soft” working materials, such as aluminum, the depth of the compressive layer and the roughness are influenced. A larger shot size always leaves—given the same intensity—a smoother surface. Reference 68 contains a report about peening with two differently sized peening materials, known as dual shot peening. The shot velocity is probably the most important parameter, as it can be easily varied by the air pressure and the revolutions per minute of peening wheel. As is the case with the shot size, the depth of the maximum compressive layer is primarily influenced and the surface tension is influenced to a lesser extent. Extremely high shot velocities may, however, lead to “overpeening effects,” that is, damage to the surfaces. Such effects coincide with reduced surface stresses. Depending on the material hardness and consolidation condition of the workpiece, such effects may lead, for example, to surface ruptures. A proper shot peening process must be carried out in such a manner that the processed surface displays a coverage of at least 100%. The original state after processing should no longer be visible. The entire shot peened area must display spherical indentations caused by the peening ma-


material should be at least as hard or harder than the working material subjected to the process, unless the surface gradient is a decisive factor. For a large number of ferrous and nonferrous working materials, this can be achieved with a peening material of the normal hardness of 45 to 52 HRC (Rockwell C). The increasing use of high-tensile steel (50 HRC and above) demonstrates that the use of especially hard peening material (55–62 HRC) is required. The compressive stress profiles

0.2 0.3 Depth, mm

Peening 1045 steel at 62 HRC with 330 shot. Courtesy of Metal Improvement Company, Inc.


Visual examination using a ten-power magnifying glass. Courtesy of Metal Improvement Company, Inc.

Fig. 10

proved to be advantageous to apply degrees of coverage at 200% and more, as it results in an increase of the subsurface residual stress. The shot impact angle and the resulting intensity or consolidation in the proximity of the edge layer is an additional important parameter for shot peening. The optimal peening angle for jet shot peening emerged at 85⬚. At this angle, the maximum power transference occurs without the following peening material being impeded by ricocheting peening material. It can be seen in Fig. 11 at 30⬚ that peening tangentially reduces the possible power transfer by 50%. The shot impact angle becomes important in the peening of boreholes and workpieces that have roundings and notches of different sizes in need of processing.

0.010" A 0.0087" A 85°

45°

Fig. 11

Prestress level, MPa 400

Resulting intensity

Impingement angle versus intensity. Courtesy of Metal Improvement Company, Inc.

Nozzle Workpiece

Tension

0.005" A

30° Impingment angle

600

0.007" A

1350 700

200 0 0


60°

⫺200 Shot peened condition ⫺400 ⫺600

Process Monitoring

Compression

⫺800

Reciprocating shot deflector

Stress peened condition

⫺1000 M

M

⫺1200 ⫺1400

0

0.2

0.4

0.6

0.8

1.0

1.2

Depth, mm

Fig. 13 (a)

Stress peening of 50 CrV 4. Courtesy of Metal Improvement Company, Inc.

Shaded area indicates peened surface

Reciprocating and rotating peening lance

(a) Acceptable shapes

(b) Unacceptable "deformed" shapes

(b) (b) Unacceptable "broken" shapes Shot peening of bores. (a) Internal shot deflector. (b) Lance method. Courtesy of Metal Improvement Company, Inc.

Fig. 12

If the depth of a borehole exceeds the bore diameter of the part, an external processing of the borehole wall cannot be properly shot peened. A peening lance with deflecting nozzle or the internal deflection method must be applied under controlled conditions. Boreholes with diameters up to 2.4 mm are peened in production by applying the internal deflection method (Fig. 12a). Using the deflecting nozzle (Fig. 12b), the internal surfaces of long pipes, oil drilling gear, helicopter rotor blades, hydraulic cylinders, and turbine blades are shot peened. Figures 2 and 3 show the residual stress profiles of different working materials depending on the special shot peening parameters. The figures clarify the potential variation in breadth in forming residual compressive stresses. Zinn listed the compressive stresses from peening with respect to welded aluminum alloys (Ref 69). For workpieces that are load bearing in one direction only and that require a durability in excess of that which can be reached by conventional shot peening, the peening is applied under prestressed condition. The workpiece is peened in a prestressed or expanded state. Stress peening generates a much higher residual compressive stress than is possible by conventional shot peening. The residual stress values generated under prestressed conditions can be as high as the yield strength of the working material. Residual stresses resulting from stress peening are shown in Fig. 13.

Fig. 14

Peening media. Courtesy of Metal Improvement Company, Inc.

There is no nondestructive testing method to determine the proper shot peening of a component. To obtain optimal shot peening results it is necessary to optimize the shot peening parameters applied and ensure that all parameters are controlled during the peening process. For an effective control of the shot peening process the parameters must be addressed in the following order: 1. 2. 3. 4.

Shot (media) control Intensity control Coverage control Equipment control

The most important shot peening parameter relates to the microstructure, chemistry, shape, size, material, and hardness of the peening material “shot.” All these variables are described in Ref 42 as well as by the condition of the peening material. The peening material must be uniform in size and fundamentally spherical in shape without sharp edges or broken particles. Broken or sharpedged peening material can be potentially damaging to the surface of the component. Examples of this are shown in Fig. 14 to 16. During the automatic shot peening process, the peening material must be sieved and sorted continuously (Ref 42). Cast steel shot is available in two hardness

Inducing Compressive Stresses through Controlled Shot Peening / 349 ranges, namely 45 to 55 HRC and 55 to 65 HRC. For steel components exceeding 200 ksi (1375 MPa) in tensile strength hard shot with a hardness range 55 to 65 HRC or ceramic shot with comparable hardness at 57 to 63 HRC should be used (Ref 42). For nonferritic materials, shot peening is carried out with stainless steel shot or using ceramic or glass beads. The decontamination of nonferritic components after shot peening with ferritic shot by using glass is a common practice to exclude cathodic corrosion. The shot peening intensity is controlled by the “Almen” strip. This is a strip of cold-rolled spring steel—SAE 1070—square-edged and uniformly hardened and tempered to 44 to 50 HRC. The Almen strip is fixed on a specified holding fixture. During the peening process, the Almen strip will be exposed to the peening material from one side. The plastic deformation on the strip surface facilitates a bending of the strip. The height of the curvature on being measured in a standard Almen gage is referred to as the arc height and is a dimension for measuring shot peening intensity.

Fig. 15

Fig. 16

The Almen block(s) with the strip can be mounted on an actual component and inserted at the critical angles of the part to be shot peened (Fig. 17). Frequently, there are no actual components available for cost reasons. A dummy representing the surfaces to be shot peened is used instead. The mounted Almen strips have to be placed in the same positions as they would be on the actual component. Also the distance between the actual surface and the reference surface incorporating the Almen strip to the nozzle must be identical (Fig. 18). There are three different types of Almen strips, namely, N, A, and C. These Almen strips are selected after determining the proper depth of compression required on the part to be shot peened and the energy level necessary to obtain that depth of compression. The details of the measurement referenced by the specification AMS-S-13165 (Ref 42) are shown in Fig. 19. Another important shot peening parameter is the coverage. The effect of controlled shot peening is considered achieved if the entire component surface is uniformly dimpled or obliterated.

The visual inspection of large areas of steel parts, fillets, cavities, grooves, or internal bores with a tenfold magnifying glass to determine a full coverage is extremely difficult, if not impossible. There are two methods to execute the second parameter of coverage control (Ref 42): ● Visual inspection using a magnifying glass

with a tenfold magnification

● Inspection using an approved liquid tracer

system. Since 1976 the Dyescan fluorescent tracer liquids have been available as they are used in the Peenscan process, an approved liquid tracer system. The working principle of this process is similar to the dye penetration method to determine cracks. Prior to shot peening, an approved fluorescent tracer liquid is brushed, sprayed, or dipped on the component, and it is allowed to dry. This forms a fluorescent elastic coating that is subsequently removed at a proportional rate to the shot peening coverage. The fluorescent tracer system reacts to deviations in shot peening intensity, incomplete coverage, and an excessively low angle of impact. By inspection under ultraviolet (UV) light the Peenscan process provides a practical method of determining the peening coverage in terms of quantity and the uniformity

Shot peening media. (a) Unacceptable. (b) Acceptable. Courtesy of Metal Improvement Company, Inc.

(a) Surface damage caused by poor shot control. (b) Acceptable surface. Courtesy of Metal Improvement Company, Inc.

Fig. 17

Almen fixture (strapped turbine disk). Courtesy of Metal Improvement Company, Inc.

Fig. 18

Almen fixture (dummy). Courtesy of Metal Improvement Company, Inc.

350 / Residual Stress During Hardening Processes of tracer removal. This process has been established to be clearly superior for determining the peening coverage to visual inspection using a tenfold magnifying glass. The process is demonstrated in Fig. 20 and 21. Only automatic shot peening plants facilitate the repeatability of the shot peening parameter and are therefore mandatory. These shot peening plants offer the possibility to monitor, control, and record all the important parameters for accurately verifying the shot peening process. Such characteristic peening parameters are the air pressure in every nozzle of the peening wheel, material flow of every nozzle or speed of every peening wheel, revolution or forward speed of the workpiece, oscillation of the nozzles, distance of the nozzles, peening time of every nozzle, and the total processing time. In the set intervals, the process parameters are compared with the maximum and minimum threshold values. On exceeding or falling below the threshold values, the machine stops itself and indicates the deviation to the operator and the quality assurance department. The mistake must be eliminated prior to the machine resuming the working process precisely from the point of stop-

page. Figure 22 shows a sketch of a computercontrolled shot peening plant. A typical operational chart of a computer-controlled MIC shot peening plant is shown in Fig. 23. Every working step is completed by the printout as proof and documentation. An interruption of the shot peening process and its causes are recorded on the printout (“ABORT” in Fig. 24). The computer printout provides the data which document that every component was treated with the same shot peening parameters as the sample component. The shot peening plants are equipped with important additional functions, such as peening material sorting by size as well as by shape in order to eliminate irregular or inadmissible particles.

Process Optimization Optimization of the effects of shot peening is achieved by a careful selection of the composition, hardness, and size of the peening material; the transferred energy at impact (which controls the depth of the compressive layer); and the percentage of coverage, in addition to component material and geometry. The many possible com-

30 ± 0.015 in. 0.031 ± 0.001 in. 0.051 ± 0.001 in. 0.0938 ± 0.001 in.

N strip Peening nozzle

A strip C strip Almen strips Shot stream

4⫺6 in.

Measuring dial

0.745 ± 0.750 in.

Hardened ball supports Arc height 3.0 in. Holding fixture

(a)

Arc height

0.75 in. Strip removed. Residual stresses induce arching (b)

Peenstress Software Peenstress (Ref 70) is a computer program that is capable of modeling the residual compressive stresses that are introduced by controlled shot peening in most of the engineering metals, mild and high-strength steels, stainless steels, carburized and carbonitrided steels, aluminum alloys, titanium alloys, and nickel alloys (Fig. 25). The Peenstress program will print out a stress curve that shows both the magnitude of the residual stress distribution and the depth profile beneath the surface, for the material and the parameters of shot peening that were selected (Fig. 26). One can use the curve to read the magnitude of the compressive stress at the surface and at depth and use that magnitude in load calculations. One can see very graphically what would be the resultant residual tensile stress on the opposite unpeened surface or in the core of a part that is peened all over (Fig. 27) and then have the opportunity to adjust the peening parameters, if necessary. Most significantly, this can now be done on a computer screen without having to resort to very expensive and time consuming xray diffraction (XRD) measurements or even laboratory and field testing of many variables. Testing is still recommended, but can be reduced to a few selected data points.

C.A.S.E. Process

Almen test strip

10/32 screws

binations of these factors make the correct choice a difficult one.

Strip mounted for height measurement (c)

Fig. 19

The Almen strip system. Courtesy of Metal Improvement Company, Inc.

Fig. 20

Shot peening coverage. (a) Partial coverage. (b) Full coverage. Courtesy of Metal Improvement Company, Inc.

Frequently, when the bending fatigue life of gears has been increased by shot peening the tooth roots, surface fatigue or pitting of the contact faces became the next mode of failure. There has been a need, particularly for automotive and aircraft transmissions, to extend the surface fatigue life beyond that provided by shot peening alone and smoothing the surface after peening has been found to be very effective (Ref 67). Unfortunately, the processes to accomplish this have been time consuming and therefore costly. The C.A.S.E. process (Ref 71) can reduce the relative finishing time and costs, after shot peening, and provide a surface which, in addition to having the compressive stresses from the shot peening, can have Rsk value of as little as ⳮ1.1. Very significant increases in surface contact fatigue (pitting) life have been observed. C.A.S.E. is an acronym for chemically assisted surface engineering and covers a twostage process. The C.A.S.E. Process requires that the gears are properly shot peened, followed by chemically assisted superfinishing. Very different surface profiles can be described using nearly the identical Ra values (Fig. 28). The aim of C.A.S.E., however, is to smooth the spherical edges and to create a profile as shown in Fig. 29. The value corresponding to this profile is:

Inducing Compressive Stresses through Controlled Shot Peening / 351 Rsk ⳱ skewness

More details are provided in Ref 72 and 73. The values in Table 1 show clearly that a surface processed with C.A.S.E. is not sufficiently described by the Ra value. The meaningfulness lies in Rsk, which has a value clearly below –1, which is the minimum value striven for. The stress profiles in Fig. 30 show the tensile stresses and the residual peening stresses as well as the C.A.S.E. influence.

X-Ray Diffraction Reading

Fig. 21

The Peenscan system. (a) Coated unpeened. (b) Peened 15 s partial coverage. (c) Peened 60 s full coverage. (d) Peened 60 s, improper nozzle angle in cavity. Courtesy of Metal Improvement Company, Inc.

A significant breakthrough in the controls of the shot peening process was recently introduced to industry. This new method entitled “Milam,” utilizes XRD readings of residual stress profiles, which are much more economical and are available in days rather than weeks. The new method permits the use of XRD profiles as quality-control measurements that can be recorded for statistical process control data. The practical Milam system has wide applications: for instance, lowvolume aircraft components, high-volume automotive transmission gears, and even in-the-field shot peening of chemical processing vessels. It can also be used to predetermine with high accuracy the shot peening parameters for process development. The Milam system actually offers three alternative applications. The first employs coupons that are essentially the same size as a standard Almen strip, 0.75 by 3 in. (19 by 75 mm), but

Display

Display Machine terminal

Air pressure

Master terminal

Manual input Manual input

Production data

Data

Product data storage Data

Shot flow

New procedures

Data

Input Master computer Data

Instruction Part motion

Instruction

Nozzle motion

Printer

Data

Data

Peening machine comput.

Procedures from storage

Status

Data collection system

Instruction

Limit switches and misc. devices

Fig. 22

Computer-controlled shot peening machine. Courtesy of Metal Improvement Company, Inc.

Fig. 23

Status

Status

Software path flow diagram. Courtesy of Metal Improvement Company, Inc.

Bulk shot handling and conditioning system


Customer Part number

: :

Specification operation

: AMS-S-13165 :

Mic procedure Shot size Intensity Coverage Saturation time 100% cover time

: : : : : :

Nozz. 01

Fig. 24

Table 1

21-8592 Ml-170R 6-10A 100% 6 minutes 6 minutes

Air press TMR Shot flow TMR Turntable TMR Speed change Max shot flow Turntable RPM

5 15 5 5 25 16.0

Sec Sec Sec Sec Lbs RPB

Mode Cycle count Cycle time

Horz NA 6:00:00

Oscillation program Pos In min Pos Home 1 30.0 32.0 11 19.5 start 2 24.0 4.0 12 19.0 3 23.5 8.0 13 18.5 4 23.0 12.0 14 18.0 5 22.5 14.0 15 17.5 6 22.0 15.0 16 17.0 7 21.5 16.0 17 12.0 8 21.0 17.0 18 12.0 9 20.5 18.0 19 12.0 10 20.0 19.0 TA 12.0

Nozzle program Nozz. Active 1 2:00:00 A 2 2:00:00 A 3 2:00:00 A 4 2:00:00 A 5 4:00:00 A 6 4:00:00 A 7 4:00:00 A 8 6:00:00 A 9 6:00:00 A 10 6:00:00 A

Hi limit

Air Shot Psi lb M 60 18.0

Nozz. 02 Nozz. 03 Nozz. 04 Nozz. 05 Nozz. 06 Nozz. 07 Nozz. 08 Nozz. 09 Nozz. 10 Turntable speed Air Shot Air Shot Air Shot Air Shot Air Shot Air Shot Air Shot Air Shot Air Shot Psi lb M Psi lb M Psi lb M Psi lb M Psi lb M Psi lb M Psi lb M Psi lb M Psi lb M RPM 60 18.0 60 18.0 60 18.0 60 18.0 60 18.0 60 18.0 40 16.0 40 16.0 40 16.0 11.0

Data

55

16.0

55 16.0 55 16.0 55 16.0 55 16.0 55 16.0 55 16.0 35 14.0 35 14.0 35 14.0

Lo limit

55

14.0

SN001

50

14.0

SN002

Abort 1:14:10 low shot flow nozz. 02 at lb min

SN002

56

16.0

Remaing cycles 0 Oscill. position

In min 2.0

Inches

6.0

50 14.0 50 14.0 50 14.0 50 14.0 50 14.0 50 14.0 30 12.0 30 12.0 30 12.0

9.0

2.0

56 16.0 55 15.0 55 14.0 56 15.0 51 14.0 52 15.0 35 13.0 34 13.0 34 14.0

10.0

6.0

9.5

5.0

56 15.0 57 17.0 56 15.0 57 16.0 55 16.0 54 15.0 36 14.0 34 14.0 34 14.0

Tue 5:19:47 PM Feb 16, 1999

Oscill. speed

10.0

Typical documentation by computer printout. Courtesy of Metal Improvement Company, Inc.

Surface characteristics (17 CrNiMo 6) Grounded and shot peened

Grounded

Grounded and shot peened and C.A.S.E.

Parameter

Axial

Tangential

Axial

Tangential

Axial

Tangential

Rz Ra Rt Rsk

0.36 0.04 0.59 0.83

1.52 0.21 1.96 0.23

0.68 0.10 0.87 0.19

0.69 0.12 0.85 0.18

0.57 0.07 0.85 ⳮ1.22

0.66 0.07 0.96 ⳮ1.35

Source: Metal Improvement Company, Inc.

Material Library Material: Al/7010 * T7651/cysp

Review library Monotonic 472

Cyclic 425

Elastic limit

(MPa)

Ultim. tensile str.

(MPa) : 560

Elongation

(%)

Endurance limit

(MPa) :

Cancel material

Young's modulus

(MPa) : 71000

Print data sheet

Poisson's ratio k factor n factor

Modify mater.

Run

: 0,300 (MPa)

Research mat. New material

: 10,00

Monotonic 607,60 0,0272

Remarks : ENSAM/Prof. Ericsson/20 cycles/1992

Cyclic 641,20 0,0446

Help Quit ENSAM—MIC

Material library. The selected material is aluminum alloy 7010 T 76. Screen printout shows the monotonic strength coefficient k and the strain-hardening coefficient, n, as well as the cyclic strengths coefficient k⬘ and the strain-hardening coefficient, n⬘, which define the true monotonic stress strain curve and the cyclic stress strain curve, respectively. Also shown are the ultimate and yield strengths, elongation, Young’s modulus, and Poisson’s ratio, for this material. Courtesy of Metal Improvement Company, Inc.

Fig. 25

In min 20.0 21.0 22.0 23.0 24.0 25.0 25.0 25.0 25.0

that are 0.25 in. (6.5 mm) thick. The coupons are designed to fit on a standard Almen block and can therefore be used on an existing Almen fixture. In this way, the Milam coupons are placed to represent the critical areas of the part to be peened. The Milam coupons are made from the same material (or even at the same temperature at the customer’s option) as the parts and heat treated along with the parts. They are shot peened after the Almen strip verification and just before the parts are processed and periodically thereafter on request of the customer. The second is an alternative to the Milam coupons but still part of the Milam system. MIC and Lambda can handle small parts directly as long as they are within the dimension of 2 by 2 by 1.5 in. (50 by 50 by 38 mm). With the third alternative, larger parts can be cut up so that the critical areas for XRD reading are available, but Lambda must do the cutting. After shot peening, the test parts are then sent to the XRD laboratory; because of their standard size, the coupons or the small parts can be etched and x-rayed at successive depth levels for residual stress readings in a very expeditious manner. This is a quick, economical method for measuring induced compressive stresses in components.

Shot Peening Applications As has already been explained, components manufactured from all kinds of materials containing metals, ranging from magnesium to steel, can be utilized for host peening and, thus, for creating a compressive residual stress in the workpiece surface. In the case of materials with a relatively low strength, slight surface faults that could be the initial cause of fatigue cracks are in turn obturated by the plastic extension and

Inducing Compressive Stresses through Controlled Shot Peening / 353

Residual stress distribution 0.2

0.1

Depth, mm

F 15 A S 400 Shot V = 29 m/s Al/7010 * T7651/C

⫺100 Residual stress, MPa

1999:2:18 Peenstress ENSAM-MIC d = 0,092 mm h = 0,005 mm

Dir. z ⫺200

Σs, MPa

⫺300

⫺310

Σm, MPa

⫺332

PΣm, mm

0.005

PΣO, mm

0.210

⫺400

Residual stress profile. Peenstress software calculates and displays the stress profile and the calculated shot velocity. The separate panel indicates the surface stress 兺s, the maximum stress 兺m, the minimum depth of the maximum stress P兺m, and the depth of compression P兺O. Courtesy of Metal Improvement Company, Inc.

Fig. 26

1999:2:18 Peenstress ENSAM-MIC 0.1

0.2

⫺100 ⫺200

⫺100 AL/7010 * T7651/C

⫺200

⫺300

⫺300

⫺400

⫺400

enclosed by the residual stress. In the case of materials that are of high strength, such as may be utilized for the manufacture of gears, for example, a higher compressive residual stress can be achieved, which will, among other things, increase the fatigue strength. The increase in the size of fatigue cracks depends on the stress factors at the peak of the crack. An increase in the size of any crack can be prevented by the stress (Ref 74) based on the following factors: ● As a rule, a fatigue crack will not spread un-

less the tensile stresses increase.

● The crack opening stretch does not occur as

long as a compressive stress remains. Stress profile in a thin plate. When the selected structure is a thin plate, the stress profile shows tensile stress compensating for the compressive stress below the surface, which is induced by the shot peening. The structure is a 0.125 in. (3 mm) thick plate, peened on both sides with equal parameters. If the peening intensity is too high, excessive tensile stress may be generated internally that will have a negative effect on fatigue. Courtesy of Metal Improvement Company, Inc.

Figure 31 shows clearly how this will operate. Figure 31(a) shows in a simplified form the distribution of stress under applied load. Figure 31(b) shows the distribution of the stress of the shot peened component. Figure 31(c) shows the distribution of stress resulting from the addition of load stress and residual stress. Figure 31(d) shows the distribution of stress after a crack has spread around the area subject to tensile stress. The broken lines denote the original distribution of the stress as shown in Fig. 31(c). Figure 31(e) shows a well-advanced stage in the formation of a crack as far as point (I). In the surrounding area there is a change in the stress. Figure 31(f) shows that the crack no longer extends within the area subject to residual compressive stress. Controlled shot peening in the manufacture of gears (Fig. 32) is to be found in the automobile industry, in commercial vehicles, in marine gears, in the manufacture of drive shafts, and extends even to the manufacture of small gears in hand machine tools and, at the other extreme, extends to its use in the manufacture of large gears used in marine engines, as well as for mining equipment. The radiuses at the base of the tooth are normally those parts of the component that are subject to most stress and should, therefore, be peened (Fig. 33 and 34) (Ref 75). In practice, it has also been found, though, that the peening results in concaving on the flanks that will retain oil and thus provide better lubrication. Wear, noise, pitting, and seizing may also be reduced, and the running temperature will drop. Gears with a low dimension tolerance or with a high level of surface quality can be lapped or honed after shot peening, provided that during the fine finishing care is taken not to remove more than 10% of the residual compressive stress layer. Compressive stresses induced by controlled shot peening may have a lot of benefits, for example, in the chemical industry applications by

Fig. 27

Negative skewness

Positive skewness

Ra = 2.4 µm

Negative

Ra = 2.5 µm

Ra = 2.4 µm

Comparison of Ra values for different profiles in C.A.S.E. processing. Courtesy of Metal Improvement Company, Inc.

Fig. 28

Positive

Fig. 29

Skewness of the amplitude distribution in C.A.S.E. processing. Courtesy of Metal Improvement Company, Inc.

354 / Residual Stress During Hardening Processes increasing of the resistance against stress-corrosion cracking. This mechanism eliminates surface tensile stress. Stress-corrosion cracking cannot occur in an area of compressive stress. Figures 35 and 36 show the measured residual stress of a welded StE 460 (P 460 N) steel plate. This material is used for manufacturing railway tank cars for ammonia. The residual stresses were measured to document the suitability of shot peening. Stresses were measured in the untreated semifinished material on the untreated welding seams as well as on the shot peened areas. During 1989 and 1990, about 60 railway tank cars used for transporting ammonia were

restored, showing no sign of stress corrosion even after ten years of operation. Shot peening is also successfully applied to chemical process vessels made of austenitic steel. The results of the laboratory tests for stress corrosion are shown in Table 2. In these tests, samples were exposed to a 42% MgCl2 solution at 145 ⬚C. In the absence of stress-corrosion cracks, the investigations into the shot peened specimens in line with exposure were discontinued at 1000 h. The respective production costs of a 5000 L tank container in different materials are compared in Fig. 37.

200 0

Residual stress (σES), MPa

⫺200 ⫺400 ⫺600

Lasershot Peening

⫺800 ⫺1000

σES Ground Ground and shot peened Ground and shot peened and C.A.S.E.

⫺1200 ⫺1400 ⫺1600 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Depth, mm

Fig. 30

Stress profile (17 CrNiMo 6). Courtesy of Metal Improvement Company, Inc.

II

I σ

∆σ

(a)

(c)

(e)

I II σ 60°

R ∆σ

(b)

(d)

(f)

Crack arrest by compressive self stress. (a) Load stress. (b) Self stress. (c) Sum of (a) and (b). (d) Crack starts. (e) Crack progressed to edge of former compressive zone. (f) Crack arrested. Courtesy of Metal Improvement Company, Inc.

Fig. 31

On the basis of the corrosion test results and the production cost considerations, tanks and other constituent parts of the plant could be manufactured from a less corrosion-resistant and therefore less expensive material. Overall costs can be reduced by 50% after allowing for the cost of shot peening. Also the resistance against corrosion fatigue will be improved by shot peening, caused by the beneficial effect of the compressive stress. Fretting fatigue can occur when a rotating component is press fitted onto a shaft. A slight relative movement of the mating surfaces caused by vibration or shifting loads will shear the high points from the top of the peaks in the mating surfaces. The resulting debris will oxidize and produce the typical rusty powder characteristics of fretted steel. This very hard debris tends to build up in one area, abrading the surface and creating stress risers that can propagate into fatigue cracks. In industry, the piston rod bushes of large diesel engines, joint faces of machine components, bearing pins, and threads are shot peened.

Lasershot peening, also a surface treatment, employs laser-induced shocks to create deep compressive stresses beyond a 0.040 in. (1 mm) depth with magnitudes comparable to that produced by shot peening. Lasershot peening has proven to significantly enhance the damage tolerance of components and has generated sufficiently impressive results to move it from a laboratory-demonstration phase into a significant industrial process technology. Until now this evolution has been slowed down by the absence of a laser system meeting the power requirements for economical processing. Commercial lasers available at present are limited to power outputs of 10 to 100 J, with repetition rates of around 0.25 Hz and a new design in development with 1 Hz capability. The estimated time required to process an area of 1 by 3 in. (25 by 75 mm) could take anything from 1 to 3 h using one of these machines. Robust laser systems have been developed that for the first time push the average power output to 200 J at 10 Hz. It enables the processing of a 3 in.2 (19 cm2) area in minutes instead of hours. With the invention of the laser, it was rapidly recognized that the intense shocks required for peening could be achieved by means of tamped plasmas that were generated at metal surfaces by means of high-energy density (˜200 J/cm2) lasers with pulse length in the tens of nanoseconds range. Initial studies on laser shock processing of materials were carried out by the Battelle Institute (Columbus, OH/USA) from about 1968 to 1981 (Ref 76, 77). Excellent recent work has also been reported in Ref 78. Laser intensities of 100 to 300 J/cm2 with a pulse duration of about 30 ns can generate shock pressure of 104 to 105 atm when absorbed on a metal surface. A thin layer of black paint on the

Inducing Compressive Stresses through Controlled Shot Peening / 355 surface provides an excellent absorber that produces a plasma burst that is inertially confined with a surface layer (tamp) such as water (Fig. 38). These shocks impart compressive stresses to depths greater than 0.040 in. (1 mm). Special techniques for controlling the temporal and spatial shape of the pulse are used to prevent the high-intensity laser from breaking down the water column or generating stimulated processes that reflect the laser energy before reaching the paint surface. With appropriate care given to the setup, impressive results can be achieved from Lasershot peening.

In order to use the high throughput capability of the laser, it is important to have manipulation hardware to rapidly and precisely move surfaces to be treated through the rapidly pulsing laser beam. The authors have designed a five-axis, computer-controlled robotics system with motion synchronized to the laser pulses. As an example of the laser process, Fig. 39 shows the residual stress induced in Inconel by Lasershot peening and contrasts it with typical results achieved by shot peening. Laser-generated shock can be tailored to develop compressive stresses deeper into the material with mag-

nitudes similar to those generated by shot peening. Additionally, corrosion takes more time to penetrate the compressive layer induced by Lasershot peening. Deep compressive stress is important for critical areas of components such as turbine blades because it prevents the foreign object damage caused by debris being sucked up into a turbine engine from becoming a crack initiation site. Most metals can be successfully Lasershot peened to very deep depths of compression (Ref 79–82). REFERENCES

Compressive stress, ksi 0

⫺25

0

⫺50

⫺ 75

⫺100

⫺125

⫺150

⫺175

⫺200

0.0015

0.05

0.10 0.0045

Depth, mm

Depth, in.

0.0030

0.15 0.0060

0.0075

0.02

0.0080 0

500

1000 Compressive stress, MPa

Fig. 32

Stress profile of carburized gear tooth root, ground, then shot peened with special hardness shot. Courtesy of Metal Improvement Company, Inc.

6000 Shot peened

Peak cyclic load, nonreversing, lb

Mean

1000

4000 None shot peened Mean 3000 500 bevel gear Spiral 3,625 D.P. Material: 8620H bar stock Heat treatment: carburized and hardened, 61 HRC Load transmitted: 135 hp, 5000 rpm Shot peening specifications: Shot size: 170H Intensity: 0.010-0.014 A Coverage: 200%

2000

1000

0

500

0 104

105

106

107

Cycles to failure

Fig. 33

Increase in fatigue resistance of spiral bevel gear. Courtesy of Metal Improvement Company, Inc.

Peak cyclic load, nonreversing, N

5000

1. W.E. Newton, Sand Blast and Its Adaption to Industrial Purposes, J. Soc. Arts, Vol 23, 1875, p 257–260 2. F.C. Brooksbank, Sand Blast Apparatus for Cleaning Castings, Iron Age, Vol 57, 1896, p 640–642 3. F.P. Zimmerli, Shot Blasting and Its Effects on Fatigue Life, Surface Treatment of Metals, American Society for Metals, 1941, p 261–278 4. F.P. Zimmerli, How Shot Blasting Increases Fatigue Life, Mach. Des., Vol 12, Nov 1940, p 62 5. J.O. Almen, Peened Surfaces Improve Endurance of Machine Parts, Met. Prog., Vol 43 (No. 2), 1943, p 209–315 6. J.O. Almen, Peened Surfaces Improve Endurance of Machine Parts, Met. Prog., Vol 43 (No. 5), p 737–740 7. J.O. Almen, Peened Surfaces Improve Endurance of Machine Parts, Met. Prog., Vol 43 (No. 8), p 254–261 8. J.O. Almen, Peened Surfaces Improve Endurance of Machine Parts, Met. Prog., Vol 43 (No. 9) 9. J.O. Almen, Shot Blasting to Increase Fatigue Resistance, SAE Trans., Vol 51 (No. 7), 1943, p 248–268 10. Minich, “Abrasive Wheel Throwing Machine,” U.S. Patent 2077636, 1934 11. R.L. Mattson and J.O. Almen, “Effect of Shot Blasting on the Mechanical Properties of Steel,” Final Report, OSRD, 3274, 4825, 6647, (NA-115), Office of Scientific Research and Development, Washington D.C., 1945 12. R.L. Mattson, H.E. Fonda, and J.O. Almen, “Final Report on Effect of Shot Blasting on the Mechanical Properties of Steel,” (NA115) (OD-177), National Defense Research Committee of the Office of Scientific Research and Development, War Metallurgy Division, 1944 13. R.L. Mattson and J.O. Almen, “Effect of Shot Blasting on the Physical Properties of Steel,” Final Report, part 3, OSRD 6647, National Defense Research Committee of the Office of Scientific Research and Development, War Metallurgy Division, 1946 14. J.O. Almen, Fatigue of Metals as Influenced by Design and Internal Stresses, Surface


15.

16. 17.

18.

Stressing of Metals, H.F. Moore, W.M. Murray, J.O Almen, O.J. Horger, and P.R. Kosting, Ed., 4–8 Feb 1946, p 33–84 ¨ berblick u¨ber die UntersuchunW. Bautz, U gen u¨ber die Dauerhaltbarkeit von Federn. Interner Untersuchungsbericht, 28.3, 1938 (in German) H. Wiegand, Oberfla¨che und Dauerfestigkeit, Berlin-Spandau, BMW-Flugmotorenbau, 1940, p 83 (in German) O. Fo¨ppl, Oberfla¨chendru¨cken zum Zweck der Steigerung der Dauerhaltbarkeit mit Hilfe des Strahlkugelgebla¨ses, Mitteilungen des Wo¨hler-Instituts, Braunschweig, 1939, p 44–59 (in German) R. Z. von Manteuffel, Dauerhaltbarkeit von Kraftfahrzeugfedern und Mo¨glichkeiten zu

Table 2

19.

20.

21. 22.

ihrer Beeinflussung, Dtsch Kraftfahrt., No. 49, 1941 (in German) H.F. Moore, Effect of Surface Stressing Metals on Endurance under Repeated Loadings, Surface Stressing of Metals, H.F. Moore, W.M. Murray, J.O Almen, O.J. Horger, and P.R. Kosting, Ed., 4–8 Feb 1946, p 1–18 W.M. Murray, Measurement of Surface Stresses, Surface Stressing of Metals, H.F. Moore, W.M. Murray, J.O Almen, O.J. Horger, and P.R. Kosting, Ed., 4–8 Feb 1946, p 19–32 O.J. Horger, Mechanical and Metallurgical Advantages of Shot Peening, Iron Age, 29 March/5 April 1945 M. Olley, “Influence of Shot Peening on

Shot peened area Grounded area

6

5

60 1

2

135

320 380 Stress data of welded StE 460 (P 460 N). Stress: location 1, ⳮ484 MPa; location 2, ⳮ515 MPa; location 2.1, ⳮ171 MPa, 1 mm subsurface; location 5, ⳮ20 MPa; location 6, ⳮ389 MPa. Courtesy of Metal Improvement Company, Inc.

Fig. 35

Results of stress-corrosion cracking tests Load, h

Material and shot peening parameter

At 50%

At 70%

At 80%

At 90%

X 6 CrNiTi 18–10 (1.4541) Not shot peened SSCW 0.8, 5 A, 100% SSCW 0.8, 12 A, 100% SSCW 0.8, 20 A, 100%

11 … … …

5 … … ⬎1000

… … … …

3.2 … … ⬎1000

X 6 CrNiTi 17–12–2 (1.4571) Not shot peened SSCW 0.8, 5 A, 100% SSCW 0.8, 12 A, 100% SSCW 08, 20 A, 100%

17 … … …

11.3 … ⬎1000 ⬎1000

… … … …

7.5 … ⬎1000 ⬎1000

X 2 CrNiMoN 22–5-3 (1.4462) Not shot peened SSCW 0.8, 5 A, 100% SSCW 0.8, 12 A, 100% SSCW 0.8, 20 A, 100%

5.3 … … …

3.3 … ⬎1000 ⬎1000

… … ⬎1000 ⬎1000

1.3 … 2 5.3

Specimen tensile tested in 42% MgCl2 medium at 145 ⬚C and at a load of 50 to 90% of the 0.2% yield point

Shot peened area Repaired area

7 9 Grounded area

320 Stress data of repair welded StE 460 (P 460 N). Stress: location 7, ⳮ357 MPa; location 7.1, ⳮ78 MPa, 1 mm subsurface; location 9, ⳮ434 MPa. Courtesy of Metal Improvement Company, Inc.

Fig. 36

90,000 80,000 100

700

600

80

500

70 Not peened

Computed stress, MPa

Computed stress, ksi

Peened

Cost of production, Euro

70,000 90

60,000 50,000 40,000 30,000 20,000

60 400

10,000 0

50 105

1.4541 106 Cycles to failure

Fig. 34

Fatigue chart of carburized gears. Courtesy of Metal Improvement Company, Inc.

107

1.4571

1.4539

1.4462

Material

Fig. 37

Cost comparison of 5000 L vessel. Courtesy of Metal Improvement Company, Inc.

Inducing Compressive Stresses through Controlled Shot Peening / 357 Mechanical Properties,” Symposium on Shot Peening, American Society for Metals, 1944 23. F.P. Zimmerli, “Shot Peening of Coil and Leaf Springs,” Symposium on Shot Peening, American Society for Metals, 1944 24. K. Walz, “Federfragen- insbesondere aus dem Gebiet der Zeitfestigkeit bei sinusfo¨rmiger und schlagartiger Beanspruchung,” Broschu¨re der Mauser-Werke, Oberndorf, 1943 25. H.O. Fuchs and R.L. Mattson, Measurement of Residual Stresses in Torsion Bar Springs, Proc. Soc. Exp. Stress Anal., Vol 4 (No. 1), 1946, p 64

26. J.C. Straub and D. May, Stress Peening, Iron Age, 21 April 1949, p 66–70 27. Manual on Shot Peening, Sp-84, Society of Automotive Engineers, 1952 28. S.W. Serensen, Zusammenha¨nge zwischen der Schwingfestigkeit, der Ober- fla¨chenverfestigung und der konstruktiven Gestaltung, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 13–39 29. N.P. Stschapow, Oberfla¨chenverfestigung im Eisenbahnwesen, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 40–55

Laser beam

Pressure Tamping material

Protective overlay for light absorption Part to be processed

Shock waves

⫺ Plasma burst causes pressure

Fig. 38

0+

Pressure wave

Residual compressive stress

Lasershot process. Courtesy of Metal Improvement Company, Inc.

Depth, mm 0

0.25

0.5

0.75

1

Shot peened 0.010 A


⫺40

⫺200 ⫺400

⫺60 ⫺80

⫺600

⫺100

Lasershot peened by MIC-LLNL

⫺800

⫺120 ⫺140

⫺1000

⫺160

⫺1200

⫺180 0

0.01

0.02

0.03

0.04

Depth, in.

Fig. 39

Stress profile of Inconel 718. Courtesy of Metal Improvement Company, Inc.

⫺1400 0.05


⫺20

⫺200

1.25 0

0

30. B.G. Gurewitsch and S.F. Jurjew, Einfluß der Restspannungen auf die Erho¨hung der Schwingfestigkeit nach der chemischen und thermischen Behandlung, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 56–78 31. B.F. Balaschow, Festigkeitserho¨hung durch Nitrieren von Maschinenteilen, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 79–99 32. I.W. Kudrawzew, Einfluß der Restspannungen auf die Schwingfestigkeit geschweißter Werkstu¨cke Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 100–118 33. M.M. Kobrin, Festigkeit der Preßverbindungen mit oberfla¨chengewalzten Sitzfla¨chen Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 119–130 34. A.W. Rabtschenkow, Oberfla¨chenbehandlung zur Erho¨hung der Schwingfestigkeit von Stahl unter Korrosionswirkungen Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 131– 152 35. I.S. Koslowski, Festigkeitserho¨hung durch einsatzgeha¨rtete Zahnra¨der im Kraftfahrzeugbau Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 153–169 36. W.T. Tschirikow, Erho¨hung der Festigkeit und Lebensdauer einsatzgeha¨rteter Kraftfahrzeugzahnra¨der, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 170–180 37. N.A. Karasjew, Erho¨hung der Dauerfestigkeit von Maschinenteilen durch Kugelstrahlen, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 181–194 38. D.S. Listgarten, Einfluß von Oberfla¨chengu¨te und Warmbehandlung auf die Schwingfestigkeit von Federstahl, Ho¨here Gestaltfestigkeit durch Oberfla¨chenverfestigung, Vortra¨ge auf der Tagung der Wnitomasch, Moscow, April 1954, p 195–217 39. Shot Peen Forming, Steel, Metalwork. Week., 7 July 1958 40. “Shot Peening of Metal Parts,” Military Specification No. MIL-S-13165, 1956 41. “Shot Peening of Metal Parts,” Military Specification MIL-S-13165 B Amendment2, 25 June 1979 42. “Shot Peening of Metal Part,” AMS-S13165 43. Werkstofftechnische Verfahr en. Techn. Betriebshandbuch der DLH Nr. TBH-90-K, 15. April 1965 44. “Spezifikation fu¨r Kugelstrahlen von Metal-


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len,” MBB-UFE-Entwurf Nr. 18/70, Aug 1970 “A 300 B-Landing Gear—Technical Information for Implementing Main Parts Repair Procedures,” Doc. No. 16171, Messier-Hispano Product Support “Shot Peening of Steel and Titanium Alloys,” Process Specification No. MA-57, Rev. B, Northrop Corp. Norair Div., 28 July 1967 “Materials and Processes Requirements for Air Force Systems,” Military Standard No. MIL-STD-1587 (USAF), 31 July 1976 “Shot Peening,” Report No. 20–10–03, WU 813, Boeing, 15 June 1969 “Shot Peening, Computer Monitored,” AMS-S-2432 “Shot Peening,” AMS-2430 “Peening Media,” AMS-2431 “Cut Wire Shot,” SAE J 441, Society of Automotive Engineers “Test Strip, Holder and Gage for Shot Peening,” SAE J 442, Society of Automotive Engineers “Cast Shot and Grit Size Specifications for Shot Peening and Cleaning,” SAE J 444, Society of Automotive Engineers “Metallic Shot and Grit Mechanical Testing,” SAE J 445, Society of Automotive Engineers “Cast Steel Shot,” SAE J 827, Society of Automotive Engineers “Specification for Low-Carbon Cast Steel Shot,” SAE J 2175, Society of Automotive Engineers “Procedures for Using Standard Shot Peening Test Strip,” SAE J 443, Society of Automotive Engineers W. Schu¨tz, “Betriebsfestigkeitsversuche mit Spurstangenhebeln und Lenkhebeln zum Typ ‘Bu¨ffel’” LBF-Bericht Nr. 961/9621/ 1058, Darmstadt, Nov 1960 W. Schu¨tz, Impact/Anwendungsbericht Kugelstrahlverfahren, Kugelstrahlen in der Antriebstechnik, Metal Improvement Company, Inc., Unna/ Deutschland

61. H. Wohlfarth, Ein Modell zur Vorhersage kugelstrahlbedingter Eigenspannungszusta¨nde. In Macherau, Hauck: Eigenspannungen—Entstehung, Messung, Bewertung, DGM Informationsgesellschaft Verlag, Oberursel, 1983, Band 2 62. H. Wohlfahrt, Residual Stress and Stress Relaxation, E. Kula and V. Weiss, Vol 28, Sagamore Army Mat. Res. Conf., Plenum Press, Paris, London, 1982, p 71 63. Shot Peening Applications, Engineering Manual, 8th ed., Metal Improvement Company 64. H.O. Fuchs, “Shot Peening Stress Profiles,” Metal Improvement Company 65. B. Scholtes, Eigenspannungen in mechanisch rundschichtverformten Wirkstoffzusta¨nden—Ursachen, Ermittlung und Bewertung. DGM Informationsgesellschaft, Oberursel 1980 66. D.P. Townsend and E.V. Zaretsky, “Effect of Shot Peening on Surface Fatigue Life of Carburized and Hardened AISI 9310 Spur Gears,” NASA Technical Paper 2047, National Aeronautics and Space Administration, 1982 67. D.P. Townsend, “Effect in Surface Fatigue Life of Hardened Gears by High-Intensity Shot Peening,” NASA Technical Memorandum 105678, National Aeronautics and Space Administration 68. A. Ahmad and E.D. Crouch, “Dual Shot Peening to Maximize Beneficial Residual Stresses in Carburized Steels,” ASM International/Reprint 8904–006 69. W. Zinn, Untersuchungen zum Dauerschwingverhalten von Stumpfschweißverbindungen aus den naturharten Aluminiumlegierungen AlMg3 Deutscher Verlag fu¨r Schweißtechnik, Du¨sseldorf, 1988 70. Y. Le Guernic, “Impact/Review of Shot Peening Technology, Peenstress Software Selects Shot Peening Parameters,” Metal Improvement Company, Inc., France 71. “Impact/Review of Shot Peening Technol-

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ogy, The CASE for Superfinishing,” Metal Improvement Company, Inc. L. Mummery, Surface Texture Analysis, Hommelwerke GmbH, VS-Schwenningen/ Germany Handbook Hommel Surface Roughness, Terminology and Parameters, Hommelwerke GmbH, VSSchwenningen/Germany H.O. Fuchs, Regional Tensile Stress as a Measure of the Fatigue Strength of Notched Parts, Mechanical Behavior of Materials, Vol II, p 478–448 J.B. Seabrook and D.W. Dudley, “Results of a Fifteen Year Program of Flexural Fatigue Testing of Gear Teeth,” American Society of Mechanical Engineers No. 63-WA199 B.P. Fairand and B.A. Wilcox, J. Appl. Phys., Vol 43, 1972, p 3893 A.H. Clauer, B.P. Fairand, and J. Holbrook, J. Appl. Phys., Vol 50, 1979, p 1497 P. Peyre and R. Fabbro, Optical Quantum Electron., Vol 27, 1995, p 1213–1229 P. Prevey, D. Hombach, and P.I. Mason, “Thermal Residual Stress Relaxation and Distortion in Surface Enhanced Gas Turbine Engine Components,” Proc. ASM/TMS Materials Week (Indianapolis, IN), 15–18 Sept 1997, ASM International S.R. Mannava, W.D. Cowie, and A.E. McDaniel, “The Effects of Laser Shock Peening (LSP) on Airfoil FOD and High Cycle Fatigue,” USAF Structural Integrity Program Conference, United States Air Force, Dec 1996 C. Brent Dane, J. Wintemute, B. Bhachu, and L. Hackel, “Diffraction Limited High Average Power Phaselocking of Four 30J Beams from Discrete ND:Glass Zigzag Amplifiers,” Postdeadline paper CPD27, CLEO ’97, 22 May 1997 J.R. Harrison and L.A. Hackel, “New Laser Technology Enables Lasershot Peening to be a Commercially Affordable Process,” SAE 981963, Society of Automotive Engineers, 1998



Residual Stress Formation during Casting R.W. Lewis, University College of Swansea, Wales K.N. Seetharamu, Z.A. Zainal, and A.Y. Hassan, University of Science Malaysia

MOST FOUNDRIES have stories about castings that flew into pieces with a bang when being machined, or even when simply standing on the floor. It is easy to dismiss such stories, but they should be viewed as warnings. They warn that, in certain conditions, castings can have such high stresses locked inside that they are dangerous and unfit for service—even though they look perfect (Ref 1). More than $50 million is attributed to thermal stress-generated casting defects. Such defects can be essentially eliminated through the application of computer predictions. If a casting were to be cooled at a uniform rate and with a uniform constraint acting at all points over its surface, then it would reach room temperature perfectly in proportion—perhaps a little large, or a little small, but not distorted. In practice, of course, the casting generally is somewhat large, or somewhat small, and not quite accurate in shape. Occasionally, it may be very seriously distorted. Again, in an ideal world, if the constraint by the mold were either zero or infinite, in both cases the casting would be of predictable size and correct shape.

Even if a casting were subjected to no mold constraint at all, it would certainly suffer internally generated constraints as a result of uneven cooling. The famous example of this effect is the mixed-section casting shown in Fig. 1(a). If a failure occurs, it always happens in the thicker section. The explanation of this behavior requires careful reasoning. First, the thin section solidifies and cools. Its contraction along its length is easily accommodated by the heavier section, which simply contracts under the compressive load since it is hot, and therefore plastic, if not actually still molten. Later, however, when the thin section has practically finished contracting, the heavier section starts to contract. It is now unable to compress the thin section, which has become rigid and strong. Thus, the heavy section goes into tension. Depending on its temperature it will either stretch plastically, hot tear, or cold crack. The example shown in Fig. 1(b) is another common failure mode. The internal walls of the castings remain hot longest, even though the casting may have been designed with even wall

or

(a)

or

(b)

Fig. 1

(a) Thick/thin-section casting showing tensile stress in the thick section. (b) Even-walled casting showing internal tensile stresses

sections. This is, of course, simply the result of the internal sections being surrounded by other hot sections. The reasoning is therefore the same as for the thick/thin-section casting in Fig. 1(a). The internal walls suffer tension at a late stage of cooling. This tension may be retained as a residual stress in the finished casting, or may lead to catastrophic failure by tearing or cracking. The same reasoning applies to the case of a single-component heavy-section casting such as an ingot, billet, or slab—especially when cast in steel, which has poor thermal conductivity. The inner parts of the casting solidify and contract last, putting them into tension. Because of the low yield point of the hot metal, extensive plastic yielding occurs. There is a further type of internal constraint that appears to be universal in castings of all sizes and shapes. It is rarely recognized, but was investigated by Weiner and Boley (Ref 2) in a theoretical study of a simple slab casting. They assumed elastic-plastic behavior of the solid, and that the yield point of the solid was zero at the melting point (not quite true, but a reasonable working approximation) and increased as the casting cooled. They found that plastic flow of the solid occurs at the very beginning of solidification. The stress history of a given particle was found to be as follows. On freezing, the particles are subject to tension, and since the yield is initially zero, its behavior is at first plastic. As it cools, the tensile stress on it increases and remains equal to the yield stress corresponding to its temperature, until such time as the rate of increase of stress upon it is less than the rate of increase of its yield stress. It then starts to behave elastically. Soon after unloading begins, the stress on the particle decreases rapidly, becoming compressive, and finally reaching the yield stress in the opposite direction. Its behavior remains plastic thereafter. To sum up their findings, in a solidifying material there will be various deformation regimes: (1) a plastic zone in tension at the solidification front, since the strength of the solid is low; (2) a central region where the stresses are in the elastic range; and (3) a zone at the surface of the casting where there is a plastic flow in compression. The overall scheme is illustrated in Fig. 2.

362 / Residual Stress Formation During Manufacturing Processes

Elastic compression

Plastic compression

Elastic tension Plastic tension

(Time)0.5

Liquid Distance Plastic Mold

Elastic

Plastic

Compression

Liquid + solid

Tension

Tensile stress 0 Compressive stress

0

0.2

0.4

0.6

0.8

1.0

Distance through solid

Fig. 2

Elastic-plastic regimes in a simple slab casting

Residual tensile stress, MPa

90 80

Gray cast iron

70 60 50 40

Al alloy

30 20 10 0

Approximate solidification time 0

Fig. 3

1

2 4 8 16 32 Time in mold before stripping

64

Residual stresses in aluminum alloy and gray iron castings as a function of stripping time

The model probably would be improved, but not fundamentally altered, by using creep flow behavior instead of the elastic-plastic flow behavior with yield stress a function of temperature. Richmond and Tien (Ref 3, 4) criticize this model on the grounds that it does not account for the friction at the casting/mold interface. When Richmond and Tien included this, they found that the casting/mold interface is no longer in compression but in tension. This is almost certainly true for large castings in metal molds, such as steel ingots in cast iron ingot molds, where the pressure between the mold and casting is high, the friction is high, and the mold is rigid. These authors explain the occurrence of surface cracks in steel ingots in this way. How-

ever, Weiner and Boley (Ref 2) are likely to be more nearly correct for smaller castings in sand molds. Here, the interfacial pressure will be less, and the surface more accommodating, reducing the restraint due to friction. Thus, their analysis probably remains the most appropriate for medium-size shaped castings. As in cases where the casting is constrained by the mold, removing the casting from the mold at an early stage would be expected to be normally beneficial in reducing residual stress. Figure 3 shows the result for iron and a high-strength aluminum alloy (Ref 5). All the observations made thus far appear to be explainable assuming that the cause of the development of residual stress is the interaction of different members of the casting cooling at different rates.

Prediction of Residual Stresses in Castings The strain DL/L due to differential contraction is determined by the temperature difference, DT, and the coefficient of thermal expansion of the alloy, ␣. Since e ⳱ DL/L ⳱ ␣DT, r ⳱ eE, results in r ⳱ ␣EDT. The stress therefore depends on the temperature difference between members. It is also worth noting that the stress is independent of casting length L. Further influence of the geometry of the threebar frame casting was found by Von Steiger (Ref 6), who measured the increase of the stress in the center bar of gray iron castings by increasing the rigidity of the end cross-members. He found that

a center bar of more than twice the diameter of the outer bars would suffer a residual stress of more than 200 MPa (30 ksi), which was sufficient to fracture the bar during cooling. The stress analysis of castings poses several problems not seen in more traditional problems in mechanics. Residual stress formation during casting is a consequence of various regions of a geometrically complicated component cooling at different rates. The stress response is the result of coupled thermal, microthermal, and stress histories. Stress predictions are strongly influenced by the thermal and microstructural histories. The accuracy of thermal and microstructural predictions is a primary factor in the accuracy of residual stress predictions. Figure 4 schematically represents the types of analyses required to completely describe a casting process (Ref 7). An overall architecture of a comprehensive solidification modeling system is shown in Fig. 5, which depicts the various modules available in the current state-of-the-art solidification simulation of casting processes, the information available from each module, and the interconnection between each module (Ref 8). The primary and most obvious phenomenon controlling casting is the transfer of heat from the cooling metal to the mold. The early models of casting cooling were straightforward heat conduction analyses. However, the mechanics of fluid flow are important for both mold-filling effects and physics-based models of interdendritic porosity formation. Buoyancy effects after the mold is full exert varying degrees of influence during the cooling cycle, depending on the thickness of the casting being produced. In addition, analysis of the flow of various chemical species is very important for crystal growth, and many thermofluid models today incorporate species flow. The heat-transfer processes occurring are complex, the cooling rates employed range from 10ⳮ5 to 1010 K/s, and the corresponding solidification systems extend from several meters to a few micrometers. These various cooling rates produce different microstructures and hence a variety of thermomechanical properties. Yu et al. (Ref 9) related the occurrence of casting defects to cooling rates. During the solidification of binary and multicomponent alloys, the concentrations vary locally from the original mixture as material may be preferentially incorporated or rejected at the solidification front. The material between the solidus and the liquidus temperatures is partly solid and partly liquid (resembling a porous medium) and is referred to as the “mushy zone.” Lewis et al. (Ref 10) have given an account of several aspects of modeling of heat transfer, fluid flow, and thermodynamics in castings. Solidification kinetics, including phase selection, nucleation, and growth, are now being investigated in several laboratories. Incorporation of these principles into the more traditional thermofluid models promises to enable quantitative microstructural predictions in the near future (Ref 9), and predictions of engineering proper-

Residual Stress Formation During Casting / 363 ties such as tensile strength and elongation will be possible before long. These predictions will enable product-design engineers to evaluate the effects of nonuniform properties and defects on the life-cycle performance of components. Finally, the coupling of mechanical analysis with thermal analysis enables the prediction of residual stresses and distortions in castings. Another important problem is the material response to the thermal cycle, as material properties are temperature dependent (Ref 11). For steels and other materials, dramatic changes in mechanical properties can occur at temperatures above 600 C (1110 F). Phase transformations, with their attendant volume changes, also play an important role in the development of residual stresses. Thermomechanical models were first applied to modeling of continuous casting and ingot casting. Elastoplastic (Ref 12–14) and elastoviscoplastic (Ref 15–17) behaviors have been considered with thermo-dependent material properties. The effect of different kinds of constitutive equations has been discussed (Ref 18), and elastoviscoplastic behavior seems to be more appropriate to model the development of strain and stress in casting and to take into account the different states of metal (liquid, semisolid, solid). Such models were recently applied to the castings of complex-shape parts (Ref 19, 20). The focus is currently on the validation of models: Do they correctly describe reality, and what must be the accuracy of materials data for models to be predictive? The great influence of thermal properties of alloys on calculated solidification time have been pointed out (Ref 21). Coupling between thermal and mechanical behavior magnifies the complexity of this problem since not only thermal and mechanical properties must be accurately known, but the way the coupling is modeled also is of importance. Chandra (Ref 22) presents the basic concepts for a comprehensive finite-element-based computer simulation method for the prediction of hot tears, hot cracks, residual stresses, and distortions in precision castings using a sequential thermomechanical analysis approach. The existing capabilities of several industry standard commercial and research finite-element codes are also reviewed. Drezet et al. (Ref 23) predict the deformation and temperature field evolution during direct chill (DC) and electromagnetic (EM) casting of aluminum alloy slabs using a transient thermomechanical model based on viscoplastic law. The model, validated on the basis of the measurements presented earlier in this article, enables prediction of the influence of casting parameters on butt curl and swell, rolling faces pulling, and residual stress state for DC and EM cast ingots. Stefanescu (Ref 24) has made an attempt to predict features such as microsegregation, microstructure length scale, fraction of phases, structural transitions, hardness, microhardness, and tensile properties. Distribution of residual porosity in castings is calculated based on a uniform solidification assumption for the particular

case of aluminum-rich Al-Cu castings (Ref 25). An analytical criterion, identifying conditions under which there will be no porosity formation, is established. Hiebler et al. (Ref 26) showed that the strength properties of in situ solidified steel near the solidus temperature can be readily determined and hence may allow development of a stress criterion in order to further improve the assurance of inner soundness even under the most critical conditions. However, Yamanaka et al. (Ref 27) found that internal cracking occurs and extends when the total amount of strain applied between zero strength temperature (ZST) and zero ductility temperature (ZDT) exceeds the critical strain, independent of deformation mode, whether continuous or intermittent. It is interesting to note that Zhang et al. (Ref

Heat-flow analysis

¥ Macroporosity (isolated hot spots) ¥ Microporosity (empirical criteria; e.g., Niyama) ¥ Primary dendrite arm spacing (empirical criteria) ¥ Secondary dendrite arm spacing (empirical criteria)

Fluid-flow analysis

¥ Better representation of the thermal field during and after mold filling ¥ Darcy flow for interdendritic porosity models

Solidification kinetics

¥ Grain size of castings via nucleation and growth laws ¥ Secondary dendrite arm spacing (coarsening relations) ¥ Solidification path

Species flow analysis

¥ Prediction of macrosegregation ¥ Prediction of microsegregation ¥ Enhanced representation of the solidification kinetics, fluid flow, and heat transfer

Thermomechanical analysis

Fig. 4

28) have presented a fast-acting simultaneous filling and solidification model based on reduction of Navier-Stokes equations to a transient Bernoulli equation and potential equation along with enthalpy method with a one-dimensional heat conduction model. Ruiz and Khandia (Ref 29) have used LS-DYNA 3D both for the filling simulation and to carry out a coupled thermal and stress analysis of casting during solidification, predicting cooling rates, residual stresses, and as-cast shapes. Magnin et al. (Ref 30) determined the elastoviscoplastic constitutive equation using an optimization model, which calculates the best rheological parameters to fit experimental stress curves. This law is then introduced in a finite-element model of billet DC casting using the commercial software package

¥ Physics-based solidification shrinkage ¥ Hot tearing from yield criteria ¥ Prediction of air gap with modification of heat transfer ¥ Prediction of residual stresses and casting dimensional control

Types of analysis available for solidification modeling, with their benefits

Initial design

Material properties (metal, mold)

Quick analysis (solidification time, modulus, etc.)

Rules (empirical charts, etc.)

Fig. 5

Special boundary conditions (interface, heat-transfer coefficients, etc.)

Rigging design

Solidification simulation (temperature, solid fraction, velocity, etc.)

Stress analysis (shrinkage stresses distortion)

Microstructural evolution (grain size, dendrite arm spacing, etc.)

Defect prediction (macro- and microporosity, misrun, etc.)

Mushy zone fluid flow (macrosegregation)

Typical architecture of a comprehensive solidification modeling system

364 / Residual Stress Formation During Manufacturing Processes MARC. A good idea of product quality and performance can often be obtained at the initial stage of the product development cycle through prediction of filling, solidification, stresses, and shrinkage (Ref 31). Examples of simulations conducted using an experimental die, an automotive housing, and a wheel in an aluminum alloy are given.

Finite Element Analysis An experimental on-site study of the influence of operating parameters on the quality of castings produced in a working steel mill would be very costly and time consuming. It is far more practical to simulate the entire complex process numerically. Any acceptable mathematical model should be capable of accommodating variations in the operating parameters as they arise in practice so that their effects on the final product can be predicted. Another requirement placed on the model is that it be suitable for designing molds so that the optimum mold type may be used for given casting conditions and steel qualities. Since the entire process is dependent on heat flow from the ingot to the mold and subsequently to the surroundings, it is logical to determine the temperature field at various stages of the process. From this temperature field, initial strains can be calculated and the resulting thermal stresses determined. Since the appearance of the pioneering paper by Sarjant and Slack (Ref 32), a number of authors have published studies on the development of mathematical models for calculation of the solidification process in steel ingots. Although the solidification of an ingot is a three-dimensional process, it appears to be possible to obtain an adequate picture of the process using a twodimensional model. It has been demonstrated (Ref 33) that for the ingot dimensions used in actual practice, a true picture of the solidification process can be obtained by calculation in a horizontal section at midheight through the ingot. The thermal model used here uses the Galerkin method (Ref 34) and eight-noded quadratic isoparametric elements and possesses the novel feature of using elements with time-varying conductivity to model the heat transfer in the air-gap that forms between ingot and mold. Calculated temperature fields may be used to evaluate the loading stresses, and in this way the thermal stress development may be determined using either an elastic formulation (Ref 35) or an elastoplastic formulation (Ref 36). The elastoplastic formulations have the disadvantage of being unable to model any time-dependent creep effects. The mathematical stress model in this article embodies a general solution procedure for determining the development of thermal stresses in an elastoviscoplastic multiphase body and is capable of accounting for time-dependent properties. The constitutive model used is of the type proposed by Perzyna (Ref 37) and first implemented numerically by Zienkiewicz and Cormeau (Ref 38). In this model the behavior of the

material is elastic if a certain function of the yield condition has a value of less than zero, while time-dependent viscoplastic flow occurs when the value of this function is positive. The model can also be used to give the purely plastic solution, in which time and viscous effects do not have real meaning but are used merely as means for attaining steady-state condition. The temperature field and the development of the thermal stress in a section at the midheight of an ingot casting are calculated and shown.

Finite-Element Formulation of the Heat-Flow Problem (Ref 39) The variation of temperature T with time in a two-dimensional region X bounded by a curve C, for both ingot and the mold, is given by: qc

T T T ⳱ kx Ⳮ ky t x x y y

冢

冣

冢

冣

(Eq 1)

q12

兺 Ni Ti(t) i⳱1

KT Ⳮ CT˙ ⳱ F

Ni Nj Ni Nj Ⳮ Ky x x y y

冢K

兺e 冮X

冣

x

e

dX Ⳮ

where T3 is the temperature of the outer wall of the mold and T is the ambient temperature. The heat-transfer coefficient h12 changes when the air gap between the ingot and the mold forms. To take this phenomenon into account, h12 is regarded as a function of position on the ingot perimeter and of time. Oeters et al. (Ref 40) have observed that the calculations are in good agreement with the actually measured heatflow densities in the gap if the breadth of the gap is taken to be of the order of 0.5 mm (0.02 in.). Thus, in the present model, the heat transfer across the gap is modeled as a conduction mode, with the conductivity being a function of time and position on the perimeter. This approach allows the effect of the lubrication used on the inner wall of the mold (Ref 40) to be modeled by using a suitable value of the thermal conductivity in the air-gap region. The heat-transfer coefficient between the outer wall of the mold and the surrounding air takes into account heat trans-

(Eq 5)

in which typical matrix elements are

(Eq 2)

(Eq 3)

(Eq 4)

where Ti is the time-dependent value at node i. The substitution of Eq 4 into Eq 1 and the application of the Galerkin method (Ref 34) results in

Kij ⳱

where T1 is the surface temperature of the ingot and T2 is the temperature of the inner wall of the mold. (2) Between the outer wall of the mold and the surroundings: q3 ⳱ h3 (T3 ⳮ T)

n

T⳱

where qc is the thermal capacity, and kx, and ky are the thermal conductivities in the x and y directions, respectively. The boundary conditions for this partial differential equation are the expressions for the heat fluxes between the ingot and mold and between the mold and the surroundings. These boundaries occur in two regions: (1) Between the ingot and inner wall of the mold: k12 ⳱ h12(T1 ⳮ T2) ⳱ (T1 ⳮ T2) d12

fer by radiation and by free convection. The variation of density and specific heat with temperature is handled as discussed by Comini et al. (Ref 41), and any phase change that occurs is treated by the method discussed by Morgan et al. (Ref 42). The thermal conductivities of the ingot and mold are also allowed to vary with temperature. The temperature fields in the ingot and the mold are computed simultaneously using a finiteelement formulation. The region of interest is divided into a number of eight-noded isoparametric elements Xe, with boundary Ce with quadratic shape functions Ni associated with each node i. In the isoparametric elements, the shape functions are used to transform the coordinates (Ref 34), and this enables better representation of any curved boundaries that may be present in the problem. The unknown temperature T is approximated in the solution domain at any time by:

兺e 冮C hNi Nj dC e

Cij ⳱

兺e 冮X

Fi ⳱

兺e 冮C

qcNi Nj dX

e

e

Ni hTdC

(Eq 6)

(Eq 7)

(Eq 8)

where the summations are carried out over each element e. The coupled system of ordinary differential equations represented by Eq 5 is solved by a finite-difference two-stage Crank-Nicolson predictor-corrector method, and in this way the complete thermal history of the region can be determined. The change in temperature in a certain time can then be used to calculate incremental initial node strains dei via

冦冧

␣DTi dei ⳱ ␣DTi 0

(Eq 9)

where ␣ is the temperature-dependent coefficient of expansion. An elastoviscoplastic stress model is then used to calculate the stress distribution resulting from the application of this initial strain.

Residual Stress Formation During Casting / 365 Finite-Element Formulation of the Elastoviscoplastic Stress Model (Ref 39) In the elastoviscoplastic stress model, it is assumed that the total strain is the sum of elastic and plastic components, together with any initial strains: e ⳱ ee Ⳮ evp Ⳮ ei

(Eq 10)

Only elastic strains are produced initially by the application of a load, and the elastic strain rate is linearly related to the total stress rate by the matrix of elastic constants D (Ref 43) according to: r˙ ⳱ D˙ee

(Eq 11)

where the overdot denotes differentiation with respect to time. The viscoplastic strain occurs only if the stress levels exceed some previously defined yield stress. This yield stress is given by the yield function:

e ⳱ Bd

(Eq 12)

Therefore, when F 0, purely elastic behavior takes place, but F 0 represents the onset of plastic deformation. The viscoplastic strain is given by: evp ⳱ e˙ vp ⳱ f (r, evp) t

冮

X

X

BTrdX ˙ ⳱ 0

(Eq 19)

Combining Eq 10, 11, and 19 then leads to:

冮

BTD(˙e ⳮ e˙ vp ⳮ e˙ i)dX ⳱ 0

(Eq 20)

which, on using Eq 17 to substitute for e, becomes:

冮

X

冮

X

BTD˙eidX Ⳮ

冮

X

BTDevpdX

(Eq 23)

The solution procedure for Eq 22 is given by Zienkiewicz and Cormeau (Ref 38). In this method, a simple Euler iterative procedure is used which can become unstable if critical time steps are too large. The selection of critical time steps has been studied by Cormeau (Ref 44), and his stability limits are followed here.

(Eq 18)

As the constitutive relation for viscoplastic problems has been specified in time rate form in (Eq 11), it is convenient to rewrite Eq 18 as

冮

R˙ ⳱

Examples

BTrdX ⳱ 0

˙ BTDBddX ⳱ 0

(Eq 21)

That is, (Eq 13) Ksd˙ ⳮ R˙ ⳱ 0

To define completely a strain-rate law, it is assumed that, in common with plasticity, the directions of straining are given by gradients of a plastic potential Q: Q r

(Eq 17)

where B is the standard matrix derived from the derivatives of the shape functions (Ref 43). The virtual work principle in this case enables the equilibrium equation to be written as:

X

F (r, evp) ⳱ 0

e˙ vp ⳱ w(F)

where d is the column vector of nodal values di. With the displacements at all points given by Eq 16, the strains at any point can be determined from the relationship:

(Eq 22)

where KS is the overall stiffness matrix and R˙ represents the total loading rate, which turns out to be

Because of the complexities and practical difficulties of experiments on ingot castings, only a limited number of experimental investigations are reported in sufficient detail in the literature to make possible a comparison with the results of a mathematical model. Oeters et al. (Ref 40) have reported extensive results of the investigation on a 6 ton ingot casting, and this is the example chosen for the present investigation. At the midheight of the 6 ton ingot, the cross section is in the form of a square with rounded corners and a side length of 600 mm (23.6 in.). Along two opposite sides of the square the surrounding mold has a thickness of 150 mm (6 in.), while this thickness becomes 166 mm (6.5 in.) along the other sides. The variation of the properties with temperature is assumed to take the form reported by Williams et al. (Ref 11). The finite-element mesh used in the analysis consists of 52 elements (illustrated in Fig. 6) and 185 nodes. The nodes are located at the element corners and at the midpoints of the element sides. The time of air-gap formation at various locations on the ingot perimeter follows roughly a parabolic law proceeding from the corner to the middle of the face (Fig. 7). Initially, the model

(Eq 14) 8

16

24

32

46

52

23

31

45

51

21

30 40 29 28 36

44

50

43

49

42

48

41

47

Viscoplastic flow laws can then be written as: w(F ) ⳱

Mold

冦

0 if F ⱕ 0 w(F) if F 0

7

Combining Eq 10, 11, and 13 results in the complete constitutive relation: e˙ ⳱ Dⳮ1r Ⳮ w(F)

Q Ⳮ e˙ i r

Air gap

6 4

15 14

5

12

22 13

27 3

(Eq 15)

11

(Eq 16)

35

39

26 2

10

18

1

9

17

34

38

25

n

兺 Ni di ⳱ NTd i⳱1

19

Ingot

The finite-element stress analysis is performed only on the ingot, which is discretized by using the same elements and shape functions as were used in the thermal analysis. If the vector u denotes the displacement field, then this may be approximated over in terms of the nodal displacements di by: u ⳱ u˜ ⳱

20

Fig. 6

Finite-element mesh for ingot, air gap, and mesh

33

37

366 / Residual Stress Formation During Manufacturing Processes 1000 Center of the side 800 Quarter of the side Temperature, ˚C

is run with intimate contact everywhere, and then the gap opens from the corner toward the center as time proceeds. In the gap, the heattransfer coefficients given by Oeters et al (Ref 40) are utilized as functions of time in the form shown in Fig. 8. Since the gap width is fixed at 0.5 mm (0.02 in.), this variation is supplied to the model as a variation in thermal conductivity of the air gap. At the start, the time steps need to be very small, on the order of seconds, and they gradually increase up to a value of 2 min in the later stages of the simulation run. The calculated temperature of the inner wall of the mold for various locations is plotted against time in Fig. 9. For the sake of comparison, the results of Oeters et al. (Ref 40) are also shown. As the exact thermal properties used by Oeters et al. are not known, it can be concluded that a reasonable agreement has been obtained. Figure 10 compares surface temperatures on the ingot as functions of time and location; the predicted temperatures are again slightly lower than those of Oeters et al. Figure 11 shows the solidification fronts determined at various time intervals; these results are in good agreement with the values determined by Weingert (Ref 45). The temperature field in the ingot is used for evaluating the thermal loads employed in the

600 Corner 400

Experimental Present results

200

0

0

20

10

30

40

Fig. 9

80

90

60

70

80

90

Experimental Present results

Temperature, °C

Time, min

70

1200

1100

20

60

Temperature curve for inner wall of mold

Center of the side

40

30

50

Time, min

1000

Quarter of the side 900 10 Corner 0

0

150

800

300

0

20

10

30

40

Distance from corner

Heat transfer coefficients, cal/cm2min °C

Fig. 7

Time for air-gap formation

Fig. 10

Average value of ingot surface temperature

viscoplastic stress analysis. A plane-strain stress analysis was performed using a Von Mises yield criterion (Ref 43). The model is used to give a purely plastic solution at steady-state conditions at each stage. The rate of viscoplastic straining is given by Eq 14, in which the flow function used is:

3.0 Center of face 2.4

1.8

1.2

0

Quarter of face

18 30

0.6 74 80 0

20

40

60

80

Time, min

Fig. 8

␾⳱ c

F Fo

(Eq 24)

52

Corner 0

50

Time, min

Average heat-transfer coefficients in the air gap

Fig. 11

Solidification fronts for one quadrant of the ingot

where Fo is some reference value of stress and c is a fluidity coefficient. The mechanical properties vary as a function of temperature and are taken from Williams et al (Ref 11). A Poisson’s ratio of 0.33 is used.

Residual Stress Formation During Casting / 367 Figures 12 and 13 show the computed stress field in the ingot at two different times. The region near the ingot surface is subjected to tension initially and, as expected, this gradually changes to compression with the passage of time. Prediction of such stress concentration regions would be particularly useful in the case of complex shapes to avoid possible failures. Next, examples of the calculation of residual stresses for pure aluminum under axially symmetric and realistic boundary conditions are given. The effects of the melt pressure and cooling conditions on the residual stresses are also reported. Molten pure aluminum at a uniform temperature equal to or above the melting temperature is assumed to start at time t ⳱ 0 when part of the boundary of the body is cooled down in an axially symmetric way to a temperature equal to or below the solidification temperature. Figure 14 shows on the r-z plane, at time t, the two-dimensional model sections. The interface velocity and location are treated as primary variables of the heat-transfer analysis, and the isostatic stress condition at the front is utilized as an initial condition in the stress analysis. The freezing interface condition as an initial rather than a bound-

Fig. 14

Tension Compression

Fig. 12

One quadrant of the principal stress field after 4 min

Model section for the solidification problem

ary condition at the time of solidification of a material print was first discussed by Richmond (Ref 46) and implemented in one-dimensional solidification problems by Richmond et al. (Ref 4, 47) and in two-dimensional plane stress applications by Zabaras et al (Ref 48). The thermal properties of pure aluminum are given in Table 1, and the temperature-dependent mechanical properties reported by Heinlein et al. (Ref 47) are given in Table 2. A viscoplastic constitutive model is needed to prescribe the inelastic deformation, which should include important effects such as rate sensitivity, strain hardening, and recovery in a rather wide range of temperatures up to the melting point of the solidifying pure metal. In the simulation reported here, a hyperbolic-sine constitutive law is used to prescribe the inelastic deformation. The details of the formulations for thermal and thermomechanical analysis are given by Zabaras et al. (Ref 49). The examples that follow will consider solidification of a cylinder initially filled with liquid aluminum at melting temperature. Part of the boundary of the cylinder will be assumed to be cooled down as follows: T0 (t) ⳱ Ta Ⳮ (Tm ⳮ Ta) eⳮQt

Tension Compression

Fig. 13

Principal stress field after 40 min

(Eq 25)

where Ta is the final steady-state temperature, Tm is the melting temperature, and Q is a cooling rate parameter. In the following examples, Ta ⳱ 500 C (930 F), Q ⳱ 0.2 sⳮ1, and Tm ⳱ 660 C (1220 F). Four-noded elements were used for the temperature analysis, while eight-noded

Table 1

Thermal properties of aluminum

Property

Value

Thermal conductivity in solid, kS Thermal conductivity in liquid, kL Heat capacity in solid, CS Heat capacity in liquid, CL Latent heat, L Density, q Initial temperature, Tin Melting temperature, Tm

0.0548 kcal/m•s•ºC 0.0548 kcal/m•s•ºC 0.2526 kcal/kg•ºC 0.2526 kcal/kg•ºC 94.44 kcal/kg 2650 kg/m3 660 ºC (1220 F) 660 ºC (1220 F)

Source: Ref 46

Table 2 num

Mechanical properties of alumi-

Coefficients of constitutive law, eN ⳱ 3/2 AeⳮC/(TⳭ273) [sin h Br] ¯ n]/r¯ s A 0.382 ⳯ 1012 /s B 0.037/MPa C 18,849 K n 3.84 Thermal expansion coefficients, ␣(T)n(a), m/m • C ⳯ 106 At 25 C 23.19 At 300 C 27.86 At 400 C 30.23 At 660 C 38.355 Poisson’s ratio (m) 0.37 Young’s modulus E(T) ⳱ F ⳮ GT, where F ⳱ 6.93 ⳯ 104 and G ⳱ 43.7152 MPa / C. (a) n: The variation of ␣(T) is assumed to be piecewise linear within the temperature intervals 25 to 300 C, 300 to 400 C, and 400 to 660 C. Source: Ref 46

368 / Residual Stress Formation During Manufacturing Processes quadrilateral elements were employed in the deformation part of the problem. In the first example, it is assumed that the cylindrical body is insulated at the top and bottom and that the rest of the surface (r ⳱ R) is cooled with the temperature history depicted in Eq 24. Plane-strain conditions with traction-free outer surface were assumed. The geometrical parameters were assumed as h ⳱ 0.04 m and R ⳱ 0.018 m. The front position and the temperature history at various locations are shown in Fig. 15 and 16, respectively. These results were compared with a one-dimensional deforming finiteelement implementation of the problem (Ref 50) and were found to coincide to within plotting accuracy. Figure 17 shows the residual stress distribution with the plane-strain assumptions on the plane z ⳱ 0.002113 m at the end of solidification, t ⳱ 8.32 s. The stress history at the location r ⳱ 0.017714 m and z ⳱ 0.002113 m near the bottom and the surface r ⳱ R is also shown in Fig. 18. As shown, the hoop stress at the outer surface r ⳱ R is compressive, while near the center of the cylinder all the stresses are tensile. Generally, the residual stress in the axial direction is tensile, but it becomes slightly com-

pressive in the region close to the surface r ⳱ R near the end of solidification. In this example, as expected, the stresses were found not to significantly vary in the axial direction. In the second example, the geometry and the temperature boundary conditions are the same as before. It is assumed that the bottom is fixed in the axial direction and the traction-free conditions are applied to the top surface and to the outer surface, r ⳱ R. It was observed that the traction conditions at the top surface affect primarily the axial stress while leaving the radial and hoop stress almost the same for both freetop and plane-strain conditions (Ref 51). Large tensile residual axial stresses appear in the region close to the center of the cylinder. Figure 19 shows the residual stress variation in the axial direction at time t ⳱ 8.3202 s, and the stress history at location r ⳱ 0.0177145 m and z ⳱ 0.0010566 m (close to the bottom and r ⳱ R) is given in Fig. 20. The hoop and axial stress histories are almost the same, an assumption used by Heinlein et al. (Ref 47) to simplify a threedimensional problem to a unidirectional one.

To demonstrate the effect of melt pressure, a longer cylinder is considered (h ⳱ 0.4 m), and other conditions are kept the same as those in the first example. In this case, the pressure at the bottom of the cylinder is about 0.01 MPa (0.0014 ksi). The displacements of three points at r ⳱ R are given in Fig. 21, where it is shown that the surface r ⳱ R near the bottom of the cylinder first expands before it starts contracting. Generally, the residual stress distribution is very close to that discussed in the first example; but early on, the differences of the displacements at r ⳱ R and the stress distribution between this and the first example can be observed. Also, the hoop stress was found to have higher values early on (Ref 51). Therefore, as is expected, one can conclude that the melt pressure has a significant effect on the stress early in the process and can play an important role in the location and time of formation of air-gaps in the solid shell/mold interface. For cases with larger Q (high cooling rate), it was observed that the solidification process proceeds faster and that the calculated stresses obtained at the end of solidification are larger than those in the first example (Ref 51).

6

Stress, MPa

Stress, MPa

Radial front position, m

4

0.01

2

0

−2 0 0

0

Fig. 15

2

4

6 Time, s

8

0.01 r, m

0

Radial stress Axial stress Hoop stress r = 0.017714 m z = 0.0021133 m

−1

−2

0.02

0

2

4

10

Fig. 17

Front position for solidification of a cylindrical body uniformly cooled at the surface at r ⳱ R

6

8

Residual stress distribution in the radial direction at t ⳱ 8.32 s using a plane-strain assump-

tion

Fig. 18

Thermal stress history with a plane-strain assumption

5

660

4

640

3

Radial stress Axial stress Hoop stress

r = 0.002918 m r = 0.002918 m r = 0.002918 m

Stress, MPa

620 600 580

0

2

4

6 Time, s

2 1

r = 0.017324 m

r = 0.018000 m r = 0.014731 m r = 0.009685 m r = 0.006980 m

560

0

r = 0.017324 m

−1 8

10

r = 0.017324 m

−2 0

Temperature history at various locations for solidification of a cylindrical body uniformly cooled at the surface at r ⳱ R

10

Time, s

680

Temperature, °C

1

Radial stress Axial stress Hoop stress z = 0.0021133 m

0.02

Fig. 16

Fig. 19

0.01

0.02 Z, m

0.03

0.04

Residual stress variation in the axial direction at time t ⳱ 8.3202 s with a traction-free top surface

Residual Stress Formation During Casting / 369 1

Stress, MPa

0

−1 Radial stress Axial stress Hoop stress r = 0.0177145 m z = 0.0010566 m

−2 −3 0

2

4

6

8

10

Time, s

Fig. 20

Thermal stress history with a traction-free top surface

In the final example, a cylinder with R ⳱ h ⳱ 0.018 m was cooled with the condition of Eq 24 at both the bottom surface and the surface r ⳱ R. The pattern of solidification is shown in Fig. 14. It is assumed that the outer surface, r ⳱ R, and the top surface are traction-free, while the bottom is fixed in the axial direction. Principal residual stresses in the r-z plane near the end of solidification are plotted in Fig. 22. Large tensile residual stresses appeared at the top around the center region, the stresses were small in the area close to the surface r ⳱ R, and the residual stresses were compressive at the bottom close to the center region. The effect of casting size and thermal boundary conditions on residual stresses and deformation has been investigated by Sathya Prasad (Ref 52).

0.02 0

Displacement, mm

−0.02 −0.04 −0.06 Radial displacement z = 0.00 m Radial displacement z = 0.20 m

−0.08

Radial displacement z = 0.40 m −0.10

Axial displacement z = 0.00 m, z = 0.40 m Axial displacement z = 0.20 m

−0.12 0

2

4

6

8

10

Time, s

Fig. 21

Radial and axial displacements at the surface r ⳱ R with plane-strain assumption and large melt pressures

0.0011 Tension Compression

1.5 MPa

z, m

0.0010

0.009

0 0

0.009 r, m

Fig. 22

Principal stresses in the r-z plane at time t ⳱ 7.3294 s for the solidification problem

0.018

Special Considerations The deformation of a solidifying material is very different from that of a standard fixed body. A solidifying body develops residual (initial) stresses immediately after solidification and is never in a state of zero stresses (stress free). Thermal stress problems carry with them difficulties not normally found in the analysis of either thermal or stress problems. The coupling between the temperature and stress fields works in both directions. It is possible to imagine cases where the basic boundary conditions for the thermal analysis are affected by the deformations, as in the formation of the air gap that controls the heat flow to the mold from the cooling ingot. Fully coupled analyses are slightly more complicated because they require deciding when to update the effect of one process to the other. Decultieux et al. (Ref 53) apply a three-dimensional finite-element coupled thermomechanical model to the solidification of the hollow cylinder. An experiment has been developed to measure heattransfer coefficients and air-gap width in permanent mold casting of aluminum-silicon alloys. Comparison between experimental and calculated temperature and air-gap width shows the validity of the coupled approach. The thermal strain fields computed from the temperature fields introduce complications. The incompressible nature of plastic deformation creates a constraint at each gauss point in an element. When the number of constraints arising from incompressibility exceeds the numbers of degrees of freedom, locking is said to occur, as there are no possible solutions for this case. The solution to this may be the reduced order of the integration for the hydraulic components of the stress, which may lead to, most notably, a failure to satisfy the patch test (Ref 54). A related effect comes from the order of the thermal strain fields within the element. If nodal temperatures are interpolated to give gauss point values, and these are used to determine thermal strains, then the thermal strain field has the same order as the displacement field in the element. The total strains, which are computed from the partial derivatives of the displacements, are one order lower. This incompatibility can also lead to locking problems. The need to avoid incompatible strain fields has been known for some time (Ref 55) and extremely large errors can result if it is not observed (Ref 56). Using linear elements in the thermal analysis and quadratic elements in the stress analysis is the most common strategy (Ref 49). Plane-strain conditions are most commonly used in the stress analysis. This condition implies that the longitudinal heat flow and longitudinal displacement are zero. Longitudinal interactions in the stress may not always be satisfied even though longitudinal heat flow is probably never very large. To compensate for this problem, extension to a generalized plane strain has been used (Ref 54) where plane sections must remain plane but may rotate or trans-

370 / Residual Stress Formation During Manufacturing Processes late with respect to one another, in which case net longitudinal stress on any cross section now becomes zero. One of the main purposes of solidification modeling is to identify casting designs that are likely to cause defects due to porosity formed when shrinkage occurs during phase change. This porosity, which frequently takes the form of interdendritic voids, affects the ultimate tensile strength of the casting and hence is to be avoided. It can be eliminated only when the liquid metal from the riser is able to travel to the hot spot location to compensate for the solidification. Experiments on cast steels have shown that when the temperature gradient at the end of the solidification falls to below 10 K/cm, porosity is observed even in well-degassed material. On the basis of solidification simulation, the solidification time can be found and the temperature gradients at that instant can be determined. Based on the contour of 10 K/cm thermal gradient, it is possible to determine the location and size of the shrinkage defect. However, it may be noted that the value of 10 K/cm is valid for a three-dimensional casting, and a different limit may have to be taken for two-dimensional simulations. Sathya Prasad (Ref 52) has predicted the size and location of shrinkage cavities for Lshaped and T-shaped castings with and without chills. Residual stress determination must also make sure that no shrinkage cavity exists in the castings. If it does, its presence must be accounted for, as there may be stress concentration around such a cavity. In the case of continuous casting of steel, compared with ingot casting, several additional difficulties are encountered when predicting the residual stresses. High stresses develop in the solidifying shell as a result of a number of forces acting externally and internally on the strand. The values of heat extraction and solidification are relatively slow for static casting (solidification time measured in hours), whereas solidification time for continuous casting is in minutes. A static casting meets with a single cooling environment over its solidification period, while a continuous cast section encounters different environments—mold, sprays, pinch rolls, radiation—before complete solidification takes place. Thus, continuous castings change rapidly from one zone to another, resulting in higher thermal stresses than in ingot castings. A continuous cast section also is stressed by pinch rolls, bending and straightening operations during solidification, mold oscillation, and misalignment of mold and roller cages. Ferrostatic pressure can also produce sufficient stress to cause bulging across the wide faces of large slabs. ACKNOWLEDGEMENTS The material presented here is collected from several papers apart from the work of the authors, who gratefully acknowledge the efforts of these fellow researchers. The authors especially thank their students Habib, Paragasam, Parthi-

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47.

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J. Num. Meth. Eng., Vol 8, 1974, p 821– 845 K. Morgan, R.W. Lewis, and K.N. Seetharamu, Modeling Heat Flow and Thermal Stress in Ingot Casting, Simulation, 1981, p 55–63 F. Oeters, K. Ruttiger and H.J. Selenz, Heat Transfer in Ingot Pouring, Information Symp. Casting and Solidification of Steel, Luxemborg, Vol 1, 1977, p 126–167 G. Comini, S. del Guidice, R.W. Lewis, and O.C. Zienkiewicz, Finite Element Solution of Non-Linear Heat Conduction Problems with Special Reference to Phase Change, Int. J. Num. Meth. Eng., Vol 9, 1974, p 109– 127 K. Morgan, R.W. Lewis, and O.C. Zienkiewicz, An Improved Algorithm for Heat Conduction Problems with Phase Change, Int. J. Num. Meth. Eng., Vol 12, 1978, p 1191–1195 O.C. Zienkiewicz, The Finite Element Method, McGraw-Hill, London, 1977 I.C. Cormeau, Numerical Stability in QuasiStatic Elasto-Viscoplasticity, Int. J. Num. Meth. Eng., Vol 9, 1975, p 109–127 H. Weingert, “Untersuchungen Uberder Temperatur-Und-Erstarrungsablanf, Schwerer Blocke Und Brammen,” Ph.D. dissertation, Clausthal, West Germany, 1968 O. Richmond, Models of Stresses and Deformations in Solidifying Bodies, Modeling of Casting and Welding Processes, AIME, 1982, p 215–222 M. Heinlein, S. Mukherjee, and O. Richmond, A Boundary Element Method Analysis of Temperature Fields and Stresses during Solidification, Ironmaking Steelmaking, Vol 59, 1986, p 59–81 N. Zabaras, Y. Ruan, and O. Richmond, Front Tracking Thermomechanical Model for Hypoelastic-Viscoplatic Behavior in a

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50.

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54.

55.

56.

Solidifying Body, Comput. Meth. Appl. Mech. Eng., Vol 81, 1990, p 333–364 N. Zabaras, Y. Ruan, and O. Richmond, On the Calculations of Deformations and Stresses during Axially Symmetric Solidification, J. Appl. Mech., (Trans. ASME), Vol 58, 1991, p 865–871 N. Zabaras and Y. Ruan, A Deforming Finite Element Analysis of Inverse Stefan Problems, Int. J. Num. Meth. Eng., Vol 28, 1989, p 295–313 N. Zabaras and O. Richmond, Analysis and Finite Element Approximations of Deformation and Thermal Stresses in Solidifying Bodies, in Computer Modeling and Simulation of Manufacturing Processes, B. Singh and Y.T. Im, Ed., ASME, 1990 B. Sathya Prasad, “Solidification Simulations of Castings Using Finite Element Method,” Ph.D. thesis, Indian Institute Technology, Madras, India, 1999 F. Decultieux, M. Menai, F. Bay, C. Levaillant, P. Schmidt, I.L. Svensson, and M. Bellet, Thermomechanical Modeling in Casting with Experimental Validation, in Modeling in Welding, Hot Powder Forming and Casting, L. Karlsson, Ed., ASM International, 1997, p 291–313 A.S. Oddy and L.E. Lindgren, Mechanical Modeling and Residual Stresses, in Modeling in Welding, Hot Powder Forming and Casting, L. Karlsson, Ed., ASM International, 1997, p 31–59 B.A.B. Anderson, Thermal Stresses in a Submerged-Arc Welding Joint Considering Phase Transformations, J. Eng. Mat. Technol., (Trans. ASME), Vol 100, 1978, p 356– 362 A.S. Oddy, J.M.J. McDill, and J.A. Goldak, Consistent Strain Fields in 3D Finite Element Analysis of Welds, J. Pressure Vessel Technol., (Trans. ASME), Vol 112 (No. 3), 1990, p 309–311



Residual Stress Formation during Casting: Continuous and Centrifugal Casting Processes D.-Y. Ju, Saitama Institute of Technology, Saitama, Japan

DETERMINATION OF RESIDUAL STRESS in manufacturing processes incorporating solidification, such as casting, welding, and so on, is important for evaluating the mechanical properties and strength of materials and to optimize manufacturing conditions (Ref 1–4). However, residual-stress formation depends not only on the thermomechanical behavior and processing effect due to the variation of microstructure and macrostructure during manufacturing of materials, but also on the interaction of heat conduction, change of phase transformation due to solidification, and stress/strain. A unified constitutive model (Ref 5, 6) that describes variation of the mechanical behavior from viscous fluid to solid and the mixture domain in the material due to solidification is necessary. This article presents some developments in thermomechanical theory and numerical analysis method incorporating solidification of material to simulate the residual-stress formation during casting. A unified inelastic constitutive relationship capable of describing both elastic-viscoplastic solids and viscous fluids to simulate the casting process is proposed and verified by experimental and numerical results. A proposal based on the finiteelement method to combine temperature and stress fields as well as deformation during solidification is also presented. The mechanism of residual-stress formation during continuous and centrifugal casting can be represented using simulation. The thermomechanical modeling was also verified by comparison with the experimental data, such as the measured residual stress and variation of casting temperature.

Inelastic Behavior and Unified Constitutive Theory of Metallic Material in Solidification When dealing with the high-temperature processes incorporating solidification, it is important to know the mechanical behavior of material

nearly up to the melting temperature, and unified constitutive models are desirable for describing characteristics of both inelastic solid and viscous fluid (Ref 7–10). Studies of constitutive relationships at high temperature have been carried out by many researchers (Ref 11–14). In particular, many constitutive models for creep and plastic behavior under some loading paths below 700 C have been developed in the 1970s to 1990s (Ref 15–22). However, it is necessary to verify whether these models are applicable to mechanical behavior at high temperature close to the melting point. Therefore, the authors first carried out tension, creep, and cyclic loading tests for type 304 austenitic stainless steel from room temperature to melting temperature, and strain rates depending on flow stress and strainhardening behavior were investigated. Some typical inelastic constitutive equations based on unified constitutive theory, such as the types of Perzyna and Bodner as well as the superposition model, are used to describe hightemperature behavior and are compared with the test results. The material parameters in the equations were identified by the data of tension tests to simulate the creep and cyclic stress/strain behavior for verification of the models.

Experimental Procedure Axial load and displacement (or strain) must be controlled in tension and creep tests, and the controlled value should be changeable independently of the time interval. A SUS 304 steel with melting point of 1399 C was tested. The chemical compositions of material and the mechanical properties at room temperature are shown in Tables 1 and 2, respectively. The specimen was shaped into a solid cylinder with two lugs as shown in Fig. 1. Four temperature levels, that is—750, 900, 1000, and 1200 C—were chosen for the experiments since the authors were interested in the material behavior at high-temperature condi-

tions. The material behaviors at lower temperatures were also examined to cover a wide range of temperatures. The temperature variation along the gage length was controlled within Ⳳ2 C. The heating rate of the specimen was nearly 8 C/min, and the test was started after the temperature was held for 60 min. The tension tests were made under strain-controlled condition with the strain rates of 1.0, 0.1, 0.01, and 0.001%/s. In the creep tests, several stress levels below the yield stress were employed.

Table 1

Chemical composition of SUS 304

Element

Composition, wt%

Carbon Silicon Manganese Phosphorus Sulfur Nickel Chromium

0.08 0.59 1.00 0.032 0.005 8.26 18.30

Table 2 Room-temperature mechanical properties of SUS 304 Property

Value

Yield stress (ry), MPa Tensile strength (rs), MPa Elongation (␾), %

274.4 607.6 62.0

φ10

M20X2.5

GL 50 33

104

33

170

Fig. 1

Shape and dimensions (in mm) of the specimen

Residual Stress Formation during Casting / 373

e˙ Iij ⳱ Kw(F) 200 750 C 150

900 C

100

1000 C

50

1200 C

0 10−4

T = 1200 °C

150

10−3

10−2 0.1 Strain rate (ε), %/s

1

10

(a)

0

T = 1000 °C

ε = 1.0%/s

50

0.01%/s 0.001%/s

900 C

10

1000 C

0 10−4

10−3

10−2 0.1 Strain rate (ε), %/s

1

100

0.01%/s

7.5 MPa

900 C 750 C

3 40.0 MPa

2

100.0 MPa 80.0 MPa

1

25.0 MPa

0 0

4

2

6

8

Time (t ), h

Fig. 5

0.001%/s

T = 750 °C

•

ε = 1.0%/s

150 0.001%/s

100

0.01%/s

0.001%/s 0.01 1.0

250 200 150 100

Creep curves at several temperature levels

0 1.0

1.5

2.0

2.5

3.0

3.5

Strain (ε), % Stress-strain curves at several temperature levels

900 C n = 5.20

10−3

10−4

10−5

0 0.5

1200 C n = 2.50

1000 C n = 3.00

750 C n = 6.25

50

50 0 0.0

Strain rate (ε), %/s

50

10−2

300 0.2 % proof stress (σ0.2), MPa

Stress (σ), MPa

ε = 1.0%/s

0

Stress (σ), MPa

1

•

150

Fig. 2

12.5 MPa

2

10

(a) Strain-rate dependence of flow stress at e ⳱ 2.0%. (b) Strain-hardening coefficient

Fig. 3 T = 900 °C

200

3.0 MPa

0

(b) 0 200

3

50.0 MPa

1200 C

•

100

5.0 MPa

4

5

150

1200 C 1000 C

25.0 MPa

Creep strain (εc), %

50

(Eq 1)

4

750 C

15

F rij

where K denotes a viscosity constant of the material. w(F) is a function of the static yield func-

•

ε = 1.0%/s 0.01%/s 0.001%/s

100

200 Stress (σ), MPa

In order to open complex relation of stress and strain under engineering environments of loading and temperature, there has been substantial development of the so-called “unified” theories of viscoplasticity in which all aspects of inelastic

dσ/dε, MPa/%

Stress (σ), MPa

200

Inelastic Constitutive Models

behavior are intended to be represented by the same variable. Here, three types of constitutive models that have some possibility of describing the experimental behavior obtained above are considered. Generally, the total strain rate e˙ ij is expressed as the sum of the elastic strain e˙ eij and the inelastic strain rate e˙ Iij , that is, e˙ ij ⳱ e˙ ije Ⳮ e˙ Iij , where the elastic strain rate is given by Hooke’s law. The models for inelastic strain are Perzyna’s model based on the excess stress theory, superposition model, and Bodner’s model. Perzyna’s Model. The excess stress theory assumes that the inelastic strain is produced as:

Creep strain (εc), %

The experimental data on material behavior at high temperature, which involve the conventional tension tests at various strain rates, creep, and cyclic straining under several stress levels, are discussed in this section. Figure 2 indicates a series of stress-strain curves under monotonic tension under several strain rates at 750, 900, 1000, and 1200 C. The variation of strain rate has a large influence on the yield and flow stresses, especially at high temperatures above 1000 C. The relation between strain and flow stress at e ⳱ 2.0% at various temperatures is depicted in Fig. 3(a), and Fig. 3(b) represents the effect of strain rate on hardening coefficient in the same conditions. Figure 4 gives the results of the yield stress depending on temperature. In creep tests, the stress level was chosen to be lower than proof stress r0.2. The creep curves are shown in Fig. 5, which shows that the creep strain at 750 C is very small, while the creep strain over 1000 C is to present enough larger value even when the stress level is lower, so the

flow mechanism of fluid rather than solid seems to govern the deformation behavior at those temperature levels. Figure 6 shows the relation between stress and creep strain in a logarithmic scale. The number n in Fig. 6 represents an exponent in the Norton law e˙ ⳱ Ar n.

Flow stress (σ0.02), MPa

Experimental Results and Discussions

Fig. 4

250

500 750 1000 Temperature (T ), ºC

1250

Relation between yield stress and temperature under different strain rates

5

10

50 100

500

Stress (σ), MPa

Fig. 6

Relation between stress and steady-state creep strain rates

374 / Residual Stress Formation During Manufacturing Processes tion F(rik , eIij , j, T) in stress space involving inelastic strain eIij , hardening parameter j, and temperature T. As a proposal of viscoplastic constitutive theory, Perzyna has proposed four kinds of functions for w(F), among which a special case w(F) ⳱ F is employed to give the viscoplastic strain rate e˙ vp ˙ ijI : ij ⳱ e 3k 2

e˙ vp ij ⳱

1/2

冬冢2 s s 冣 3

kl kl

n

ⳮ ry

冭

sij (3J2)1/2

(Eq 2)

where J2 is the second invariant of deviatoric stress sij , and ry denotes the yield stress. In order to deal with viscous fluid, the authors chose k ⳱ 1⁄3l with the viscosity l. When the value of parameter n tends to unity, Eq 2 is reduced to a uniaxial stress-strain relation under monotonic tension and is then expressed as:

e˙ I ⳱ k(|r| ⳮ ry)

eIij ⳱ eijp Ⳮ eijc

Viscosity (µ), GPa • s

(Eq 4)

The superposition model has various possibilities, but only two forms are employed here. First, a simple superposition model (model A) is considered. The plastic strain and creep strain are simply added to represent the inelastic response of the material. The plastic strain rate epij is given as: skl s˙kl sij (4/9)ry2dry/d e¯ p

(Eq 5)

Here, yield stress ry is identified as a function of equivalent plastic strain ep as:

1200

ry ⳱ r0{1 ⳮ l exp(ⳮb¯ep)}

(Eq 6)

800

where r0, l, and b are material parameters. A classical creep equation of Norton’s law is used to describe the creep strain rate e˙ cij :

400

e˙ cij ⳱ mA 1/mr¯ (nⳮm)/m(¯ec)(mⳮ1)/mSij 0

0

300

600

900

1200

Temperature (T ), C

Fig. 7

Variation of temperature-dependent viscosity

200

Stress (σ), MPa

(Eq 3)

from which the parameter k, or viscosity l is to be identified. The superposition model assumes that the inelastic strain eIij can be decomposed into the time-independent plastic component epij and the pure time-dependent (creep) strain ecij such that:

e˙ Iij ⳱

Experiment Superposition Bodner

150

ε = 1.0%/s

100

rr ˙ 2 r2ydry/d e¯ p

Ⳮ mA1/m(ec)(mⳮ1)/mrn/m

50 0 200 Experiment Perzyna Perzyna + creep ε = 1.0%/s 0.01%/s

100

(Eq 8)

Another superposition model (model B) is chosen that is a combination of the Perzyna’s viscoplastic model and the Norton’s creep equation (Eq 7). When Eq 8 is adopted to be the relationship for the creep process, the inelastic model under uniaxial stress is then expressed as:

0.01%/s

150

(Eq 7)

where r represents the von Mises equivalent stress and ec indicates the equivalent creep strain, while A, n, and m are material constants. Therefore, the constitutive form under the uniaxial stress can be written as: e˙ I ⳱

0.001%/s

Stress (σ), MPa

r |r|

e˙ I ⳱ c(|r| ⳮ ry)

r Ⳮ Ar¯ n |r|

(Eq 9)

Bodner’s Model. A form of Bodner’s model is employed as:

冢 2 冤3J 冥冣 J

e˙ ijI ⳱ D0 exp ⳮ

1 Z2

2

sij 1/2 2

(Eq 10)

50 0.001%/s 0

Fig. 8

0

1

2 3 Strain (ε), %

4

5

Stress-strain curves under different strain rates at 900 C

On the basis of “incremental isotropy” of the flow, the scalar hardening variable Z ⳱ ZI Ⳮ ZD in the model is taken to consist of the parameters of isotropy Z, and directional components ZD. The simple form of the model under the uniaxial stress can be derived:

e˙ I ⳱

冢冤冥冣 |r|

2 1 Z2 D0 exp ⳮ 3 2 r2

r

(Eq 11)

where parameter D0 in Eq 10 and 11 is a material constant.

Simulated Results by Some Constitutive Models Some results of simulated stress/strain behavior using the constitutive models described in the previous section are presented. The parameters of the constitutive models are identified from the conventional experimental data stated in the section “Experimental Procedure.” The temperature-dependent viscosity l in the Perzyna’s model is plotted in Fig. 7, and the parameter n of the superposition models A and B is chosen to be of the same value. Using these parameters, experimental stress-strain curves under compression with results simulated by the three models are shown in Fig. 8. The calculated creep strain by superposition model B is given in Fig. 8, which is compared with the experimental data. In order to explain the work-hardening behavior by these models, Fig. 9 shows two examples of stress/strain behavior under the cyclic path at 900 and 1100 C, which are compared with the experimental data. From Fig. 8, the effect of the work hardening is revealed to be very small when the temperature is above 900 C. The creep curves simulated by superposition model B and experimental data show almost no difference, and the model reflects the mechanical behavior under the cyclic strain path at high temperature. Because the model can be regenerated as a constitutive relationship for viscous fluids, one can say that the Perzyna’s model B superposed by creep can be used to describe the mechanical behavior of the material near melting temperature. Among these models, the Perzyna’s model may also be found to be most suitable to simulate ultrahightemperature behavior including liquid state since it is reducible to the model of the Newtonian fluid above melting temperature.

Numerical Analysis Method of Thermomechanical Problems in Casting One must often resort to a numerical analysis in order to obtain quantitative solutions of nonlinear equations in continuum mechanics. However, regardless of the initial assumptions and the methods to formulate such a problem in evaluating the results by numerical methods, the continuum is, in fact, approximated by a discrete model in the solution process. One such approach, based on the idea of approximating continuous fields, is referred to as the finite-element method. Its simplicity and generality is very attractive, and it is applied to a wide range of nonlinear problems.

Residual Stress Formation during Casting / 375 The thermomechanical problem incorporating solidification processes is a complicated frame of coupling equations, which are not only related to solid mechanics, fluid mechanics, or heatconduction problems, but also involve inelastic constitutive relationships. The finite-element method is a powerful tool for finding the numerical solution to simulate such thermomechanical behavior in casting. This section discusses numerical analysis technology, when the finite-element method is applied to the thermomechanical problem, and what kind of algorithm is employed to solve nonlinear equations in practice. Special attention is placed on the phase transformation in solidification processes in the numerical analysis, and the effects of latent heat and dilation due to phase transformation are considered.

Governing Equation of Thermomechanical Fields From the continuum thermomechanics viewpoint, solidification is a complicated phenomenon characterized by the interaction between temperature and stresses as well as phase transformation from liquid to solid, and the state in solidifying material termed the mushy zone, which is a mixture of solid and liquid phases. In the case of some kinds of casting processes discussed later in this article, molten metal is poured directly into a mold in addition to the existing material. Figure 10 shows boundary movement with increasing volume as well as interface movement during solidification. Here, an initial domain V 0 at time t including liquid and solid is considered, and C0 is an initial boundary for the body. DV and DC denote the increments of volume and boundary during time period Dt. Hereafter any material parameter v is assumed to be expressed by the mixture law using the parameters of solid vs and liquid vl such that: v ⳱ vsns Ⳮ vlnl

冮qu˙ dV ⳱ 冮 i

V

冮

d qu˙i dV ⳱ dt V

d dt

冮 q冢2 u˙ u˙ 1

i i

V 0 rij nj dC Ⳮ

冣

Ⳮ e dV ⳱

Ⳮ hi)ni dC Ⳮ

ⳮ qlsn˙ s ⳱ qf

冮

DV qbi dV

冮

V

冮

C

(Eq 14)

ⳮk

T ni ⳱ h(T ⳮ Tw) xi

(Eq 19)

ⳮk

T ni ⳱ g(T 4 ⳮ T 4w) xi

(Eq 20)

where Tw is the temperature of the coolant, and h and g are the heat-transfer coefficient and Stefan-Boltzmann coefficient, respectively.

Kinetics of Phase Transformation in Solidification

(rij u˙j

q(c Ⳮ bi u˙i)dV

qu¨ ⳱ rij ,j Ⳮ qbi qe ⳱ qc ⳮ

To identify the volume fraction of the solid phase ns during solidification (Eq 18), a phase diagram for the alloying system is employed, and the volume fraction of the solid phase ns is assumed to be determined by the Scheil equation:

(Eq 15)

hi Ⳮ rij e˙ ij xi

ns ⳱ 1 ⳮ ␾ⳮ1(1ⳮk0) and n1 ⳱ 1 ⳮ ns

Here, ␾ is a dimensional function that is dependent on temperature:

(Eq 17)

␾⳱

100

900 C ε = 0.001%/s

0.5

1.0

0

100 1.0 (b)

Hysteresis loop of stress at (a) and (b) 900 C and (c) 1100 C

1100 C ε = 0.01%/s

0

Experiment Perzyna Perzyna + creep Bodner Superposition

50

0.5

0.0

0.5

1.0

100 1.0

Strain (ε), %

Strain (ε), %

(Eq 22)

50

50

0.0

(T ⳮ Ts)/ms (T ⳮ Ts)/ms Ⳮ (T1 ⳮ T )/m1

where ml and ms are the gradients of the liquidus and solidus temperature Tl and Ts with respect to

50

0.5

(Eq 21)

(Eq 16)

Substituting the Fourier law h ⳱ –k(grad T) into Eq 17, one can obtain a heat-conduction

50

(Eq 18)

where c, ls, and f are the specific heat, latent heat, and heat supply, respectively. The boundary condition of heat transfer and thermal radiation can be written as:

(Eq 13)

where e and hi are the internal energy and the heat flux, and c is the heat supply carried by the additional volume of growing body discussed later. Applying Gauss’s theorem to Eq 14 and 15, the local forms of the equation of motion and the energy equation are obtained:

Stress (σ), MPa

Stress (σ), MPa

冮

V

100

0

(a)

d d ˙ i dV DV q u

冢冣

where bi is body force. The total energy balance in the combined region with the surface normal ni is represented by:

50

Fig. 9

冮

T qcT˙ ⳱ k ⳮ rij eijvp xi xi

where q, q0 represent the density of each part. Then the global momentum balance in the combined domain can be represented by:

900 C ε = 0.01%/s

100 1.0

0 0 ˙ i dV Ⳮ V0 q u

equation coupled with heat generation due to mechanical work rij eijvp and latent heat ls as:

Stress (σ), MPa

100

(Eq 12)

with the volume fraction of solid phase ns. When the initial velocity and stress in the domain V 0 are denoted as u0i , and r0ij , and the components in DV are udi and rdij , the linear momentum in the combined body V ⳱ V 0 Ⳮ DV with C ⳱ C0 Ⳮ DC having the velocity ui is reduced to:

0.5

0.0 Strain (ε), %

(c)

0.5

1.0

376 / Residual Stress Formation During Manufacturing Processes the alloying element on the phase diagram, respectively, and k0 is a distribution coefficient representing the segregation effect. When the segregation effect is assumed to be neglected, as in this article, Eq 22 can be reduced to the simple form: ns ⳱

must also be used. Since the viscoplastic strain increment of the element at the kth time step may be written by Taylor’s expansion: {Devp}k ⳱ {˙evp}kDt Ⳮ hHk{Dr}kDt

placement rate ui different from vi. Then, the material-time derivative of any time-dependent scalar, vector, or tensor function w(xi,t) is reduced to:

(Eq 25) w ˙ ⳱

where h 僆 [0,1] and Hk ⳱ ({˙e }/{r})k. Here, the stress increment can be represented by: vp

(T1 ⳮ T)/m1 (T ⳮ Ts)/ms Ⳮ (T1 ⳮ T)/m1

(Eq 23)

{Dr}k ⳱ [De]{Dee}k ⳱ [De]({De}k

which is called the lever rule.

ⳮ{Devp}k ⳮ {Dem}k ⳮ {DeT}k)

Formulation of Numerical Analysis This section considers formulations of finiteelement method in order to simulate the steadyand unsteady-state problems in the casting process. Formulation of Finite-Element Method for Unsteady-State Casting. By using Gauss’s theorem and a weighted residual method on the heat-conduction equation (Eq 18) and boundary condition (Eq 20 and 21), one can obtain a system of finite-element formulation in the weak form of Galerkin type:

⳱ {Qh} Ⳮ {Qf} Ⳮ {Qm} Ⳮ {Qn} Ⳮ {Qr}

qcVi

with the elastic stress-strain matrix [D ]. By substituting the stress increment in the form of Eq 25 into Eq 26, the elastic-viscoplastic stressstrain matrix [Dvp] leads to:

(Eq 24)

where [P], [Hk], [Hh], and [Hf] are the matrices related to capacity, conductivity, heat transfer, and heat radiation, respectively. {Qh}, {Qf}, {Qm}, {Qg}, and {Qr} are the vectors of heat transfer, heat radiation, latent heat, and heat supply due to stress power by the increasing molten metal. Due to the time dependence in the finiteelement equation (Eq 24), time discretization is needed, and a differential scheme based on the Crank-Nicholson method is employed. With regard to the nonlinear solution of the thermal stress problem, an incremental approach

T T ⳮ k ⳮ rij evp ij xi xi xi

冢冣

ⳮ qlsVi

ns ⳱ 0 xi

(Eq 30)

The temperature in each element is expressed by: [Dvp]k ⳱ ([1] Ⳮ [De]hHkDt)ⳮ1

(Eq 27) T ⳱ [N]{T}e

Using the variational principle, the finiteelement equation for stress analysis finally can be obtained as: [K]{Du} ⳱ {DFf} Ⳮ {DFvp} Ⳮ {DFm} Ⳮ {DFT}

˙ Ⳮ ([Hk] Ⳮ [Hh] Ⳮ [Hf]){T} [P]{T}

(Eq 29)

When the term of (w)/t in Eq 29 vanishes for steady state, heat conduction Eq 18 is now reduced to:

(Eq 26) e

w w Ⳮ vi t xi

(Eq 31)

in which [N] is a trial function matrix. The finite element formula of heat conduction equation is obtained by allying the Galerkin method to Eq 30 with the boundary conditions (Eq 19, 20); thus, an integral form is obtained:

(Eq 28)

where [K] is the stiffness matrix, and {DFf}, {DFvp}, {DFm}, and {DFT} are the incremental vectors of load included by body force, effect on inelastic deformation and thermal expansion, and phase transformation, respectively. Formulation of Finite-Element Method for Steady-State Continuous Casting. In the continuous-casting process, the material flows in space, so that the fields of temperature and stress/strain can be generally described in a spatially fixed Eulerian coordinate system xi instead of a Lagrangian coordinate Xi being moved with the material with velocity Vi. In the case of casting, the material velocity Vi is assumed to be a sum of the casting speed vi and the small dis-

冮

V

冢

[N]T qcVi ⳮ

T ns ⳮ rij evp dV ij ⳮ qlsVi xi xi

冣

冮 k[G] [G]{T}dV ⳮ 冮 T

V

T C[N] qdC

(Eq 32)

where [G] ⳱ []T[N]

(Eq 33)

and []T is a differential matrix. The thermal flow q can be calculated by Eq 19 or 20. From Eq 32, the formation for finite element analysis is obtained: ([P] Ⳮ [H]){T} ⳱ {Qs} Ⳮ {Qh} Ⳮ {Qq}

∆V

V εi = Vεi+ ∩ V εi –

Vi– Γi

Γ i ∩ ∆Γ

[P] ⳱

Vi+

兺e 冮VV q]T xi [N]{m}dV

Vi+ Γεi +

Fig. 10

Model considering growth of domain and solidified mushy zone

(Eq 34)

The first term of the right-hand side of Eq 34 represents the latent heat generation due to solidification, and the second and third terms correspond to the heat flows through boundaries Sh and Sq, respectively. Here, there are two terms dependent on the casting speed, which are generally formed by:

∆V

Γ

Γεi Γi+

∆Γ

⳱ 0

(Eq 35)

T

{Qs} ⳱

兺e 冮V qls冤 i ns冥 x

[N]{m}dV

(Eq 36)

When the vector of displacement rate {u} and strain rate {e} in a finite element are interpolated by the nodal displacement vector {u} in the forms:

Residual Stress Formation during Casting / 377 ¯ ˙ }e and {˙e} ⳱ [B]{u˙}e [u˙} ⳱ [N]{u

(Eq 37)

with the strain-displacement matrix [B] dependent on coordinates, the system of stiffness equation in incremental form is derived from Eq 37 by applying the principle of virtual work as: [K]{u˙} ⳱ {L˙ b} Ⳮ {L˙ T} Ⳮ {L˙ m} Ⳮ {L˙ v}

(Eq 38)

The terms in the above equation are summed up with the element matrices generally shown as: [K] ⳱

兺e 冮V [B]T[De][B]dV

(Eq 39)

{L˙ b} ⳱

¯ T [b] 兺e 冮V [N] 冢 xi [N]冣{m}dV

(Eq 40)

{L˙ T} ⳱

兺e 冮V [B]T([␣¯ ]grad[N]){m}dV

(Eq 41)

{L˙ m} ⳱

兺e 冮V [B]T[De]冢[b](ns xi [N]冣{m}dV ¯

(Eq 42)

Here, the temperature and the volume fraction of solid phase at the central point of the element are used in calculation of these matrixes. Total matrix [K] denotes a total stiffness matrix, and [De] represents the elastic stress-strain matrix, while {r} and {V} are the vectors of deviatoric stress and casting speed. Other vectors {␣}, {b}, and scalar w are: [De]ⳮ1{r} T

(Eq 43)

¯ [b] ⳱ [b] ⳮ [De]ⳮ1{r} ns

(Eq 44)

[␣] ¯ ⳱ [␣] ⳮ

x ⳱

冢

1 ry 1 ⳮ 2l (3J2)1/2

冣

(Eq 45)

Algorithm of Numerical Analysis In the process incorporating phase transformation, the coupling effect between the fields of temperature, microstructure of material, and stress/strain are essentially to be taken into account in the analysis. As stated in the previous section, however, the numerical analysis of steady-state temperature distribution coupled with solidifying phase change is made independently followed by stress analysis based on obtained temperature field. Here, and assumption is made on the velocity field in both analyses that the casting velocity vi is large enough compared with the displacement rate ui in the case of uniform casting, which follows that the velocity {v} in Eq 35 to 42 is to be replaced by the uniform casting speed {v}. Liquidus and solidus lines are determined by solving the finite element Eq 24 by neglecting the first term {Qs} on the right-hand side repre-

senting latent heat generation in the first approximation. By use of the lever rule, the volume fraction of solid ns is identified, and the term {Qs} is evaluated. The same iteration procedure was repeated to obtain the converged distributions of temperature and phase. The obtained result is applied to determine the displacement rate vector {u} in Eq 37, and displacement ui, strain eij, and stress rij can be evaluated by integrating the rate e˙ ij , and r˙ ij . Moreover, Eq 24 and 38 derived in the previous section are nonlinear with respect to the temperature {T} and displacement rate {u}, respectively, and special attention is necessary in solving the equations. Equation 34 has only one term for latent heat generation determined by volume fraction of solid ns, thus, it employs the simple method of iteration. As for stress analysis, on the other hand, the nodal forces on the right-hand side of Eq 38 are the nonlinear functions of temperature T and structural change ns being dependent on the rate {u}. Furthermore, in the region of molten state, a large strain rate is produced in spite of a small variation of nodal forces. A modified NewtonRaphson scheme, or initial method, was adopted to solve the nonlinear equation.

Residual Stress Formation during Semicontinuous Casting Vertical semicontinuous direct-chill casting process is one of the most efficient methods of producing ingots of aluminum alloys and other metals. It is beneficial for optimizing the operating conditions to simulate the thermomechanical field in the solidifying ingot. Many reports have been published concerning such finiteelement analyses of the temperature distribution incorporating solidification, but a few papers treat the induced stress/strain field: simulations of thermal stress in continuous-casting slab were made using an elastic-plastic constitutive model, for example, Grill, Brimacombe, and Weisenberg (Ref 23) and Sorimachi and Brimacombe (Ref 8), and viscoplastic stresses were simulated based on the solidification analysis by Williams, Lewis, and Morgan (Ref 1). However, in their studies, the influence of casting speed was neglected, so that the numerical simulation along with the variation of casting conditions cannot be realized. In order to solve this problem, Ju and Inoue (Ref 24–26) proposed a numerical simulation method by Eulerian coordinate, and application to the continuous-casting process of steel slab was carried out. The aim of this section is to apply the coupled method of temperature and stresses incorporating solidification to semicontinuous direct-chill casting of aluminum alloy. When the bottom block plate is located at the upper position and the length of the growing ingot is small, the temperature, liquid/solid interface, and stresses in the ingot vary with time, both in the sense of space and of material. However, when the ingot becomes long enough, the physical field in the

upper part is regarded to be time-independent or steady in the spatial coordinate fixed to the system. In the first part of this section a steady-state heat-conduction equation with heat generation due to solidification is formulated in a spatial coordinate system when considering the material flow. A numerical calculation for the temperature in the solidifying ingot as well as the simulation of the location of liquid/solid interface is carried out by finite-element analysis. Most metallic materials at low temperature may be treated as an elastic-plastic solid. However, if they are heated beyond the melting point, the materials can be regarded as viscous fluid, and they behave in a time-dependent inelastic manner at high temperature close to the melting temperature. Therefore, a unified constitutive model needs to be established to describe the elastoplastic and viscoplastic behavior of the solidified part of the ingot as well as the viscous property of the liquid state. Taking into account the effects of such phenomena, a modification of Perzyna’s constitutive model as in other sections of this article is presented in the second part of the section, and some experimental results of the viscosity appearing in the model are presented for the aluminum-zinc type alloy employed. Using the model, elastic-viscoplastic stresses are calculated in the ingot to find the residual stress distribution and are verified by the measured data from the hole-drilling strain-gage technique. Finally, results of numerical simulation are presented on the influence of operating conditions on temperature and stresses, such as ingot size, casting speed, initial temperature, and so on, to give fundamental data for optimizing the operating condition.

Finite-Element Model and Casting Conditions The theory and the procedure developed as discussed previously are now applied to the simulation of the vertical semicontinuous directchill casting process shown schematically in Fig. 11. The material treated is an aluminum-zinctype alloy with 5.6% Zn and 2.5% Mg. A quadrilateral finite-element mesh pattern of 600 elements with 1941 nodes illustrated in Fig. 12 is employed for both analyses of temperature and stress fields. The boundary condition for heat conduction is assumed in such a way that the temperature of the meniscus of molten metal is prescribed to be w0, and that heat is insulated along the central line and the bottom of the ingot as well as the surface contacted with the refractory. The cylinder facing to the mold is regarded as the boundary Sq on which heat flux is given, and the other part of the surface Sh is given by a heattransfer boundary due to cooling of water. Figure 13 depicts the measured heat flux q absorbed by the mold, and heat-transfer coefficient h depending on flow rate of water is shown in Fig. 14. Other data used for temperature calculation incorporated with solidification are shown in Table

378 / Residual Stress Formation During Manufacturing Processes 3. Characteristic results of calculated temperature and residual stresses for an ingot 1 m in length with the diameter of 240 mm are compared with experimental data to verify the method. Simulations in other cases of different

Molten metal

Refractory

operating conditions such as casting velocity, size of the ingot, and cooling rate are also made.

Results of Simulation Figure 15 indicates a bird’s-eye view and an isothermal representation of calculated temperature distribution. The lines denoted by Tl and Ts in the figure are the liquidus and solidus tem-

Mold Water flow

Billet

Heat flux (q), cal/mm2 • s • °C

Cooling water

0.8

0.6

0.4

0.2

0 0

Bottom block

Withdrawal

Fig. 11

Schematic of semicontinuous vertical directchill casting

Refractory

r

Mold

Heat-transfer coefficient (h), kcal/m2 • h • °C

Fig. 13

V

40

80

120

Distance from top of mold (d ), mm Variation of heat flux from top of the mold

1.6

Wl = 145 l/min 115 85 1.2

0.8

0.4 0

100

200

300 1000

Distance from top of mold (d ), mm

Fig. 14

Table 3

Distribution of heat-transfer coefficient depending on discharge of cooling water

Material properties of aluminum 7075

Heat conductivity, cal/(mm • C) Density, g/mm3 Specific heat, cal/(g • C) Latent heat due to solidification, cal/g Casting speed, mm/min Liquidus temperature, C Solidus temperature, C Gradient of liquidus line, C/% Gradient of solidus line, C/% Young’s modulus, MPa Poisson’s ratio Viscosity, MPa • s Initial yield stress, MPa Hardening coefficient, MPa

z

Fig. 12

Finite-element mesh pattern for semicontinuous vertical direct-chill casting

perature, respectively. Figure 16 shows the data replotted to give the temperature change at the center and on the surface, while the circles represent the measured temperature by thermocouples. The fact that the calculated temperature on the surface coincides well with the measured data may indicate the validity of the simulation method. Change of the volume fraction ns at four characteristic points along the distance from meniscus is represented in Fig. 17, which may give the information on progressing mode of solidification and thickness of solidified shell. For the simulated results of temperature and solidification mode presented above, stress analysis was carried out for the entire area of the ingot, including the molten metal, by use of the finite-element equation (Eq 28) based on the elastic-viscoplastic constitution model (Eq 2). The displacement mode is depicted in Fig. 18. Contour of radial, tangential, and axial stress distributions rr, rh, and rz are shown in Fig. 19. The contours of stress distribution are represented in Fig. 20. Examples of the calculated stress distribution by elastic-viscoplastic constitutive model and the one by time-independent elastic-plastic model are shown in Fig. 21. When compared with each other, the viscoplastic stress analysis gives smaller results, at least on the surface, than elastic-plastic stresses. The stresses are found to generate at the location where the solidification starts (see Fig. 19 and 20), and the radial distribution becomes steady going downward owing to the flatter temperature distribution. In order to examine this effect, the stress distributions at several locations are given in Fig. 22, in which the distribution at the very end of the ingot (Fig. 22d) can be regarded to be residual stresses. Open-circle data points in the figure indicate the experimentally measured residual stresses by a hole-drilling strain-gage method (Ref 27). The fact that the experimental data coincide well with the analytical results suggests the validity of the simulation procedure based on the viscoplasticity developed here. As seen from Fig. 22, the shear stresses are insignificant in the area of mol-

Thermal expansion coefficient, 1/C Dilation due to solidification

k1 ⳱ 0.0425; ks ⳱ 0.0125 Ⳮ 0.0583T q ⳱ 2.8 ⳯ 10ⳮ3 c1 ⳱ 0.015 Ⳮ 0.00173T; cs ⳱ 0.083 Ⳮ 0.00267T ls ⳱ 93.16 V ⳱ 80.0 T1 ⳱ 638 Ts ⳱ 600 m1 ⳱ 3.69 ms ⳱ 9.09 E1 ⳱ 500.0; Es ⳱ 75000.0 ⳮ 76.3T m ⳱ 0.33 l ⳱ 3700.0 (T ⱖ 346 C) l ⳱ 0.007178T 2 ⳮ 21.1698T Ⳮ 10160.7 (T 346 C) ry0 ⳱ 2.0 (T ⱖ 346 C) ry0 ⳱ 150.0 ⳮ 0.428T(T 346 C) H ⬘ ⳱ 350.0 ⳮ 0.13333T (T ⱕ 150 C) H⬘ ⳱ 330.0 ⳮ 1.683 (T ⳮ 150) (150 T 346 C) H⬘ ⳱ 0.132 (T ⱖ 346 C) ␣1 ⳱ 33 ⳯ 10ⳮ6; ␣s ⳱ 21.8 ⳯ 10ⳮ6 Ⳮ 0.2T ⳯ 10ⳮ7 b ⳱ ⳮ7.5%

Residual Stress Formation during Casting / 379 ten state, and the normal stresses rr, and rz (see Fig. 19 and 21) are regarded to be hydrostatic stresses, which means that the constitutive equation employed here reveals modified deformation of the liquid.

fect of temperature and stress distributions on the casting speed, size of the ingot, and cooling condition. Figures 23 and 24 represent examples of temperature profiles for different casting speed and the radius of ingots with various cooling rates. The effect of discharge of cooling water on thickness of the mushy zone at the center is summarized in Fig. 25. The effects of casting speed and ingot radius on the stress rh are represented in Fig. 26 and 27, respectively, and the relation between stresses and casting speed is

Simulations for Other Operating Conditions Let us apply the procedure to cases with other operating conditions. Focus is placed on the ef-

Temperature (T ), C

TI Ts

1000

600 800 400 600 200

40

s (r

diu

Ra

200 120

om

e fr

anc Dist

80

), m m

Fig. 15

), s (z

400

0

mm

cu enis

m

0

Calculated temperature profile. V ⳱ 80 mm/min

800 Experimental Calculated r = 120 mm

1.0 Volume fraction of solid, ξs


600

400 Center 200 Surface

0.8 0.6 0.4

r = 0 mm r = 380 mm r = 76 mm r = 120 mm

0.2 0

0 0

100

200

300

80

400

Temperature variations at the center and the surface of the ingot. V ⳱ 80 mm/min

Displacement (Ur), mm

Fig. 16

100

120

140

Fig. 17

Volume fraction of solid along the distance from meniscus. V ⳱ 80 mm/min

1000

0.2 800

0.0 600

0.2 400

0

Ra

40

diu

200

80

s (r

120

), m

0

m

Fig. 18

160

Distance from meniscus (z ),mm

Distance from meniscus (z ), mm

Displacement mode. V ⳱ 80 mm/min

nce

a Dist

from

r (z

te cen

m

), m

summarized in Fig. 28. The simulated stresses varying with the discharge of cooling water is also plotted in Fig. 29. The calculated results shown above seem to simulate the characteristics of temperature and stresses depending on operating conditions. If the data of such simulation is accumulated at different operating conditions as shown in Fig. 23 to 27, it would be possible to optimize the design of the system.

Residual Stress Formation during Centrifugal Casting From the viewpoint of the solidification microstructure, materials present various solidifying types: for example, solidification of pure media and eutectic material should be a smooth interface between liquid and solid (Ref 28, 29); however, solidification of the alloy has no obvious interface, but has been a mixture domain of liquid and solid. Furthermore, as stated in the section “Numerical Analysis Method of Thermomechanical Problems in Centrifugal Casting,” solidification with growing domain is a practical process, and it has many important effects in some practical engineering problems such as centrifugal casting, welding, and so on. It is necessary to consider the thermomechanical process accompanied by heat supply due to increment or input of the material as time goes on. Because moving the total domain as well as the boundary will cause an energy variation in the total system, this problem has general significance. However, because it is difficult to consider the entire phenomenon, the beginning of the study only considers a static problem involving a moving boundary due to increment of domain, and this section discusses an unsteadystate solidification process. In order to describe the inelastic behavior using a unified mathematical model, two aspects are emphasized. One is that the process is associated with a nonlinear problem with a moving external boundary depending on time and location, and the other is characterized by the fact that it incorporates phase transformation such as solidification based on the mixture theory. For the numerical analysis of the solidification and growth of domain, a finite-element scheme proposed in the section on numerical analysis is used. Here, heat input due to successively increasing liquid metal was introduced into the heat-conduction equation by adding the newly developed elements in the finite-element scheme. Moreover, latent heat generation due to solidification is also taken into account by varying fraction of solidified volume, which can describe the state of the mushy zone. Simultaneously, a method of stress analysis based on the obtained temperature distribution is developed, where an elastic-viscoplastic constitutive relationship capable of describing the viscoplastic solid as well as viscous fluid is employed. Here, in order to simulate stress and deformation, one assumes that the velocity along direction Vr is small and has the same stress state on contacted

380 / Residual Stress Formation During Manufacturing Processes boundary. Examples of numerical calculation of temperature with solidification and stress are presented for some practical cases of centrifugalcasting processes, and the validity of calculated temperature field under several operating conditions is discussed in comparison with the experimental results. Stress (σr ), MPa

1000 800

100 600

50 400

0.0 40 80

200

Stress (σ ), MPa

m

), m

mm

e fro

anc

Dist

0.0

1000 800

100 0.0 100 0 40 80

600 400

us (

200

m

e fro

anc

Dist

0.0

isc men

z ),

mm

Stress (σz ), MPa

1000 800

100 0.0 100 0 40 80

600 400

cus

200

m

e fro

anc

Dist

0.0

Fig. 19

s (z

cu enis

is men

(z ),

mm

Contour of radial (rr), tangential (rh), and axial (rz) axial stress distributions. V ⳱ 80 mm/min

0

σθ

σr

σz

1000

0

24

48

72

96 120

Radius (r ), mm

Fig. 20

0

24

96 120

0

24

48

MPa 10 .2

MPa

MPa 54.2

Pa 72

Radius (r ), mm

40.5

Pa 43.1 M

Pa 0M

7 5.

2.76 MPa

48

12 6.0 M

167.2

800

23.7 MPa

MPa

32.1 MPa

98.7 M

1.02 MPa

600

49.5 MPa

70.1 MPa

400

Pa

13.6 MPa

Distance from meniscus (z), mm

200

72

96 120

Radius (r ), mm

Isostress contours. Radial (rr), tangential (rh), and axial (rz) axial stress distributions. V ⳱ 80 mm/min

Analysis Models and Casting Conditions Centrifugal casting is one of the most efficient processes for producing pipes, tubes, cylinder sleeves, and so on. It is well known that the technique utilizes the centrifugal force generated by a rotating cylindrical mold to fit the molten metal on the mold wall and to form the desired shape, as shown in Fig. 30. Many problems still remain in the process regarding thermal and mechanical behaviors, for example, progressive domains of molten and solidified metals, moving interface between both parts, and development of stresses along the solidified field. Centrifugal-casting methods have been developed to make many machine parts and structures. However, there are no numerical analyses of the casting process, because it is difficult to solve temperature field, solidification, and residual stress field due to the growing domain in the casting process. In order to simulate the process, the authors applied the above-mentioned analytical procedure to the casting practice. In this section, centrifugal casting that produces rolled products and pipes are calculated. An axisymmetrical model as shown in Fig. 31(a) is employed for finite-element analysis for the first model (I), where both ends of mold are fixed during casting process and the casting roll is long (L ⳱ 5 m) with a large diameter (internal diameter of mold do ⳱ 1270 mm). Moreover, in order to evaluate the distribution of temperature and stress fields in the end corner of a pipe, the authors chose another model (II) with finite length (L ⳱ 1 m) as shown in Fig. 31(b). In model I, the material used for the pipe is a nickel-chromium alloy, and the metal mold is made of a carbon steel. The rotating speed and the initial mold temperature is x ⳱ 440 rpm and T0 ⳱ 100 C, respectively. The initial temperature of molten metal was Ti ⳱ 1330 C with liquidus temperature Tl ⳱ 1230 C and solidus temperature Ts ⳱ 1140 C. Since the heat is transferred from the mold surface to air, the heattransfer coefficient is taken as h ⳱ 2.78 ⳯ 10ⳮ3 cal/(mm2 • s • C). The materials of the metal mold and pipe of model II are both 7075 aluminum alloy, as used in the process described in the section “Residual Stress Formation During Semicontinuous Casting.” The initial mold temperature and molten metal temperature are chosen as T0 ⳱ 650 C and Ti ⳱ 680 C, and liquidus and solidus temperature are Tl ⳱ 638 C and Ts ⳱ 600 C. The heat-transfer coefficient is chosen as h ⳱ 5.56 ⳯ 10ⳮ3 cal/(mm2 • s • C). The rotating speed is kept to x ⳱ 540 rpm, and the time period of


0 6M Pa

1000


6 7.

5M Pa

Pa

1 6

3

M

Pa

124 M

MPa 12 .8

27.8 MPa

v = 80 mm/min

640 C

1 1

MPa 52 .5

MPa 76.2 164 M

Pa

600

79.5 M

Pa

400

800

24

48

72

96 120

0

24

48

72

v = 95 mm/min

640 C

640 C

250

82 0

Radius (r ), mm

Fig. 21

v = 70 mm/min

Mold refractory

20 MPa

200 Distance from meniscus (z), mm

28.1 MPa

0.0

85

96 120

110

Radius (r ), mm

500

Calculated stresses (rh) by (a) elastic-viscoplastic and (b) elastic-plastic models. V ⳱ 60 mm/min

0

120 0

120 0

120

Radius (r ), mm Isothermal lines for different casting speeds

v = 70 mm/min

0.0

v = 60 mm/min

200

Stress, (σr, σθ, σz), MPa

100

0.0

100

200

100

0.0

100

0

24

48

72

98

120

200

0

24

Radius (r ), mm



100

0.0

640

640

110

110

72

98

500

120

0

150 0

250 0

300

Radius (r ), mm

Fig. 24

100

0.0 σr σz

100

0

24

48

72

98

120

200

Radius (r ), mm

Fig. 22

660 C

Isothermal lines for different ingot radii

200

100

(c)

48

(b) 200

660 C

400

Radius (r ), mm

(a)

200

640

110

Thickness of mushy zone (ts), mm


200


660 C

v = 35 mm/min Mold refractory

Fig. 23

σθ τrz 0

24

48

72

98

120

38

v = 80 mm/min 36

34

32

30 80

Radius (r ), mm

100

120

140

150

Discharge of cooling water (wt), l/min

(d) Stress distribution in several sections of ingot. (a) z ⳱ 121 mm. (b) z ⳱ 400 mm. (c) z ⳱ 850 mm. (d) z ⳱ 1000 mm

Fig. 25 water

Relation between thickness of mushy zone at the center depending on discharge of cooling

382 / Residual Stress Formation During Manufacturing Processes outer surfaces, where solid lines represent the results of coupled calculation that considered the heat supply of stress power, while dashed lines are the uncoupled results without effect of stress power. The simulated temperature is compared with experimental results represented by open circles measured by radiation thermometer. Figures 33 and 34 depict the distributions of density and volume fraction of solid in radial direction as the parameter of time. From the results, it can be seen that the cooling rate on the inner surface tends to be slow because of the latent heat generation due to solidification, while the rate becomes larger after the solidification was completed. The distribution stress associated with

Results of Simulation for Model I. As the result of temperature, lines in Fig. 32 show the temperature variations with time on the inner and

v = 60 mm/min

1000

0

24

72

Fig. 26

v = 80 mm/min

0

24

48

2.76 MPa 23.7 MPa 7 5.0 12 MP 6.0 a MP a

a

98.7 M

Pa

MP 83 .2

72

Pa

32.1 MPa

Pa .0 M

167.2 M

12 6

31.6 MPa

169.1 M 96 120

Radius (r ), mm

3.51 MPa

MPa

Pa

MPa

99.5

5 48

12 8

800

27.6 MPa

164 M

Pa

600

2.5

76.2 M

Pa

MPa

400

23.4 MPa

200 Distance from meniscus (z), mm

v = 75 mm/min

30.1 MPa

0

Stress (σz, σθ), in solid shell, MPa

Results of Numerical Analysis

96 120

0

w l = 112 L/min

48

72

96 120

Radius (r ), mm

w l = 142 L/min

0

45

w l = 245 L/min

0

11.0 MPa

10.9 MPa

9.9 MPa

2 55.


.7 57

500

σθ

35 σz 30 25 55

85 70 Casting speed (v), mm/min

100

Relation between stresses at the center of ingot and casting speed

40

σz σθ

20

0 70

500

r = 120 mm w l = 115 mm

40

Fig. 28

Stress distributions (rh) for different casting speeds

0

50

60

24

Radius (r ), mm

development of solidification is represented in Fig. 35. Compared with the data of volume fraction of solid shown in Fig. 34, stress in liquid state, in fact, vanishes, while drastic variation of the stresses is observed in the mushy zone between liquid end and solid front. Simulated results of the residual stresses are plotted in Fig. 36 when the cast region and mold cooled down to room temperature at t ⳱ . Results for Model II. Figure 37 shows the temperature distribution at different time steps. Figures 38 and 39 represent the variation of density and volume fraction of solid. It follows from the results that the variation of temperature, density, and volume fraction of solidus in the corner of model II is increased very rapidly due to cool-

Stress in solid shell, MPa

the pouring molten metal is 3 s. Mechanical parameters of the alloy as shown previously also are employed. The same thermal radiation coefficient g ⳱ 7.028 ⳯ 10ⳮ7 cal/(mm2 • s • K4) is used for two models, and the radiation condition is situated on the inner surface of pipe. In model I, heat insulation condition is assumed on both sides of the model, while it is also imposed on the outer surface of the mold in model II.

110 130 90 Discharge of cooling water (wt), t/min

Relation between stresses at the center of ingot and discharge of cooling water. V ⳱ 80 mm/ min. z ⳱ 112 mm

Fig. 29

500 Ladle Molten pool

−35.4

150 Radius (r ), mm

−129.0

Metal mold −35.7 −82.5

−46.7 1000

0

Fig. 27

−113.0

126.0

80.7

10

4.0

10

1.7

.5

86

1000

1000 0

250 Radius (r ), mm

150

0

20

300

Bearing

Radius (r ), mm

Stress distributions (rz) dependent on effect of ingot diameter and cooling water rate. V ⳱ 80 mm/min

Fig. 30

Schematic of centrifugal casting

Residual Stress Formation during Casting / 383 and fluid velocities in both liquid phase and solid phase. On the other hand, due to the symmetry to the central line, a half part of the model shown in Fig. 42(b) is treated for the analysis.

Calculated Results of Material A

Strip continuous casting by twin-roll method is a promising technology. Not only can the casting method save energy, but it can also reduce production costs in the manufacturing of material. However, it is difficult to control the quality of the strip because of the existence of the deformation of the strip itself, due to thermal expansion or thermal stress. Here, there are two key points: first, if the solidification is completed before the liquid reaches the minimum clearance point between the rolls, then the strip will incur a fixed gap. Therefore, one key point is controlling solidification. Another key point is that the viscoplastic deformation incorporating material flow has to be considered in this thermomechanical process.

Continuous Casting by Twin-Roll Method The twin-roll continuous-casting system is schematically illustrated in Fig. 42(a). In this process, molten metal is sent between two rolls rotating in opposite directions with some angular velocity. The level of the molten metal is always kept constant by overflowing the excess molten metal from the nozzle. As soon as the molten material is poured into the rolls, solidification takes place on the roll surface, which is cooled by circulating water inside the roll. Therefore, the problem then is to find this steady solidification profile and the distribution of temperature

The procedure developed above is now applied to the simulation of the thin-slab casting process under some operating conditions. The results are summarized as follows. Figure 43 represents the finite-element discretization of the whole region of the strip and roll. The approximate velocity field based on the incompressibility condition and boundary conditions of velocity due to rotation of roll is shown in Fig. 44. The roll surface as well as the boundary in contact with the roll and strip is assumed to belong to heat-transfer boundary and the surface of the strip to the heat-radiation boundary. In order to verify the numerical analysis method proposed in the section on numerical analysis, two kinds of casting material are taken into consideration: one kind of material (material A) is a low-melting-point alloy (tin-bismuth alloy), and the other (material B) is SUS 304 steel mentioned in the section “Inelastic Behavior and Unified Constitutive Theory of Metallic Material in Solidification.” The casting speed is set at Vc ⳱ 77.2, 64.5, and 51.1 mm/s. The thickness of the slab is 3 mm. The initial temperature of the molten metal is T0 ⳱ 190.0 and 185.0 C, respectively. The material coefficients of tinbismuth alloy are used for the temperature calculation and stress analysis. The initial temperature of rolls is chosen as Tm ⳱ 10 C. The liquidus temperature and solidus temperature of tin-bismuth alloy are Tl ⳱ 150 C and Ts ⳱ 138 C. When the casting process of SUS 304 is considered, the thickness of the slab is 1 mm, and two casting speeds are set: Vc ⳱ 400 and 600 mm/s. The properties of material can be found

Simulated results of steady temperature distribution in both the strip and roll are shown in Fig. 45(a) for the casting speed of 77.2 mm/s with T0 ⳱ 190 C on the meniscus, and Fig. 45(b) depicts the volume fraction of solid phase, in which the line indicated by ns ⳱ 1.0 shows the solid front. Measured temperature distribu-

1200 Temperature (T ), C

Analytical Models and Parameters

Residual Stress Formation During Strip Continuous Casting by TwinRoll Method

in the section “Inelastic Behavior and Unified Constitutive Theory of Metallic Material in Solidification.”

Measured Uncoupled method Coupled method

800

400

0

0

1000

Fig. 32

2000 3000 Time(t ), s

4000

Temperature distribution (model I)

2010

1050 × 10−3 Density, (ρ), g/mm3

ing from both ends. Figure 40 shows the development of equivalent stress in the growing domain under the solidification process. Residual stresses at the end of cooling are shown in Fig. 41.

480

8.0

7.5

t = 210 s 7.0 500

550

600

635

Radius (r ), mm

Fig. 33

500

2010

850 mm

Volume fraction of solid, ξs

r = 635

Additional element

r = 108

114 mm

1050

Additional element

Fig. 31

6

Metal mold

(a)

Density distribution (model I)

5.0

(b) Finite-element division. (a) Model I. (b) Model II

510

1.0

t = 210 s 0 500

550

600

635

Radius (r ), mm

Fig. 34

Distribution of volume fraction of solid (model I)

384 / Residual Stress Formation During Manufacturing Processes ure 53 shows that temperature distribution on the slab surface at the roll outlet presents violent fluctuations due to latent heat generation by solidification domain. When the casting speed Vc is raised, the temperature fluctuation toward a small range is presented on the slab surface. The distribution of the horizontal stress rx from meniscus to the junction point at the roll outlet is represented in Fig. 54. From these figures, the high-level stress field by rapid cooling is found to occur near the shell surface, and the equivalent stress distribution on the slab surface at the roll outlet also presents violent fluctuations due to the temperature fluctuation. The equivalent stress analysis results based on several constitutive equations are plotted in Fig. 55. In the section of slab at the roll outlet, calculated equivalent stress by three types of constitutive equations is approximated to the same distribution. However, when casting speed is lower, the effect of creep strain is evident.

Calculated Results of Material B Simulated results of steady temperature field in both the strip and roll are shown in Fig. 51(a) and (b) for the casting speed of 400 and 600 mm/ s. The fraction of solid phase in solidified region of the strip with liquidus and solidus temperature Tl ⳱ 1460 C and Ts ⳱ 1399 C is depicted in Fig. 52. Temperature distribution along the central line is plotted in Fig. 53. In the early stage of rapid cooling by the roll, the solidified shell is seen to grow gradually toward the central part. The change in casting speed is known to affect the distribution of temperature and shell thickness. As the casting speed becomes faster, the position of liquid line moves downstream. Fig-

in some casting processes, which include semicontinuous casting, centrifugal casting, and continuous casting by twin-roll method. A method to simulate solidification and temperature as well as stress distribution in casting is formulated, and the implementation by finite-element cal-

100 Mold

0 50 σr σe σz

100 150 200 500

Concluding Remarks

600

550

650 700

750 800 850

Radius (r ), mm

Fig. 36 Temperature (θ ), C

This article provides a general discussion on the framework of thermomechanical theory incorporating solidification, and a series of practical analytical schemes based on the finiteelement method are proposed. These schemes are applied to simulate thermomechanical fields

Casted region

50 Stress, (σr, σθ, σz), MPa

tion by thermocouples along the central line and surface of the strip are plotted by data points in Fig. 46 and 47, while the solid lines indicate the calculated temperature results. It may be suggested from the figure that the simulations give fairly good agreement with the experiment. The stress distribution is shown in Fig. 48, and the results at several locations are given in Fig. 49. The distribution at the very end of the strip can be seen to grow up again, which may become the origin of residual stresses. Figure 50 gives the comparison of the measured data of the thickness with the calculated results.

700 400 0 100

t = 0.5 s 200

Di

t = 450 s

Residual stress distribution (model I)

Solid front

σr σe σz

t = 300 s

Liquid end

Temperature (θ ), C

z

st a 300 pl nce an fr e om ( 400 ), ce m nt m ra l

700

108 112 Radius (r ), mm

400

t = 2.0 s

0 100 200

l ra nt ce m m fro ), m ce (z an e st lan Di p

t = 210 s

300

400

20

Liquid front

112

104

400 0 100

t = 4.0 s

200

20 500

Casted region

700

300

400

Mold

600

l ra nt ce m m fro ), m ce (z an e st plan

t = 30 s

0

800

112

Radius (r ), mm

Fig. 35

108

Radius (r ), mm

700

Di


t = 90 s

Temperature (θ ), C

t = 120 s

Stress distribution (model I)

108

104

Radius (r ), mm

Fig. 37

Temperature distribution (model II)


200

st an 300 of ce m fro ol m d, b 400 m ott m om

108 112 Radius (r ), mm

2.8 2.6

t = 2.0 s 2.4 100 200

Di

st

400 Di

Variation of density (model II)

112 108

1.0

104 Radius (r ), mm

0 400

l

st an pl ce an fr e om ( ), ce m nt m ra

200

0.1 0

100

z

Di

104 108 Radius (r ), mm 112

400

t = 1.0 s

300

1.0

200

0.5

z

100

0

104 108

Radius (r ), mm 112

t = 2.5 s 300

Di

st a 200 pl nce an fr e om ( ), ce m nt 100 m ra l

108

112

104 Radius (r ), mm

Fig. 39

0.3 0.2

t = 2.0 s

300

st a pl nce 200 an fr e om ( ), ce m nt 100 m ra l

104 112 Radius (r ), mm

Fig. 38

108 Radius (r ), mm

0

z

an 300 of ce m fro ol m d, b 400 m ott m om


Di

112

300

l

t = 1.0 s

2.4 100

1.0

400

t = 0.5 s

an pl ce an fr e om ( ), ce m nt m ra

2.6

t = 1.0 s

st 200 a pl nce an fr e om ( ), ce m nt 100 m ra l

Di st

112 Radius (r ), mm

2.8

300 Di

Variation of volume fraction of solid phase (model II)

400 300

t = 1.5 s

10.0

an pl ce an fr e om ( ), ce m nt m ra l

108

400

200

5.0

z

100

0

104

Di st

Di 200 st an 300 of ce m fro ol m d, b 400 m ott m om

0

Equivalent stress (σ), MPa

t = 0.5 s


2.4 100

1.0

4. D.Y. Ju and T. Inoue, Metallo-Mechanical Simulation of Centrifugal Casting Process of Multi-Layer Roll, J. Mater. Sci. Res. Int., Vol 2 (No. 1), 1996, p 18–25 5. H. Matsui, D.Y. Ju, and T. Inoue, Inelastic Behavior and Unified Constitutive Equations of SUS 304 at High Temperature, J. Soc. Mater. Sci. (JSMS), Vol 41 (No. 466), 1992, p 1153–1159 6. D.Y. Ju, T. Inoue, and H. Matsui, ViscoPlastic Behaviour of SUS 304 Stainless Steel at Ultra-High Temperature, Advances in Engineering Plasticity and Its Application, D. Lee, Ed., 1993, p 521–528 7. P. Perzyna, Thermodynamic Theory of Viscoplasticity, Advance of Applied Mechanics, Vol 11, Academic Press, 1971, p 313–354 8. K. Sorimachi and J.K. Brimacombe, Improvements in Mathematical Modeling of Stresses in Continuous Casting of Steel, Iron Steel., Vol 4, 1977, p 240–245 9. K.S. Chan, S.R. Bodner, K.P. Walker, and U.S. Lindholm, A Survey of Unified Constitutive Theories, Proc. Second Symp. Nonlinear Constitutive Relations for High Temperature Applications (Cleveland, OH), 1984, p 108–112 10. P. Perzyna, The Constitutive Equations for Rate Sensitive Plastic Materials, Arch. Mech. Stos., Vol 20, 1968, p 499–512 11. S.R. Bodner and Y. Partom, Constitutive Equations for Elastic-Viscoplastic Strain Hardening Materials, J. Appl. Mech., Trans. ASME, Vol 42, 1975, p 385–389


2.6

z

Density (ρ = 103), g/mm3

2.8

REFERENCES 1. J.R. Williams, R.W. Lewis, and K. Morgan, An Elastic-Viscoplastic Thermal Stress Model with Applications to the Continuous Casting of Metals, Int. J. Num. Meth. Eng., Vol 14, 1979, p 1–9 2. T. Inoue, Metallo-Thermo-Mechanical Coupling—Analysis of Quenching, Welding and Continuous Casting Processes, Berg. Hu¨tten. Monatsh., Vol 132, 1987, p 63–75 3. T. Inoue and D.Y. Ju, Thermo-Mechanical Simulation of Some Types of Steady Continuous Casting Processes, Advances in Continuum Mechanics, O. Bruller, V. Mannl, and J. Najar, Ed., Springer-Verlag, 1991, p 389–406

z



posed in the section on numerical analysis are verified by comparing the calculated results with the experimental data for temperature on the inner surface. The relaxation of temperature variation along time dependence of increment of molten metal and the occurrence of the latent heat in solidifying domain is displayed.

may describe the stress and deformation in the entire region of the solidifying process including liquid and solid states. ● In the simulation of stress field, the development of stresses with a following increment of molten metal is presented. On the other hand, when the effects of centrifugal force are considered, the residual stresses in the casting process would occur with the compressive stress.


● The theory and method of simulation pro-

● The unified inelastic constitutive equation


culation is presented in this article as an example of the application of theory and procedure developed in the proceeding. A modification of Perzyna’s viscoplastic constitutive relationship is proposed, which reflects actual liquid-solid phase transformation during the casting process. The results of simulation are also verified by comparing with experimental data, and application of the technique to other operating conditions is carried out to obtain the fundamental data of optimal design of the system. A new algorithm for solving the solidification problem with growing domain has been presented as an application of the theory in the section on numerical analysis. From simulated results of the centrifugal-casting process, the following conclusions can be drawn:

108 Radius (r ), mm 112

Fig. 40

Equivalent stress at initial stage (model II)

386 / Residual Stress Formation During Manufacturing Processes Molten steel Steel roll Steel shaft 400

Stress (σr), MPa

× 102

Free boundary 300

x

o


l

1.0

+

200

0

1.0

ym

r Cooling water

Di

108 Radius (r ), mm 112

b

z

100

104

+

ω

Copper roll sleeve 0′

Steel pinch roll

400

× 102

Roll

+

300

bo

200

0 2.0

100

108

Vo

Free boundary

z

Cast strip

Di

104 Radius (r ), mm 112

(a)

Fig. 42

(b)

y

Twin-roll casting system (a) and model for simulation (b)

400

× 102

300 l

2.0


200

0 2.0

100

Di

104 108 Radius (r ), mm

Fig. 41

z

112

Residual stresses at the end of cooling (model II)

20

0

Distance from meniscus (y), mm

Stress (σz), MPa

+

l

2.0


Stress (σθ), MPa

Strip

20

40

Detail of region A

60

A

80

100 50

Fig. 43

40 30 10 20 Distance from center (x), mm

0

Finite-element division for continuous casting by twin-roll method

Fig. 44

Velocity field. Vb ⳱ 77.2 mm/s


20 1.1 14 18 21 25 28

40 60

142

111 95

80



190 C 179 170 167

0

100 50

25

178 169 162 140

20 13 17 20 25

40 60

108 50 0

80

Fig. 46


0.15

60

1.0

25

40

80 100

80

0

0

20 0.15 40

0.83

60

1.0

25

0

80

50

Distance from center (x ), mm

25

0


Distribution of temperature (a) and volume fraction of solid (b) (material A). To ⳱ 190 C

σx

σy

200 Calculation 150

Experiment

V = 77.2 mm/s 100

0



0

0.0

20

8 12

40

4 MPa

60 4 80

20 30 4 MPa

40

60

40 50

80

5

V = 51.1 mm/s

0.0

20

18

50 0

20

40

60

80

100

100


Fig. 47

Variation of temperature on the surface of the strip (material A). To ⳱ 190 C

25

20

15

10

5

0

100


Fig. 48

100

Variation of temperature along the central line (material A). To ⳱ 190 C

100 50

Temperature (T ), C

60

V = 51.1 mm/s

20

20

0.83

20



0

40

V = 51.1 mm/s

100

92

50

V = 77.2 mm/s

150

30

0

V = 77.2 mm/s

20 Distance from meniscus (y), mm

190 C 0

100


Fig. 45

200

V = 51.1 mm/s

20

Temperature (T ), C

V = 77.2 mm/s

20

Isostress line in the strip (material A). V ⳱ 77.2 mm/s

25

20

15

10

5


0

388 / Residual Stress Formation During Manufacturing Processes 12. S.R. Bodner and A. Merzer, Viscoplastic Constitutive Equations for Copper with Strain Rate History and Temperature Effects, J. Appl. Mech., Trans. ASME, Vol 100, 1978, p 388–394 13. J.L. Chaboche and G. Rousseler, On the Plastic and Viscoplastic Constitutive Equation (Part 1), J. Pressure Vessel Technol., Trans. ASME, Vol 105, 1983, p 153–158 14. J.L. Chaboche and G. Rousseler, On the

15.

16.

17. 20

10

0

Stress, MPa

0


20

40 20 0

18.

20 40

19.

20 40

Plastic and Viscoplastic Constitutive Equations (Part 2), J. Pressure Vessel Technol., Trans. ASME, Vol 105, 1983, p 158–164 P. Ackermann, W. Kurtz, and W. Heinemann, In Situ Tensile Testing of Solidifying Aluminium and Al-Mg Shells, Mater. Sci. Eng., Vol 75, 1985, p 79–86 T. Suzuki, K.H. Tacke, and K. Schwerdtfeger, Influence of Solidification Structure on Creep at High Temperatures, Metall. Trans. A, Vol 19A, 1998, p 2857–2859 T. Inoue et al., Benchmark Project on the Application of Inelastic Constitutive Relations in Plasticity-Creep Interaction Condition to Structural Analysis and the Prediction of Fatigue-Creep Life, Part I, Proc. of Subcom. Inel. Anal. High Temp. Mater., JSMS, Vol 1, 1991, p 1–5 P.J. Wray and M.F. Holmes, Plastic Deformation of Austenitic Iron at Intermediate Strain Rates, Metall. Trans. A, Vol 6A, 1975, p 1189–1196 P.J. Wray, Onset of Recrystallization Dur-

20.

21.

22.

23.

24.

0 20 200

40

Roll boundary 60

Strip thickness (δ), mm

20 0

σx σy σz

20 40 20 0

80

20

5

10

25.

150 100

26. Experiment Calculation

100 50

0

0

20


Fig. 49

60

100

27.

Casting speed (v), mm/s

Stress distribution at several locations (material A). V ⳱ 190 mm/s

Fig. 50

Computing and measuring results of strip thickness (material A)

28.

100

100

29.

A

400

300

1200 C

200

1240 C

C 1280

100

1470 C 1400 1000

360 C 420

400

A

500 600 1.5 600 400 (a)

● T.P. Battle and R.D. Pehlks, Mathematical of

100 200 300

1470 C 1400 1000

● ●

300 C 360 420

400

A 600

0 300

SELECTED REFERENCES

A

400

500

200

100

600 400

0


Fig. 51

0

1240 C 1280 C

0

1200 C


200


200

ing the Tensile Deformation of Austenitic Iron at Intermediate Strain Rates, Metall. Trans. A, Vol 6A, 1975, p 1197–1203 C.E. Pugh and D.N. Robinson, Some Trends in Constitutive Equation Model Development for High Temperature Behavior of First-Reactor Structural Alloys, Nucl. Eng. Des., Vol 42, 1978, p 269–278 T. Inoue and S. Nagaki, A Constitutive Modeling of Thermo-Viscoelastic-Plastic Materials, J. Thermal Stress., Vol 1, 1978, p 53–61 D. Kujawski and Z. Mroz, A Viscoplastic Material Model and Its Application to Cyclic Loading, Acta Mech., Vol 36, 1980, p 213–230 Grill, J.K. Brimacombe, and F. Weinberg, Mathematical Analysis of Stresses in Continuous Casting of Steel, Iron Steel., Vol 1, 1976, p 38–47 D.Y. Ju, T. Inoue, and N. Yoshihara, Simulation of Vertical Semicontinuous Direct Chill Casting Process of Cylindrical Ingot of Aluminum Alloy, Trans. Jpn. Soc. Mech. Eng. (JSME), Vol 55 (No. 513), 1989, p 1236–1243 (in Japanese) D.Y. Ju and T. Inoue, Simulation of Solidification and Evaluation of Residual Stresses During Centrifugal Casting, Proc. Third Int. Conf. Residual Stresses, Vol 1, Elsevier, 1991, p 220–225 D.Y. Ju and T. Inoue, Simulation of Solidification and Viscoplastic Deformation in the Twin Roll Continuous Casting Process, Trans. Jpn. Soc. Mech. Eng. (JSME), Vol 57 (No. 537), 1991, p 1147–1154 (in Japanese) S. Redner and C.C. Perry, Factors Affecting the Accuracy of Residual Stress Measurements Using the Blind Hole Drilling Method, Proc. Seventh Int. Conf. Experimental Stress Analysis (New York), Aug 1982, p 604–616 A. Boley and J.H. Weiner, Theory of Thermal Stresses, Wiley, 1960 L.I. Rubenstein, The Stefan Problem, American Mathematical Society, 1971

300

200

100

0

● ●

Distance from center (x ), mm (b)

Distribution of temperature (material B). (a) Vc ⳱ 400 mm/s. (b) Vc ⳱ 600 mm/s

●

Microsegregation in Binary Metallic Alloys, Metall. Trans. A, Vol 22A, 1991, p 957–980 R.M. Bowen, Theory of Mixture, Continuum Physics, A.C. Eringen, Ed., Vol 3, Academic Press, 1976 M.C. Flemings, Behavior of Metal Alloys in the Semisolid State, Metall. Trans. A, Vol 22A, 1991, p 957–980 H. Gouin, Variational Theory of Mixture in Continuum Mechanics, Eur. J. Mech., B/Fluids, Vol 9, 1990, p 469–491 T. Inoue, in Thermal Stresses, R.B. Hetnarski, Ed., Vol 3, Elsevier Science, NorthHolland, 1989 D.Y. Ju and T. Inoue, A Thermomechanical Model Incorporating Moving Liquid/Solid

Residual Stress Formation during Casting / 389 200 100 Distance from meniscus (y), mm


100

100 Equivalent stress (), MPa

200

0 100 ξs = 0.1 ξs = 1.0

200 300 400

0 100 ξs = 0.1 ξs = 1.0

200

Perzyna (n = 1) Perzynna Perzyna + creep 50

0 1.5

300

0.5

1.0

0.0

Distance from center (x ), mm (a)

400 500

600 400

300

200

100

600 400

0

300


200

100

0


(a)

Fig. 52

Distribution of solid fraction (material B). (a) Vc ⳱ 400 mm/s. (b) Vc ⳱ 600 mm/s

Equivalent stress (), MPa

100 500

Perzyna (n = 1) Perzynna Perzyna + creep

50

0 1.5

0.5

1.0

0.0


1500

Dependence of constitutive relationships on stress distribution. (a) Vc ⳱ 400 mm/s. (b) Vc ⳱ 600 mm/s

Fig. 55

Center of slab Surface of slab

1100

0

0

100

100

900

700 300

400

500

(a) 1500 Center of slab Temperature (T ), C

1300

σ x = 1 MPa

600

Surface of slab

1100

σ x = 1 MPa

200

5 10

0

300

400


200


Stress (σx ), MPa

100


0

0 1.5

900

1.0

0.5

0

300

400

0 1.5

0

Distance from center (x), mm

500

5 10

200

Stress (σx ), MPa

Temperature (T ), C

1300

500

1.0

0.5

0

Distance from center (x), mm

700 0

100

200

300

400

500

600


600 160

(b)

Fig. 53 600 mm/s

Temperature variation at center and surface of slab (material B). (a) Vc ⳱ 400 mm/s. (b) Vc ⳱

120

80

40

600 160

0

Distance from meniscus (x), mm (a)

Fig. 54

120

80

40

Distance from meniscus (x), mm (b)

Distribution of stress rx (material B). (a) Vc ⳱ 400 mm/s. (b) Vc ⳱ 600 mm/s

0

390 / Residual Stress Formation During Manufacturing Processes Interface and Its Application to Solidification Process, Proc. Sixth Int. Conf. Mechanical Behaviour of Materials (Kyoto), JSMS, 28 July 1991, Vol 5, p 119–120 ● D.Y. Ju, Y. Oshika, and T. Inoue, Simulation and Temperature in the Centrifugal Casting Process, J. Soc. Mater. Sci. (JSMS), Vol 40 (No. 449), 1991, p 12–18 (in Japanese) ● D.Y. Ju, S. Takemura, and T. Inoue, Analysis of Coupled Mode of Solidification and Stresses the Centrifugal Casting Process, J.

Soc. Mater. Sci. (JSMS), Vol 41 (No. 464), 1992, p 751–757 (in Japanese) ● J.B. Leblond, G. Mottet, J. Devaux, and J.C. Devaux, Mathematical Models of Anisotropic Phase Transformation of Steels and Predicted Plastic Behavior, Mater. Sci. Technol., Vol 1, 1985, p 815–822 ● K. Miyazawa and J. Szekely, A Mathematical Model of the Splat Cooling Process Using the Twin-Roll Technology, Metall. Trans. B, Vol 20B, 1989, p 391–390

● D. Peirce, D.F. Shih, and A. Needlemen, A

Tangent Modulus for Rate Dependent Solid, Int. J. Comput. Struct., Vol 18, 1984, p 875– 887 ● T.L. Sham and H.W. Chow, A Finite Element Method for an Incremental Viscoplasticity Theory Based on Overstress, Int. J. Comp. Mech., Vol 34, 1989, p 143–156 ● O.C. Zienkiewicz, The Finite Element Method, McGraw-Hill, 1977



Residual Stress Formation Processes during Welding and Joining W. Zinn and B. Scholtes, Universita¨t Kassel, Germany

KNOWLEDGE ABOUT FORMATION and consequences of welding or brazing residual stresses has increased considerably during the past decades. A number of papers have made fundamental contributions to this topic (Ref 1– 3), and general aspects about origin and distributions of welding and brazing residual stresses are now classified. Considerable interest in this subject is based upon the fact that welding or brazing residual stresses have various impacts on the behavior of joined components. In this context, the most important viewpoints are:

Temperature

Time t 0 = 0 s

● High amounts of total stresses as a conse● ● ● ● ● ● ● ●

quence of superimposing loading and residual stresses Influence on local yield strength of components, depending on sign and multiaxiality of residual stress state Formation of cracks without external loads Increasing the risk of brittle fracture by high local stress values and/or highly multiaxial residual stress states Influence of residual stress distributions on loading modes of existing cracks Influence on fatigue strength and fatigue life Influence on elastic stability, for example, buckling Influence on stress corrosion sensitivity in the case of corrosive environment Consequences of existing residual stress distributions on distortion of joined components

Subsequently restricted to metallic materials, an overview is given about origin and assessment of welding and brazing residual stresses. A focal point is put on the basic principles of residual stress development and the influence of important process parameters on amount and distribution of residual stresses. Residual stresses are always consequences of inhomogeneous elastic and/or plastic deformations on a macroscopic or microscopic scale (Ref 4). Consequently, all processes or process parameters of the welding or brazing operation that introduce or influence inhomogeneous deformations have to be considered, if the origin of joining residual stresses has to be outlined. In the following chapters, only macro residual

Time t 1 > t 0

y

x

x

HAZ Cold

Seam Hot

HAZ Cold

Impeded longitudinal shrinkage • High value of longitudinal residual stresses • Low amount of shrinkage

Transverse shrinkage not impeded • Low value of transverse residual stresses • Noticeable amount of shrinkage

Fig. 1

Shrinkage and impeded shrinkage as a consequence of inhomogeneous temperature distribution. HAZ, heataffected zone. Source: Ref 6

392 / Residual Stress Formation During Manufacturing Processes stresses are considered, which are assumed to have similar consequences on components as loading stresses (Ref 4, 5).

Welding Residual Stresses Welding residual stresses are the consequences of the fluctuating inhomogeneous temperature distributions arising in the course of the different welding processes in and around the weld seam. Heating, as well as the cooling period, is of importance. This section outlines different aspects and influencing parameters that contribute to the amount and distribution of welding residual stresses.

Residual Stresses Due to Shrinking Processes. A very important origin of welding residual stresses is impeded shrinkage processes, which occur when heated and cooled regions are neighbored. The basic principle is that heated volumes shrink during the cooling-down process according to their coefficient of thermal expansion and the existing temperature difference. It is assumed that melted volumes do not exert forces on surrounding volumes. Consequently, weld seams and surrounding volumes that have not been melted during the welding process exhibit different thermal and, thus, residual stresses (Fig. 1) (Ref 6). If shrinking is not impeded, thermal stresses relax completely and no residual stresses remain after cooling down to room tem-

Distributions of longitudinal and transverse residual stresses parallel and perpendicular to a two-pass welded aluminum plate. TIG, tungsten inert gas; ry and rl, stresses parallel to the weld toe; rx and rt, stresses transverse to the weld toe. Source: Ref 7

Fig. 2

perature. In the case of the weld seam, starting from the stress-free state of the melting pool, tensile thermal stresses build up during the cooling process, which reach the temperature-dependent yield strength of the material. Consequently, at the end of the cooling process, tensile residual stresses exist in the weld seam. If the amount of restricted shrinkage is high enough, they may reach the yield strength of the weld seam material. Materials volumes that are at a certain distance from the weld seam and are not melted during the welding process undergo impeded thermal strains during the heating period as well. It follows that compressive thermal stresses build up, yielding compressive plastic strains when the compressive temperature-dependent yield stress is reached. These volume shrinkages build up tensile stresses when thermal contraction during cooling is impeded. The amount of tensile residual stresses, in this case, is directly related to compressive strains during the heating process. For equilibrium reasons, longitudinal residual stresses change sign over the width of the plate (Fig. 2) and result in an inhomogeneous distribution of longitudinal residual stresses (Ref 7). Up to now, only longitudinal residual stress components have been considered. But, as a consequence of inhomogeneous longitudinal stresses, inhomogeneous shrinkage in transverse direction results as well. Because inhomogeneous shrinkage also means impeding of shrinkage, residual stresses build up, also in the transverse direction, even if no external forces impede shrinkage in the transverse direction. However, residual stress amounts in transverse direction reach only about one-third of the values in longitudinal direction. On the other hand, transverse residual stresses may also reach the yield strength of the material, for example, after multipass welding. Because the amount of restraint is usually higher at repair welds compared to new constructions, residual stresses are typically more severe and especially have to be taken into account. Residual Stresses Due to Quenching Processes. Particularly in the case of thicker plates, considerable temperature differences build up between the near surface and the core layers of the plate during the cooling process. The resulting thermal residual stresses may exceed the yield strength of the material, resulting in plastic deformations. Obviously, these inhomogeneous plastic deformations lead to residual stresses after cooling. If no other processes were active, compressive residual stresses in near surface layers and tensile residual stresses in the core would be expected. However, in most cases, by far, quenching residual stresses develop together with residual stresses due to shrinkage processes and, if present, residual stresses due to phase transformations. Residual Stresses Due to Phase Transformations. Residual stresses as a consequence of phase transformations during welding processes

Residual Stress Formation Processes during Welding and Joining / 393

Time = t 1

Temperature

Transformation

t1 < t2

Temperature

Time = t 2

Tra S n Im sfor hrin mi ma ka g Tra nent tion e a ns t for rans ffec te m f Sh atio orm d a ti rin n o ka aff ge ec n ted

y

Fig. 3

x

x

Shrinkage and expansion in example of phase transformation of sufficient highly treated areas. Source: Ref 6

Table 1 Materials data for the calculation of brazing residual stresses Material

E, GPa

m

␣,10ⴑ6Kⴑ1

ZrO2 Si3N4 Ag CK 45

210 280 73 188

0.3 0.27 0.3 0.3

10.6 2.5 20.0 14.0

E, Young’s modulus; m, Poisson’s ratio; ␣, coefficient of thermal expansion. Source: Ref 12

Interaction of impeded shrinkage and transformation for different cooling velocities. Example 1, low velocity; Examples 2 and 3, high velocity. Re, yield strength; r, stresses; ␣, coefficient of thermal expansion; E, Young’s modulus; DT, temperature differences; S, stiffness. Source: Ref 6

occur if, during the cooling-down period of the heated weld seam, phase transformation processes connected with volume changes occur locally (Fig. 3)(Ref 6). Inhomogeneity of transformation processes, which is a necessary prerequisite for the formation of residual stresses, may be attributed to different reasons, for example, different peak temperatures during the welding process, different cooling velocities, or local changes of chemical composition. In the case of steels, transformation from austenite to ferrite, bainite, or martensite is connected with a characteristic volume increase. Consequently, one would always expect compressive residual stresses in transformed volumes, if transformations occur simultaneously and balance tensile residual stresses in adjacent volumes.

In practice, this is not the case. Moreover, shrinkage and transformation processes overlap, and the amount as well as the sign of the resulting residual stresses strongly depend on the temperature range in which transformation takes place. The consequences are schematically outlined in Fig. 4. It shows, as a function of temperature, the tensile or compressive yield strength of a ferritic-pearlitic or a bainitic microstructure. Starting at high temperatures, tensile stresses build up due to shrinkage processes and according to the temperature-dependent yield strength of austenite. If phase transformations occur as a consequence of volume increase, tensile stresses rapidly decrease and change to compression. If, in the transformed volume, a ferritic-pearlitic microstructure develops, maximum compressive stresses are limited by the respective compressive yield strength of the phases created (Example 1 in Fig. 4). If a martensitic transformation takes place, because of the high yield strength, the highest compressive stresses can develop. At the end of the transformation process, compressive residual stresses decrease because of continuous temperature decrease along with accompanying shrinkage (Examples 2 and 3 in Fig. 4). Depending on Young’s modulus, E, the stiffness, S, of the component, the coefficient of thermal expansion, ␣, and the remaining temperature difference, DT, up to room temperature, compressive or even tensile residual stresses result. Highest tensile residual stresses are expected if the transformation process is finished at relatively high temperatures. In that case, the tensile yield strength of the ferritic-pearlitic microstructure may be reached by the residual stresses. From the schematic diagram in Fig. 5, it can be seen that the lower the transformation temperature, the more effective the consequences of transformation processes on the resulting residual stresses will be. Consequently, pronounced effects of transformation processes

Fig. 4

Fig. 5

Influence of heat input on transformation temperature, Tt, and resulting consequences on shrinkage tensile or transformation compressive residual stresses. RS, residual stress. Source: Ref 8

394 / Residual Stress Formation During Manufacturing Processes perpendicular to the weld seam. In the case of low heat input (Curve 3, see also Fig. 4 and 5), one can see that shrinkage and, especially, transformation processes lead to a reduction of tensile residual stresses or even compressive residual stresses, resulting in a characteristic W-shape of the residual stress distribution. In the case of high heat input (Curve 1), one can expect that immediately after phase transformation in the heated weld seam area compressive stresses exist and that cooling down to room temperature results in a buildup of high tensile stresses across the weld seam. The influence of the chronological sequence of the transformation processes is especially pronounced in voluminous components. In this case, a considerable time may elapse before transformation processes in the fast-cooling outer layers and the slow-cooling core volumes are finished. If transformation-induced stresses resulting from the inhomogeneous volume changes lead to plastic deformations, after temperature compensation residual stresses occur with positive sign in volumes having undergone transformations first and negative sign in volumes transformed last. In practical cases, however, this effect always occurs in connection with residual stresses due to pronounced temperature gradients in directions perpendicular to the weld

on the resulting residual stress distributions can be expected, for example, for steels with high yield strength at high temperature or for extremely high cooling rates. The diagram sketched in Fig. 6 shows the influence of increasing heat input on the distribution of transverse residual stresses along a line

RS 1

RS

y x

x

RS Weld toe

x

HAZ

ea

ti

3

H

x

np

ut

RS

Fig. 6

Influence of heat input on transverse residual stress distribution. RS, residual stress. Source:

Ref 9

Brazing temperature

Room temperature

seam. As a consequence, transformation-induced compressive residual stresses are often observed with smaller amounts in surface layers compared with volumes near the core. Summary. Welding residual stresses are a consequence of the interaction of the following separate processes: ● Impeded expansion and shrinkage as a result

of inhomogeneous temperature distributions

● Quenching effects ● Phase transformations

Consequently, the algebraic sign and amount of residual stresses in the weld seam and the heataffected zone depend on the transformation temperature, Tt, which is determined by the timetemperature-transformation diagram of the material and also the cooling velocity. Obviously, the local chemical composition plays an important role. In addition, the local temperature-dependent yield strength of the material and the degree of stiffness of the construction is decisive. One can see that the basic processes of the development of welding residual stresses are widely understood. A prediction of welding residual stresses in individual cases, however, is quite difficult because of the relatively great number of influencing parameters and their interdependencies. To that end, further consequent research and the correct inclusion of the experimental experiences in appropriate finite-element (FE) models are necessary.

Brazing Residual Stresses

αthA > αthB

Fig. 7

Distortion and residual stresses shown schematically in a brazed two-layer compound. Source: Ref 12

Normalized thermal residual stresses at the surface, MPa/K

2.0

Variations with hb (0 ≤ hb ≤ 0.3) mm

1.5 1.0 0.5 0.0 –0.5 –1.0

ZrO2

hc Si3N4

–1.5

steel

hs steel

–2.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

hb

● The solidification behavior of the solder ● The differences in the thermal expansion be3.5

hc/hs

Fig. 8

In modern structures, components are very often required to possess complex properties such as sufficient ductility together with resistance against abrasive wear and high temperatures. These requirements cannot be satisfied by monolithic materials alone. In these cases, brazed compounds have been demonstrated to be very useful because materials of different properties can be joined by this method. Very important examples include cemented carbide tools and brazed ceramic-metal compounds combining hardness and chemical resistance with strength and ductility of appropriate metallic partners. In the case of brazing, joining of two partners is achieved by a melted hard solder, while the materials joined remain well below their solidus temperature. Special active solder materials have been developed to meet the needs of economical industrial applications. During the cool down from joining temperature, brazed compounds develop a complex residual stress state. The most important influencing parameters are:

Influence of the thickness ratio hc /hs of the ceramic and the steel on brazing residual stresses in the outer surfaces of the compound. hc, thickness of ceramic; hs, thickness of steel; hb, thickness of solder. Source: Ref 12

havior of the joint materials

● Elastic and plastic properties of the joint part-

ners

● Geometry of the joint compound ● Cooling down conditions (Ref 10, 11)

Residual Stress Formation Processes during Welding and Joining / 395 Thermal residual stresses during the cool down from brazing temperature and residual stresses after cooling may be detrimental for the compound and cause distortions or failure during the manufacturing process or in service. Therefore, knowledge about residual stress states and their variation with brazing and geometrical conditions is of high importance in order to realize compounds optimized for practical applications. Characteristic Residual Stress Distributions in Brazed Components. Basic principles of the development of brazing residual stresses can be outlined with the aid of Fig. 7. It schematically shows a two-layer compound with layers A and B and thermal expansion coefficients ␣thA ⬎ ␣thB (Ref 12). Starting from a stress-free state, thermal stresses build up as soon as the solidified braze material leads to adhesion between the two layers, because of the differences between the thermal expansion coefficients. This is outlined on the right hand side of Fig. 7. In addition to a global bending of the compound, local bending effects on the lateral surfaces also can be detected. Consequently, a relatively complex residual stress distribution results. In this case and if similar thicknesses and elastic properties of the layers are assumed, compressive (tensile) residual stresses occur at the outer free surfaces of layer A (B). Near the joining face, residual stresses with opposite sign develop. Consequences of important parameters on resulting residual stress distributions and amounts have been studied theoretically using analytical as well as FE models (Ref 12). In most cases, purely elastic behavior is assumed, which, however, is not always justified. As an example, Fig. 8 shows the influence of thickness ratio hc /hs (hc, thickness of ceramic; hs, thickness of steel) for compounds of steel Society of Automotive Engineers (SAE) 1045 and Zr02 or Si3N4 ceramic. The calculations are based on a three-layer plate with silver as braze material and the materials properties listed in Table 1. The longitudinal residual stresses, normalized to the temperature difference, DT, are plotted as a function of thickness of the compound layers. The coefficient DT is the temperature difference during cooling

Examples of residual stresses determined in different brazed metal-ceramic compounds. Source: Ref 12

Fig. 9

from brazing temperature, for which the brazing solder shows elastic behavior. In each component, linear stress-depth distributions occur, resulting from a superposition of bending and tension or compression loading. In Fig. 8 one can clearly see that tensile residual stresses in the ceramic surfaces decrease considerably with decreasing thickness ratio. If hc /hs ⱕ 0.5, compressive surface residual stresses in the ceramic surfaces always exist. Because differences in thermal expansion coefficients are smaller for SAE 1045/Zr02 compounds compared with SAE 1045/Si3N4, amounts of brazing residual stresses are also larger in the latter case. In most cases, experimental residual stress determinations in brazed compounds are carried out by x-ray or mechanical methods. The results presented in Fig. 9 confirm the calculations of Fig. 8. In this case, x-ray measurements were carried out on the outer surfaces of plates with the dimensions 20 ⳯ 20 mm2and the thicknesses indicated. A considerable uncertainty of calculations exists in the ignorance about plastic deformations in the brazed components during the cooling process, if thermal stresses exceed the temperature-dependent yield strength. In a number of cases, neutron stress analyses showed clear evidence of plastic deformations in brazed metallic components and also in the metallic part of ceramic-metal joints (Ref 13). A typical example is presented in Fig 10. The diagram shows the distribution of residual stresses across the center of a 19 ⳯ 19 mm2 brazed SAE 1045/WC-Co compound. In this case, a Cu-Mn-Co hard solder was used. In the WC-Co cemented carbide, a linear distribution of the residual stresses as a function of the distance from the surface is observed with a maximum tensile residual stress of approximately 550 MPa immediately at the free surface. Near the solder layer, compressive residual stress amounts of more than –600 MPa are found. In the steel plate, compressive residual stresses of about –250 MPa exist at the free surface, which decrease linearly and change sign at a distance of about 1.5 mm from the surface. Near the solder layer, a layer of about 2 mm

Fig. 10

thickness with constant tensile residual stresses of about 250 MPa is observed. Measurements using x-ray diffraction or hole-drilling techniques confirm these distributions in near surface layers. In the meantime, more complex residual stress states in brazed components have also been analyzed. A characteristic example is the examination of joints of steel and cemented carbides similar to cutting tools (Ref 13, 14). The typical geometry investigated is shown in Fig. 11. Cemented carbide tungsten-carbon containing 10 wt% cobalt and 17.3 wt% titanium, tantalum, and niobium was brazed into a slit of a steel block made of SAE 4140. Brazing was carried out using copper as braze foil together with a nickel mesh in order to keep the thickness of the brazing gap constant during the brazing process. FE-calculations as well as experimental stress analyses were carried out. Residual stresses near the surfaces of the components are essentially determined by local or global bending moments due to different amounts of shrinkage during cooling and also influenced by the geometry of the parts under investigation. One can see a rather good agreement between measurement and calculations. Such investigations are very helpful to assess strength or failure behavior of real components. Already during the brazing operation, thermal tensile stresses may produce cracks in brittle materials. In addition, location of crack initiation as well as direction of crack propagation under fatigue conditions is clearly determined by existing residual stress fields (Ref 16). Summary. Brazing residual stresses play an important role for the correct function of components during service. Because of the different thermal expansion coefficients and the temperature cycles involved during the brazing process, they are, in most cases, inevitable. Because of the number of influencing parameters, however, strategies can be developed to avoid detrimental residual stress distributions, if the basic processes are well understood. In this context, adapted geometries play an important role. Me-

Depth distribution of residual stresses rxRS in the center of an SAE 1045/WC- Co compound determined by neutron diffraction. Source: Ref 13


Neutron diffraction FE calculation

a σRS X

y

σRS (MPa) Y

σRS (MPa) X


a y

σRS Y Cemented carbide

x

x z

z

a Distance a, mm


σRS (MPa) Y

σRS (MPa) X

y

σRS X

Distance a, mm

Fig. 11

a

a

Steel

a σRS Y y x

x z

2a

c

a = 12.7 mm b = 5 mm c = 2/3 a


a

b

Distance a, mm

z

Distance a, mm

RS Calculated and measured residual stress distributions in a model tool geometry made of steel SAE 4140 and cemented carbide. Left, rRS x component; right, ry component; above, residual stresses in steel; below, residual stresses in cemented carbide. Source: Ref 15

chanical as well as diffraction techniques for residual stress analysis are available. Analytical and FE-methods to predict brazing residual stress distributions and to assess the importance of individual process parameters are also well developed. REFERENCES 1. E. Macherauch and H. Wohlfahrt, Origin of Welding Residual Stresses, Materialpru¨fung, Vol 19, 1977, p 272–280 (in German) 2. H. Christian and F.-X. Elfinger, Residual Stresses in Weld Seams, Der Maschinenschaden, Vol 51 (No. 3), 1978, p 124–130 (in German) 3. H. Wohlfahrt, Welding Residual Stresses, Origin, Calculation, Assessment, Eigenspannungen, E. Macherauch and V. Hauk, Ed., DGM-Verlag, Oberursel, 1983, p 85– 116 (in German) 4. E. Macherauch and K.-H. Kloos, Origin, Measurement and Evaluation of Residual Stresses, Proc. Int. Conf. Residual Stresses in Science and Technology, Vol 1, Garmisch-Partenkirchen, DGM-Verlag, Oberursel, 1986, p 3–26 5. V. Hauk, Structural and Residual Stress Analysis by Nondestructive Methods, Elsevier, Amsterdam, 1997

6. H. Wohlfahrt, Consequences of Austenite Transformation for the Formation of Welding Residual Stresses, Ha¨rterei-TechnischeMitteilungen, Vol 41 (No. 5), 1986, p 248– 257 (in German) 7. W. Zinn, Investigation of the Fatigue Behaviour of the Butt Welded Al-Alloys AlMg3 and AlMg4.5Mn, Schweißtechnische Forschungsberichte, Bd. 34, DVS-Verlag, 1990 (in German) 8. T. Nietschke-Pagel and H. Wohlfahrt, The Generation of Residual Stresses Due to Joining Processes, Residual Stresses—Measurement, Calculation and Evaluation, V. Hauk, H. Hougardy, and E. Macherauch, Ed., DGM Informationsgesellschaft Verlag, 1991, p 121–134 9. T. Nietschke-Pagel, “Residual Stresses and Fatigue Behaviour of Welded Fine-Grained Steels,” Ph.D. dissertation, University Kassel, 1994 (in German) 10. O.T. Janeu, D. Munz, B. Eigenmann, B. Scholtes, and E. Macherauch, Residual Stress State of Brazed Ceramic/Metal Compounds, Determined by Analytical Methods and X-Ray Residual Stress Measurements, J. Am. Ceram. Soc., Vol 73, 1990, p 1144– 1149 11. L. Pintschovius, N. Pyka, R. Kußmaul, D. Munz, B. Eigenmann, and B. Scholtes, Experimental and Theoretical Investigation of

12.

13.

14.

15.

16.

the Residual Stress Distribution in Brazed Ceramic-Steel Compounds, Mater. Sci. Eng., A 177, 1994, p 55–61 B. Scholtes, Recent Investigations on the Origin and Distributions of Residual Stresses in Ceramics and Metal-Ceramic Compounds, Contraintes residuelles et nouvelles technologies, CETIM, 1990, p 61–71 K. Bing, “Residual Stresses and Distortion of Different Metallic Materials Brazed with Steel SAE 1045,” Ph.D. dissertation, University Karlsruhe (TH), 1995 (in German) L. Pintschovius, B. Schreieck, and B. Eigenmann, Neutron, X-Ray, and Finite-Element Stress Analysis on Brazed Components of Steel and Cemented Carbide, MAT-TEC 97, A. Lodini, Ed., ITT-International, Gournay sur Marne, 1997, p 307– 312 K. Bing, B. Eigenmann, B. Scholtes, and E. Macherauch, Brazing Residual Stresses in Components of Different Metallic Materials, Mater. Sci. Eng., A 174, 1994, p 95– 101 B. Schreieck, B. Eigenmann, and D. Lo¨he, “Residual Stresses and Failure of Brazed Joints of Cemented Carbide and Steel Similar to Cutting Tools, in Joining Ceramics, Glass and Metal,” DVS-Berichte Band 184, DVS-Verlag GmbH, Du¨sseldorf, 1997, p 140–144



Residual Stresses in Powder-Metal Processing P. Ramakrishnan, Indian Institute of Technology, Bombay, India

POWDER METALLURGY (P/M) is concerned with producing metal and alloy powders and converting them to semifinished or finished parts for several consumer and industrial products, including simple household appliances, computer disk drives, surgical implements, and sophisticated components of satellites. Products of P/M include porous materials, self-lubricating bearings, filters, a variety of ferrous and nonferrous structural parts, electrical contacts, tool steels, cemented carbides, diamond tools, friction materials, refractory-reactive and high-tem-

perature materials, and metal-matrix composites. The P/M process conserves energy and raw materials, and minimizes machining and scrap losses, resulting in cost reductions. Thus, the process competes with traditional metalforming processes such as casting, working, machining, rolling, forging, and so forth. Powder processing involves a sequence of operations depending on the end-product requirements as shown in Fig. 1. These include the traditional low-cost components produced by the press-sinter technique, another category of cost-effective and high-per-

Metal powder production (Atomization, chemical, electrochemical, and mechanical processes) Mixing (additives and lubricants) Compaction

Warm compaction

Hot Die pressing Isostatic pressing Rolling Spraying Pressureless sintering

Cold Die pressing Isostatic pressing Rolling Slip casting Injection molding

Sintering (Atmosphere, vacuum, high temperature)

Fig. 1

Solid phases

Activated

Liquid phase

Infiltration

Rolling

Finishing:

Repressing

Extrusion

• Machining

Resintering

Wire drawing

• Heat treatment

Sizing

Forging

• Rapid prototyping

General P/M process

formance parts that require advanced P/M processing techniques, and those components in which the P/M approach will lead to enhanced mechanical properties and improved performance characteristics. Thus, in addition to the widely used press-sinter method a variety of processing techniques such as hot pressing, isostatic compaction, powder rolling, powder extrusion, powder preform forging, high-temperature sintering, hot isostatic pressing (HIP), injection molding, warm compaction, rapid prototyping, and so forth, have been developed, and their use is increasing in P/M processing. Powder metallurgy has emerged as an advanced manufacturing technology for the mass production of precision net-shape high-performance components for the automotive, general engineering, electrical, electronic, and aerospace industries. According to the information released by the U.S. Department of Commerce, Bureau of the Census, the U.S. metal powder market in 1996 was of the order of $1.9 billion and included iron, aluminum, copper, tungsten, molybdenum, titanium, tantalum, superalloys, precious metal, and other nonferrous metal powders, paste, and flakes. The North American P/M parts business is estimated to be of the order of $2 billion, and is the largest P/M market in the world, twice the size of Europe and Japan, each of which account for about $1 billion in sales of conventional P/M parts. During the 1998 Powder Metallurgy World Congress and Exhibition in Granada, Spain, it was reported that the metal powder shipments increased almost 12% in 1997 to 440,843 metric tons. North American iron powder markets have invested heavily in new capacity and new products with iron powder production capacity exceeding 590,000 metric tons (Ref 1). Powder metallurgy is reported to be a high-growth industry and a 21st century technology. It has a significant impact on design viability and economics in key industries. In the aircraft industry, the cost of a design using P/M components is 37% lower than a machined component. This has resulted in a market growth from a 0% share in 1986 to nearly 50% in 1997. It has been reported

398 / Residual Stress Formation During Manufacturing Processes that new commercial jet aircraft engines made by Pratt and Whitney and General Electric Company contain a total weight of P/M superalloy extruded forging ranging from 680 to 1995 kg/ engine (Ref 2). Powder metallurgy is the only way to produce certain high-temperature alloys.

Powder-Metallurgy (P/M) Processing Ferrous P/M Parts The use of high-performance sintered ferrous materials has been increasing steadily in recent years in the automotive sector because of the cost-effective manufacturing capability of P/M to produce products with improved structural and functional performance along with reliability. The commercial use of sintered iron bearings as a less expensive substitute to the expensive bronze bearings initiated by General Motors, USA, during early 1930s. Germany developed sintered iron driving bands as a substitute to copper during the mid-1930s. During World War II, both Germany and the United States produced limited quantities of large sintered iron bearings for machine components and war vehicles, thereby demonstrating the economic viability of sintered ferrous products as a substitute for cast and machined steel components. A major consumer of P/M parts is the automotive market, accounting for about 70 to 80% of total produc-

tion. One can expect the continuing influence of the automotive industry on the fortunes of the P/M industry. According to the forecast of industrial experts, the global car production will grow from its 1994 level of 35 million units/yr to 40 million units/yr by the year 2005, thereby providing ample opportunities for P/M parts production (Ref 3). Furthermore, a typical 1998 American family vehicle contains 14.7 kg of P/M parts, about 5% increase over 1997. The forecast indicated a family vehicle will contain 22.6 kg of P/M parts by the year 2000. Automotive major growth areas for P/M include engine transmission, exhaust systems, and antilock brake systems (ABS). Powder-forged connecting rod and steel bearing caps are recognized examples of reliability, innovation, and cost savings. The American automotive industry is seriously considering the use of P/M in pinions and pinion carrier frames in automatic transmissions to improve dimensional accuracy and reduce manufacturing costs. The major material in the powder blend would be steel, consuming about 81,700 metric tons, which represents about 24% of the total current shipments of iron and steel powder annually for all applications in North America (Ref 4). It is expected that the pinion carrier frame market will be an important new application for steel powder during the next decade. The market for stainless steel products is increasing because of the newer demand of exhaust system flanges, sensor rings in ABS systems, and so forth. The stainless steel powder shipments are expected to grow more than 10%

Metal powders, additives, and lubricants

Mixing

Compacting

Sintering Infiltration

Repressing

Sizing

Resintering Finished part

Fig. 2

Basic P/M process for steel parts

Finished part

Finished part

in 1998 in the United States. Powder metallurgy high-speed steels are finding increasing usage for cutting automotive gears, aerospace parts, tooling for injection molding, and P/M dies. The world P/M tool steel market is of the order of 12,000 metric tons. Powder Metallurgy Parts Manufacturing. The widely used press-sinter P/M steel parts manufacturing process is shown in Fig. 2. Carefully selected metal powders are mixed with suitable additives and lubricants to get the desired alloy composition, compacting the powder mixture in a shaped die under pressure at room temperature so as to produce a green compact of required density and strength. The compaction pressure will depend on the characteristics of the powder such as whether it is elemental or prealloyed, its particle size, shape, size and shape distribution, microstructure, phases present, chemistry, and residual stresses in the powder and the size, shape, and green density of the compact. After the application of pressure through the punches, the compact has to be ejected from the die to produce the green compact. Carbon is usually added as finely powdered graphite and 0.5 to 1% dry powdered lubricant such as wax, stearic acid, or metallic stearate to reduce the friction during compaction. Green compacts are sintered at elevated temperature below the melting point of base metal in a sintering furnace with suitable atmospheres. During sintering, the mechanical bonds of the powder particles are converted to metallurgical bonds, thereby leading to densification and improvement in mechanical properties. The dimensional changes during sintering will depend on the composition of ferrous alloys and the density of the green compact. Powder metallurgy provides precise control of materials and properties and permits wide variation in physical and mechanical properties, at the same time ensuring performance characteristics of consistent uniformity. Practically any desired metal, alloy, or mixture of metals, including those combinations not available in wrought form, can be processed through P/M. A variety of controlled porosity products are available, ranging from metal foams, filter, and self-lubricating bearings to porous products to diffuse the flow of gases or liquids. Powder metallurgy products permit quieter and smooth operation by damping vibration and noise. Another advantage is the production of complexshaped parts and the capability to reduce the subassemblies by a proper die design and tooling or joining during sintering or infiltration. The additional operations such as repressing and resintering and/or metal infiltration can provide an increase in the density and mechanical properties of the P/M product. The physical properties of the P/M steel part can be optimized by a postsintering heat treatment, which requires proper selection of materials, heat treating parameters, and processing equipment. If necessary the parts may be machined, heat treated, or densified by infiltration, repressing, and resintering. Although the P/M technology has been used to produce net-shape products, occasionally some machining operations such as tapping, threading, and transverse holes may be necessary. In such in-

Residual Stresses in Powder-Metal Processing / 399 stances, machinability of P/M parts can be improved with appropriate treatments. Powder metallurgy products may be subjected to mechanical working as in the case of cast product or may be directly processed from powders by rolling, extrusion, or forging with additional advantage. Parts may be consolidated to full density by hot pressing or by HIP as in the case of alloy steel powders. Other relatively more recent consolidation techniques include high-temperature sintering, warm compaction, and metal-injection molding (MIM) and rapid prototyping.

Powder Characteristics The basic raw material for P/M processing is the metal powder, and successful processing will depend on the characteristics of the powders. A knowledge of the characterization of powders is fundamentally important in many critical stages of the processes such as mixing, compaction, sintering, and postsintering operations that will govern the final structure and properties of the products. However, the characterization of powders presents many challenges because of the complexity of properties and the large number of variables involved (Ref 5, 6). Even for a single particle, one can distinguish between the characteristics of the material and the characteristics introduced by the manufacturing method. The material characteristics include chemical composition, theoretical density, melting point, and structure. The characteristics introduced by the manufacturing method include particle size, shape, microstructure, density, reactivity, and surface conditions. Since the powders generally consist of a large number of particles with varying characteristics, it is essential to distinguish the characteristics of a mass of powder, including size and shape distribution, surface area, apparent density, tap density; flow and friction conditions of the powders; size, shape, and distribution of porosity and microstructure within the powders; and internal stresses and compressibility. Thus, there are large number of variables and properties, and the general characteristics of the powders depend on the manufacturing method and treatment of the powders. Powder Production. Important methods for the production of powders can be classified into (1) atomization of molten metal, (2) chemical reactions, (3) electrochemical methods, and (4) mechanical processing of solid materials. Several techniques are available in each category; for example, the atomization of molten metal can be achieved by liquids such as water, oil, different gases, vacuum, ultrasonic, and centrifugal methods. Chemical methods are reduction of metal oxides and other compounds with carbon or other gases, decomposition of metal hydrides and carbonyls, condensation of metal vapors, and precipitation of metals from salt solutions. Electrolytic deposition can be from aqueous solutions or fused salts. Various types of milling and machining methods are used in the mechanical processes. In addition, a variety of techniques are used to produce ultrafine and nanopowders with special characteristics. The

selection of a particular method will depend on the desired characteristics and intended application of the powders and the economics of the process. Iron and steel powders represent a major part of the metal powders currently produced. Among the steel powders, the stainless steel and tool steel powders share is relatively low, of the order of 5%; however, one can expect a high growth rate on account of their increasing usage. Although a large number of methods are available for the production of iron powders, the reduction of iron oxide and atomization of molten metal dominated the market by virtue of their inherent technical and economic development potential. The major difference in the two powder production processes lies in the development of the crude powders (Ref 7). In the sponge iron process, crude powder is porous and irregular, while in the atomizing process the particles are denser and more regular. The raw material iron ore or mill scale is reduced in one or two steps. The single-step reduction process consists of reduction of oxides by hydrogen in a belt furnace or in a fluidized bed, while in the two-step process—such as Hoganas—the iron ore or mill scale is first reduced to an intermediate product known as sponge iron in tunnel kilns. The sponge is crushed and ground, and the powders further reduced and annealed to the final iron powder. In the atomization process, a high-carbon (4% C) iron is air atomized and annealed for decarburizing the particle core and reduction of the particle surface oxide. Another method consists of shotting or atomizing high-purity pig iron into rather coarse particles, which after ball milling are treated in a reduction annealing process to remove carbon and oxygen, as in the case of Quebec metal powder process. In the Domfer process, the shots are ball milled and mixed with fine mill scale and then annealed to make iron powder. Direct-water atomizing a molten steel to the desired particle size distribution and then annealing was subsequently adopted by the leading manufacturers throughout the world. For P/M structural parts, iron powder or alloyed iron powder is mixed with copper, graphite, nickel, other elemental additives and a lubricant before compaction. Recent advances are in the development of highly compressible powders, alloying methods, and mixing technology of the constituents. To improve the homogeneity of steel powders, prealloyed powders have been developed by melting alloying elements with iron and then atomizing the melt. These powders have similar chemical characteristics but a reduced compressibility, and this reduction in compressibility is proportional to the type and amount of alloying elements. However, the loss in compressibility can be made up by techniques such as repeating the basic compaction and sintering stages or by hot pressing, HIP, or by powder forging. The compressibility of prealloyed steel powders could be improved with a small addition of molybdenum. Another development is the partially

prealloyed powders, in which alloying elements are bonded by diffusion to iron powder particles in order to minimize powder segregation and compositional variations in the individual sintered components. Many ferrous alloy compositions with copper, nickel, and molybdenum have been developed (Ref 8, 9). The mixing of powders is influenced by the powder characteristics such as particle size, shape, size and shape distribution, and composition. Often in the diffusion-alloyed powder, diffusion of alloying elements during sintering is incomplete, leading to heterogeneous microstructures in the product. The mixed powders have some drawbacks such as demixing, poor flow and die fill, dusting of fine particles, and relatively lower green strength after compaction. These problems have been solved by utilizing a new concept in which a binder acts as a glue to bond the smaller particle size alloying elements to the larger iron-base particles (Ref 10–12). Different alloying methods for ferrous powders are shown schematically in Fig. 3. Thus, the alloying method of ferrous materials significantly influences the distribution of alloying elements, compressibility, and the nature of porosity and microstructure of the sintered product. Molybdenum and nickel are commonly used in low-alloy P/M steel powders for increasing the strength, hardenability, toughness, and fatigue resistance. The oxides of these elements could be reduced during the annealing treatment of the water-atomized powders. However, these alloying elements are more expensive, and efforts are being made to replace them with less expensive manganese and chromium. In P/M steels, these elements are generally maintained below 0.3% because of the difficulty in reducing the oxides during annealing (Ref 13). However, this problem can be solved by mixing the base iron or prealloyed powders with higher-carbon ferrochrome and ferromanganese and sintering at 1250 ⬚C for the reduction of chromium or manganese oxides. Sintered parts containing chromium and manganese have a tendency to produce larger dimensional changes, and the same have been overcome with the addition of nickel (Ref 14). Oxygen pickup of manganese- and chromium-containing steels can be reduced by using oil as the atomizing medium instead of water. Further oil atomization can be used for carbon-containing (⬍6% C) rapidly quenched powder with low oxygen content (Ref 15). Iron powder as well as high-alloy steel powders are produced with an oxygen content lower than 100 ppm (0.01%) by oil atomization (Ref 16). The P/M stainless steel sector is an important and growing part of industry because of their oxidation and corrosion resistance and good physical and mechanical properties. Powders are produced by water atomization with irregular characteristics, while gas atomization using nitrogen or argon will provide spherical shape. Considerable progress has been made in the atomization techniques including real-time visualization (Ref 17, 18). Commercial grades include AISI 410, 440C, 446, 304L, 304, 347,

400 / Residual Stress Formation During Manufacturing Processes 316L, 316, and 317. Tool steel powders are also produced by either water atomization, or gas atomization with argon or nitrogen. These powders have uniform composition and fine microstructure, resulting in excellent hardness with less distortion during heat treatment. The P/M approach also enables production of newer tool steels with higher alloy content but without the segregation of alloying elements. Rapid solidification is another possibility in the case of atomization of molten steels. This will reduce the micro- and macrosegregation continuously with increasing solidification rate. Other advantages include increased solid solu-

bility and the formation of metastable or glassy alloys. In principle, the latter case represents zero segregation since the liquid state is preserved to room temperature with minor changes in the atomic rearrangement. The dendrite arm spacing as a function of solidification rate for metals is shown schematically in Fig. 4. Ingots and large castings have a solidification rate of 10 to 10ⳮ3 K/s; subsonic gas atomization induces solidification at about 10 to 102 K/s, water atomization at 102 to 104 K/s, and ultrasonic gas atomization at about 103 to 105 K/s. Metallic substrates of 20 lm have a solidification rate of about 104 to 106 K/s, while finer metallic sub-

Fe

Fe

Fe

Fe

Fe

Fe

Fe

Fe

(a)

(b)

Fe Fe

Fe Fe (c)

Fig. 3

(d)

Schematic distribution of alloying elements in different alloying methods. (a) Admixed. (b) Partially alloyed. (c) Binder bonded. (d) Prealloyed

103 Casting

Dendrite arm spacing, µm

100 Gas atomization Water atomization 10

Ultrasonic/centrifugal atomization Gun splat

1

0.1

0.01 10−3

10−1

10

103

105

107

109

1011

Cooling rate, K/s

Fig. 4

Cooling rates and secondary dendrite arm spacing of metal powders/substrates for different atomization techniques

strate of 10 lm to submicron thickness have a solidification rate of the order of 106 to 1010 K/ s (Ref 19). A variety of centrifugal atomizing processes have been developed to produce powders of finer particle size. Gas dissolution in metal melt and gas atomization have been developed to produce steel powders of less than 20 lm in size (Ref 20). The growing interest in MIM has increased the demand for finer iron and steel powders. Iron micropowders produced by decomposition of carbonyl iron process have spherical particle shape, fine particle size, and average size in the range of 4 lm or lower with good sinterability (Ref 21). Improvements in the commercial atomization process has enabled production of steel powders with mean particle size in the range of 4 lm for MIM (Ref 22). Extremely fine iron powders of the order of 50 ˚ have been prepared by the evaporation and A condensation method (Ref 23). Although mechanical processing is generally used for the production of powders of hard and brittle materials, the milling process is commonly used as a secondary operation in the production of iron powders from spongy cakes of oxide-reduced, sintered, or agglomerated, atomized, and electrolytic powders. Milling is also used for producing powders from cast iron scrap, cryogenic milling, or hydrogen embrittlement of steel swarf (Ref 24, 25). Different types of hammer, disk, rod, ball, vibratory, and fluid-energy mills are used for this purpose. For making finer powders or solid-state alloying, high-energy mills such as attrition, vibratory, or large-diameter tumbler mills are used. There is an increasing use of high-energy mills for producing alloy and composite powders having unique microstructures through mechanical alloying. The technique is used as another nonequilibrium processing such as rapid solidification for reproducing a wide variety of materials such as solid solutions, intermetallics, amorphous, and nanocrystalline materials (Ref 26). Hard steel materials have been fabricated with matrix of chromium carbide by mechanically alloyed powders containing 30 to 50% Cr and 2.3 to 4.8% C with better wear resistance than Stellite (Ref 27). Mixing and Blending of Powders. Iron and steel powders of the required characteristics are to be produced by blending different size fractions of the metal powders to obtain the desired apparent density and flow of the powders for die filling. Powders of different constituents are to be added to produce the desired alloys during sintering. Lubricants are to be added to assist compaction, reduce wear, and increase the die life. Depending on the mixing device—such as rotating drum, double cone or twin shell, screw mixer, or a blade mixer—the mechanisms of mixing may be predominantly diffusion, convection, or shear. Double-cone and twin-shell mixers, with or without internal intensifier blades, are used for dry mixing of iron and steel powders. In forming processes such as injection molding (Ref 28), powder-binder feedstock have to be prepared with uniform distribution of binder and ferrous powder particles throughout

Residual Stresses in Powder-Metal Processing / 401 the feedstock. The binders may be thermoplastic mixtures of polymers, waxes, oils, lubricants, and surfactants. Thermoplastic binders are mixed at intermediate temperatures where shear is dominant by using screw or plunger extruders or sigma blade mixers. The powder binder mixes and subsequently granulates before injection molding. For injection molding, fine steel powders in the micron-size range are used to produce intricate shape and improved sinterability with the binder in the range of about 40 vol%, depending on the packing characteristic of the powders.

Compaction in Rigid Dies Unidirectional compaction is the most widely used manufacturing method for structural steel components. Powder pressing is carried out in rigid steel or carbide dies under pressures of the order of 150 to 900 MPa. Lower pressures are used for porous ferrous bearings, and the pressure gradually increases with increasing density such as low-density, medium-density, and highdensity products with less than 10% porosity. The compacts maintain shape by cold welding and interlocking of powder grains within the mass. The green compacts must be sufficiently strong to withstand ejection from the die and subsequent handling and transport to the sintering furnace. The final shape and mechanical

properties are related to the level and uniformity of the as-pressed density known as green density. Compaction cycle for a single-level part is shown in Fig. 5. A desired amount of mixed iron powders is automatically gravity fed into the die along with core rod to produce a hollow shape from the hopper through a feeder shoe and compacted with the help of upper and lower punches at a pressure, depending on the density requirements of the part. The upper punch is withdrawn, the lower punch ejects the pressed compact, and the feeder shoe slides the part away from the die cavity. The cycle is automatically repeated by charging, powder filling of the die. Compaction cycle can be classified as single, double, or multiple action depending on the complexity of the part to be produced. Movement of only the upper punch is usually termed single action, while relative motion of two members—either both punches with stationary die or upper punch and die with lower punch stationary—is termed double action. Multiple action utilizes several tool members arranged in order to support each level of the component separately. Depending on the complexity, P/M components can be classified into one of the four classes (Ref 29): ● Class I: components are single level with single shape and low length-to-diameter ratio that will allow single-action compaction. ● Class II: compounds are single level with higher length-to-diameter ratio and require double action.

Upper punch

Powder from hopper Die

Lower punch

Core rod Cycle start

Charging-powder die filling

Compaction begins

Green compact

Compaction completed

Fig. 5

Compaction cycle for a single-level part

Ejection of part

Recharging die

● Class III: components have two levels and are

termed external- and internal-flanged components and require double-action compaction. ● Class IV: components have three or more levels. These are multilevel parts of different thickness and contour, and they have to be pressed with multiple forces from two directions. A variety of compacting presses are available with wideranging pressing capacities and production rate capabilities. Compacting presses are mechanically or hydraulically driven, but can incorporate a combination of mechanically, hydraulically, or pneumatically driven systems. The tool design should take into consideration the nonuniform transmission of pressure to the mass of powder in the die, limited lateral flow, as well as the ejection of the compacted part from the die in the direction of pressing. The density within the green compact decreases with increasing length of the compact since the powders do not behave like liquids under pressure and the applied pressure is not uniformly transmitted. Double-action compaction can improve the pressure distribution, but generates a lowerdensity region in the middle of the compact. Therefore, length-to-diameter ratios exceeding 3 to 1 are not generally recommended. Normally reentrant grooves, reverse tapers, and lateral holes are difficult to incorporate in the compact because of the difficulty of ejection and, thus, machining. Efforts have been made to overcome this limitation by designing flexible die assemblies. Bevels requiring feather-edged tools that are fragile should be modified to a small flat end. Parts with abrupt changes in section should be avoided as they introduce stress raisers that may lead to crack formation as a result of the stresses induced by the elastic expansion or springback during ejection of the part from the die. The size of production rate of the part will depend on the press capacity, complexity of the part, and the number of punch motions required during compaction. The double-action tooling system is used to produce class I and II parts. Force is applied to the top and bottom of a part simultaneously. In this case, the die is stationary and the punches have the same travel rate. The floating-die tooling system can also give a similar effect in which the die is mounted on a spring or a yielding mechanism using hydraulic or pneumatic cylinders for an adjustable resisting force. When the upper punch enters the die and starts to compact the powder, friction between the powder and die wall causes the die to move down, which will have the same effect as an upward movement of the lower punch. When the compaction is complete, the die moves upward to its powder fill position, and the lower punch ejects the part from the die. Multiple-motion die-set process can produce complex P/M parts using floating die and withdrawal tooling methods. For very high production rates of simple parts of the order of 60,000 to more than 100,000 pieces/h, me-

402 / Residual Stress Formation During Manufacturing Processes chanically driven rotary presses or anvil presses are used.

Isostatic Compaction Some of the constraints of rigid-die compaction such as long thin-wall cylinders and parts with undercuts, and so forth, can be overcome by isostatic compaction. In cold isostatic pressing, water or oil is used as the pressure medium. The powder is contained in a flexible mold such as polyurethane and is compacted with the same pressure in all directions through the fluid pressurizing medium (Ref 30). Pressure ranging from 200 to 400 MPa or more of the order of 800 MPa can be used. When the elastomeric mold along with the powder can be removed from the pressure vessel, the technique is known as wet bag tooling, while the technique in which the elastomeric mold is fixed to the pressure vessel is known as dry bag tooling. Since the pressure is applied isostatically over the entire surface of the part, more uniform density is achieved through the entire part than in the case of rigid die pressing. Isostatic pressing is used in the manufacture of 30 cm cylinder liners (Ref 31), P/M tool steels, stainless steels, and alloy steels. Other compaction processes include triaxial compression by simultaneous isostatic and uniaxial compression, high-energy-rate compaction, explosive forming, slip casting, and vibration compaction (Ref 32, 33). Compaction in rigid dies at very high pressures of the order of 3 GPa have also been carried out using T15 highspeed steel dies and punches. These steels are manufactured by HIP of inert-gas-atomized powders with a composition weight percentage of 12 W, 5 V, 5 Cr, 5 Co, and 1.6 C. The process known as cold sintering (Ref 34) or high-pressure consolidation at ambient temperature has been used for processing T15 high-speed steel and 410L stainless steel with improved properties. Full-density fine iron nickel powder composites with 80 vol% VC and Cr3C2 have been successfully consolidated by cold sintering.

Sintering Green ferrous parts produced by compaction are sintered at elevated temperatures in a con-

trolled atmosphere so as to produce sintered parts with the desired microstructure and mechanical properties. Sometimes loose powders are also sintered to consolidate them for certain applications, such as porous filters and electrodes or for model experiments to study sintering. Sintering is a key operation for the development of sintered ferrous alloy components intended for structural applications. It is a thermal treatment of the powder or a compact at a temperature below the melting point of the main constituent to increase its strength by bonding the particles together. A variety of physical, chemical, and metallurgical transformations occur during sintering, and these are influenced by sintering conditions such as temperature, time, atmosphere, and cooling rate as well by the chemical composition of the powder mass. During sintering, atomic diffusion takes place, and the neck formed among the powder particles as a result of bonding will grow, leading to improvement in mechanical properties. In the case of atomized prealloyed powder particle, the microsegregation within the powder particle, if any, will be eliminated. The reaction between the sintering atmosphere and the surface oxides or adsorbed gases on the powder particles will clean the surface, thereby promoting the diffusion process. When the alloying additions are in the form of elemental powders, the diffusion process will lead to the beginning of alloying. As the sintering proceeds, recrystallization and grain growth may follow, the pores tend to become rounded, and the total porosity decreases, resulting in densification. Depending on the constituents and nature of initial powder mass, the lower-meltingpoint constituents melt with the formation of liquid phase, or the liquid phase may be eutectic or transient, which will facilitate rearrangement and diffusion resulting in faster pore elimination and densification. Alloying additions such as copper and phosphorus in iron will result in the formation of liquid phase during sintering at a lower temperature than those of silicon, iron, or tool steels. As the sintering continues with increasing temperature, there is likely to be more densification and more homogeneous alloying. After sintering, the sintered mass is cooled to room temperature. Depending on the composition of ferrous alloys and cooling rate, the resultant structure may be annealed, normalized,

Slow cooling zone Loading green parts

Fig. 6

Preheat, lubricant burn-off zone

Sintering zone

Schematic presentation of a continuous mesh-belt sintering furnace

or quenched; the process chosen will govern the mechanical properties of the final product. Sintering Furnaces and Atmospheres. Different types of continuous production furnaces are used for sintering. These include the mesh belt conveyer furnace, the pusher furnace, roller hearth furnace, and walking-beam furnace. In addition, different batch-type furnaces and vacuum furnaces are also used. The longitudinal section of a muffle-type continuous production furnace is shown in Fig. 6. The first section of the furnace is the preheat or delubrication/burnoff zone, into which, after loading, the green parts enter and the compacting lubricant is removed from the green P/M compact. Next is the sintering zone, in which the parts are sintered at a specific temperature and time in a suitable atmosphere. This is followed by a short, slowcooling zone to reduce the thermal shock and develop the microstructure and a final cooling zone with water cooling and a protective atmosphere to a sufficiently low temperature so that oxidation does not occur when the sintered parts are unloaded. In a continuous mesh belt conveyor furnace sintering is carried out at 1120 ⬚C. The function of the sintering atmosphere is to control the chemical reactions between the ferrous materials being processed and the furnace surroundings. An atmosphere may be used as source for one or more chemical elements as in the case of addition of carbon to iron in a carburizing furnace atmosphere. The atmosphere may also prevent loss of alloying elements present in the materials, or the atmosphere may be used to remove the decomposition products of the lubricants from the furnace, thereby preventing their deposition in the furnace interiors. In the case of iron and steel components, the atmosphere will aid the reduction of the oxides on the surface of the metal particles in the compact and control the carburization and decarburization. The oxidation and decarburization are caused when oxygen, water vapor, and carbon dioxide are present in improper proportions with respect to the hydrogen and carbon monoxide content in the sintering atmosphere. Iron oxides are reduced by hydrogen, carbon, and carbon monoxide, while carburization is caused by hydrocarbons such as methane or by carbon monoxide. Typical atmosphere compositions, atmosphere functions, and corresponding tempera-

Hanging curtains Cooling zone

Hanging curtains Final cooling zone

Unloading sintered parts

Residual Stresses in Powder-Metal Processing / 403 tures for sintering steel are shown in Fig. 7. The most frequently used sintering atmospheres are endothermic gas, exothermic gas, dissociated ammonia hydrogen, and vacuum. The composition of principal furnace atmosphere constituents, such as conventional and synthetic nitrogen-base atmospheres, along with the chemical requirements, such as the ratios of various atmospheric constituents for different furnace operations—for example, reduction of surface oxides, carburization, decarburization, and burning lubricant vapors—are given in Tables 1 and 2. Now consider sintering a green compact made out of elemental powders of iron, copper, graphite, and lubricant. The product should be free from soot and the admixed graphite should be uniformly diffused into iron particles as combined carbon, resulting in an optimal pearlitic microstructure during cooling with minimum carbon loss. After melting, copper should be uniformly distributed over all particle surfaces in the part. Good bonding between the particles and relatively rounded pores are required for structural integrity. At least five stages are required to complete the sintering process, which will occur in five different zones of the furnace, outlined in Fig. 7 and summarized in Table 2. While sintering iron graphite powder, the temperature has a profound effect on the amount of combined carbon formed for a given sintering time. Furthermore, the cooling rate after sintering also influences the strength and hardness. Sintering of iron-copper involves bonding of iron to iron, iron to copper, melting of copper, solution and diffusion of copper in solid iron, and solution and precipitation of iron in liquid copper. Iron-copper-carbon sintered products

• 425–625 °C

• 625– 1040 °C

give high strength due to the combined effect of copper causing precipitation strengthening and increasing hardenability of steel, but they lack toughness. Sintering of alloy steel will depend on the type of alloying such as elemental, prealloyed, diffusion alloyed, or a hybrid mix. Mixing elemental powders provides high compressibility, but for homogenization and uniform composition good diffusion rates must be maintained during alloying. During sintering, partially alloyed steels containing nickel, molybdenum, and copper will form numerous nickel-rich areas of austenite, sometimes surrounded by high-carbon martensite because of the slow diffusion of nickel and faster diffusion of copper and molybdenum. High-Temperature Sintering. High-temperature sintering is currently used to sinter at temperatures above 1120 ⬚C, which is difficult to handle in the conventional belt furnaces. Depending on the alloy system and processing conditions, typical temperatures for high-temperature sintering of ferrous alloys are in the range of 1180 to 1350 ⬚C. The advantages of hightemperature sintering include: ● The use of reactive elements such as man-

ganese, chromium, silicon, and so forth, which would otherwise oxidize at conventional sintering temperatures ● Possibility of extending the sintering techniques to new alloy systems and materials structures that are not possible at lower sintering temperatures, such as full-density tool steels, stainless steel with improved corrosion resistance, and metal-matrix composites ● Improve the distribution of alloying elements

• 1040– 1120 °C

Preheating zone Loading green compacts Atmosphere functions

Atmosphere composition

Fig. 7

Delubrication zone

• 1120–815 °C

• 815 °C to ambient

Slow cooling zone Water cooling zone

Hot zone

• Convey heat quickly and uniformly

• Reduce surface oxides

• Copper melting coating, or infiltrating

• Carbon control

• Cooling

• Burn and sweep out lubricants to front exit

• Carbon diffusion

• Bonding

• Cooling rate control

• Prevent oxidation or controlled light oxidation

• Lightly oxidizing

• Highly reducing

• Reducing

• Reducing

• Slightly reducing or neutral or slightly oxidizing

• Neutral to carbon

• Neutral to carbon preferred

• Neutral to carbon preferred

• Carbon control

Schematic of typical furnace condition for sintering steel

Unloading sintered products

such as nickel molybdenum, copper, and so forth through enhanced diffusion at higher temperatures; the increase in diffusion rate also results in better densification and spheroidization of porosity ● The formation of liquid phase at higher temperatures further helps in the densification of the product. However to take full benefits of high-temperature sintering, the critical processing steps must be identified and controlled (Ref 36, 37). These include the variations in sintering parameters such as time, temperature, and atmosphere, as well as their influence on the sintered product. High-temperature sintering has been used as a means of reducing the oxygen content in powder preform forging, although the process was not adopted for the production of sintered steel until 1970. This is mainly due to the lack of development in high-temperature sintering furnaces, higher cost of production for making components in batch-type high-temperature sintering furnaces, and inadequate knowledge on hightemperature sintering of ferrous alloys. Subsequently, interest in high-temperature sintering revived with improvements in furnace technology for processing full-density tool steels and specific ferrous alloys with improved properties. Stainless Steels. Corrosion resistance of powder metallurgy stainless steels is inferior to that of the wrought alloys of the same composition, and so there is a need to investigate and improve the properties of these sintered products. Hightemperature sintering in appropriate atmospheres with controlled cooling rate can produce sintered stainless steels with higher density and mechanical properties and improved corrosion resistance. Studies of stainless steel indicate that higher sintering temperature of 1350 ⬚C reduces the deleterious interstitial elements and increases sintered density, strength, and corrosion resistance. Nitrogen in the sintering atmosphere provides alloy strengthening; however, nitrogen control is important for corrosion resistance. Rapid cooling from the sintering temperature of the order of 200 ⬚C/min or faster is required to prevent the absorption of excess nitrogen with the formation of Cr2N. The formation of chromium oxide or nitride reduces the corrosion resistance. It has also been reported that the poor corrosion resistance of 316 stainless part with 5100 ppm nitrogen, 3000 ppm oxygen, and 0.12% C can be improved by sintering in 75H/ 25N atmosphere for 30 min at 1205 ⬚C followed by fast cooling. The oxygen content is found to be 3000 ppm, while nitrogen content reduced to 2100 ppm and carbon to 0.07%. Excessive carbon is generally caused by residual lubricant, while high oxygen content is due to the high dewpoint of the atmosphere. Low dewpoint gas atmosphere of –40 ⬚C or vacuum sintering is required for optimal corrosion properties. Precipitates of chromium nitride or carbide will not only reduce the amount of chromium available to form a protective oxide film, but will also

404 / Residual Stress Formation During Manufacturing Processes change the chemical potential of the matrix depleted of chromium from the remaining material to form a protective oxide film and results in a galvanic couple, thereby accelerating intergranular corrosion. Sintering studies based on relative contribution diagrams of 316L stainless steel filters have shown that corrosion resistance will depend on the average pore size (Ref 38). Filters produced by sintering at higher temperature are found to have better corrosion behavior in NaCl, although they had the same extent of sintering as measured by the final porosity. The improved corrosion resistance is attributed to the healing of fine pores, which are detrimental. Improved corrosion resistance with increased sintering temperature of some stainless steels is reported in Fig. 8 (Ref 39). Liquid-phase formation as a result of hightemperature sintering will lead to more complete alloying, improved densification, and even attainment of full density. Theoretical density can be achieved in the Fe-0.5B-0.6C, wt% at 1300 ⬚C, because of the formation of increasing

Table 1

amounts of the eutectic by the diffusion of iron (Ref 40). The shrinkage and the sintered density is a function of boron content and is strongly affected by the carbon content. In the iron-silicon system, sintering is promoted by a transitory liquid phase that disappears at higher temperatures. However, the sintering is activated by the presence of silicon, which stabilizes the ferrite phase where diffusion is higher. Other ferrite promoters such as tungsten and molybdenum improve the density. However, the ferrite formation does not allow heat treatment, but hardening can be achieved by the formation of molybdenum and tungsten carbides. Tool Steels. Many of the problems related to the conventional cast and wrought high-speed steels can be overcome by adopting P/M methods. In this approach, powders of the required composition are produced by gas or water atomization of the molten metal. The gas-atomized powders are spherical and are densified by canning followed by HIP or hot extrusion in the solid state at about 1100 to 1150 ⬚C. The primary

MC and M6C carbides in this process are finer, of the order of 1 to 2 lm. However, these billets require extensive finish machining to produce the end products. The water-atomized powders are irregular and can be die pressed or cold isostatically pressed to green compacts of 70 to 75% density followed by vacuum sintering at about 1240 to 1330 ⬚C to full density. This method can produce near-net-shape components, but the use of higher sintering temperatures results in coarser carbides of the order of 2 to 15 lm. Hot isostatically processed components are more expensive, but will have superior properties and performance as dies and cutting tools particularly for complex broaches and gear hobs. The general application of P/M tool steels can be classified as: high-speed cutting and machining operations, cold working, processing and molding of engineering plastic, hot (warm) working, die casting, and precision wear parts. The selection of a particular P/M tool steel for a given application depends on a number of factors such as the service life required, the oper-

Composition of principal furnace atmosphere constituents Key ratios(a)

Atmosphere

AGA class

Air-tonatural gas ratio

Dewpoint

Nominal composition, vol %

⬚C

⬚F

Nitrogen

Hydrogen

Water

Carbon monoxide

Carbon dioxide

Lean exothermic Rich exothermic Endothermic Associated methanol Associated ammonia Hydrogen Nitrogen

101 102 302 … 601 … …

9.0 6.0 2.5 … … … …

20(a) 20(a) 5 15.5 ⳮ50 ⳮ60 ⳮ60

68(b) 68(b) 40 60 ⳮ60 ⳮ80 ⳮ80

84.7 69.8 38.2 … 25.0 … 100

1.2 12.2 40.4 65.6 75.0 100 …

2.5 2.5 0.8 1.7 0.004 0.001 0.001

1.4 10.2 19.8 32.4 … … …

10.2 4.9 0.3 0.4 … … …

Methane

Hydrogen to water

Carbon monoxide to carbon dioxide

Hydrogen to carbon monoxide

… 0.4 0.5 … … … …

0.5 4.9 51 39 19,000 100,000 …

0.1 2.1 66 81 … … …

0.9 1.2 2.0 2.0 … … …

Note: For nitrogen-base atmospheres, composition, dewpoint, and key ratios can be synthesized over a broad range, depending on which of the above generated atmospheres is blended with the high-purity nitrogen gas. (a) Control carburization or decarburization, oxidation or reduction, or combination of these. (b) Dewpoint is ⳮ6 ⬚C (10 ⬚F) above temperature of cooling water; dewpoint may be reduced to 5 ⬚C (40 ⬚F) by refrigeration or to ⳮ45 ⬚C (ⳮ50 ⬚F) by absorbent tower dehydration. Hydrogen-to-water changes accordingly. Source: Ref 35

Table 2

Furnace zones, sintering phases, and atmosphere requirements to sinter an iron, 2% copper, 1% graphite, and 1% lubricant part Atmosphere composition (a), %

Temperature Furnace zone

⬚C

⬚F

Time, min

Sintering phase

1 delube

425–650

800–1200

10–30

2 preheat

650–1070

1200–1960

5–15

3 high temperature

1070–1150

1960–2100

10–30

Particle bonding

4 slow cool

1150–815

2100–1500

5–15

Carbon restoring

5 cool down

815–50

1500–120

30–90

Cooling down, optionally oxidizing

Delubing

Elimination of particle surface oxides

Sintering subphases

Atmosphere requirement

Hydrogen (b)

Methane

0–0.1

Water

0.5–1.5

Flow

Circulation

Lubricant vaporizing, vapor burning, flushing vapors to entrance Oxide reducing, graphite diffusing, copper melting, and coating particle surfaces Copper diffusing, neck (bond) growing, pore rounding Carbon transferring, homogenizing

Fast, uniform heat transfer, slightly oxidizing

2–7

High toward Highly entrance desirable

Highly reducing to surface oxides, neutral to carbon fast, uniform heat transfer

5–15

0.1–0.3

0.01–0.03 High toward Desirable entrance

Neutral to carbon reducing

3–8

0.2–0.5

Uniform slow cooling, slightly carburizing

2–7

0.3–1.0

Pearlite forming, part cooling down, preventing oxidation or controlling light oxidation

Slightly reducing or neutral (optionally oxidizing) to iron, uniform fast cooling

0–2

0–0.1

0.01–0.02 Medium toward entrance 0.01–0.02 Medium toward entrance 0.01–0.02 Low to medium partially toward exit

Desirable

Highly desirable Highly desirable

(a) Balance is essentially nitrogen with or without small amounts of carbon monoxide and carbon dioxide. (b) Hydrogen can be derived from hydrogen storage vessel, dissociated ammonia, endothermic gas, or dissociated methanol. (c) If slightly oxidizing atmosphere is required, water is relatively higher or a small amount of air is introduced along with nitrogen in water-cooled section at a selected location. Source: Ref 35

Residual Stresses in Powder-Metal Processing / 405 ating conditions anticipated, compatibility with coating operations, materials availability, and cost. Some of the P/M high-speed steel compositions are reported in Table 3 (Ref 41). Processing of P/M tool steels requires controlled high-temperature sintering for obtaining full-density products with controlled microstructure. The temperature range available for sintering to full density is extremely narrow—of the order of 3 to 5 ⬚C—necessitating uniform temperature distribution in the furnace (Ref 42). Actual sintering temperature will depend on the chemical composition, but may be between 1180 and 1300 ⬚C. The linear shrinkage for full densification can be of the order of 10%. The formation and sustenance of the liquid phase play an important role in the density and desired microstructure of the sintered tool steel (Ref 43– 45). A rise in the critical sintering temperature of the order of 5 ⬚C can lead to rapid austenite grain growth of continuous carbide films MC or M6C, depending on the composition of steel, between adjacent grains. While sintering at lower temperature below the solidus, the carbide dispersed in the structure will interfere with the grain growth and densification. When the sinter-

ing temperature is raised to solidus, a certain amount of the carbides will dissolve, thereby reducing the interference from the carbide dispersion, leading to grain growth and densification. The required structure with small austenite grains and finely dispersed carbides can be produced only by getting the correct amount of liquid phase and by controlling the temperature and time of sintering. High-speed tool steel T15 has a wider sintering temperature range than M2 steel because of the differences in the chemical composition and carbides predominantly M6C in the case of M2 and MC for T15 steel. Optimization studies on the vacuum sintering of a T15 steel (1.55C, 4.41Cr, 0.14Mo, 2.24Co, 4.27V, 12.80W, 0.094O, balance Fe) with a Fisher subsieve particle size of 13.6 lm have shown their optimal microstructure and bend strength could be achieved by sintering at 1265 ⬚C for 30 min (Ref 45). Another important development is the attainment of enhanced properties in high-speed steels through improved cleanliness (Ref 46). Knowledge about the role of oxide inclusions on the functional properties of high-speed steels has initiated considerable measures to control the in-

clusion in the steel by improved refining. In a high-alloy high-speed steel such as ASP 30 (8.5Co, 6.4W, 5Mo, 4.2Cr, 3.1V, 1.28C), inclusion control is achieved by employing a totally closed system, from atomizing molten-metal tundish to encapsulation of the powders, in order to prevent the dust contamination and by the oxygen inclusion refining to an active slag treatment by the electroslag heating (ESH) tundish process. These improvements in the P/M processing of high-speed steels have resulted in increasing the mechanical properties. Substantial improvements in fatigue properties could be achieved by electroslag heating of tundish. In conventional high-speed steels (M2), when surface defects from tool preparation are eliminated, individual carbides and stringers act as stress raisers. In the P/M high-speed steels (ASP 30), inclusions act as stress raisers and directly affect the microchipping resistance. Minimization of the unfavorable inclusions through the modified process improves the microtoughness of P/M steels (Ref 47). A reduction in the number of inclusions with critical size is important in many applications. Molds for optical lenses, medical parts, compact disks, and encapsulation of integrated circuits may not permit nonmetallic inclusions as small as 15 to 20 lm, as the presence of these will result in the rejection of the molds. The newer P/M tool steels have a significant positive effect on both manufacturing properties, such as electrodischarge machining ability, polishability, and mechanical properties. They have also exhibited improved tool performance in applications such as cutting tools, molds requiring high surface finish fine blanking tools, powdercompacting tools, and highly stressed cold-forming tools.

Treatment of Sintered P/M Parts

Fig. 8

Corrosion resistance of various P/M stainless steels. Hours of immersion by open beaker method in 5% NaCl solution until 1% of surface is covered by rust or stain. Source: Ref 39

Although sintered parts can be used as such, some of the parts are sized or repressed in order to maintain closer tolerances or higher densities. Certain sintered products require additional treatments such as infiltration, oil impregnation, machining, joining, steam treatment, plating, and other corrosion-protection treatments and heat treatment. Infiltration is a process of filling the pores of P/M parts with a metal or alloy of lower melting point to increase the density, strength, hardness, ductility, or impact resistance of the component. The properties of sintered iron P/M parts have been improved with the infiltration of copper. It is important to control the infiltration temperature for developing proper microstructure and hence the mechanical properties (Ref 48). Joining P/M components can be used to produce complex shapes or to produce products with different properties by joining P/M parts with different materials, including conventional components. Joining can be achieved by sintering, infiltration, or by projection welding, arc, resistance, or electron beam welding. Sintered P/M parts can also be brazed with special braz-

406 / Residual Stress Formation During Manufacturing Processes ing materials. Other joining methods include gluing, press fitting, upsetting, riveting, and bolting. Oil impregnation will provide the part selflubrication, as in the case of bearings, or greater resistance to corrosion. Impregnation can be accomplished by soaking the parts in an oil bath or by a vacuum process. Machining is minimal in P/M components and is limited to operations such as undercuts, cross holes, or threads. Frequently, machining operations such as tapping, threading, drilling, or surface grinding are necessary for sintered P/ M parts. Since the sintered materials are porous, it is necessary to keep the cutting tool sharp. The factors affecting the machinability of P/M steels are composition, porosity, microstructure, processing conditions, inclusions, and machining parameters (Ref 49). The effect of various machinability-enhancing additives or composition

Fig. 9

Effect of density on the hardenability of P/M steels

Table 3

changes to sintered products has dominated most of the investigations, and these additives have included lead, bismuth, tellurium, selenium, CaO, MoS2, and MnS. Although porosity is necessary for certain applications such as self-lubricants, it has a detrimental effect on machining, leading to interrupted cut and acceleration of tool wear and poor surface finish of the product. In this context, studies on the machinability and enhancing additives are very significant for increasing the application range of sintered products. Sintered materials are more susceptible to atmospheric corrosion than solid materials because of the porosity that will not only increase the reactive surface, but will also provide favorable sites for condensation of liquids that may cause corrosion. The extent of corrosion depends on porosity, which is governed by the sintered density of the material. The porosity can be closed by resin impregnation or steam treatment. For impregnation resins such as polyester, resin diluted with styrene is found to be suitable, and the impregnation is carried out in an autoclave followed by hardening the resin using heat treatment. Resin-impregnated sintered components are also useful for pressure-tight applications. These components can also be plated with copper, nickel, chromium, cadmium, zinc, and so forth for improving surface corrosion or the appearance of the sintered parts. Steam treatment is another method to close the porosity of sintered parts and/or to increase the corrosion resistance and mechanical properties (Ref 50). Steam treatment is carried out in special furnaces with overheated steam at around 550 ⬚C for 1 to 2 h. This treatment will provide a black iron oxide (Fe3O4) layer of about 5 lm thick on the surface that is hard and wear resistant. Heat Treatment. Sintered steel components are often subjected to heat treatment in order to

optimize the physical and mechanical properties of the product. These heat treatments include annealing, through hardening, and case hardening. While heat treating P/M parts, special consideration needs to be given to the density, composition, quenching or cooling method, temperature, atmosphere, and the equipment-related variables such as temperature uniformity and atmosphere control. The response of a P/M part to a particular heat treatment will depend on its thermal conductivity, which is related to the density of the sintered part. High-density P/M parts and wrought material parts have high thermal conductivity, ensuring rapid heating and cooling, while parts with low density take longer to heat and cool, thereby necessitating special quenching or cooling methods. Another factor to take into consideration is hardenability, which decreases with increasing porosity. During case hardening, case depth may increase with increasing porosity, as shown in Fig. 9 (Ref 51). Another factor to be considered is the surface morphology—the amount of open porosity at the surface. The amount of surface open porosity increases with decreasing density. Accordingly, decisions have to be made about the type of quenchant, the type of equipment (such as salt bath) to be used, and so forth for hardening. The micrograph in Fig. 10 shows the effect of surface morphology on the ability to carburize FC-0202 (0.2C, 2Cu) materials (Ref 51). Alloying elements have a direct influence on the hardenability of ferrous P/M materials. The compositions of some P/M structural steels are given in Table 4. The alloying elements are carbon, copper, nickel, and molybdenum. As the alloying content increases the eutectoid of the steel generally shifts to a lower carbon content in the phase diagram, while the critical cooling rate is reduced and the transformation nose of

Nominal compositions of P/M high-speed steels Designation

Composition, wt%

Tradename(s)

AISI

UNS

JIS

Werk. No.

C

W

Mo

Wear-resistant high-speed steels containing 3–4% V ASP23, APM 23, CPM M3, Micromelt M3, FAX 31, DEX 20, KHA 32 CPM M4, Micromelt M4, Isomatrix S690, HAP M4

M3 M4

T11323 T11304

SKH53 SKH54

1.3344 …

1.3 1.4

6.25 5.75

5 5

SKH 55 … …

1.3243 … …

1 1.5 1.3

6 5.75 6.25

SKH10 … … … … … …

1.3202 … … … 1.3241 … …

1.6 1.5 1.5 1.6 2.3 2.1 2.2

12 10 8 11 6.5 14 12

… …

… …

1.3 1.8

6.25 12.5

Heat-resistant and superhigh-speed steels containing 5–12% Co and 2–6.5% V CPM M35 M35 … CPM Rex 54 … … ASP30, APM30, CPM Rex 45, Micromelt HS 30, Isomatrix S790, … … FAX 38, DEX 40, HAP 40, KHA 30 CPMT15, Micromelt T15, FAX 55, DEX 61, HAPT15, KHA 50 T15 T12015 CPM Rex 76, Micromelt HS 76 M48 T11348 HAP 50, DEX 62 … … Isomatrix S390 … … ASP60, APM60, KHA 60 … … DEX 80 … … HAP 70 … … Cobalt-free superhigh-speed steels CPM Rex 20 CPM Rex 25

M62 M61

T11362 T11361

Co

Weq

Hardness, HRC

3 4

… …

16.25 15.75

65–67 65–67

5 5 5

2 4 3

5 5 8

16 15.75 16.25

65–67 66–68 66–68

… 5.25 6 2 7 6 9

5 3 4 5 6.5 5.5 5

5 8.5 8 8 10.5 12 12

12 20.5 20 15 20.5 26 30

66–68 67–69 67–69 66–68 67–69 68–70 69–71

… …

27.25 25.5

66–68 67–69

10.5 6.5

V

2 5

Note: All of the P/M high-speed steels contain about 4% Cr for hardenability in large sections. Silicon, manganese, and sulfur contents are typically 0.50%, 0.30%, and 0.03% maximum, respectively. For select applications requiring improved machinability, sulfur contents are increased to 0.10 or 0.22% with corresponding increases in the manganese contents. Source: Ref 41

Residual Stresses in Powder-Metal Processing / 407 the continuous-cooling curve shifts to the right. Increasing the carbon content tends to increase the tensile strength. Maximum strength occurs at a carbon level between 0.8 and 0.9%. However, above the carbon level of 0.77%, the austenite that forms at the grain boundaries results in a brittle structure. The addition of copper also strengthens and helps to sinter harden some lowalloy steels. Copper has a strong influence on dimensional change, and precise control of copper and carbon is required to maintain consistent dimensional change. Addition of nickel to 2% and in certain cases up to 6% improves the heat treated properties of the steel. Nickel lowers the austenitizing temperature and increases hardenability. Molybdenum additions in the range of 0.5 to 1.5 are useful since it has a higher diffusion rate than nickel. However, more care should be taken in the heat treatment of molybdenumcontaining steel, and the molybdenum carbide formed during tempering can provide secondary hardening. Powder metallurgy parts may be oil quenched, which is less severe than water and

brine due to improved distortion control and minimized cracking. Fast oil with improved heat transfer characteristics is preferable. Since the P/ M part can absorb oil, proper care should be taken during cleaning. In addition to oil, water, brine, or aqueous polymer solutions can be used with improved rate of heat transfer, but accelerate the part corrosion on account of the residual quenchant that can be trapped in the surface of pores. For hardening and case hardening, the temperature must be high enough to fully austenitize the material so that it will quench to a martensitic structure. A higher austenitizing temperature is required for oil quenching than for water or brine quenching. Tempering and steam treating are performed below the austenitizing temperature, a uniform distribution and dissipation of heat are needed to ensure consistency of the end product. With increasing carbon and nickel content, the austenitizing temperature is decreased, while other alloying elements slightly increase the austenitizing temperature and time. More than double the soaking time is required for less-dense P/M products than for wrought material because of the lower thermal conductivity. Considering the atmosphere of endothermic gas, a nitrogen/methanol atmosphere or a nitrogen-base atmosphere can be used as long as the carbon potential is controlled to prevent oxidation or reduction. During case hardening, the atmosphere should be neither carburizing nor decarburizing to the materials. The amount of additive gases such as methane, propane, and/or ammonia should be a function of density and degree of open porosity in the part. Sintered steel parts with low density and with highly open surface will have less uniform case depth and less well-defined interface between case and core. These defects can be minimized by controlling the relative amounts of additive gases. Important heat treatments of P/M steel parts include hardening by austenitizing and quenching; processes

Table 4

that improve surface properties such as the case hardening methods of carburizing, carbonitriding, nitrocarburizing, and nitriding; tempering; and annealing. Carburizing is carried out on P/M parts with relatively large cross-sectional thickness to obtain maximum fatigue and impact properties. Parts with more than 15% porosity are not recommended for carburizing. Carburizing materials generally contain nickel, molybdenum, and copper with a combined carbon level of 0.3 to 0.35% for a porosity of 10 to 15% and the combined carbon is reduced to 0.15 to 0.25% for porosity of less than 10%. These steels are generally gas carburized at about 900 to 930 ⬚C for shorter cycles with a higher carbon potential than for wrought material. Carbonitriding is a gas-carburizing process in which about 10% ammonia gas is introduced into the gas-carburizing atmosphere at about 800 to 850 ⬚C. The ammonia dissociates, and the nitrogen formed diffuses into the steel surface simultaneously with carbon, thereby retarding the critical cooling rate on quenching, leading to a more consistent martensitic transformation. Care should be taken to avoid excessive nitrogen diffusion, which will lead to embrittlement. Carbonitriding, because of its lower operating temperature, provides better control of distortion than carburizing. In plasma nitriding, an ion discharge or plasma of positive ions and electrons is set up between two electrodes in a vacuum chamber containing low-pressure nitrogen gas. The ions bombard the P/M part that forms the cathode, heating to temperatures of the order of 470 to 570 ⬚C, cleaning them by dislodging surface atoms and depositing active nitrogen, which is created by ion collision with nitrogen molecules in the gas. Induction hardening is recommended for those parts requiring a hard and wear-resistant

Composition of P/M structural steels Composition limits (b), %

Description

P/M iron and carbon steels

Iron-copper and copper steels

Iron-nickel and nickel steels

Copper-infiltrated steels

Low-alloy steels Influence of surface effect on the ability to carburize on FC-0202 (0.2C, 2Cu) material. Top to bottom open surface, closed surface, core. Closed surfaces allow for more uniform absorption and diffusion of carbon. Etchant: 2% nital

Fig. 10

MPIF (a) designation

C

Ni

Cu

Fe

Mo

F-0000 F-0005 F-0008 F-0200 F-0205 F-0208 FN-0200 FN-0205 FN-0208 FN-0405 FN-0408 FX-1005 FX-1008 FX-2005 FX-2008 FL-4205 FL-4405 FL-4005 FLN-4205

0–0.3 0.3–0.6 0.6–0.9 0–0.3 0.3–0.6 0.6–0.9 0–0.3 0.3–0.6 0.6–0.9 0.3–0.6 0.6–0.9 0.3–0.6 0.6–0.9 0.3–0.6 0.6–0.9 0.4–0.7 0.4–0.7 0.4–0.7 0.4–0.7

… … … … … … 1.0–3.0 1.0–3.0 1.0–3.0 3.0–5.5 3.0–5.5 … … … … 0.35–0.55 … 1.70–2.00 1.35–2.50(c)

… … … 1.5–3.9 1.5–3.9 1.5–3.9 0–2.5 0–2.5 0–2.5 0–2.0 0–2.0 80–14.9 80–14.9 15.0–25.0 15.0–25.0 … … … …

… … … 93.8–98.5 93.5–98.2 93.2–97.9 92.2–98.0 91.9–98.7 91.6–98.4 89.9–96.7 89.6–94.4 82.5–91.7 82.2–91.4 72.4–84.7 72.1–84.4 95.9–0.85 96.3–98.9 94.5–97.5 93.95–97.75

… … … … … … … … … … … … … … … 0.50–0.85 0.70–1.00 0.40–0.80 0.50–0.85

(a) Metal Powder Industries Federation. (b) Other elements total by difference equals 2.0% max, which may include other minor elements added for specific purposes. (c) At least 1% of the nickel is admixed as elemental powder.

408 / Residual Stress Formation During Manufacturing Processes surface such as cams, bevel gears, spur gears, and so forth. Since the inductance of P/M materials, because of porosity, is lower than in wrought materials of similar composition, a higher power setting is required to reach a given depth of hardening. Further rapid transfer to the water-quench solution containing some rust-preventive additive to avoid internal corrosion is also required. Nitrocarburizing is carried out within the ferritic region at about 570 to 600 ⬚C, involving the addition of nitrogen and carbon to the surface of P/M parts. Nitrogen forms a thin layer of hard and wear-resistant e-iron nitride on the surface. The atmosphere usually consists of a 50:50 mixture of endothermic gas and anhydrous ammonia, and the metal powder should have a density of more than 90%. Nitrocarburizing improves resistance to sliding wear and fretting and also increases the strength and reduces the notch sensitivity of P/M parts. Annealing is used in cases such as P/M forging to improve machinability. Forgings are austenitized at a temperature appropriate for carbon content, followed by rapid cooling to an isothermal transformation temperature determined by the TTT diagram for the steel. A combination atmosphere and vacuum continuous heat-treating system is shown in Fig. 11 (Ref 51). Typical ferrous P/M applications include hardening, carburizing, carbonitriding, and tempering of automotive transmission and drive-train components, hydraulic valves, cams, and actuators. Sinter hardening allows P/M parts to be hardened in the sintering furnace while cooling from the hot zone. The material should be selected with sufficient alloy content so that it is air hardenable. Parts made out of nickel, molybdenum, and low-alloy steel powders with blended addition of 2% Cu and 0.8% C have been found to develop satisfactory properties by sintering at

1120 ⬚C followed by tempering at 177 ⬚C. During accelerated cooling from the sintering furnace, these parts transform to martensite. Although the sinter-hardening process may not produce complete transformation to martensite, the resultant microstructure/property relationship provides considerable flexibility to the P/M fabricator. The incomplete transformation provides a tensile strength of the order of 70 to 80% of tempered martensite, and the remaining microstructure consists of porosity, bainite, and pearlite. The economic advantage of the process includes the elimination of a separate heat treatment step such as quenching and tempering, thereby providing a cleaner process with better dimensional uniformity and yield. Depending on the variations of belt speed and cooling system, the percentage of martensite can be altered from 28 to 84% with corresponding hardness values of 16 to 36 HRC (Ref 52). It is essential to heat treat P/M tool steels to develop their properties. Powder metallurgy tool steels use the same heat treatments as those used for conventional tool steels, but the former respond more rapidly because of the uniform microstructure and finer carbide size. The heat treatments include preheating, austenitizing, quenching, and tempering; the optimal heat treating temperatures depend on the composition, and the recommendations by the manufacturers should be followed (Ref 53). Powder metallurgy grade tool steels are segregation-free, and hence the variations in dimensional changes after heat treatment are smaller than those in conventional tool steels. Cooling rates have a profound influence on the properties of P/M austenitic stainless steels. With very slow cooling, precipitation occurs preferentially at grain boundaries, resulting in an increase in strength and loss in ductility. The carbide precipitation is detrimental for machinability. When the cooling

Combination atmosphere and vacuum continuous heat treating system. Typical ferrous P/M applications include hardening, carburizing, carbonitriding, and tempering of automotive transmission and drive-train components, hydraulic valves, cams, and actuators

Fig. 11

rates are normal precipitation at grain boundaries is reduced, while rapid cooling such as water quenching suppresses the precipitation of carbides and nitrides, thereby providing maximum ductility.

Hot Pressing The majority of sintered parts are made by cold compaction in rigid dies followed by sintering. Since metals are softer at elevated temperatures, it is possible to achieve higher densities using hot pressing or pressure sintering. The powder or green compact is subjected to heat and pressure. Resistance sintering under pressure, electrically activated pressure sintering, and spark sintering are the variations of hot pressing. The die material in hot pressing may be alumina, silicon carbide, superalloys, refractory metals and their alloys, or graphite, and the latter can be heated by direct resistance or by external resistance or induction heating. Depending on the die materials, temperatures as high as 2200 ⬚C and pressures of the order of 160 MPa can be used. The atmosphere may be reducing, inert, or vacuum. Investigation on the hot pressing of iron powders between 100 and 1000 ⬚C indicates that the compaction rate is larger during ␣-c transformation than at temperatures just below or above the transformation. Furthermore, the compaction rate is much larger below the Curie point than above (Ref 54). High-carbon steel powder containing 1.89% C produced by nitrogen gas atomization has been vacuum hot pressed at 700 ⬚C to more than 99% of theoretical density at 0.9 ks at 160 MPa and for 7.2 ks at 100 MPa (Ref 55). The analysis of densification showed the superplastic flow of each powder plays an important role in the densification process. Hot Isostatic Compaction. Some of the limitations of hot pressing such as problems in producing higher length-to-diameter ratios, complex shapes, and larger components can be overcome by HIP. The temperature of HIP varies from 400 to 3000 ⬚C and pressures of the order of 20 to 300 MPa, depending on the material. Heating elements such as graphite, tungsten, tantalum, platinum, molybdenum, kanthal, and nichrome are used, and the pressurizing medium can be inert gas such as nitrogen, argon, helium, or vacuum. A typical HIP unit consists of a pressure vessel, gas storage, handling system, power supply, controls, and instrumentation (Ref 56). Schematic representation of the section of a HIP pressure vessel with furnace is shown in Fig. 12. Since the equipment must be able to withstand high isostatic pressures at elevated temperatures, a cold pressure vessel with an internal furnace is preferred. The powder to be consolidated is packed in a gastight sealed preshaped container or cold isostatically pressed. The container materials may be glass, ceramic, or a metal or alloy and should not react with the powder materials, but should be able to transmit the load to the powder at elevated temperature. The heat is supplied by the furnace, which is kept inside the

Residual Stresses in Powder-Metal Processing / 409 pressure vessel. The powder-filled container is hot degassed and sealed under vacuum. The required gas pressure is generated either by pumping the gas to an intermediate pressure to the workpiece, followed by heating to obtain the final temperature and pressure or by heating the workpiece to the required temperature while maintaining a low pressure of the order of 7 MPa followed by pressurization that is hot loading. Pressure-assisted sintering is another method in which the P/M parts density could be increased to near-theoretical density at pressures of the order of 2 to 12 MPa. This will reduce the equipment cost of pressure vessels and associated facilities, gas consumption, and sintering time, thereby reducing the operating cost substantially (Ref 57). Initially, the sintering is carried out to attain closed porosity, followed by the application of pressure at or near the sintering temperature to produce a full-density product. Since the HIP equipment and process is expensive, alternate approaches have been developed, such as Ceracon process, rapid omnidirectional compaction, and STAMP process. In the Ceracon (CERAmic CONsolidation) process, a granular ceramic medium is used to transfer the pressure, instead of a gas, on HIP (Ref 58). The preform is prepared by cold compaction and then heated in a controlled atmosphere to the consolidation temperature. At the same time, the ceramic granules are also heated and charged into the die. The heated preform is inserted into the ceramic medium so that the preform is completely surrounded by the ceramic grains. The heated assembly is then transferred to a consol-

idation press, and an axial load is applied to the ceramic grain by moving the ram mechanically or hydraulically. The preform experiences axial and lateral forces, resulting in deformation and full densification with the correct processing variables. The consolidated part is ejected along with the granules from the die and separated from the ceramic granules. Preforms of alloy steels have been consolidated to full density by this process, and the surface finish of the product is influenced by the size and shape of the ceramic grains. The process is simple, and economic advantages include inexpensive tooling when low dimensional tolerances are adequate. Products such as low-alloy steel ratchet wrenches have been produced economically by this technique. Rapid omnidirectional compaction is another isostatic compaction method in which a powderfilled cavity is surrounded by a mass of fluid die material, such as AISI 1020 steel or a Cu-10Ni alloy, which is capable of plastic flow at temperatures of the order of 1000 ⬚C and pressures of the order of 800 MPa. This consolidation pressure is applied to the fluid die from a uniaxial ram of a compaction or forging press and tooling. The pressure is transmitted to the powder through the fluid die in an omnidirectional way as in the case of isostatic compaction. The thick fluid elements permit consolidation of complex shapes, including holes, reentrant angles, and irregular shapes. The powder is filled in the welded die assembly, evacuated and sealed, and then heated to the consolidation temperature, placed in a pot die and subjected to uniaxial ram force. The ram force is transmitted through the plastic fluid die elements and reacted

End closure Wire-wound vessel W o r k l o a d

Temperaturecontrolled hot zone

W o r k

Furnace insulation mantle Furnace heater

l o a d Support and bottom insulation Thermocouple feedthrough Power feedthrough

Fig. 12

Hot isostatic pressure vessel and furnace

by the pot die inner surface, thereby applying pressure to the powder from all directions. Highspeed tool steel milling cutters have been processed by this technique to fully dense, near-net shape with very fine microstructure resulting in superior performance in comparison with a coarse-grained sintered product with some residual porosity (Ref 59). The STAMP process is an integrated one in which the molten metal poured from a tundish is horizontally atomized with nitrogen or inert gas (Ref 60). The powders, after sieving, are hermetically sealed in a sheet metal container by welding. These are then heated to about 1100 ⬚C and transferred to a hydraulic press and consolidated to about 95% theoretical density. The billet weight may range from 50 to 2500 kg. These billets are then hot worked to final shape. Lowalloy steels, stainless steels, and tool steels have been consolidated. The process is energy efficient and economical with improved hot workability of the billet on account of its microstructural homogeneity.

Roll Compaction Direct rolling of powders into a compacted green strip with sufficient strength for handling is achieved in roll compaction. In this process, the powder from the hopper is carried toward the roll gap under the roll nip with its apparent density, depending on the powder characteristics in the static condition forming the incoherent powder zone. Under dynamic conditions when the rolls are rotating, the friction between rolls and powder and interparticle friction along with gravity will carry the powder into the roll gap, and it will be compacted into a green strip when using a horizontal mill (Ref 61). The incoherent powder zone extends over an angular distance ␣ and on the entry side of the rolls with diameter R and is continuous with the compacted strip on the exit side of the rolls (Fig. 13). Powder rolling is used initially for single-layer strip with different porosity. Tooling has been added to guide powders into the roll compaction zone, and control blades have been designed to regulate the flow rate of the powder into the mill. Other modifications include a system of side entrants at the ends of the rolls to prevent the powder from spilling out of the compaction zone and a system for continuously dressing the surface of the rolls to maintain a steady-state friction condition between the rolls and powder. Multilayer strip is also being produced by simultaneously feeding separate streams of powders with different layers into the roll gap. By modifying the powder feeding system, a vertical mill can also be used for roll compaction. Considering the principle of metal powder compaction in general, it may be noted that in the case of compaction, in rigid dies friction inhibits the compaction process, while in roll compaction friction assists the compaction. In addition to direct roll compaction of steel powders, efforts have also been made to produce a porous billet by sintering followed by different

410 / Residual Stress Formation During Manufacturing Processes mechanical working operations such as rolling, cold or hot rolling to produce sheets, or forging and extrusion to produce seamless tubes or cold extruded products. The conventional way of producing thin steel from rough ingot to the final coiled strip is capital and energy intensive with considerable losses in the materials through edge trimming, reheating, and pickling. Direct roll compaction of powders followed by sintering and hot and cold rolling as shown in Fig. 13, will reduce the cost of capital and energy with substantial improvements in the materials utilization. Another method is a slurry process in which a slurry is made out of the steel powder, which is deposited on a suitable substrate followed by roll compaction and sintering followed by hot and cold rolling (Ref 62). Evaluation of the large-scale production of mild steel sheets and tubes including seamless tubes and extruded steel parts have shown that the process is very attractive and economical. Hot extrusion of powders to full density utilizes a combination of hot pressing and hot mechanical working (Ref 63– 65). The hydrostatic forces along with the unidirectional forces cause the compact to flow through the die. Microstructural control of the product is achieved by the manipulation of extrusion variables such as temperature, extrusion ratio, and so forth. The frictional forces produce a shear component, and the energy expended in shear presents almost half of the energy needed for extrusion. Different methods of powder extrusion are extrusion of loose powder through a die, extrusion of cold or hot pressed compact, and extrusion of powder in a sealed container, canned powder extrusion. Seamless P/M stainless steel tubes are commercially manufactured by hot extrusion. In a typical case, gas-atomized stainless steel powders of composition 22Cr5Ni-3Mo-0.015N-0.003C, balance Fe, are loaded into a mild steel can to a density of about 70% and sealed. The can is cold isostatically compacted to a density of about 85% and then hot extruded to full density at about 1200 ⬚C using glass lubricant. Technical and economic advantages of this process include improved mi-

crostructure and mechanical properties, along with improved yield of the tubes (Ref 66). A typical example of the use of these stainless steel tubes is in the lift tower of the Grande Arche at La De´fence, Paris (Ref 67). More than 150 tons of P/M grade stainless steel tubes ranging in diameter from 60 to 244 mm were used because of their special surface finish, allowing freedom from maintenance.

Powder Forging Powder forging is a hot densification process in which an unsintered, presintered, or sintered preform made out of powders is forged to higher densities. It has the advantage of powder metallurgy such as dimensional accuracy and minimum materials waste, along with the high strength of forging. Plastic deformation and volume change of the sintered powder materials is different from those of the conventional cast materials because of the porosity in the former case. In powder preform forging, the preform design has a significant effect on the metal flow, structure, distribution of the stresses in the material, and properties of the final product. The mode of densification during powder forging will depend on the repressing or upsetting conditions. During repressing, the extensive flow of the materials in the lateral direction is prevented by die-wall constraints as the outside diameter of the preform is close to the outside diameter of the forged part, and with the approach of full density a hydrostatic condition prevails. A spherical pore becomes ellipsoidal on collapse, with the long axis close to that of the original pore diameter. The limited lateral flow of the repressed part restricts anisotropic properties, while in upsetting forging considerable lateral flow of the materials takes place. The stress state around a pore is a combination of normal stress and shear stress, and the spherical pore becomes flattened and elongated in the direction of lateral flow. This can result in some amount of anisotropy in upset forging that is much less than that in wrought material.

Powder Hopper

α

R α

Compaction rolls

Compacted strip Hot rolling

Cold rolling

Sintering Coiler

Fig. 13

Rolling of metal powders to strip

Conventional forging requires few dies and forging steps, while powder forging can usually produce a fully formed component with a single forging step. Powder forging is energy efficient and utilizes maximum materials with minimum scrap. The actual savings in materials will depend on the complexity of the product. Powder forging consumes less energy and provides longer tool life. The properties of the powderforged component depend on a number of processing parameters such as powder characteristics, compaction, sintering, or forging parameters such as forging temperature, pressure, speed of press, chilling of the preform by the tooling, and the amount of material flow. A variety of iron and steel parts have been powder forged, and their number is increasing because of the economic advantages (Ref 68). A large number of powder-forged components are produced for automotive applications for transmissions, engines, and differentials. These include connecting rods for engines, valve seats, stator cams, chain saw sprockets, gears, and so forth. The increasing demand for light weight, low cost, close control of balance, weight, improved material properties, and endurance limits by the automotive industry has resulted in the introduction of powder-forged connecting rods. Powder metallurgy offers homogeneous microstructure without any material textures and anisotropic properties. Powder forging in closed dies without lateral flow results in high density and strength levels. Premixed powders such as FeCu-C or prealloyed powders such as Fe-Cr-NiMo-Mn with additional amounts of free carbon and heat treatment enable generation of customer-tailored properties with preferable microstructures. Strength levels more than 1500 MPa can be achieved by powder forging, and hence individual alloy design offers the possibility of lightweight connecting rods. Chemical compositions of some of the ferrous alloys used for powder forging are given in Table 5. The production sequence of the powder-forging process is shown in Fig. 14 (Ref 70). The prealloyed powders are compacted on an eightaxis computer-numerical-controlled (CNC) servohydraulic multiplaten powder press to a density level of 6.4 to 6.6 g/cm3. A sophisticated tool concept allows close control of the movements of the individual compacting punches and guarantees a homogeneous distribution of sectional densities and therefore also determines the total and balance weight of the components at minimum weight scatter. A subsequent balance system then provides a 100% weight check and guarantees close tolerances and balance weights. The highly precise weight control system guarantees consistent properties of the component as well as optimal conditions and tool endurance for the following precision net-shape forging in closed dies. The preforms are then positioned by a robot pick-and-place system directly onto the conveyor belt of the sintering furnace or into an intermediate buffer-system in order to provide flexibility for tool changes or maintenance work. Sintering is carried out at 1120 ⬚C for 15 min,

Residual Stresses in Powder-Metal Processing / 411 Table 5

Chemical composition requirements for powder forged parts Composition, wt%

Element

Ni (max) Mo (max) Ma Cu Cr (max) S (max) Si (max) P (max) C O Fe

P/F-10xx

P/F-10Cxx

P/F-11xx

P/F-11Cxx

P/F-42xx

P/F-46xx

P/F-44xx

P/F-49xx

0.10 0.05 0.10–0.25 0.30 max 0.10 0.025 0.03 0.03 (b) (c) bal

0.10 0.05 0.10–.025 1.8–2.2 0.10 0.025 0.03 0.03 (b) (c) bal

0.10 0.05 0.30–0.60(a) 0.30 max 0.10 0.23(a) 0.03 0.03 (b) (c) bal

0.10 0.05 0.30–0.60(a) 1.8–2.2 0.10 0.23(a) 0.03 0.03 (b) (c) bal

0.40–0.50 0.55–0.65 0.20–0.35 0.15 0.10 0.03 0.03 0.03 (b) (c) bal

1.75–2.00 0.50–0.60 0.10–0.25 0.15 0.10 0.03 0.03 0.03 (b) (c) bal

0.10 max 0.80–0.95 0.08–0.18 0.15 0.10 0.03 0.03 0.03 (b) (c) bal

0.10 max 1.4–1.6 0.08–0.18 0.15 0.10 0.03 0.03 0.03 (b) (c) bal

(a) Covers manganese sulfide additions of from 0.3 to 0.5 wt%. The manganese content in solution is similar to P/F-10xx or P/F-10Cxx, i.e., 0.10–0.25 wt%. (b) Carbon content specified by the purchaser. (c) When required, maximum oxygen content shall conform to the amount specified by the purchaser. Source: Ref 69

Automatic handling

100% weighing

Sintering

Compacting Buffer

Shot-peening

Fig. 14

Automatic handling

Protective atmosphere

Signing

Forging

Production route of powder-forged connecting rods

Powder filling

Ejecting Compacting

Preform inserting

Forged connnecting rod Ejecting

Forging

Fig. 15

Tooling configuration for powder forging of connecting rods

and the process parameters such as temperature, belt speed, dewpoint, and so forth are monitored and registered. A second robot system transfers the sintered hot parts under a protective atmosphere of nitrogen into the forging cavity of the CNC hydraulic forging press. Forging is done in a manner similar to the tool concept of compaction in fully capsulated closed dies when any lateral material flow and the possibility of generating flashes or burrs are avoided. This compaction step therefore only provides a reduction of the component height so that all geometrical features and weight accuracy of the green part are transferred into the forged preform. The specified densities of more than 7.6 or even 7.8 g/cm3 are achieved in the most stressed transition zone from gudgeon pin end to shank section. Consistent forging results are obtained through the control of uniform tool temperature and proper lubrication. The tooling configuration for powder forging of the connecting rod is shown in Fig. 15. After ejection, the forged connecting rods will be cooled down to room temperature under controlled conditions in a protective atmosphere. Shot peening is performed to remove the connecting rod forging pale. Density and sectional distribution as well as carbon and oxygen content are analyzed at regular intervals. All dimensions are checked on a statistical process control (SPC) base and recorded. An assessment of the cost of manufacturing connecting rods by different manufacturing techniques indicates a minimum cost for powder forging. Besides reduced energy and fluid costs for machining, the environmental aspect due to drastically reduced removal of chips and machining coolant volume gains more importance under modern ecological management audit schemes. Powder-forged connecting rods have reduced engine weight and improved engine performance on account of their improved weight control and dimensional control along with reduced component weight. Furthermore, powder forging has proved to be competitive in relation to conventional forging, resulting in an overall cost reduction. Millions of powder-forged connecting rods are currently in use by leading auto manufacturers throughout the world, and their number is steadily increasing.

412 / Residual Stress Formation During Manufacturing Processes Metal-Injection Molding Metal-injection molding (MIM) has been established over the past decade as an emerging technology for the manufacture of small, precision components of complex shapes in both small and large volumes. Metal-injection molding components are finding new applications in industries such as automotive, business equipment, computer hardware, chemical, biomedical, aerospace, and armaments. Specific components include airbag components and other automotive parts, micro-electronic packages, computer disk drives, orthodontic brackets, firearm components, camera and business machine parts, cutting tools, wire bonding and other assembly tools, wristwatch cases, jewelry, thread guides, spray nozzles, wear components, oxygen sensors, surgical tools, biomedical implants, radiation shields, cutters, clippers, connectors, turbochargers, and valves. The important steps involved in the MIM process are shown in Fig. 16. Ferrous powders of suitable characteristics are hot mixed with a binder and granulated to form the feedstock, which is molded somewhat similarly to those used in plastic-injection molding. The molded part is then subjected to debinding and sintering to form the product. The powder particle size and shape distributions are important for injection molding, as spherical or near-spherical shapes will provide a high packing density while fine powders sinter more readily than coarser powders. Generally, a mean particle size of less then 20 lm is preferred. Such powders are produced by carbonyl process or by water or gas atomization. The applications of

Steel powder

these ferrous powders include soft magnetic materials, low-alloy steels, stainless steels, and tool steels. The prominent binder categories are thermoplastic, thermosetting, water-based, inorganic, and gelatin systems. The binder systems consist of a binder, a plasticizer to reduce the viscosity of the binder, and surfactants to lower the surface energy for mixing. Wax polypropylene system is a typical binder system for MIM. The ratio of metal powder to binder or the solids loading determines the viscosity, debinding rate, dimensional control, and shrinkage. The mixing should result in a homogeneous powder/binder mixture free from segregation, and the binder constituents should fill all the interstitial spaces between particles, at the same time forming a thin layer around each particle. The mix is granulated into solid pellet feedstock that can be stored or fed into the injection molding machine. The rheological properties of the feedstock are important; the viscosity at the molding temperature should allow the feedstock to flow smoothly into the die cavity without segregation, and the mix should become rigid on cooling. The feedstock is extruded into the die cavity and is heated with careful control of the nozzle and die temperature of the injection molding machine. Molds with multiple cavities can produce several parts during each injection, thereby reducing the unit cost of the parts. The parts are subjected to debinding by heating the green compact, and this will lead to the melting, decomposing, and/or evaporation of the binder. This process will take several hours, depending on the section thickness of the product. Catalytic debinding could reduce the debinding

Binder

Premixing Granulation

Hot mixing Granules

Debinding

Mold

Hot plunger Molding

Sintering

Fig. 16

Metal-injection molding process

Sintered parts

time. Other debinding techniques depending on the binder system include wicking, solvent extraction, vacuum extraction, and air drying. After removing the binder, the brown parts are sintered at suitable temperature, time, and atmosphere to obtain metallurgical bonding and densification. Since the debound brown parts are porous, large shrinkage occurs, and the sintering atmosphere and temperature must be closely controlled to retain the composition and shape of the product. The density of the sintered part is usually greater than 97% and approaches theoretical density. The properties of the sintered parts can be improved by postsintering. Metal-injection molding has now become a mass-production technology for small net-shape parts of about 25 g weight, exhibiting design and economic benefits over cast and wrought components in such fields as electronic equipment, machine tools, watches, cameras, and medical equipment. Recent developments in binder systems and instrumentation for injection molding and sintering equipment have resulted in the expansion of MIM products to larger parts such as a 2 kg boat propeller and newer areas such as automotive engine parts (Ref 71, 72.)

Spray Forming This is a potential manufacturing process for producing semifinished and finished engineering components economically. In this process, molten metal or alloys are atomized in an inert gas atmosphere at high pressure to give a spray of liquid particles that is directed onto a substrate, where they impinge, flatten into thin disks or splats, coalesce, and solidify to produce a coherent deposit. The process gives a short route from a melt to a product with fine grain size, freedom from segregation, and enhanced mechanical properties. The product can be a strip that can be subsequently hot and cold rolled, a shape that can be forged, or a billet that can be extruded or deposited on a cool substrate that can be withdrawn as a continuous tube. The process offers a reduced number of operations and increased material yields, resulting in significant economic benefits (Ref 73). Many metallurgical benefits are possible through rapid solidification such as fine grain size, no segregation, and low oxygen content for high-alloy materials. Spray deposition is also attractive for new alloy composition, special products such as laminates, and metal-matrix composites. Spray forming in the Osprey mode has become a viable technology for the production of near-net-shape preforms. Scientific knowledge has been utilized in process control and optimization of spray forming. The process is being developed commercially for the cost-effective fabrication of tubular and billet-shaped products from stainless steels, cast iron, and tool steels. The alloys fabricated by spray forming frequently exhibit improved mechanical properties over ingot metallurgy products (Ref 74). High-quality seamless stainless steel tubes, high-speed steels, and other high-alloy materials

Residual Stresses in Powder-Metal Processing / 413 with superior properties have been processed by spray forming. Efforts are also being made to produce billets up to 400 mm in diameter and 1200 kg in weight by spray forming of D2 (1.5C, 12Cr, l.0Mo, 1.0V, wt%) cold-work tool steels. Other tools steels such as T15 high-speed steel (1.5C, 4.5Cr, 12.5W, 5V, 5Co, wt%) and H13 hot-work tool steel (0.4C, 1.5Si, 5Cr, 1.5Mo, 1V, wt%) are also being evaluated (Ref 75). Spray forming appears to offer a route for the manufacture of billet products with structures equivalent or superior to remelted materials and comparable to P/M products. It is also expected that these materials will have enhanced forgeability to convert the billet to final form.

Warm Compaction Powder metallurgy end users are demanding densities higher than the traditional values of less than 7.1 g/cm3 and improved mechanical properties for ferrous P/M parts. Traditionally, higher-density cores are obtained by copper infiltration, double pressing and double sintering, high-temperature sintering, or by powder forging. However, these techniques involve secondary processing and a significant increase in the cost of production. Relative costs of P/M processes versus part density is shown in Fig. 17 (Ref 76). Warm compaction is a technique by which higher densities and improved mechanical properties are achieved by single compaction, using heated powders and tooling in the range of 75 to 150 ⬚C, in a standard compacting press. When the powder is heated, the compressive yield strength of the powder is reduced substantially, depending on the temperature, resulting in higher densities at lower compaction pressures. Since the powder and tooling are heated to 130 to 150 ⬚C, special lubricants have to be developed to perform at these temperatures. However, the enhanced lubricity of the lubricant at elevated temperatures results in a lower amount of lubricants of the order 0.6% instead of the traditional 0.75% in conventional compaction, resulting in the attainment of higher green and sintered densities (Ref 77). Among the advantages of warm compaction, mention may be made of

Fig. 17

Relative cost versus ferrous part density of several P/M processes

the attainment of higher densities with reduced pressing force, increased green strength, more homogeneous density distribution, better dimensional control, improved static and dynamic properties, and good hardening and machining characteristics. The results of warm compacted Densmix powders heated to 130 ⬚C and compacted in heated tooling could achieve in production scales of complex parts densities in the range of 7.2 to 7.4 g/cm3 with 10 to 15% improvement in mechanical properties (Ref 78). The usefulness of warm compaction has been demonstrated in the production of automotive hubs for high-performance engines, helical gears, gears with complex forms, spiral gears, lock components, and so forth. The warm compaction technology offers both technical and economic possibilities to fill the gap between conventional single pressing and double pressing and extends the use of P/M into new applications.

Rapid Prototyping Rapid prototyping (RP) processes allow for the production of prototypes directly out of three-dimensional computer-aided design (CAD) data. Complex shaped parts, including those with undercuts or hollow inserts, can be manufactured without the use of molds or tools within hours. The three-dimensional description of the object can be CAD design, computer tomograph, finite-element analysis, or from the digitization of a master pattern. The development of stereolithography (SLA) has enabled use of the digital information to create a part directly from the CAD solid model. The file of the part is sectioned by a software program into thin horizontal slices. With the introduction of appropriate process parameters, the part is manufactured by the RP machine. Subsequent to the introduction of SLA process, other RP processes were developed that convert powders into objects by using machine movements determined by algorithms that systematically section a computer rendering of a part. The commercial RP processes produce parts in layers using free-forming material. Among the established RP processes, mention may be made of laser sintering, selective laser sintering (SLS), direct metal laser sintering (DMLS), laser cladding three-dimensional printing, and multiphase jet solidification (MJS) (Ref 79). Most MIM powder materials can be processed by MJS. Excellent properties for 316 stainless steel, where yield strengths double that of wrought annealed bar with no sacrifice in ductility are routinely achieved by laser-based direct-fabrication processing. A chromium/molybdenum hot-work die steel, H13, was directly deposited for three-dimensional components, as the material is commonly used for the die-casting tooling industry (Ref 80). This process can reduce the time for die production by about 40%. The advantages of RP include reducing the product cost and development time for a new product.

Residual Stresses in P/M Processing Residual stresses are of considerable interest and importance to both basic and applied studies because of their influence on the geometrical conditions, processing parameters, and service behavior of products. They contribute over a wide range from inhomogeneous microlevel such as the lattice imperfections to homogeneous micro- and macrolevels. Many processes such as mechanical, thermal, chemical, or any combination of these treatments can lead to the origin of residual stresses. A variety of techniques such as x-ray diffraction, ultrasonic, acoustic emission, photoelasticity, nuclear magnetic resonance (NMR) imaging, neutron diffraction, and so forth have been used to evaluate residual stresses. The Versailles project on Advanced Materials and Standards (VAMAS), technical working area, has taken up residual stress measurement using neutron diffraction. It is reported that this is the only technique currently available for nondestructive measurement of residual stresses deep inside components due to the high penetration depths of neutron beams (Ref 80). More details about residual stresses, their origin, measurements, and their contribution to various properties are reported in the literature (Ref 81, 82) as well as in different sections of this handbook. In powder processing, residual stresses can be generated during metal or alloy powder production, blending, compaction, sintering, mechanical working operations such as powder rolling, forging, and extrusion, machining, heat treatment, and special treatments such as coatings to improve the performance of the product. An understanding of the contribution of residual stresses is of considerable importance since these can influence the dimensional stability, distortion, and properties during processing and end uses resulting in adverse functioning of the component and its reliability during service life. The capability of powder metal processing for making production rates of finished and semifinished parts with good dimensional tolerances is considered to be one of the prominent economic advantages. The effect of traditional P/M processing at various stages on the dimensional stability is shown in Fig. 18. It is evident that stages such as heat treatment decrease the dimensional stability, while stages such as sizing provide improved tolerances to the product. Furthermore, as the number of processing steps increases from the top to the bottom of figure the mechanical properties also increase. Although residual stresses may originate and contribute to the dimensional stability and properties of P/M product, relatively limited published literature is available, and there is considerable scope for research and development in this underexplored area.

Powder Production Residual stress can originate during the production of metal and alloy powders by different

414 / Residual Stress Formation During Manufacturing Processes techniques. These include thermal gradients during atomization of liquid metals, evaporation and condensation, nucleation, and growth processes leading to micro- and macrolevel structural inhomogeneties. The magnitude of microlevel residual stresses in powders will increase in nonequilibrium processes such as rapid solidification or due to environmental interactions with oxygen, moisture, and so forth. The effects of cooling rates and secondary dendrite arm spacing for production of metal powders for different atomization techniques are given in Fig. 4. Different techniques such as gas, water, ultrasonic, or centrifugal atomization can increase the cooling rate from 10 to 106 K/s, thereby reducing the dendrite spacing from several microns to less than 0.1 lm. This will have an effect on the macro- and microsegregation as well as on the homogeneous micro- and inhomogeneous residual micro stresses in the powders. The level of residual stresses in powders is also influenced by the powder characteristics such as size, shape, internal porosity, surface conditions and reactivity of powder. More details about powder characteristics and powder production methods have already been discussed in the earlier sections of this article. Now the defect porosity, which is very much detrimental to the P/M processing, is considered. Many factors during powder manufacturing such as alloy composition, reactivity, melt temperature, viscosity and surface tension of the molten metal atomizing media, pressure, design geometry of the atomization nozzle, flow, surrounding atmosphere, and quenching rate can contribute to the formation of porosity of powders. Furthermore, the porosity in the powder increases with particle size. The porosity in the powder particles will increase the residual

Dimensional stability Decreasing

Medium

Increasing

Pressing

stresses and reduce the apparent and tap densities, thereby creating problems during compaction, uncontrolled dimensional change during sintering, and hot consolidation, and may give rise to residual micropores in the final product, resulting in inferior fatigue and fracture properties of the product. Many commercial methods of production of ferrous powders by electrolytic and chemical methods require some amount of size reduction by milling. In addition, high-energy milling operations are used to produce alloy and composite powders by nonequilibrium process such as mechanical alloying. Mechanical alloying is carried out in the solid state to synthesize alloy powders of very different melting temperatures, nanocrystalline and amorphous materials, and a variety of metal and nonmetal composite powders. The process is carried out using elemental or alloy powders with other constituents in highenergy mills such as large-diameter horizontal ball mill, planetary mill, SPEX shaker mill, or attritor. During the process, the collision of milling balls with powder particles and the container and impeller results in the fracturing and welding of the particles. The repetitive deformation, fracturing, and welding of the particles during mechanical alloying produce an equilibrium composite powder structure in which the oxide or other added dispersoid and/or naturally occurring oxide films is about the same as the welded interlamellas. The laminated structure is further refined as fracture takes place and the thickness of the lamella is decreased. Schematic of variation of properties with processing time during mechanical alloying is shown in Fig. 19. As the processing time increases, initially welding predominates in ductile materials with an increase in the particle size, followed by size reduction and a decrease in particle size. The lamellar spacing decreases, while the hardness of the powder particle increases due to strain hardening and improved distribution of dispersoids. The mean strain at fracture of the particle initially decreases rapidly as the larger particles initially

will have severe flow, and eventually the smaller particles will contain less severe flow and are more likely to withstand the severe strain required for welding. These powders will have considerable residual stresses due to strain hardening during the process and the heterogeneity in the microstructure of the composite powders. Oxide-dispersion-strengthened iron-base alloys for high-temperature applications are processed by mechanical alloying. A typical example is the Inconel alloy MA 956 with composition Fe20Cr-4.5Al-0.5Ti-0.5Y2O3, processed by mechanical alloying in bar, plate, sheet, tube, and wire form (Ref 83). In addition to powder production, stages such as blending and mixing to prepare powders of desired characteristics in terms of apparent density, or addition of lubricants and/or alloying constituents such as carbon and other elemental powders prior to compaction can also introduce internal stresses to the powders. A longer mixing time in an appropriate mixer device can lead to more power consumption, cause excessive wear and tear of the equipment, and introduce internal stresses in the powder through strain hardening, and the latter will adversely affect the compaction of the powders.

Compaction of Metal Powders Residual stresses play an important role during compaction in widely used P/M structural steel parts production. The compaction cycle for a single-level part is shown in Fig. 5. Application of pressure is followed by die filling with the upper and lower punches, and the powder particles will initially undergo rearrangement followed by elastic and plastic deformation. With the increase of pressure, the powder packing is improved, resulting in a decrease in porosity and an increase in strain hardening of the powders. The work-hardened materials undergo fragmentation, resulting in further densification and bulk deformation of the compact. After compaction, the upper punch is removed and the lower punch

Sintering Welding predominates Heat treatment

Resintering

Sizing

Effect of P/M processing on the dimensional stability

Mean strain at fracture

Particle size Lamellar spacing

Heat treatment

Fig. 18

Hardness

Variations in properties

Heat treatment

Grinding predominates Sizing

Processing time

Fig. 19

Schematic representation of variation of properties with processing time during mechanical alloying

Residual Stresses in Powder-Metal Processing / 415 is used to eject the compact, and the cycle is repeated. During compaction, the powder particles undergo plastic and elastic deformation, and the component is constrained in the radial direction by the die cavity. During ejection, more and more of the component is freed from the die cavity, thereby the radial constraint is removed, leading to the springback to relieve the elastic deformation. When the compact is emerging from the die cavity, it will expand in the horizontal direction due to internal elastic strain release accompanied by the weakening of the interparticle bond. If these stresses exceed the green strength of the compact, then the compact will develop cracks perpendicular to the pressing direction. The effect of strain hardening during compaction of iron powder has shown three characteristic regions: an initial stage of rapid densification, followed by an almost linear variation in slope, and the third stage in which the slope decreases rapidly. By incorporating the strain hardening of the materials, the second stage of compaction behavior can be accurately predicted, while the third stage is concerned with a mechanism incorporating the closure of microscopic defects and pores (Ref 84). In iron powder, consolidation is promoted by the presence of porous fines that deform readily and bind the larger particles. The irregular particle shape causes a symmetrical loading between particles, creating shear stresses, interparticle sliding, and consequent frictional welding. The green strength is developed by a combination of mechanical interlocking and frictional welding. During compaction, the transition from first stage to second stage occurs when the pressure exceeds the bulk yield stress of the material, which is when the plastic flow becomes homogeneous instead of local. Hence the model of compaction assuming homogeneous plastic flow can become valid at the beginning of second stage. In the case of gas-atomized spherical powders, plastic deformation occurs at the point of interparticle contact, and the particle shape changes from spherical to polyhedral with the compaction pressure below the yield stress of the material, indicating the first stage of compaction. The plastic deformation and strain hardening of the powders during compaction have been confirmed by x-ray diffraction and microhardness analysis (Ref 85). In spite of the plastic deformation, the powders exhibited inadequate compaction and green strength on account of limited interlocking, sliding, and frictional welding because of the spherical powder characteristics leading to little or no shearing. In rigid-die compaction, with the movement of punches in the vertical direction the green density within a compact decreases with increasing length of the compact, since the transmission of stress through the mass of powder will not be uniform. With increasing complexity of the product, the die design and punches with multiple levels and motions will be more involved, and the problems related to residual stresses and their contribution during compaction also increase and should be tackled carefully to obtain

a sound green compact (Ref 86). Another factor to be considered is the deflection in compaction tooling. A better understanding of the densification of the powder and the resulting stress and deflections in the tooling will provide a means of balancing deflection and springback, thereby avoiding some of the compaction defects. This is particularly important because of the tendency to produce high-performance parts with higher green densities where the density gradients and springback problems become increasingly common. Although the defects in the compacts are due to many causes and are interrelated in a complicated way, the solution to quality problems must be addressed in a simple relationship with leading causes. In this respect, tool stress monitoring—particularly during pressure release and the ejection—can provide useful information for identifying the main causes of cracks in the green compact (Ref 87, 88). A majority of the cracks originate primarily during consolidation prior to sintering, although some cracks may not become evident until sintering has occurred. These defects can be eliminated if most of the causes of cracks in green P/M components are properly understood and addressed. Nonuniform densification of metal powders during die compaction is a problem to be addressed for a better understanding of the process. Lower green strength may result from incomplete compaction or the development of residual stresses that may cause either compact failure on unloading or difficulty in subsequent handling. Variations in densities may also interfere with subsequent processing through inhomogeneous sintering, infiltration, or deformation during forging. The rate-independent models for powder compaction require a yield function to represent the transition from elastic to inelastic behavior. The experimental results suggested that the current yield functions characterized by an elliptical shape in pressure-derivatic stress space may be incorrect and that a yield function reminiscent of granular behavior may be more appropriate. Furthermore, the two state variables— density and interparticle cohesion—are necessary to characterize yield (Ref 89). Simulation of compaction processes to predict the density distribution in compact and/or shape of the compact through constitutive equations has been attempted. The two-dimensional simulation of compaction behavior of powder by particulate modeling has been improved by three-dimensional simulation that incorporates plastic deformation and actually measures interparticle friction. The constitutive equations applied to simulation of powder behavior in forming processes using continuum approach could provide useful information on microscopic behavior of powder assemblies such as density distribution, stress state, and shape of the compact during or after compaction process. However, the effect of particle characteristics such as friction and cohesion cannot be investigated, as these constitutive equations are not related to the particle characteristics. The development of computers has attracted further studies on the simulation of

compaction of powders based on the particle modeling in three-dimensions, incorporating plastic deformation of particles and experimentally measured interparticle friction. Simulations have been carried out for various types of compaction such as closed-die isostatic and threedimensional compaction (Ref 90). Although the pressure/density relationship obtained agrees qualitatively well with the experimental observation and also with the prediction of yield surfaces, there is still much to be done to develop a realistic interparticle force low in the simulation to quantify with the experimental observations. Generally, the optimization of the tool geometry and the die sequence in net-shape powder compaction is currently carried out incrementally and empirically. Efforts have been made to develop a physically based micromechanical model of powder compaction to allow for the computer-based design procedures. The volume density of the compact D is defined as a ratio of solid volume to the total volume, and the deformation of powder is viewed as the material indentation of powder particles. During the first stage of compaction when the density is less than 0.8 D, the contacts between particles are assumed to be independent, and the plastic dissipation by frictional sliding or by plastic flow is small relative to the work done by indentation (Ref 91). A contact law has been proposed for the normal frictionless indentation of dissimilar rigid viscoplastic spheres based on a self-similar deformation and within the infinitesimal strain regime (Ref 92). Further investigations have included the effects of elasticity and finite deformation. During the second stage of compaction when density is greater than 0.8 D, the compact is viewed as a porous body. In a recent study on the micromechanics model of powder compaction, finite-element calculations have been used, taking into consideration the effects of die-wall friction and the effect of material and friction parameters on the final density distribution of a syncor-hub and a valve guide (Ref 93). For a highly constrained geometry of the valve guide, the relative density quickly reaches the value D ⳱ 1 in the vicinity of sharp corners as a result of shearing. A die wall friction of 0.3 leads to the competition between sliding and shear yielding near the wall. The top portion of the material is fully densified, and when the frictional resistance of the material becomes larger than the shear yield stress of the compacted material, the latter shear within in a thin layer and stick to the wall surface, leaving debris on the die wall. Because of the less-confined geometry of the syncor-hub, a high friction of 0.3 does not cause this phenomenon. In addition, the variations in the relative density of the syncor-hub are small in the top wide portion and is of the order of 0.84 to 0.86 of D, while the variation is larger in the thin outer cylinder. The final density distribution is extremely sensitive to the choice of friction coefficient, is moderately sensitive to the initial density D start and is insensitive to the reference density Do and the elastic modulus.

416 / Residual Stress Formation During Manufacturing Processes Although computer simulation of die compaction has been investigated in the past, the commercial possibility has been explored seriously only recently. Finite-element analysis can be applied successfully to simulate powder die compaction. However, the simulation of the compaction stage must account for the complex mechanical behavior of the powder, as well as frictional interaction between the powder and tool set, including complex tooling motion in the case of multilevel part geometry. In the relaxation stage, the springback of the part is small, but the simulation must also account for the complex material behavior and friction, since this can lead to further densification of the powders or green part failure as a result of cracking or end capping. During this stage it is also necessary to take into account whether the part is within the die, since as it emerges from the tool set radial straining takes place. All of the above stages are interdependent, and hence it is essential that a fully integrated model is developed to represent the complete process, which will enable the industry to make products with consistent and improved properties.

Sintering of Metal Powders Some aspects of sintering including furnaces, atmospheres, and systems such as stainless steels and tool steels, and other related high-temperature consolidation techniques have already been reported. This section emphasizes the material transport mechanisms, dimensional changes, the role of stresses, and process modeling. The materials transport during sintering of powders is brought about by a combination of processes of surface, grain boundary, and volume diffusions. Since the diffusion rates are exponentially rated to temperatures, high-temperature sintering is being used for high-alloy steels, stainless steels, and tool steels to produce highperformance parts. Although changes in pore shape can occur very much faster by surface diffusion than by volume diffusion, the former cannot contribute much to the changes in pore volume and to the overall densification of the compact. Densification proceeds by a combination of volume and grain-boundary diffusion, and significant reduction in pore size occurs when the pores are connected to grain boundaries, suggesting that grain boundaries act as sinks for vacancies. Thus, for high rate of sintering the initial grain size can be reduced by reducing the particle size, but the chances of contamination and bulk flow characteristics of loose fine powders may restrict their utilization. During sintering, when the pores reach a limiting size they are unable to contribute to the grainboundary migration resulting in grain growth, and a reduction in densification will take place. In multicomponent alloy systems, the reactions to sintering depend on the relative surface energies, diffusion rates, and solubility of the constituents. When the constituents are extensively soluble in one another, Kirkendall effects become significant and give rise to vacancy fluxes

in response to concentration gradient. Eliminating the problem of shrinkage during sintering of metallic powders in the solid state will be possible with a better understanding of creep phenomenon, viscous plastic flow, internal friction, and diffusion. In the case of liquid-phase sintering, three stages—such as the rearrangement of the particles of the residual solid phase by viscous flow in the liquid phase, dissolution and reprecipitation processes, and coalescence—can be distinguished. A typical ferrous system of commercial importance in which liquid-phase sintering can lead to interesting dimensional changes is the iron-copper system. During the sintering of iron powder, shrinkage takes place at about 1150 ⬚C, but the addition of about 2% Cu powder to iron powder will eliminate the shrinkage. At the sintering temperature, the copper melts, enveloping the iron particles by the rearrangement process, which is accompanied by solution of iron from convex parts of the surface and reprecipitation on the concave neck surfaces. The other process is the solution of copper into the c-iron, causing the expansion of c to leave small pores at the sites of copper and expansion of the compact. Increasing the copper content from 2% to 8%— the limit of solid solubility of copper in c-iron— at about 1150 ⬚C will allow maximum expansion of the compact to take place. This expansion of the compact can be controlled by the addition of 1% graphite, which will result in the formation of ternary Fe-Cu-C eutectic liquid phase at a temperature lower than the sintering temperature, leading to shrinkage and thereby counteracting the expansion of the compact. In Fe-10Cu, it has been reported that swelling of the compact can take place by melt penetration. The additional melt in prior contact areas and at prior grain boundaries in the interior of the iron particles caused dilation leading to microscopic swelling (Ref 94). However, the melt penetration along grain boundaries can be suppressed if carbon is present in the alloy. During sintering of a green component, annealing, stress relieving, recovery, chemical reactions to form new phases or compounds, composition homogenization, shrinkage, and grain growth may take place. On cooling—depending on the system—changes such as precipitation hardening, or other phase transformation, chemical reaction, or the introduction of residual stresses in the product may be expected. In the initial stages of sintering atomic diffusion takes place, the particle contacts formed during compaction grow, residual stresses are relieved, recrystallization and grain growth may follow, the pores tend to become rounded, and the total porosity decreases, resulting in densification. Considerable emphasis is laid on sintering to obtain maximum density, resulting in shrinkage, but one of the advantages of P/M lies in the production of finished components requiring little or no machining. There are many factors influencing the dimensional change of a component during sintering. The decrease in dimensions as a result of densification is due to the elimination

of pores. However, this shrinkage can be influenced by other factors such as entrapped gases, which may expand resulting in an increase of volume. Other factors influencing the expansion include hydrogen reduction of surface oxides, and oxidation as a result of poor atmosphere control. Shape changes can also occur due to variations in green densities of a component. Finer powder generally provides higher shrinkage than coarser material during sintering, but the apparent powder density and green density of the former are lower than the latter powders. However, the atomic process in the fine powders takes place more rapidly during sintering because of larger surfaces, grain boundaries, and lattice distortions during compaction. The initial stages of sintering at constant temperature for a compacted nanometric iron powder of mean particle size of 30 nm, giving a self-diffusion coefficient of D ⳱ 6.1 ⳯ 1024 m2 /s at 325 ⬚C, provided an activation energy of 59 kJ/ mol, which is four times smaller than the one traditionally used for sintering microscopic powders, that is, 239 kJ/mole (Ref 95). Thus, even if surface diffusion is important and shrinkage experiments cannot take this process into account, mass flux between grain boundary and neck surface is an important process in the initial-stage sintering of ultrafine powders. For a better understanding of the process, sintering may be subdivided into three stages. The first stage consists of solid-state sintering when interparticle necks are formed by surface and grain-boundary diffusion. In the second stage, the particles are still connected by isolated contacts with open pore space, and the diffusion field of the necks now overlap. With further densification, the three dimensionally interlinked pore channels close at the narrow sections with a transition to the third stage, which is characterized by closed and isolated pores. The densification in the third stage is accompanied by grain coarsening. During compaction, the powder particles are subjected to strain hardening and the extent of strain hardening increases with increasing compaction pressure. In the initial stages of sintering at lower temperatures, the particles will relieve the strain hardening through recrystallization as a result of annealing. However, the high shrinkage rates of real compacts in the initial stage of solid-state sintering cannot be explained with diffusion as the elementary materials transport mechanism. This stage is characterized by the existence and formation of high densities of various types of defects as well as high rates of densification. The quantitative defect analysis made on the basis of positron lifetime measurements demonstrates the existence of vacancy clusters and dislocations as well as their time-related density change and interaction (Ref 96). There is a drastic decrease of the mean defect density and considerable shrinkage as well as a high rate of shrinkage. The excess vacancies originating in the course of restructuring the mechanical contact into a high-angle boundary agglomerate into clusters in the contact region. They interact

Residual Stresses in Powder-Metal Processing / 417 with dislocations introduced by pressing and newly formed dislocations in such a way that the viscosity of contact substance is lowered, and a cooperative materials transport mechanism will take place. On the basis of dislocation flow, this process should be assumed to allow the entire particle to move along with the softened contact boundary region, or if this mechanism is exhausted then the contact substance flows into the pores in a dislocation viscous state. Studies on the solid-state sintering assume the transport mechanisms of grain boundary and surface diffusion have developed constitutive equations using finite-element simulations of the sintering process for the three stages. Although some of the predictions of the models are confirmed by experiments, particularly the dependence of the bulk viscosity on the density, the sintering stress and the ratio of the shear to bulk viscosity could not be predicted (Ref 97). Modeling of sintering phenomena has been developed from finite difference calculations of geometric details of necks between two particle models to finite-element simulation of shrinkage of compacted powders. Earlier work on simulations could explain some of the deviations between idealized and more realistic neck geometry and other deficiencies of analytical solutions for describing neck growth and shrinkage. Later came the development of sintering diagrams in which dominating mechanisms for neck growth and shrinkage were outlined as a function of temperature and neck radius or time (Ref 98). However, the predictions from these simpler geometries were found to be deviating when quantitatively applied to real experimental results where particles of different sizes, irregular shapes, and of heterogeneous packing characteristics. Furthermore, the data collected from simple and independent experiments will differ from those of the powder particles with considerable lattice defects and surface contamination. Several groups are working on the development of advanced numerical models for simulating solidand liquid-phase sintering (Ref 99). However, it is necessary to check the physical soundness of analytical and numerical approaches before their application to industrial practice. These studies have already led to the prediction of distortion of sintering parts with complex shapes on the basis of appropriately fitted parameters in the constitutive equations. The demand for better-quality P/M components with minimum dimensional scatter is increasing, and secondary operations such as sizing will increase the production cost. Furthermore, it is difficult to carry out the sizing operation on high-strength P/M components because of their high hardness. The requirement of lowest cost coupled with high strength makes it necessary to improve the dimensional tolerance for P/M parts after sintering. The dimensional scatter on P/M component can be estimated by using a mathematical model that includes the variations in mix composition and important compacting and sintering variables (Ref 100). By using the model, it is now possible to com-

pare different powders, alloys, and manufacturing processes to find the most efficient alternative to achieve the best dimensional precision of P/M parts.

Pressure Sintering and Hot Isostatic Pressing Hot pressing, hot isostatic pressing (HIP), and other hot consolidation processes are potential methods for the manufacture of high-quality, high-strength steel, stainless steel, and tool steel components. During hot pressing or pressure sintering of powder compacts, the stress gradients and the stress level present are much higher than during pressureless sintering. The external pressure applied may be in the range of a few to several hundred MPa and will alter considerably the stress state caused by curved free surfaces of coarse powders in the 100 lm range. These altered high stresses yield accelerated material transport by major mechanisms, which are active during pressureless sintering and can provide additional transport mechanisms as plastic deformation and power-law creep. A volume reduction of 30 to 40% may make the part susceptible to nonuniform shrinkage and nonhomogenous microstructural development and also can cause considerable differences in local deformation. In HIP the powder is packed in a thin shell container in the form of a preform, the gas pressure is applied, and the temperature is raised. During this operation, the densification is not uniform because heat diffuses into the powder, the hotter surface layer sinters faster than the interior, giving a denser skin. Heat is conducted through this dense layer faster than through the less dense interior, thereby further adding to the temperature difference between the surface and interior. This will result in a densification front propagating inside, leading to large changes in the shape. A simple one-dimensional model for coupled heat flow to a hydrostatic pressure gas has been successfully developed (Ref 101). However, modeling of the densification of three-dimensional bodies during HIP when rapid densification of one part of the body may constrain the remaining part in a way that inhibits densification, leading to unexpected changes of shape, is yet to be worked out. The mechanisms that contribute to the different stages of densification have been identified and studied. However, it is necessary to check and refine the calculations. Furthermore, the materials properties are so variable that a refining process in which equations are to be calibrated to the results of real industrial HIP process. The HIP process is expensive, and it is very difficult to predict the shape and density of the final product. Finite-element calculation of the thermodynamic behavior of the powder has proved very useful to optimize the process and may result in important savings on energy and materials. Theoretical and experimental work has been carried out using appropriate constitutive equations for numerical simulation. A uni-

fied formalism has been proposed, and an adapted numerical tool developed, integrating different models that can be compared among each other and tested against industrial practice (Ref 102). These studies indicate that the constitutive equations on numerical simulation should be more precisely analyzed, and more experimental and theoretical investigations are necessary to improve the mechanical behavior of metal powders at high temperatures.

Heat Treatment of P/M Steel Parts Special consideration has to be given during the heat treatment of sintered steel components because of the presence of porosity. The hardenability of wrought steel is primarily influenced by the chemical composition and grain size, while in P/M steel the hardenability is significantly influenced by the interconnected porosity, degree of sintering, graphite segregation, and so forth. When a P/M steel part is quenched from the austenitic range, the external surface may experience higher cooling rates than the interior, resulting in mixed microstructures and inconsistent hardness values. These variations are also related to the quantity and type of porosity— size, shape, open, or interconnected—and the complexity of the P/M part. When the porosity is eliminated by forging of P/M parts, the heat treating practice will be the same as for those of conventionally processed steel of similar composition. The heat treatment of full-density P/M products including tool steels and problems related to dimensional change and distortion is considered next. The quenching may experience large temperature differences between surface and interior and between light and heavy sections, which can create shape distortion because of the thermal and mechanical stresses produced by martensitic transformation. This problem is aggravated if the hardenability of steel is so slow that a fast cooling rate is required to get the full hardness. For controlling the distortion of the part, special quenching procedures such as martempering and austempering may be useful. If permissible, localized methods of heating and quenching such as flame hardening, induction hardening, electron beam, or laser hardening will be helpful to reduce the distortion. The presence of retained austenite in heat treated tool steel can slowly transform and produce distortion if the materials are subsequently heated or subjected to stresses. Tool steel products such as gages and blocks must retain their exact size and shape over long periods. If the composition of tool steel provides the required hardness after tempering at relatively high temperature, then it is possible to reduce the amount of retained austenite and the internal stresses by multiple tempering. The first tempering reduces the internal stresses and conditions the retained austenite so that it can transform to martensite on cooling from the tempering temperature. A second or third tempering is carried out to reduce the internal stresses set up by the transformation

418 / Residual Stress Formation During Manufacturing Processes brazing, welding, and so forth prior to heat treatment. These are removed by a stress-relieving treatment in which the material is heated, and the steel will yield plastically when the hot yield strength is equal to the residual-stress level. The P/M processing of steels, stainless steels, and tool steel is discussed in other sections of this article. Powder metallurgy steels, are produced from water- or gas-atomized alloy steel powders by compaction, sintering, high-temperature sintering, extrusion, forging, or HIP. Powder metallurgy tool steels have significantly improved toughness and grindability over conventionally processed tool steels. Powder metallurgy tool steels are free from macrosegregation and porosity and are characterized by uniform distribution of extremely fine carbides. Microstructures of P/M T15 and conventional T15 high-speed tool steels are shown in Fig. 20 (Ref 103). The conventional tool steel (b) microstructure consists of coarse carbides and carbide segregation while the P/M microstructure (a) is characterized by finer carbides with uniform distribution. These characteristics are favorable for providing deeper hardening, less distortion, higher hardness, and faster response to heat treatment and are particularly useful for molybdenum-containing high-speed steels, which tend to decarburize rapidly at the austenitizing temperature. The out-of-roundness of heat treated conventional AISI M2 and P/M ASP 30 tool steels are shown in Fig. 21 (Ref 103). It is evident from the figure that the out-of-roundness distortion of P/M tool steel is substantially lower than that of the conventional tool steel. Powder metallurgy also enables production of grades that are difficult to produce by the conventional method and also newer grades with more alloying additions to provide improved properties. Surface hardening by carburizing is used to enhance the fatigue strength and tribological properties of P/M steel gears. The surface-hardened layers are characterized by microstructural and microhardness evaluation along with residual-stress measurement by x-ray diffraction. The results of the analysis indicate moderate com-

pressive surface residual stresses on the green compacted gear. A slightly higher residual-stress value obtained after sintering is attributed to the limited oxidation registered at the end of sintering. A more pronounced increase in residual stress is evident after carburizing the gear. It is concluded that x-ray diffraction is a useful tool for strict control at different production stages of P/M technology (Ref 104). Special attention is to be paid during heat treatment to minimize the percentage of residual austenite and the component geometry, as the latter can influence thermal shrinkage during quenching of the gear. The residual austenite and thermal shrinkage can influence the surface residual stresses to a great extent. Although P/M technology has been used to produce net-shape products of various sizes and shapes, frequently it is necessary to use secondary machining operations to obtain the final product as discussed earlier. Some of the P/M products are also resin-impregnated in order to seal the porosity for specific applications. These resin impregnated products have improved machinability, but not much information is available regarding the level of residual stresses. Investigations have been carried out by conducting drilling experiments to compare the residual stresses in P/M products with and without resin impregnation (Ref 105). Residual stresses were measured by using an advanced x-ray stress analyzer based on solid-state linear image sensor technique that enables conversion of x-rays directly into electrical signals. The basic system consists of a goniometer and is capable of measuring residual stresses in metallic materials without conducting 2h scanning of the detector. The x-ray tube has a maximum output of 2 kW and can measure residual stresses in microareas by means of a small focal spot size capability. An integrated PC-based control system is used for measurement, data collection, analysis, and display of results. The analysis of the results indicates that the magnitude of residual compressive stresses increases with resin impregnation, and the machining of resin-impregnated parts produces even greater residual compressive stresses compared to nonimpregnated machined parts. These findings are of significant value in understanding machinability and mechanical properties of sintered steels.

Microstructures of high-speed tool steel. (a) CPM T15. (b) Conventional T15. Carbide segregation and its detrimental effects are eliminated with the CPM process, regardless of the size of the products. Source: Crucible Material Corporation

Out-of-roundness measurements on test disks after hardening. (a) Conventional, AISI M2. (b) P/M high-speed tool steel ASP 30

of retained austenite. In plain carbon and lowalloy steel that must be tempered at low temperature to achieve the required hardness, single or repeated low temperature treatment below martensite finish (Mf) temperature can cause most of the retained austenite to transform to martensite. The low-temperature treatment is carried out in a commercial refrigeration unit at about – 70 to –90 ⬚C, either before or after the first temper. If the tool materials tend to crack because of the additional stress induced by dimensional expansion during low-temperature treatment, it is preferable to carry out the treatment after the first tempering of the tool. When the low-temperature treatment is applied after the first temper, the amount of retained austenite that transforms the treatment may be considerably less than that desired because some of the austenite might have been stabilized by tempering prior to low-temperature treatment, and in such cases the tools must be retempered after return to room temperature following low-temperature treatment so as to reduce the internal stresses and to increase the toughness of the newly formed martensite. It is desirable in some tools to retain a small percentage of retained austenite for improving toughness and providing a favorable internal stress pattern that will help the tool withstand the service stresses, and in such cases it is necessary to avoid the full stabilizing treatment. Distortion of the tool steel can also occur due to a higher austenitizing temperature or due to surface chemical reactions. Higher-temperature austenitizing of tool steel will lead to grain growth and more stabilized austenite. These conditions, along with larger thermal gradients during heating and quenching, will result in irregular dimensional changes of the products. Surface reactions such as carburization and decarburization can change the surface temperature and subsurface transformation, causing compressive or tensile stresses leading to cracking or distortion. Residual stresses can also originate from mechanical or thermal treatments such as forming, grinding, and machining, or during

Fig. 20

Fig. 21

Residual Stresses in Powder-Metal Processing / 419 Other P/M Processes Dimensional changes, defects, and residual stresses are also important in P/M processes such as metal infiltration, spray forming, warm compaction, MIM, and rapid prototyping. However, very limited investigations have been carried out in the area of residual-stress evaluation. Metal infiltration of ferrous materials is carried out using copper-base alloys. The infiltrant is placed in contact with the green ferrous compact and sintered at a temperature above the melting point of the infiltrant. The sintering of iron particles is promoted by the infiltrant drawn into the ferrous compact by capillary action. Infiltration can also be carried out as a second step after the sintering of the green ferrous compact. The porosity can be partly or completely eliminated by infiltration, resulting in improved density and mechanical properties of the product. However, as discussed in the sintering of the iron-copper system, care should be taken to avoid the growth as well as the possibility of surface erosion of the compact. Adequate measures should be taken to avoid the contribution of residual stresses as a result of liquid-solid transformation of the infiltrant on cooling. Metal injection molding consists of stages such as mixing, molding, debinding, and sintering. The densities of the MIM green compact can be as low as 50% in comparison with about 80% green density of the traditional P/M part. One way of reducing the distortion is to provide a higher green density by using a higher powder volume in the feedstock with a wider particle size distribution in order to obtain a high packing density. To obtain the desired dimension of the final product, the mold dimension is kept oversized, and the solids loading and final densities will govern the extent of oversize. The isotropic linear shrinkage (LS) for the molded dimension to the sintered part dimension (Ref 106), can be given by: LS ⳱ 1 ⳮ [Di(1 ⳮ WL)/Df]1/3

where Di is the density of green molded part, Df is the density of sintered part, and WL is the total weight loss from molded to the sintered part expressed as a fraction. The mold shrinkage factor is (green dimension/sintered dimension) ⳱ 1/[1 ⳮ LS]. However, for complex components the mold shrinkages are not isotropic. The anisotropic shrinkage arises due to variations in powder orientation, binder orientation, nonhomogeneous powder/ binder separation, gravitational force, thermal gradients during sintering, and so forth. In such cases, the mold shrinkage factors for each particular dimension are to be evaluated by initial trials. The debinding process should be selected carefully, and the debinding cycle has to be optimized so that the product is free from macroscopic defects such as blisters, cracks, and so forth, as well as from microscopic defects arising out of powder segregation. Computer simulation has also been carried out for the sintering den-

sification of injection-molded M2 tool steel, taking into consideration sintering densification, distortion, and microstructure coarsening (Ref 107). During heating, solid-state sintering occurs initially, followed by liquid-film formation and spread on the grain boundaries, resulting in rapid grain growth. A time-temperature sintering window is computed for full density without extensive carbide coarsening or shape distortion. The simulation compares favorably with distortion and densification findings of this steel, and is characterized by a narrow sintering window. The problems related to the dimensional changes and stress levels in warm compaction are of a different magnitude in relation to cold compaction. The expansion of the green compact for equivalent density is lower for warm compaction, because lower compaction pressures are required to achieve the same density. However, as the green density increases, since the final green densities of the warm compacts are higher than cold compacts, with the increased density the tooling load will increase, resulting in greater expansion of the product. Again, with the increase in tooling loads it is necessary to use thicker stress rings for greater tool deflection. Adequate care should be taken for the increased expansion as the same can cause microlaminations particularly in multilevel parts. Microlamination can lead to reduced structural integrity of the sintered product. A major advantage of warm compaction is not only the attainment of increased density, but also the increased uniformity of density, which will result in increased load-carrying capacity of the component. The management of residual stresses and resultant distortion is an important factor in the rapid prototyping of three-dimensional components. The chromium-molybdenum hot-work H13 die steel is widely used by the tool and die industry, but at the same time it is a difficult alloy for direct-metal deposition because of the residual-stress accumulation from martensitic transformation. Direct-metal deposition of H13 tool steel was carried out with a laser power of 1000 W and powder feed rate of 5 g/min for fine processing. The thickness of each deposited layer was 250 lm, and the pattern was repeated to create a three-dimensional component (Ref 108). Since residual-stress accumulation is the biggest cause of cracking, an estimation of residual stress per layer was first established. After the deposition of a predetermined number of layers, stress relieving was carried out before further layers were deposited. This strategy is useful in the fabrication of a full-size component. Thus, understanding and estimation of residual stress play an important role in the successful fabrication of three-dimensional components by direct metal-deposition of alloys such as H13 tool steel.

Microstructural Development and Properties Microstructural development of elastically strained crystalline system has been of great in-

terest, as in the case of the coarsening of coherent precipitates. The equilibrium morphology of a coherent precipitate is dictated by the interfacial free energy and the elastic strain energy. Computational technique has been used to analyze the elastic state associated with arbitrarily shaped precipitates whose elastic constants are different from those of the matrix phase. Earlier approaches failed to describe the coherency strain accurately. Recently, a new technique termed the discrete atom method (DAM) has been developed to examine the general coherency problem, based on chemical statistical mechanics and linear elasticity (Ref 109). The DAM appears to be an answer for the study of predicting microstructural evolution in many stressed alloy systems. The phase decomposition behavior from d to (d Ⳮ c) phases at elevated temperature has been investigated in the two-phase stainless steel powder of Fe-24Cr-8Ni alloy, associated with the amount of strain stored through mechanical alloying. Mechanical alloying was carried out in a vibrating ball mill, and with increasing milling time the strain stored within the d powder increased and the hardness increased from 250 to 600 HV for 360 ks milling, without any change in the crystal structure of the powder. An allotropic transformation from d to c can be induced by heating the powder to high temperature, owing to the increased driving force in c nucleation, prior to the equilibrium-phase decomposition to (d Ⳮ c) phases. The strain energy stored through mechanical milling can influence the allotropic d-c transformation, resulting in grain refinement (Ref 110). At temperatures higher than 1300 K, the microduplex structure of (d Ⳮ c) markedly coarsened, but addition of the 2 vol% of alumina powder was found to be very effective in suppressing grain growth. The influence of residual stresses on recrystallization has been a controversial issue (Ref 111) and recently this has been investigated in oxide-dispersion-strengthened mechanically alloyed sheet steel MA 956 containing 20.8Cr, 5.0Al, 0.5Y2O3, and 0.5Ti. Mechanically alloyed powders were hot isostatically pressed, and the billets were cold rolled to produce 0.5 mm thick sheet. These were annealed at temperatures between 1300 and 1380 ⬚C, and the recrystallization was established by light and transmission electron microscopic investigations (Ref 112). Recrystallization initiated rapidly at the sheet center line, designated as stage I, resulted in plate-shaped grains oriented parallel to the rolling direction at the sheet center line. Stage II is characterized by slower planar growth through the sheet thickness and finally a very coarse grain structure, sometimes with a single grain through the sheet thickness. The recrystallization kinetics are characterized by incubation time with an activation energy of 506 kJ/mole followed by a decreasing rate of boundary migration with further increasing time and temperature. The microstructural evolution is further discussed in terms of residual stresses, deformation texture, dislocation structure, and oxide

420 / Residual Stress Formation During Manufacturing Processes dispersion on the recrystallization process. The center-line-initiated recrystallization might be attributed to the residual compressive stresses at the center line of the sheet, although the compressive stresses are maximum at the surface of the sheet as determined by hardness measurements. The residual-stress profile from the sheet surface to the center line indicates that compressive stress at ⳮ725 MPa was measured at the surface, while the same becomes negligible at a depth of 0.02 mm. Two opposing regions of tensile stress, which balance the compressed stress, were broader, ranging from 0.02 to 0.19 mm with a peak tensile stress of 80 MPa. The remaining region around the center line of the sheet is slightly compressive at ⳮ20 to ⳮ30 MPa. The high surface compressive stresses are consistent with the highly deformed near-surface areas of the sheet as indicated by the high-density shear bands. This unique recrystallization process in MA 956 sheet appears to be influenced by the strong deformation texture gradient and powerful high- and low-angle boundary pinning by the fine oxide dispersions. In the development of new types of high-temperature materials for the propulsion system and so forth, there is a need to withstand severe heating and oxidation along with a steep temperature gradient. Appropriate combination of functionally gradient materials is a possible solution to withstand such severe conditions. Functionally gradient materials from 304 stainless steel powders and stabilized zirconia (ZrO2-3mol%Y2O3) have been prepared by hot pressing. These materials were evaluated by burner heating using H2 /O2 combustion flames. The heat insulating properties of these materials were satisfactorily evaluated by the thermal resistance value, but the sample surface developed cracks during the cooling cycle (Ref 113). Thermal-stress analysis showed that compressive stress in the biaxial state was generated in the areas channeled by combustion flame at the sample surface, yielding appreciable plastic deformation, which is responsible for the generation of large tensile stresses exceeding the fracture strength of zirconia during the cooling cycle. Improvements in the contact wear resistance of high-speed tool steel can be achieved by reinforcement with aluminum oxide powder, but will result in a decrease in the tensile strength. The loss in strength can be recovered by selective lamination of layers of different reinforcing content, which will make a functionally gradient material (Ref 114). The sintering time and temperature could influence residual-stress distribution, taking full account of relaxation process and volume change due to phase changes. Experimental stress analysis measurements served to validate the analytical predictions. Considerable attention has been paid to investigate the improvements in the fatigue life of sintered steel products by appropriate surface modification treatments such as surface rolling or shot peening. The enhanced fatigue behavior of the steel could be attributed to the microstructural features and residual-stress distributions.

Surface rolling could improve the fatigue strength by a factor of 1.6 in the case of sintered Fe-1.5Cu alloy and a factor of 1.3 in the case of Fe-8Ni-1Mo-0.5C alloy (Ref 115). The improvement is caused by interactions such as surface densification, increased hardness, improved surface roughness, and buildup of compressive residual stresses. The residual stresses were determined by x-ray, and through-thickness residual-stress measurements were carried out by incremental removal of very thin surface layers. The hardness of high-strength alloy steel is much higher than that of iron-copper alloys because of the higher content of martensite. The maximum values of the compressive residual stresses at the surface of as-sintered states were caused by surface machining. However, when the surfaces are rolled, the compressive residual stresses are no longer determined by prior machining, but by the level of yield stress and rate of densification, and therefore these values are higher than those of the sintered and machined surfaces. The amount of improvement in fatigue life is related to the stress-concentration factor, and the compressive residual stress fields at a depth of 0.2 to 0.6 mm will retard the propagation of surface cracks. In the development of high-strength powderforged connecting rods, the fatigue strength is governed by the surface defects such as decarburized layer, surface roughness, and nonsintered areas. The nonsintered area is attributed to defective bonding caused by oxidation of the interface in the manufacture of connecting rods. The oxidation may begin at the surfaces and proceed deeper during the transfer of porous preforms, heated to high temperature, from the sintering furnaces to the forging die in the normal atmosphere. Controlling nonsintered areas and imparting residual compressive stresses to the surface are found to be the most effective means of improving the fatigue strength (Ref 116).The compressive stresses are produced by shot peening, which could improve the fatigue strength by about 30% and could result in the production of a 10% lighter connecting rod. The continuous efforts to improve the strength/weight ratio without affecting reliability have motivated further work, including the optimization of shot peening and the evaluation of the magnitude of residual stresses of powder-forged connecting rods. Residual-stress measurements were made using x-ray diffraction techniques. Maximum fatigue strength is obtained at a shot-peening intensity in the range of 15 to 20 A (Almen). Further increase in peening intensity resulted in a decrease in fatigue life (Ref 117). This decrease in properties is attributed to overpeening, resulting in surface extrusion faults. This phenomenon can form cracks at the surface of the component and lower its fatigue life. Optimization of the peening process on fatigue test specimens resulted in an increase of 55% improvement; when the process was carried out on forged connecting rods (composition Fe-0.5C-0.1S-2Cu) using an optimal peening intensity, an improvement of 27% of fatigue strength over the unpeened rods at 90% reliability level resulted.

Conclusions The P/M process has emerged as an advanced manufacturing technology for the mass production of precision parts for general engineering, automotive, electrical, electronic, and aerospace industries. The process has become competitive with other metalforming technologies, and there is a continuous growth in the areas of steels, stainless steels, tool steels, and metal-matrix composites, which are difficult or impossible to produce by conventional methods. The growing powder-processing technologies include warm compaction, liquid-phase sintering, high-temperature sintering, hot isostatic pressing, powder forging, metal injection molding, and rapid prototyping. Studies of residual stresses during the various stages of powder metal processing are very fascinating and important from the view point of producing quality products. These include the production of metal powders by atomizing, nonequilibrium processing such as rapid solidification and mechanical alloying, compaction of metal powders, sintering, hot pressing and hot isostatic pressing, heat treatment and working such as powder forging, and other P/M processes. However, only very limited investigations have been carried out in P/M processing, and the major reported areas include heat treatment, microstructural evolution, and increasing the fatigue life of sintered and powder-forged components. In these cases, the residual-stress measurements have been carried out using hardness and x-ray techniques, and more powerful techniques such as neutron diffraction are yet to be investigated. There is a need to develop prediction methods and measurement techniques for residual stress measurements in P/M products, and a better understanding of optimized residual stresses can offer benefits such as enhanced service behavior and reliability to the components. REFERENCES 1. D.G. White, Global Growth Trends at PM98, Granada Spain, Int. J. Powder Metall., Vol 34 (No. 8), 1998, p 9 2. A.J. Clayton, P/M Growth Reported in Las Vegas, Int. J. Powder Metall., Vol 34 (No. 5), 1998, p 9 3. S. Pickering, The Road Ahead: PM’s Future in the Automotive Industry, Powder Metallurgy in Automotive Applications, P. Ramakrishnan, Ed., Science Publishers, 1998, p 15 4. D.G. White, The Challenges of Growth: State of the P/M Industry North America, Int. J. Powder Metall., Vol 34 (No. 5), 1998, p 27 5. P.N. Singh, P. Ramakrishnan, and J.K. Beddow, Characterization of Iron Powders by Fourier Analysis Techniques, Advances in Particulate Technology, M. Ramanujam, Ed., I.I.T. Madras, 1986, p 17 6. P.N. Singh and P. Ramakrishnan, Powder

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lation of Hot Isostatic Pressing of Metal Powder: Influence of Constitutive Equations, Proc. Powder Metallurgy World Congress (Paris), Vol 1, European Powder Metallurgy Association, 1994, p 725 Harry Chandler, Ed., Heat Treaters Guide—Practices and Procedures for Iron and Steels, 2nd ed., ASM International, 1995, p 844 G.M. La Vecchia, R. Roberts, A. Bertasio, and G.P. Marconi, Surface Residual Stress Measurements on As-Sintered and Carburized Steel Parts, Proc. Powder Metallurgy World Congress (Paris), Vol 11, European Powder Metallurgy Association, 1994, p 855 I. Shraf and K.H. Boswell, Residual Stress Measurements in Machined P/M Steel, Advances in Powder Metallurgy and Particulate Materials, Vol 8, Metal Powder Industries Federation, 1995, p 183 K.M. Kulkarni, Factors Affecting Dimensional Precision of MIM Parts under Production Conditions, Advances in Powder Metallurgy and Particulate Materials, Vol 5, Part 19, Metal Powder Industries Federation, 1996, p 157 R.M. German, Computer Model for the Sintering Densification of InjectionMolded M2 Tool Steel, Int. J. Powder Metall., Vol 35 (No. 4), 1999, p 57 J. Mazumder, J. Choi, K. Nagarathanam, J. Koch, and D. Hetzner, The Direct Metal Deposition of H13 Tool Steel for 3D Components, JOM, Vol 49 (No. 5), May 1997, p 55 J.K. Lee, Stress Induced Microstructural Evolution via Desecrate Atom Method, Int. Mater. Rev., Vol 42 (No. 60), 1997, p 22l

110. S. Takaki and Y. Kimura, Grain Refining of (d Ⳮ c) Two Phase Stainless Steel Powder Compact through Mechanical Milling Treatment, Proc. Powder Metallurgy World Congress, Y.O. Bando and K. Kosuge, Ed., Jpn. Soc. Powder Powder Metall., Part 1, 1993, p 151 111. J. Nutting, S. Ubhi, and T.A. Hughes, Frontiers of High Temperature Materials, J.S. Benjamin, Ed., Inco MAP, 1981, p 33 112. R.C. Klug, G. Krauss, and D.K. Matlock, Recrystallization in Oxide Dispersion Strengthened Alloyed Sheet Steel, Met. Mater. Trans., Vol 27A, July 1996, p 1945 113. R. Watenabe, A. Hibino, and A. Kawasaki, Thermomechanical Properties of Disc Shaped Functionally Gradient Material Fabricated by Hot Pressing, Advances in Powder Metallurgy and Particulate Materials, Vol 9, Metal Powder Industries Federation, 1992, p 81 114. R.A. Queeney, Residual Stresses and Mechanical Responses in Al2O3 Reinforced M2 HSS Gradient Components, Int. Conf. Powder Metallurgy and Particulate Materials (Vancouver), 20–24 June 1999 115. C.M. Sonsino, F. Muller, and R. Muller, The Improvement of Fatigue Behavior of Sintered Steels by Surface Rolling, Int. J. Fatigue, Vol 14 (No. 1), 1992, p 3 116. K. Takahashi, E. Hoshina, and M. Ogino, Development of High Strength Powder Forged Connecting Rods, Proc. Powder Metallurgy World Congress (Paris), Vol 111, European Powder Metallurgy Association, 1994, p 2227 117. R.A. Chernekoff, S. Mocarski, and D.A. Yeager, Increased Fatigue Strength of Powder Forged Connecting Rods by Optimized Shot Peening, Powder Metall., Vol 38 (No. 3), 1995, p 196



Residual Stress Formation and Distortion of Rail Steel F.D. Fischer and G. Schleinzer, Montanuniversita¨t Leoben, Austria

RESIDUAL STRESSES AND DISTORTION OF RAIL STEEL are important to security and comfort in railway traffic. In fact, some derailments were found to be initiated by residual stresses, and the buckling of rails has already caused some serious accidents. Fortunately, great disasters are a rare occurrence in railway traffic. Still wear, and thus maintenance costs, are influenced by residual stresses. Due to increasing speed and rising wheel loads of freight cars, more and more research interests have been directed to the railway system, and railway administrations demand straightness and low tensile or—even better—compressive residual stresses in the head and in the foot near the surface to improve crack growth resistance. In Fig. 1 different steps of the life of a rail are illustrated. Two production steps in particular offer the possibility of enhancing the properties of a rail of given metal composition (i.e., the cooling process and the straightening of the rail). Of course, nobody expects significant deformation during the service of a rail (that is, the deformation of a rail under wheel loads); thus, the residual stress state is highly influenced by the very localized nature of the stresses caused by wheel/rail contact. In the case of a wavy or rough rail surface (e.g., due to asperities), the localization of the contact is even stronger.

The Cooling Process The main geometrical feature of a rail is obviously the fact that it has only one symmetry with respect to a plane orthogonal to the rail foot. In addition to the single symmetry, the mass distribution along this plane varies significantly. The rail head represents a mass concentration of roughly square shape. However, the web and the two halves of the foot can be approximated by plates. Inevitably the cooling process of a rail

Metal composition

Fig. 1

Hot rolling

A rail from production to service

profile with an initially spatially constant temperature distribution results in a strong inhomogeneous temperature field and a thermal stress state. If the rail is free from external constraint, of course, neither a resultant moment nor a resultant force can appear due to pure cooling. Although the understanding of such a temperature field is of a certain technical interest and has been a topic of research for many years, little literature exists on the residual stress state due to cooling. We use the word “certain,” because some experts argue that only the stress state after the roller straightening process, which follows the cooling process, is of any relevance. However, if one wants to understand why the rail is curved after cooling and if there are ways to reduce the curvature as much as possible, one has to study the cooling process very carefully. Evidently, the curved size after cooling is the input information for the straightening process. The residual stress state due to cooling, however, is fully eliminated during the straightening process. One of the first papers dealing with residual stresses in rails after cooling was published by Mayer in the 1930s (Ref 1). Mainly experimental work is reported. The method of cutting the rail profile into small square columns (the “sectioning” method) was used, which obviously is too inaccurate to give a really clear picture. A paper later published by Asbeck et al. (Ref 2) also discusses experimental results. One of the reasons for the near-absence of numerical and analytical work on residual stresses in rails is the “difficult” geometry. Therefore, the first real progress toward a better understanding of the history of the residual stress state and the deformation of the rail could be achieved by applying the finite element method (FEM), as in one of the first works in this field by Marcelin et al. (Ref 3). This paper could not provide a clear picture about the development of the residual

Cooling

Straightening

stress state and the distortion of the rail because the authors investigated a single rail in vertical position; however, its merit has been to show a way of applying FEM to this difficult problem. To the knowledge of the writers the most comprehensive numerical study was presented in a thesis by Hinteregger (Ref 4). Two accompanying papers were published, one dealing mainly with the transient temperature field and the related residual stress state in a rail profile (Ref 5), and the second paper considering long rails and the variation of the residual stress state along the rail (Ref 6). After the discussion of the temperature field and the method for calculating the residual stress state, the problem of long rails, the “rail end problem,” is treated again in detail. Furthermore, it should be mentioned that mainly the results of Hinteregger et al. (Ref 6) are discussed in this chapter. Of course, finer meshes would be applied today; however, the concept followed can be considered as absolutely up-to-date. Also, a distinct rail profile must be assumed for the numerical calculation. The widely used UIC54E profile is applied. The thermal material behavior of this fine pearlitic material can be found in Fischer et al. (Ref 5). The austenite to pearlite transformation occurs during cooling between ca. 690 C and 610 C. The rail is represented by a layer of generalized plane-strain elements (see the mesh in Fig. 2). The base plane of this layer is defined to remain in the plane of the coordinate system. The cover plane, however,

Mounting and welding

Fig. 2

Finite element mesh. Source: Ref 4

Residual Stress Formation and Distortion of Rail Steel / 425 dependence of the heat conductivity k, the specific heat capacity cp, and the mean coefficient of thermal expansion ␣m as a function of the current temperature T, ␣m (T), expressed by:

(1) (3) (2)

␣m ⳱

Fig. 3

( kgkJ• K ( 1.0

K

Tref

␣(H)dH/(T ⳮ Tref)

(Eq 1) ˙ ri,j ⳱ ui,j • ei • ej • r • Ai(T i4 ⳮ T j4) Q

Rails on the cooling bed. Source: Ref 4

may displace in the longitudinal direction and may also rotate with respect to a rotation vector, which is fully free. The global equilibrium conditions enforce no resultant longitudinal force, no shear force on the cross section and no resulting moment. Consequently the rotation of the cross section, and thus the distortion of the rail, can be calculated. The thermal boundary conditions are explained in the next subchapter. All calculations (thermal and mechanical) were performed with the program ABAQUS (Ref 7). The Cooling Boundary Conditions and Heat Transfer. It is assumed that the temperature of the rail is spatially constant at 1030 C (1303 K) over the entire cross section at the beginning of the cooling procedure. This is the measured surface temperature after the rail has left the rolling mill. Cutting and transportation take usually about 4 min until the rail reaches the cooling area. Most of the rails cool down with contact and thermal interactions with the neighboring rails as shown in Fig. 3. A single cooled rail is a special case that rarely occurs in the course of rail production. At temperatures higher than 500 C cooling is mainly determined by radiation. Heat transfer by convection becomes more important at lower temperatures. Figure 4 shows the temperature Cp

T

冮

surface radiates to another area of the same body. Because of the small temperature differences the heat flux by self-radiation is rather small. Therefore, mainly the radiation into the surroundings is of interest. The heat flux is governed by (Ref 8):

where ␣(H) is the instantaneous linear coefficient of thermal expansion at temperature H including both the temperature-induced and the transformation-induced volume changes. Tref is chosen to be 900 C. As mentioned, the austenite-pearlite transformation takes place in the temperature range between 690 and 610 C. The latent heat q˙ in W/ m3 set free during this phase transformation can be represented either as a heat source on the right side of the heat conduction equation or, approximately, by an artificial increase qDcp of the specific heat capacity qcp according to the relation with the time t: q(cp Ⳮ Dcp)

qDcp

T T ⳱ div(k grad T) Ⳮ q˙ ⇒ qcp t t ⳱ div(k grad T) T qDcp ⳱ q˙ (Eq 2) t

DT ⳱ q˙ Dt

qDcp ⳱

q˙ Dt DT

(Eq 3)

This practice was applied in the study explained here. Each point of the rail surface absorbs or transmits energy by radiation to the surroundings and by self-radiation, which means that an area at the

( mW• K (

αk(K 1) 25.016

50

and ui, j ⳱ 1⁄2(sin ␣1 Ⳮ sin ␣2)

Cp

1

20.016

40

2 3

4

αm

5

6.1 0.6

15.106

30

6 α = 15 α2 = 83

0.4

7

10.106

20 0

200

400

600

800

1000

1100

Temperature, C 15 14 13

Fig. 4

Dependence of the heat capacity, cp; conductivity, k, and the mean coefficient of the thermal expansion, ␣m, on temperature. Source: Ref 4

(Eq 5)

˙ ri, j is the heat flux from the plane i to the where Q plane j; ei,ej are the emissivity coefficients; r ⳱ 5,67 • 10ⳮ8(W/m2K2) is the Stefan-Boltzmann constant; Ai is the area of plane i; Ti,Tj are the temperatures of the planes i and j, respectively; ui,j is the radiation shape factor; and ␣1,␣2 are the angles between the normal of the examined element and the tangent to the rail surface as shown in Fig. 5. The comparison between the total heat flux and the heat flux due to radiation into the surroundings after 6 min cooling time is shown in Fig. 6. The numbers indicate the fraction of heat flux into the surroundings in percent. On the lower side of the rail head 87% of the total heat flux is radiated into the surroundings. The other part is the heat flux from the head to the web and the foot, respectively. The surface temperatures at the web and the foot are lower than the head temperature, and therefore, the heat flows from the head to the other points. A positive heat flux leaves the body. The total heat flux in a point at the web is the sum of the positive heat flux by radiation into the surroundings and the negative heat flux by radiation from the neighboring areas of the profile. Because the total heat flux is smaller than the heat flux into the surroundings, values greater than 100% may

k

0.8

(Eq 4)

Fig. 5

10 12 11

9

8

Angles ␣1 and ␣2. Source: Ref 4

426 / Residual Stress Formation During Manufacturing Processes occur. The heat flux leaving the body is approximately the same as the heat flux entering the body in a point at the rail foot. The total heat flux is very small or zero, due to a thermal insulation, symbolized in Fig. 6 by two thick lines at the foot surface. The percentage tends to infinity in this area. The heat transfer is predominantly conductive in the contact area to the neighboring rails. This fact is taken into account in the computer model by combining the head and the foot surface of the same rail with six node interface elements for heat transfer, as symbolized in Fig. 6 by the shaded area. Below 500 C convection becomes more and ˙ ci from a plane to more relevant. The heat flux Q the surroundings is defined as: ˙ ci ⳱ Aih(T ) • (Te ⳮ T ) Q

(Eq 6)

where h(T ) is the heat-transfer coefficient, and Te is the temperature of the surroundings. It is convenient to approximate the contour of the cross section by straight lines for calculating the heat-transfer coefficients (Fig. 7). Simplified empirical relations for the heat transfer coefficient h for free convection from various surfaces to

the air at different temperatures are given in Holman (Ref 8) as: 1/4

冢冣

DT h ⳱ 1.42 L

(Eq 7)

for a vertical plane, 1/4

冢L冣 DT

h ⳱ 1.32

(Eq 8)

2o 3o

6o

4u

2u

Fig. 7

7 5u

3u

6u Approximated cross section for convection. Source: Ref 4

96

57 25

89

5o

4o

1

100 100

93

for a horizontal plane facing upward, and 1/5

冢L冣

h ⳱ 1.61

DT

(Eq 9)

for a horizontal plane facing downward. DT (C) is the temperature difference between the surface and the ambient temperature; L is the vertical or horizontal dimension (m). The unit of the heat transfer coefficient h is W/(m2K). No further details are given with respect to the calculation procedure because a transient temperature calculation is now state of the art. For more information see Ref 7. It should be mentioned that the thermal and mechanical processes are uncoupled in so far as the thermoelasticity effect (contribution to entropy via strain energy) is neglected since it is of no practical relevance. The cooling process starts with free cooling during the first four minutes. Then an interaction takes place with the neighboring rails at the same temperature level (Fig. 4, 8). After 100 min the surface temperature reaches approximately 200 C, and the rail is lifted off from the cooling area. The cross section has reached ambient temperature after 10 h cooling time. Generally the rail foot cools down more quickly than the head due to the mass difference of the head in relation to the foot. Measured and computed temperaturetime histories are in good agreement. Figure 8 shows the temperature distribution after 4 min. However, the situation is different in the case of head-hardened rails. After hot-rolling, the head of the rail is plunged into a quenching fluid for 21⁄2 minutes. Then the rail is air-cooled as usual. The temperature distribution in such a head-hardening rail after 41⁄2 minutes cooling time can be seen in Fig. 9. The composition of the quenching fluid and, therefore, the heat transfer coefficient are treated as a certain industrial secret. More details on the head-hardened rail can be found in Moser et al. (Ref 9).

87

87

800

780 760

103

103

740 740 720 97

97

680

680 112

107 720 660 640

Fig. 8 Fig. 6

Heat flux into the surroundings in percent of the total heat flux. Source: Ref 4

Ref 4

680

740 720

680 660

Temperatures in C of a rail with interaction with other rails after 4 min cooling time. Source:

Residual Stress Formation and Distortion of Rail Steel / 427 The analysis of a residual stress state during quenching or cooling can now be assumed as a well-established concept. Specifically, the kinetics of the phase change phenomena, as well as their mechanical appearance due to a transformation eigenstrain, must be understood. Here, the writers refer, for example, to a widely accepted paper by Inoue et al. (Ref 10) and for details to a paper by Tanaka et al. (Ref 11). In the case of a diffusional transformation such as the austenite-pearlite transformation, a volume change of a few percent occurs. Note that the transformation volume change itself is included in the mean coefficient of thermal expansion. This volume change cannot be accommodated by elastic straining. Therefore, a local plastifi-

h pl TP eij ⳱ eel ij Ⳮ eij Ⳮ eij Ⳮ eij

(Eq 10)

where eel ij is the elastic part of the strain tensor; ehij the thermal part being ␣m(T ⳮ Tref)dij; dij denotes the unity tensor, epl ij the plastic part and, as mentioned, eTP ij the TRIP part. The TRIP part (see Fischer et al., 1996) is derived as: e˙ TP ij ⳱

490

where ry* is a weighted yield stress of both phases; f represents the volume fraction of pearlite; w( ˜ f ) describes the pearlite transformation kinetics; sij is the global (locally averaged) stress deviator; and d is the transformation volume change. Such a modification of the constitutive law was not available when Hinteregger (Ref 4) worked out his thesis. Therefore, the “softening” due to the TRIP-effect was taken into account by a reduction of the yield stress, as seen in Fig. 10. Also, the Young’s modulus, Poisson’s ratio, the mean coefficient of thermal expansion, and the stress-strain curves are taken into account with respect to their temperature dependence. For the stress calculation the generalized plane-strain model explained previously is used. It allows a longitudinal displacement and rotations of the cross-section. Figures 11 and 12 show the thermal longitudinal stresses along the symmetry

cation is activated which interacts with the global load stress state. This phenomenon is denominated as transformation induced plasticity (TRIP). Refer to a detailed overview by Fischer et al. (Ref 12). As a practical device, an additional plasticity term eTP ij is introduced with respect to the additive strain tensor eij decomposition:

3 dw ˜ ˙ K f sij 2 df

K⳱

5 1 d 6 ry*

(Eq 11)

520 580

610 670

640

670 640

640

Temperatures in C of a head-hardened rail after 4.5 min cooling time. Source: Ref 4

Fig. 9

100

Yield stress, αy 0.001(N/mm2)

100

50

150

100

50

0

Fig. 11

Longitudinal stresses in MPa along the axis of symmetry after 20 min cooling time. Source: Ref 4

Fig. 12

Longitudinal stresses in MPa along the axis of symmetry at the end of cooling. Source: Ref 4

75 "Mixture" rule 50

Trip 25

0 600

650 700 Temperature, C

750

Temperature dependence of the yield stress during the austenite-pearlite transformation. Source: Ref 4

Fig. 10

100

50

0

50

100

428 / Residual Stress Formation During Manufacturing Processes axis for different time steps of a cooling procedure, taking into account full interaction with the surrounding rails as shown in Fig. 3. It can be shown that the influence of TRIP on the final residual stress state is significant; this may be one of the reasons for the wide scatter of measured residual stresses in railroad rails. These results were calculated on the assumption of a rail-by-rail arrangement on the cooling bed, however, without frictional contact, which is discussed subsequently. It is important to note that the residual stress distribution in a single rail differs significantly from Fig. 11 and 12 due to the different temperature field of a simple rail. If the rail is fixed with respect to its transversal deformation (a “fork-type” positioning of the rail), an additional constraint is imposed on the rail leading also to a modified picture of the residual stress state. Head-hardening changes the picture of the residual stress distribution, as shown in Fig. 13. It is interesting to note that the residual stress distribution is nearly independent of the lateral constraint of the rail in the case of head-hardened rails. Due to the changing temperature differences between the head and the foot, the contraction of the foot at the beginning of the cooling process is greater than the contraction of the head. This tendency changes several times during the cooling period. The sag f for a rail section of 30 m in length versus time t is plotted in Fig. 14, considering a positive sag if the center of the curvature is at the head-side. One can see that the sag changes significantly with time. Weight and Friction: Rail End Problem. In the treatment just described a cross section of a rail is investigated under a given time-dependent temperature field, and the assumption of a generalized plane-strain state only allows the analysis of an infinitely long rail. Furthermore, no weight or friction is taken into account. However, actual rails have a length of 30 m (98 ft) to more than 100 m (328 ft) and are subjected to their own weight. The friction on the cooling bed

prevents the rail from deforming in transversal direction. This fact leads to the surprising effect that very long rails (approximately 100 m, or 328 ft, length) show an almost perfectly straight middle section “M” of at least 60 m (195 ft) length on the cooling bed and two deformed “rail ends.” Of course, after lifting the rail with a crane and releasing the frictional forces, the rail becomes suddenly curved with a sag of some meters. Also, cutting a very long rail on a cooling bed leads to a sudden change of the deformation shape because the friction force distribution depends on the length of the rail. This phenomenon has caused some severe accidents in the shops. The first authors to describe the rail end problem of a heavy rail on a rough surface during a cooling process were Fischer and Rammerstorfer in 1989 (Ref 13). The rail is modeled by a bar with cross section A. For easier understanding assume an elastic bar; its stiffness is EJ; E, Young’s modulus; and J, cross-section inertia moment. The bar is primarily loaded by a temperature field T(z,t), which does not depend on the longitudinal coordinate x, leading to a temperature moment: mh(t) ⳱

冮 E␣ T(z,t)z dA A

(Eq 12)

m

Since the bar may move on the rough surface (representing the cooling bed) a transversal friction force, p, can be activated during the sliding, thus: | p(x)| ⳱ lq

(Eq 13)

where l is the coefficient of Coulomb friction (e.g., 0.45), and q is the weight per length unit of the rail (e.g., 54 kg mass for a UIC54E rail per meter length). Since this is a sliding process, p(x) is always oriented in the negative direction of the transversal velocity w/t with w being the transversal displacement. p(x) is, therefore, sectionally

constant and changes its sign at locations xi(t), i ⳱ 1, 2, … N where w t

冷

xi

⳱ w ˙ | xi ⳱ 0

(Eq 14)

Fischer et al. (Ref 13) were able to show that there are no “sticking” intervals. The differential equation for the rail is: 2w 1 ⳱ ⳮ (M(x,t) Ⳮ mh(t)) x2 EJ

(Eq 15)

where M(x,t) is the moment due to the friction force distribution (Fig. 15). Now in the middle section “M” of the rail w(x,t) is observed to be w(t)|M 0. Since also its second derivative is zero, Eq 15 leads to: M mh ⳱ ⳮ t t

冷

(Eq 16)

M

Since equilibrium enforces M ⳱ Q x

2M Q ⳱ tx t

(Eq 17)

Q being the resultant shear force in transversal direction, it follows immediately from Eq 16 that: Q t

冷

⳱

M

ⳮmh ⳮ x t

冢

冣冷

⳱0

(Eq 18)

M

Due to the initial conditions mh(0) ⳱ 0, w(x,0) ⳱ 0, M(x,0) ⳱ 0, Q(x,0) ⳱ 0, it follows also that: Q(x,t)|M 0

(Eq 19)

and, therefore: Q x

冷

⳱ ⳮp(x)|M 0

(Eq 20)

M

Equation 20 allows the conclusion that the middle section “M” is not affected by any friction force during cooling: M(x,t)|M ⳱ ⳮmh Q(x,t)|M ⳱ 0 p(x,t)|M ⳱ 0

(Eq 21)

L • 30 m

f, cm

f 50 0 3

6

9.103

t, s

50 100 150

Fig. 13

100

50

0

50

100

150

200

Longitudinal stresses in MPa of a head-hardened rail along the axis of symmetry at the end of cooling. Source: Ref 4

Fig. 14

Sag, f, of a rail with a length of 30 m on a frictionless support. Source: Ref 4

Residual Stress Formation and Distortion of Rail Steel / 429 Thus, the middle section “M” of the rail can be considered as a long beam with an external moment ⳮmh on both ends. It is now a very difficult problem to find the sequence xi(t), i … N. The most surprising effect is that the two equilibrium conditions: xN

冮

0

xN

冮

p(x)dx ⳱ 0

0

p(x)(xN ⳮ x)dx ⳱ mh

together with the conditions (Eq 14): w ˙ |xi ⳱ 0, i ⳱ 1, … N

yield a system of N Ⳮ 1 differential/algebraic equations for N unknowns xi, i ⳱ 1, … N (Ref 14). This obvious paradox can be solved only if N is assumed as N → . A detailed description of the solution routine is presented in Ref 14 going back to an earlier work (Ref 15). Dimensionless interval boundaries n i: ni ⳱

xi l*

l* ⳱ (mh(t)/lq)1/2

(Eq 22)

are introduced. A numerical procedure gives: n 1 ⳱ 1.041,

n 2 ⳱ 2.387,

n 3 ⳱ 2.802,

n 4 ⳱ 2.948,

n 5 ⳱ 3.003,

n 6 ⳱ 3.024, …

It can be seen that the interval boundaries come closer and closer with increasing n. The se-

quence n n, n → , reaches a limit value n ⳱ 3,029. It is interesting to note that Stupkiewicz and Mroz (Ref 16) found the same solution independently. Recently Mogilevsky et al. (Ref 17) published a concept for a finite-length beam with a sequence of friction intervals with changing friction force sign. The finite value of n points to a perfectly straight middle section “M” of the rail. Of course, since the material is assumed to be elastic and mh vanishes for a rail at room temperature, no final deflection would occur. Nevertheless, this elasticity friction study leads to a better understanding of the complicated phenomenon of the moving/sliding of the rail on the cooling bed. The investigation of the real situation of an elastic-plastic rail on a real cooling bed consisting of a grid with discrete supporting bars with spacing being orthogonal to the rail was elaborated by Hinteregger (Ref 4), Fischer et al. (Ref 18), and Hinteregger et al. (Ref 19). In the following text the results for a 100 m (328 ft) rail, which is placed on a grid, are reported. The rail was modeled by an overlay of six bars (B32 beam elements of Type ARBITRARY) adequately representing the area, as well as the moment of inertia of a UIC54E rail profile. The same constitutive law was assumed for the beam cross section as in the two-dimensional study just described. The stick-slip effect of a supporting bar is represented by an elastic-ideally plastic material with the yield stress rpy ⳱ (lqa/ As), As being the cross section of the supporting y

z W(x, t ) z T(z, t )

x

z x

x

x0

m (t )

bar. The Young’s modulus E p of the supporting bar is selected as E p ⳱ 100E. Since the supporting bar is modeled as a truss element fixed at one end, using the constitutive law explained previously, the correct sign of the friction force with the magnitude lqa is automatically taken into account. According to the calculated temperature field, the temperature is defined in 32 points of the cross section with spatial linear interpolation. In each equivalent point with respect to the longitudinal x-direction, the same time history of the temperature T( y,z,t) is defined. Both the transversal displacement w(x,t) and the longitudinal stress rx(x,y,z,t) are calculated. In the middle section “M” the rail remains almost totally straight, which corresponds to a “fork-type” positioning of the rail. Therefore, the residual stress state calculated due to this constraint in the previous section can be used to check rx( y,z,t)|M. The partial plastification of the rail during cooling leads to a deformed shape. Figure 16 shows the deformation shape of a half 100 m rail, with the length counted from the middle of the rail. Furthermore, Fig. 16 shows that only the “rail end” is deformed, covering roughly a range of 25 m. Figures 17 to 19 demonstrate the longitudinal residual stress rRx (x,y,z) at room temperature after lifting of the rail. rRx calculated by the overlay-beam-model at hand agrees well with the calculated values from the two-dimensional model with a “fork-type” positioning of the rail in the middle section “M.” Experimental Results. The findings of the previous section on a long rail led to a new view on the results of experimental investigations of the residual stress state. Usually a certain part of a rail (with a length of about 1 m, or 3.28 ft) is cut out and experimentally investigated. Figures 17 to 19, however, demonstrate that the residual stress state varies significantly within the last 25 m (82 ft) of a long rail. That means the place where a part of the rail has been cut out for experimental investigation must be defined precisely. Of course, for sake of comparison, it should be cut out from the middle section “M.”

22

– µq + µq

2

x

1

11

3

x2(t ) x3(t ) x i (t ) xN(t ) End portion

L( t )

Straight middle part

Width, cm

x1(t )

7

0

6 11

5

22

∂w ∂t

33 0.0

4 10.0

20.0

30.0

40.0

50.0

Length, m Displacement of a 100 m rail depending on the cooling time. 1, 400 s; 2, 660 s; 3, 920 s; 4, 1200 s; 5, 3600 s; 6, 6000 s; 7, 36,000 s. Source: Ref 4

Fig. 16

Fig. 15

Frictional forces on a continuous cooling bed. Source: Ref 4

430 / Residual Stress Formation During Manufacturing Processes The strong variation of the residual stress state in the rail-end region is obviously one of the reasons for a significant scatter of the experimental results reported in the literature (Ref 1, 2, 20). If the reported results on residual stresses are depicted in one graph, a scatterband emerges depicted as a shadowed region in Fig. 20. It is interesting to note that specifically the results published by Kolmogorov et al. (Ref 20) fit well the calculated results of this work relating to the middle of a fairly long rail. Also, the results found by Marcelin et al. (Ref 3) agree well, both

100 3

σ, N/mm2

50 0 2 1 2

50 3

100

1 150 0

10

20

30

50

40

qualitatively, and in part, quantitatively, with the results reported here. A further comment is necessary with respect to experimental investigations. Often, the holedrilling method is applied, which is assumed to be an established technique (Ref 21). However, a numerical simulation of this hole-drilling process by Fischer et al. (Ref 22) has revealed that the evaluation method of surface deformations by strain gages leads to wrong results if there is a steep stress gradient in the virgin material. This is a real shortcoming and has led to many misinterpretations of the residual stress state in rails since just near the head of the rail one can often observe a very steep gradient after the cooling process and the subsequent straightening process. As a conclusion, one must accept that rails, after cooling on a cooling-bed, are curved at room temperature. However, several attempts are under way to achieve a straight rail after the cooling process. This can only be performed with a specific cooling procedure, such as by contact with copper bars as discrete “heat extractors” on the surface of the rail. Several rail producers are working on such a procedure but maintain strict silence on the outcome.

Length, m

Fig. 17

Longitudinal stresses of a rail lifted off the cooling bed. Source: Ref 6

After hot rolling, the rails cool down on a cooling bed. Due to the different cooling velocities in the cross section, the rails are distorted after having reached room temperature. Since there are certain requirements for the rail straightness, not the least of which is to ensure passenger comfort, a further production step—a straightening step—must be added. Although there are different possibilities (e.g., stretch

100 2

2

1

1

σ, N/mm2

50 0 2 3 1

50 3

100

Roller Straightening

straightening), roller straightening, as used for other long products, is the most common method. Roller straightening is much faster than other methods because it allows continuous operation, and the underlying principle is fairly simple. The cool, distorted rails are drawn through the straightener by a series of driven rollers, which are located alternately below and above the rail. While the rail is passing through the rollers in the longitudinal direction, it is bent up and down. Thus, the initial distortion is homogenized and decreased by the plastic deformation caused by a combination of bending, shear, and roll contact stresses. This operation is quite important because it is the final deformation process of the production route, which determines the residual stress pattern (Fig. 21). There is always a springback effect when the outer forces are released after a plastic deformation. Thus, a new equilibrium of forces and moments caused by residual stresses are achieved. A typical residual stress pattern develops during the straightening, which is nearly independent of the initial rail distortion before the straightening operation. As tensile residual stresses promote the initiation and propagation of cracks, railway producers try to achieve low residual stresses. The most critical point here is the foot, where both the longitudinal tensile stresses due to the wheel loads and the residual stresses superpose. However, obtaining a straight rail and reducing residual stresses are

+

+

+

+

+

+

+

+

Roller deflection

Fig. 21

Roller-straightening process

3

150 0

10

20

30

50

40

Length, m

Fig. 18


100

3 3

50 σ, N/mm2

1 0

1

2 2

50

100

3

2

1 150 0

10

20

30

40

50

Length, m

Fig. 19


150

Fig. 20

100

50

0 N/mm2

50

100

150

Scatterband of longitudinal residual stresses of unstraightened rails from literature. Source: Ref 4

Residual Stress Formation and Distortion of Rail Steel / 431 difficult tasks because the straightness also depends on the distribution of the residual stresses. The roller deflections can be changed on an existing roller straightener in order to improve the residual stress pattern and the straightness of the rail. Up to now the setup of the roller positions has been a matter of trial and error, largely influenced by the skills and expertise of the operator. Railway administrations demand low residual stresses in rails (e.g., that the longitudinal resid-

Strain gage 1m 20 mm

Saw cut

Fig. 22

Measurement of the longitudinal stresses at the rail foot according to a CEN draft standard

300 200 100

0

100

200

300 MPa

Head

Web

Foot

Fig. 23

300

370 BHN, neutron 370 BHN, sectioning

200 Stress, MPa

Scatterband of the longitudinal residual stresses taken from Hodgson. Source: Ref 25

100 0

100

200 300

0

Fig. 24

100 50 Rail height, mm

150

Longitudinal residual stresses of a 370 BHN new roller straightened rail. Source: Ref 30, 31

ual stress, which is the most critical component, must not exceed 250 MPa, or 36 ksi, in the middle of the foot). According to a European Committee for Standardisation (CEN) draft standard (Ref 23), the measurement of this residual stress component has to be performed in the following way: A strain gage is attached in longitudinal direction in the middle of the rail foot. Then, a saw cut in front of and behind the gage position and normal to the longitudinal direction relieves the residual stresses. The stress relief causes an elastic strain, which can then be measured by the strain gage. Finally, the original longitudinal stresses can be calculated using the Young’s modulus (Fig. 22). Residual Stresses in Unused RollerStraightened Rails. Generally speaking, the longitudinal residual stress pattern in the cross section is a “C” shape with tensile stresses in the head and the foot and compressive stresses in the web. A comprehensive study about stresses in roller-straightened rails was done by the ORE Committee (Ref 24), which used destructive sectioning methods. Due to the sectioning, the rail parts expand or shrink elastically when separated from one another. The resulting elastic strains can be calculated by measuring the length changes, or they can be directly measured by strain gages. Of course, these measurements must be done very carefully so that the cutting or frictional heating does not influence the results. Also, the spatial resolution is not very high. Hodgson (Ref 25) summarized the results of the ORE Report in a scatterband of the longitudinal stresses (Fig. 23). Similar results are reported in Ref 26 to 28. An equivalent scatterband can be found in Wineman et al. (Ref 29). The accuracy of the measurements can be verified by checking the force and moment equilibrium in the cross section. Later, in 1992, the European Rail Research Institute (ERRI) (Ref 30) reported new measurements by neutron diffraction performed by Webster et al. (Ref 31). Neutron diffraction is a nondestructive testing method. In contrast to x-rays, neutrons can penetrate material more easily, allowing the measurement of residual stresses in the interior of the material. However, it is a rather expensive and very time-consuming method; moreover, a nuclear reactor is necessary to provide the neutrons. Monochromatic neutrons can be scattered at the lattice planes of a crystalline material. If the beam path length between the planes is a multiple of the wavelength of the neutron, then constructive interference occurs. Therefore, only under certain beam angles will diffraction take place. Also, if stresses in the material alter the lattice distances, the scatter angle changes. For more details about the neutron scattering method see the article “Methods for Determination of Inhomogeneous Residual Stress Fields” in this Handbook. Unfortunately, the investigation of the interior of the specimen is limited. Due to the scattering, fewer and fewer neutrons reach points deep inside the material. To ensure that a reasonable amount of neutrons reach the detector, a certain total beam path

length should not be exceeded. In steel, for example, the maximum path length is only a few centimeters. Webster (Ref 31), therefore, chose a longitudinal and a normal plate of the rail for the analysis. The gage volume was 2 ⳯ 2 ⳯ 2 mm3, which is typical for neutron diffraction. Hence, the results are averaged values inside this volume. In qualitative terms, his results are well in accordance with the ORE Report (Fig. 23 and 24). Just near the head surface a certain stress reversal was observed. The longitudinal tensile stresses dropped from a maximum beneath the surface to a lower value at the surface. Already the ERRI report mentioned that results near the specimen surface must be interpreted with caution due to the extrapolation of the data. An additional problem near the surface is parasitic peak shifts if the neutron gage is not entirely immersed in the specimen. Hauk and Kockelmann (Ref 32) also reported a steep stress gradient near the surface with compressive stresses at the surface. The stresses were measured by xray diffraction. But in their paper the longitudinal residual stresses changed from compressive to tensile stresses within 0.1 mm beneath the surface. Thus, the general stress pattern seems to be clear, although near the surface there are still uncertainties (Fig. 24). Behavior of Rail Steel under Plastic Deformation. There are different types of rail steel: the plain carbon, the alloy, and the heat treated qualities. The different qualities should maximize the lifetime of the rails under different operating conditions. In this case the focus is on describing the behavior of these steels under cyclic plastic deformation. Plastic deformation causes the material to undergo a certain change in shape and remains after the removal of the outer forces. In the case of straightening of rails and rails in service, the loading occurs repeatedly and with changing signs. Therefore, the emphasis is on the cyclic plastic deformation. Plastic deformation is based mainly on the gliding of lattice planes in the crystalline structure of metals; this gliding requires dislocations in the lattice. Although a certain amount of dislocations are always present in a metal, they are also generated by the plastic deformation itself. On the other hand, the piling up of dislocations decreases the mobility of the dislocation again, and the material shows hardening. If loading is reversed, it has often been observed that the elastic limit increases in one loading direction while it decreases in the opposite loading direction. This is called the Bauschinger effect and has to be considered in the case of cyclic loading (Fig. 25). Polycrystalline materials in the virgin state are isotropic. von Mises assumed that only the second invariant of the stress tensor accounts for the elastic limit. The material shows elastic behavior as long as the stress state stays within the von Mises yield surface. Thus, his theory is also called J2-flow theory, which is a good approximation of real metal behavior. After plastic deformation the material is no longer isotropic, and additional internal state

432 / Residual Stress Formation During Manufacturing Processes variables must be used to define the hardening of the material. A common approach for cyclic plasticity uses the decomposition of the hardening into kinematic and isotropic parts. These models still contain the von Mises yield function and evolution laws for the internal state variables such as the yield stress rY, which defines the radius of the elastic range (Mises cylinder) and the backstress tensor ␣ij, which describes the shift of the Mises cylinder in the principal stress space (Fig. 26). The main issue of a material model is to describe the evolution of elastic yielding and the state variables during plastic deformation. In 1979 Chaboche et al. proposed a multiple component non-linear hardening model. Today this model is widely accepted and a basis for further developments in plasticity models. The decomposition of the stress tensor into a hydrostatic and deviatoric part gives:

2 J2(Sij ⳮ ␣ij) ⳱ 1⁄2(Sij ⳮ ␣ij)(Sij ⳮ ␣ij) ⳱ 1⁄3rY (Eq 24)

p

rY ⳱ rY,0 Ⳮ Q(1 ⳮ e ⳮbeeqv)

The flow rule is modified to: e˙ pij ⳱ k(Sij ⳮ ␣ij)

(Eq 25)

where k is a constant dependent on deformation

M

400

␣˙ nij ⳱

0 0.005 0.000 200

0.005

ε 0.010

400 600 800 σ/Pa 800 Stress, MPa 600

600

400

400

200 200 0 0.005

0.005

0.010

0.005 0.000 200

0.005

ε 0.010

400

200

600 400 800

600

Fig. 25

Cyclic loading of rail steel UIC 900A

σ/Pa 800 600

p ε• ij

σ3

400 200

Sij

0

Sij αij

0.010

0.005 0.000 200

0.005

ε 0.010

400

αij

600

σ1

Fig. 26

800

σ2

(a) Measurement: cyclic tension-compression test (b) compared with a linear kinematic material model and (c) Multiple component model of Chaboche.

Fig. 27

von Mises yield surface and its shift due to kinematic hardening in the principal stress space

(Eq 27)

2 n p p c e˙ ij ⳮ c n␣nije˙ eqv 3

(Eq 28)

200

Then a modified von Mises yield surface for kinematic hardening is necessary, where rY is the common elastic yield value in a simple tensile test:

0.010

兺 ␣nij n⳱1

where each backstress component evolves due to a nonlinear law:

600

(Eq 23)

Strain 0.010

(Eq 26)

where rY,0 is the initial yield stress, Q and b are hardening parameters, and epeqv is the accumulated plastic strain. Next, the backstress tensor is decomposed into an arbitrary number of components: ␣ij ⳱

σ/Pa 800

0.010

rij ⳱ rdev Ⳮ rhyd ⳱ Sij Ⳮ dij 1⁄3tr(rij) ij ij

history. The evolution of the yield radius is assumed to be:

c n and c n are the kinematic hardening parameters, which are different for each backstress component. The kinematic hardening equations take into account the transient hardening effects in each stress-strain loop. The merit of Chaboche’s model is its easy mathematical structure, which allows a simple way to determine model parameters. The parameters can be determined from a simple cyclic uniaxial tension-compression test. Chaboche’s model allows an almost exact representation of the hysteresis curve under cyclic loading if the material shows no “out-of-phase hardening.” This out-of-phase hardening or additional hardening may occur if the strain paths change from longitudinal to shear paths and vice versa during the loading. Such nonproportional paths occur during the roller contacts. A comprehensive study about the latest developments in material models can be found in the thesis of Jiang (Ref 33) and in Chaboche (Ref 34) (Fig. 27). Because rail steel shows no “out-of-phase hardening,” a good representation of the plastic response of the material can be obtained with Chaboche’s multiple component plasticity model. The use of a simpler material model requires caution because it can strongly influence the calculated results on residual stresses. Simulation of the Roller Straightening. Different attempts were made to simulate the roller straightening. Bru¨nig (Ref 35) used beam elements of different widths accounting for the special cross section of the rail. He already used an enhanced two-surface plasticity model. Because elements covering the whole width do not allow a variation of stresses along the width, his results are, at best, average values. He also stated that the contact pressure at the rollers had only a minor influence on the residual stresses. Naumann (Ref 36) investigated a full three-dimensional FEM model with an explicit integration method, a coarse mesh, and linear kinematic hardening. However, he did not publish residual stress results from his calculations. In contrast to Bru¨nig, Naumann stated that the pressing of the rollers into the rail head and foot is in fact responsible for the residual stress pattern. Weiser (Ref 37) applied straightening mechanics on a slice of

Residual Stress Formation and Distortion of Rail Steel / 433 that the submodel was loaded with the correct forces and bending moments (Fig. 28). The straightening simulation was repeated with the submodel, still including the contact of the rollers with the rail. The global model was calculated with ABAQUS/Explicit. The explicit integration had the advantage of being able to handle contact problems more easily. For the submodel ABAQUS/Standard was used because the standard integration allowed a fine mesh. Eight node brick elements with reduced integration were used for both models. The rollers were modeled with analytical rigid surfaces. Thus, the total calculation time on a single node workstation could be reduced to about two weeks (Fig. 29).

The results of this simulation showed a Cshaped residual stress pattern. The submodeling technique was also tested with two-dimensional models and was found to be correct. Thus, new evidence was found with this model that the general idea of the residual stress pattern is true. Already Wineman (Ref 29) and others stated that a shortening of the material in the rail head and foot due to the rolling contact leads to tensile residual stresses. In Fig. 30 the total strains of a subsurface element in the middle of the rail head during the straightening process are shown. The dominant mechanism is that a small element in the head or base near the roll becomes shorter in length (e33), shorter in height (e22), and wider (e11). This leads to a mismatch in length between

200 200

150

150

50

σ/MPa

100 50

100

0 50 50

50 150

100 0

0.2

0.4

0.6

Foot

0.8

1.0

Mesh of the submodel of a UIC60 rail and longitudinal residual stresses in MPa along the symmetry line after the straightening and as a contour plot

Fig. 29

20 16

ε11

12 8

3

4 0 ε33

4 8 ε22

16

Submodel

+ Fig. 28

+

+

+ +

+

0 200

Head

12

+

0

50

Strain, 10

rail. He implemented the roller contact with an overlay of Hertz-type contact pressure. The results correspond qualitatively with the measurements. Finstermann et al. (Ref 38) applied moments and forces of a beam model on a three-dimensional FEM model of a piece of rail in order to bend it around a top and bottom roller. The repeated contact with the top and bottom roller was supposed to give a good approximation of the real roller contact. The results show compressive stresses at the head and foot surface that are much higher than the ones hinted at in the measurements of Webster or Hauk. Varney et al. (Ref 39) again used a beam model with a linear kinematic hardening law. The result is a zig-zag pattern of longitudinal stresses. Henderson et al. (Ref 40) modeled the process by a series of three-point bendings and linear kinematic hardening. A first result had only little resemblance to measured U- (or C–) shaped patterns. After the material parameters had been adjusted to unstraightened and straightened conditions, the simulation gave better results. Although these studies explain many mechanisms of straightening and offer help in understanding the process, none of them has yet solved the formation of residual stresses quantitatively. The key problem is that limited computing resources made various simplifications necessary, either by using beam or two-dimensional elements, neglecting the rolling of the rollers or using linear kinematic hardening for the material. Especially two-dimensional simulations with linear kinematic material hardening lead to zig-zag patterns of the longitudinal residual stresses, which are not in agreement with the measurements. In addition, the residual stresses after straightening, which are calculated in a two-dimensional model, strongly depend on the plasticity model used. However, an FEM simulation is quite time consuming, and contact problems make the time problem even worse. Nevertheless, the authors tested a new concept for a full three-dimensional simulation of the roller straightening process with a minimum of simplification. In order to save computation time, the simulation was split into two FEM processes. In the first step a global model, 16 m long with a coarse mesh and linear kinematic hardening law, was applied. In the second step a submodel, only three times as long as the height of the rail with a fine mesh and Chaboche’s multiple component hardening law, was used. The front and back surface of the submodel was driven by the nodal displacements of the global model. This ensured

+

Roller 2

+

Driving a small submodel through the roller straightener

Roller 3

Roller 4

Roller 5

Roller 6

Roller 7

Roller 8

Time

Fig. 30

Total strains in the subsurface layer in the middle of the head during roller straightening. e11 is the vertical strain (width), e22 is the horizontal strain (height), and e33 is the longitudinal strain.

434 / Residual Stress Formation During Manufacturing Processes flanges and web and gives the C-shaped longitudinal stress distribution.

Rails in Service Temperature Influence. The influence of ambient temperature on the residual stresses should be mentioned. Like all other materials, steel has a certain thermal expansion coefficient. Therefore, rails expand or shrink due to temperature changes. With an expansion coefficient of ␣ ⳱ 12 ⳯ 10ⳮ6 the longitudinal stresses shift by 25 MPa (4 ksi) with a temperature change of 10 C. Under hot conditions rails can buckle, while under cold conditions again tensile stresses increase the possibility of rail fracture. Therefore, railway administrations try to mount the rails at average temperatures. Residual Stresses due to Welding. Railway rails are produced in lengths up to about 100 m. In the past bolting was the common method of joining rails on the track, but at these joints repeated impacts occur, increasing the possibility of rail failure. Also, a different residual stress pattern at the rail ends—the longitudinal stresses in the head and in the base change to vertical tensile stresses in the web—support web cracks. And finally, passenger comfort is decreased by the bumps and additional side forces in curves. Currently rails are joined by welding. As a result, the rail is continuous, and no bumps or

vertical residual stresses at the rail ends occur. During welding the rail ends are heated up and the former residual stresses vanish. Then, the new joint cools down again, and new residual stresses develop. The most common method for joining rails on the track is aluminothermic (termite) welding: The two rails become bonded by superheated metal, which is the result of a highly exothermic reaction of iron alloy, iron oxide, and aluminum powder. The cooling of the welded gap then forms new residual stresses. Although this welded joint is of superior quality, some welds fail. Again, Webster et al. (Ref 41) investigated residual stresses in and near the welded joint of a rail. They reported tensile longitudinal stresses in the web region with steep gradients to high compression in the head and the foot. The stress pattern almost looks completely opposite to the distribution in new rails (compare Fig. 23 and 31). The length of this zone depends on the length of the mold, which has an insulating effect. However, it was found that approximately 90% of aluminothermic welds fail due to porosity caused by dampness that can arise if the molds are not thoroughly dried before welding. Residual Stress Formation in Rolling Contact. Many investigations of residual stresses of rails in service have been made. The motion of a wheel on a rail has a complex character consisting of elasto-plastic rolling and sliding under many circumstances (braking, acceleration of the locomotive, running in curves). Wheel passages on a rail cause plastic deformation in the running surface layer and lead to particular changes of the stress distribution in a rail head. Under heavy traffic, wheel loads can be so severe that rails fail due to the plastic deformation. A zone 1 to

2 mm (0.04 to 0.08 in.) deep is sheared relative to the bulk material, and the strains can exceed 100% deformation. This deformation is caused by the high normal and tangential forces of the wheels. Each pass of a wheel leads to additional plastic flow until the shakedown limit is reached. The following is a brief overview of the results of experimental and theoretical investigations that are an important step toward understanding the mechanisms of railway track failures. Webster et al. (Ref 31) reported neutron measurements of used 370HB and 340HB rails. The tensile longitudinal stresses in the subsurface layer of the rail head of new rails are reduced to zero or even negative values during operation. This of course enhances the crack resistance of the running surface (Fig. 32). Also, Bower et al. (Ref 42) showed measurements of residual stresses of used rails, which are definitely compressive near the running surface. Looking at theoretical investigations different approaches have been proposed to evaluate residual stresses after two-dimensional rolling contact. Sehitoglu and Jiang (Ref 43) proposed an analytical method for the determination of residual stresses in elasto-plastic rolling contact. They found compressive longitudinal stresses that reach a maximum at a distance of approximately 0.5 to 1 times the contact half length “a” beneath the surface. In 1997 McDowell proposed a new hybrid scheme (Ref 44) that asymptotically approaches the solution of Sehitoglu and Jiang. Zochowski et al. (Ref 45), who applied FEM, showed the additional effects of acceleration or braking of a wheel on residual stresses (Fig. 33). In the free-rolling case Zochowski found ten-

0

0 3

2

1

1

2 3 1

σ, MPa 200

200

1

4

400

Longitudinal residual stresses in an aluminothermic weld. Source: Ref 42

y/a

Fig. 31

0

y/a

400

2

2


300 New Used

200

3 100 0 4

100 Foot 200

0

Fig. 32

Web

Head

50 100 Rail height, mm

150

Change of the longitudinal residual stresses during service. Source: Ref 31

1 2 3 4

3

Free rolling q = 0.3 q = 0.75 q = 1.0

0.255 0.17 0.085 0

4

0.085 0.17

res σx/po

(a)

1 2 3

Free rolling q = 0.3 q = 0.7

0.34 0.255 0.170.085 0

0.085

res σx/po

(b)

Longitudinal residual stresses rx due to free rolling, q ⳱ 0, (a) acceleration q 0 and (b) braking q 0. y is the depth, a is the contact half length, p0 is the maximum of the Hertz contact pressure distribution, and q is the ratio of normal and tangential force. Source: Ref 46

Fig. 33

Residual Stress Formation and Distortion of Rail Steel / 435 sile stresses at the surface, where McDowell’s results tend to zero. Nevertheless, the general residual stress patterns of both investigations are similar. Zochowski’s results also show that braking and acceleration lead to compressive stresses at the surface. These theoretical results agree with the measurements of Webster et al. (Fig. 32) in the sense that where the theoretical results show the generation of compressive stresses in the subsurface layer of a formerly stress-free material, the measurements exhibit a decrease of the tensile residual stresses. ACKNOWLEDGMENT We gratefully appreciate the cooperation with Voest-Alpine Schienen GmbH & Co KG, which has been supporting our research for more than 15 years. We also want to express our gratitude ¨ stertoward the Austrian Science Foundation O reichischer Forschungsfo¨rderungsfonds (FFF project no. ZL 3/12384) for its financial support.

10.

11. 12. 13.

14.

REFERENCES 1. H. Mayer, Residual Stresses in Railroad Rails, Organ f.d. Fortschritt des Eisenbahnwesens, Vol 91, 1936, p 320–329 (in German) 2. H.O. Asbeck and M. Heyder, Residual Stresses in Unused Rails after Cooling and Straightening, Eisenbahntechnische Rundschau, Vol 26, 1977, p 217–222 (in German) 3. J.L. Marcelin, M. Abouat, and J.L. Chenot, Analysis of Residual Stresses in Hot-Rolled Complex Beams, Comp. Meth. Appl. Mech. & Eng., Vol 56, 1986, p 1–16 4. E. Hinteregger, “Residual Stresses and Distortion of Rails after Rolling before Straightening,” Ph.D. thesis, Montanuniversita¨t Leoben, 1990 (in German) 5. F.D. Fischer, E. Hinteregger, and F.G. Rammerstorfer, The Influence of Different Geometrical and Thermal Boundary Conditions and the Phase Transformation on the Residual Stress State in Railroad Rails after HeatTreatment, International Conference on Residual Stresses, ICRS 2, G. Beck, S. Denis, and A. Simon, Ed., Elsevier Applied Science, London and New York, 1989, p 467– 471 6. E. Hinteregger, F.D. Fischer, F.G. Rammerstorfer, and A. Jo¨ller, “Calculation of the Longitudinal Residual Stresses of Long Rails during Cooling,” Berg- und Hu¨ttenma¨nnische Monatshefte (BHM), Vol 135, 1990, p 437–441 (in German) 7. ABAQUS Finite Element Analysis Products, Hibbit, Karlsson & Sorensen Inc., www.hks.com 8. J.P. Holman, Heat Transfer, 4th ed., McGraw-Hill-Kogakusha Ltd., Tokyo et al., 1976 9. A. Moser, P. Pointer, and G. Prskawetz,

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27.

28.

29.

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31.

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36.

37.

pru¨fung, Vol 32, 1990, p 181–185 (in German) “Railway Applications—Track Heavy Rail, Part 1: Flat Bottom Symmetrical Railway Rails 46 kg/m and Above,” CEN/TC256/ WG4 Draft Standard, 1997 Studies Concerning the Measurement and Improvement of the Level of Residual Stresses, ORE D 156/Report 4, Utrecht, the Netherlands, 1987 W.H. Hodgson, Residual Stresses in Rail. Rail Quality and Maintenance for Modern Railway Operation, J.J. Kalker et al., Ed., Kluwer Academic Publishers, the Netherlands, 1993, p 61–73 J. Szelazek, Ultrasonic Measurement of Thermal Stresses in Continuously Welded Rails, Nondestruct. Test. Eval., Vol 25, 1992, p 77–85 C. Urashima and K. Sugino, Generation Mechanism of Residual Stresses in Rails, International Conference on Residual Stresses, ICRS 3, H. Fujiwara, T. Abe, and K. Tanaka, Ed., Vol 2, 1992, p 1489–1493 S.V. Kolmogorov, Y.D. Makarov, and O.N. Mikhailov, Formation of Residual Stresses in Heat Treatment Hardened Rail, Steel USSR, Vol 17, 1987, p 271–273 S.J. Wineman and F.A. McClintock, Residual Stress and Web Fracture in RollerStraightened Rail, Residual Stress in Rails, O. Orringer, J. Orkisz, and Z. Swiderski, Ed., Vol 2, 1992, p 1–22 “Measurement of Residual Stresses of Grade A and Two Head Hardened Rails with Neutron Diffraction,” ERRI D 173/Report 4, Utrecht, the Netherlands, 1992 (in German) P.J. Webster, G. Mills, X. Wang, and W.P. Xang, Residual Stress Measurements in Rails by Neutron Diffraction, Rail Quality and Maintenance for Modern Railway Operation, J.J. Kalker et al., Ed., Kluwer Academic Publishers, the Netherlands, 1993, p 307–314 V. Hauk and H. Kockelmann, “Residual Stress State in the Running Surface of a Rail,” HTM-Ha¨rterei-technische Mitteilungen, Vol 49, 1994, p 340–352 (in German) Y. Jiang, “Cyclic Plasticity with an Emphasis on Ratchetting,” Ph.D. thesis, University of Illinois–Urbana, 1993 J.L. Chaboche, Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity, Int. J. Plast., Vol 5, 1989, p 247–302 M. Bru¨nig, “An FE-Model for the Simulation of the Roller Straightening of Heavy Profiles,” Mitteilung, 89–5, Ruhr-Universita¨t Bochum, 1989 (in German) N. Naumann, “Straightening of Long Products about the Main Axis of Maximum Inertia,” Ph.D. thesis, Montanuniversita¨t Leoben, Austria, 1998 (in German) J. Weiser, “Analysis of the Formation of Residual Stresses During the Roller Straightening of Rails,” Ph.D. thesis, Otto-von-

436 / Residual Stress Formation During Manufacturing Processes Guericke-Universita¨t Magdeburg, Germany, 1997 (in German) 38. G. Finstermann, F.D. Fischer, G. Shan, and G. Schleinzer, Residual Stresses in Rails Due to Roll Straightening, Steel. Res., Vol 69, 1998, p 272–278 39. B.E. Varney and T.N. Farris, Mechanics of Roller Straightening, 39th Mechanical Working and Steel Processing Conf., Iron and Steel Society of AIME, Warrendale, PA, Vol 35, 1998, p 1111–1121 40. S. Henderson, W.T. Cook, L. Woollard, A.D. Richardson, and M.J. Wood, Control of Straightening Operations for Optimisa-

tion of Product Properties, EUR 18540 EN, Office for Official Publications of the European Commission (eur-op.eu.int), Luxembourg, 1998 41. P.J. Webster, G. Mills, X.D. Wang, W.P. Kang, and T.M. Holden, Residual Stresses in Alumino-Thermic Welded Rails, J. Strain Anal., Vol 32, 1997, p 389–400 42. A.F. Bower and K.L. Johnson, Shakedown, Residual Stress and Plastic Flow in Repeated Wheel-Rail Contact, Rail Quality and Maintenance for Modern Railway Operation, J.J. Kalker et al., Ed., Kluwer Academic Publishers, the Netherlands, 1993, p 339–349

43. H. Sehitoglu and Y. Jiang, Residual Stress Analysis in Rolling Contact, Rail Quality and Maintenance for Modern Railway Operation, J.J. Kalker et al., Ed., Kluwer Academic Publishers, the Netherlands, 1993, p 349–358 44. D.L. McDowell, An Approximate Algorithm for Elastic-Plastic Two-Dimensional Rolling/Sliding Contact, Wear, Vol 211, 1997, p 237–246 45. M. Bijak-Zochowski and P. Marek, Residual Stress in Some Elasto-Plastic Problems of Rolling Contact with Friction, Int. J. Mech. Sci., Vol 39, 1997, p 15–32



Residual Stresses during Gear Manufacture K. Funatani, Nihon Parkerizing Co., Ltd., Japan

peak of residual stress vary, depending on distribution of carbon, quench condition, and properties of the steel used. Various investigations on the residual stress state of case-hardened steels have been done, and many simulation models are being developed to estimate the distribution of residual stress in relation to various controlling factors as follows (Ref 1–7): ● Distribution of longitudinal, tangential, and

axial residual stresses

● Difference of residual stress of carburized and

pseudocarburized steel

● Influence of carburizing condition and carbon

gradient

● Influence of quenching media and cooling

condition

● Influence of steel grades and their hardena-

bility

ments of the core. When the carbon concentration becomes higher than 0.75 or 0.8% C, retained austenite is observed in relation to alloy elements and results in a decrease of surface hardness as retained austenite volume increases. Generally, 20 to 30% of residual austenite is observed when surface carbon percentage is around 0.85 to 0.9%. The amount of retained austenite increases by increasing carbon concentration at the surface layer. Distribution of Residual Stress in Carburized-and-Hardened Steels. The surface layer of carburized-and-hardened steels has compressive residual stresses as shown in Fig. 1, and the compressive residual stresses counteract applied tensile stresses and improve bending fatigue strength. The typical profile of residual stress produced in carburized-and-hardened steel

● Influence of specimen or work size and case

depth

800

Residual Stress in Carburized-andHardened Steels Carbon, %

Carbon Gradient, Hardness, and Residual Stress in Carburized Steels. The typical distribution of hardness, carbon gradient, and longitudinal residual stress in case-hardened steels are shown in Fig. 1. The surface hardness is about 700 to 850 HV and gradually decreases to the same hardness as the core or center of hardened steel. Effective case depth (ECD) is the depth from the surface at which 513 or 550 HV, equivalent 50 or 55 HRC is maintained. Total case depth (TCD) is the depth at which the carbon content is 0.04% higher than that of the core. The TCD varies depending on steel chemistry, time, temperature, and carbon potential of the carburizing process. The ECD is affected by the carburizing condition similar to that of TCD, quenching condition, hardenability of the core, and mass and size of the workpiece. Surface hardness varies depending on carbon concentration, which is controlled by carburizing atmosphere and the amount and types of alloying ele-

700 A

0.8

600 500

0.6

Hardness, HV

● Influence of microstructure and other factors

0.4 B

0.2 Residual stress, kg/mm2

CARBURIZING is a commonly used process for improving fatigue strength and wear resistance of mechanical components such as gears and many other automotive components. The surface and core hardness and case depth are specified in design drawings, which influence the strength of carburized-and-hardened steels. The hardness and case depth are influenced by steel hardenability and various processing variables such as carburizing and quench condition. Along with heat treatment results affecting with hardness, carburizing and quenching operations introduce compressive residual stress into the surface layer of steels. Compressive stress contributes very effectively to the fatigue strength of case-hardened products by reducing applied tensile stresses. Surveys of various investigative results showed that measured peak compressive residual stresses ranged from –200 to ⳮ550 MPa. It is very important to introduce compressive residual stress into the surface of carburized parts; this is performed by appropriate component design and proper processing technologies. Similar compressive residual stress is attainable by surface induction hardening, which also has a large influence on bending fatigue strength. Additional posttreatment such as shot blasting and/or double-hard peening can further increase the surface compressive residual stress and contribute more to the improvement of fatigue strength than can the traditional shot peening methods. This article explains the fundamental state of residual stress of carburized-andhardened steels in relation to each factor. Case hardening by carburizing or carbonitriding and quench processes provides the major benefit of introducing large compressive residual stress into the surface of the parts. It results from uneven volume expansion caused by transformation from austenite to martensite. The residual stress at the surface of case-hardened steel is generally compressive because of the larger expansion of high-carbon and/or nitrogen layer into martensite during transformation. The compressive residual stress at the surface layer is effective for increasing fatigue durability of the case-hardened steels. However, distribution and

0 −10 C

−20 −30 0

0.4 0.8 1.2 Depth from surface, mm

1.6

Carbon gradient, hardness, and longitudinal residual stress produced in carburized-andhardened steel. Carburized 5 h at 925 C, quenched at 860 C. A: SCM 22, 9 mm diam; B: S15CK, 25 mm diam; C: SCM 420, 9 mm diam. Source: Ref 6

Fig. 1


Tensile stress

Case

Core

Radial

0 Compressive stress

Longitudinal Tangential

some distance from the surface.

● Distribution of residual stresses in longitudi-

nal and tangential directions is nearly the same, but that of radial direction differs. ● The excessive case carbon concentration increases retained austenite, which decreases surface hardness and compressive residual stresses. ● Maximum value and distribution of residual stress are influenced by heat treatment methods such as carbon potential of carburizing atmosphere and quenching. Although some investigators concluded that the influence of steel type and the conditions of carburizing and quenching are minor (for example, Ref 3, 7, and 9), these factors have a profound influence on the performance of carburized-andhardened products as explained later in this article. Influence of Steel Grade on Residual Stress. Steel grade has a profound influence on distribution of residual stresses. Figure 3 shows the distribution of residual stresses of two casehardening grades steels, nickel-chromium alloy K13NiCr12 steel (Fig. 3a) and straight carbon C15 steel (Fig. 3b). Residual stress of alloy steel shows lower stress near the surface due to retained austenite, and plain carbon steel shows the highest stress at the surface. Influence of Size and Workpiece Shapes. Size and shape of testpiece or work have profound influences on magnitude and profiles of residual stresses. Figure 4 shows the influence of specimen size on distribution of residual stresses. Generally, as the size of the specimen increases, the maximum compressive stress increases, and also the highest stress peak gradually moves inward. However, residual stress profile near the surface not only varies depending on carbon concentration and cooling process, but also is affected by complicated vaporizing and rewetting phenomena during cooling.

Methods of Measuring Residual Stress

● ● ● ●

Parallel beam counter methods Cr K␣, 30 kV, 8 or 10 mA, vanadium filter Count range: 200 cps, time constant: 16 s Dispersion angle: 0.35, focus: l ⳱ 2 ⳯ w ⳱ 5 or 6 mm ● Sin2 W: W ⳱ 0, 15, 30, 40 The distribution of residual stresses are measured under these conditions, and about 5 to 10 20 σra* 0 Residual stress, kg/mm2

● Compressive residual stresses have a peak at

for the effective penetration depth of x-ray and changes in residual stress resulting from layer removal. Layer removal with the x-ray method has shown excellent agreement when used to evaluate residual stress distribution. Measurement of the residual stress discussed in this section used scanning x-ray method under the following conditions (Ref 5,6):

σtg

σax*

20 σtg* 40

σax 60 80

0

0.4

0.2

0.6

0.8

1.0

0.8

1.0

Depth from surface, mm (a) 20 σ ra * 0

−20 σtg* −40

σtg

−60 σax*

−80

σax

−100

−120

0

0.2

0.4

0.6

Depth from surface, mm (b)

0

Depth

Fig. 2

nonmartensitic phases such as bainite, troostite, or pearlite to form. Also, when surface carbon concentration increases to higher than 0.9% the surface microstructure retains more austenite and reduces hardness and compressive residual stress by reducing the expansion that accommodates the transformation to martensite. Generally, distribution of residual stress as shown in Fig. 1 and 2 has the following characteristics:

Residual stress, kg/mm2

is shown in Fig. 2. Residual stress distribution, especially at the surface, varies depending on steel properties and carburizing-and-hardening conditions such as carbon potential, time, quench media, and cooling method as explained later in this article. Generally, residual stress profiles in the longitudinal and tangential direction are similar, while that of axial direction differs from the other two directions. High compressive residual stresses are produced by expansion of carburized case at the end of quench-cooling process, which balance with the tensile stress in the core. The state of residual stresses introduced in hardened case of carburized-and-hardened steel is generally in compression. Low-carbon casehardening steels are carburized and quenched in selected quench media. During quenching, the subsurface portion of the core transforms first at a high temperature to ferrite and pearlite, bainite, or low-carbon martensite (700–550 C, depending on steel grade) in relation to transformation plasticity. Later, at a lower temperature (lower than 300 C), the carburized case transforms to martensite with volume expansion under influence of the transformation plasticity caused by the preceding transformation phase of the core. High-carbon case of 0.8% C expands nearly 1.2%, while that of low-carbon core of 0.2% C is about 0.3%, and this large difference in carbon level and expansion determines the sequence of phase transformation and resultant development of compressive stress in the case. Compressive residual stress in the case is influenced by core hardness or strength; however, the relation between core strength and residual stress is not simple and is explained in later sections. However, the control of carburizing-andhardening conditions is very important to prevent introduction of tensile residual stress at the surface. Especially, when the surface layer has considerably thick grain-boundary oxidation, the quenching time after pullout from the furnace and the subsequent cooling speed should be optimized to reduce formation of nonmartensite phases. The lack of surface hardenability results from grain-boundary oxidation and low-carbon contents easily cause transformation products of

Schematic of residual stresses in carburized-andhardened steels. Source: Ref 8

X-Ray Stress Analysis Methods. There are several methods of measuring residual stresses, such as distortion measurement, strain gage, xray diffraction, and neutron radiation methods. Distribution of residual stress can be measured by repeating mechanical or chemical methods to remove core portion or outer layer and correcting

Distribution of residual stresses measured by xray produced in gas-carburized hardened steels. (a) K13NiCr12; ECD: 0.4–0.6 mm, carburized and double quenched. (b) CK15 (AISI 1015); ECD: 0.5–0.6 mm carburized and hardened. rax, rtg, and rra are measured residual stresses in axial, tangential, and radial directions, respectively. Curves with asterisk show corrected curve of measured residual stress distribution. Source: Ref 7

Fig. 3

Residual Stresses during Gear Manufacture / 439 lm surface layer of specimen is chemically etched repeatedly. Calibration on the influence due to removal of surface layer is calculated from the thickness of removed layer determined by the diameter and residual stress measurements before chemical etching. This procedure is repeated to obtain distribution of residual stresses. This conventional method measures only one of the ⳲW incidental angle directions. It is thus unclear whether the direction of the principal stress is perpendicular or inclined to the sample surface. Therefore, the measured residual stresses have certain variance and are not as accurate as measurements by the recently developed position-sensitive proportional counter (PSPC) method. The technology in residual stress measurement by x-ray diffraction has made great advancement, and PSPCs or position-sensitive proportional detectors (PSPDs) are widely accepted. Compared to old scanning methods, which took many hours, equipment with a PSPD, such as PSPC, can measure residual stress in a short time. The PSPC is a linear counter that obtains diffracted x-rays simultaneously, counting over a section of 50 to 100 mm or 20 range (2h range) in the longitudinal direction (Fig. 5). New systems measure both ⳲW tilt directions to ascertain the direction of the principal stress. Also, recently developed x-ray analysis equipment enables residual stress measurement of microscopic areas of 0.15 mm diameter in combination with incident collimator (Ref 10). In addition, recently developed equipment uses computers for immediate data processing with a data base on diffraction and materials constant, and it is a very effective tool for residual stress research. However, it is very important to set the focus precisely when investigating ma-

terials with fiber flow or sharp distribution of residual stresses, and also care should be taken to avoid errors in measurement of small diameter bar or rod and corner or fillet of workpieces such as gear tooth roots. It is necessary to apply lowangle diffraction methods to measure residual stress for investigation of highly oriented microstructures and sharp stress profiles. The positivepole figure analysis for highly oriented microstructures is recommended.

Residual Stress Variation in Testpieces and Gears Residual Stresses in Testpieces The distributions of carbon content, hardness, and residual stress in three 9 mm fatigue test specimens carburized and quenched in cold oil shown in Fig. 6 have small variations (Ⳳ3 kg/ mm2). On the other hand, the residual stress distribution of rectangular plate and cylinder rod carburized and quenched in hot oil shown in Fig. 7 has large fluctuation. This variation seems to be caused by the difference in the cooling process; the 9 mm testpieces were cooled more uniformly than the rectangular plate. During cooling of the plate and rectangular bars in hot oil, a vapor blanket formed in the early stage of cooling at the surface broke nonuniformly, and the resulting fluctuation of cooling speed caused the

variation of residual stresses observed in Fig. 7. The wavy distribution of residual stresses shown in Fig. 7 was introduced in the testpiece quenched in still hot oil, where the vapor blanket surrounding the workpiece varied, depending on the testpiece shape, causing an unstable oil flow and temporary change of surrounding quenching condition. However, the surface residual stresses produced in carburized plates and rods quenched in hot oil are within a range of agreeable variance. Table 1 compares total area in compression of agitated conditions with that of quenching in still hot oil, which increases slightly with increasing quench oil agitation.

Residual Stresses in Production Gears The durability of gears used for automotive transmission should be qualified by standardized processing condition of carburizing-andhardening operation carried out in the heat treatment plant. Fatigue strength of those gears varies as influenced by processing variables such as carburizing and quenching conditions. The quality of produced gears is usually evaluated based on surface and core hardness, case depth, and microstructure of testpieces carburized simultaneously with gears. In some cases, metallurgical quality is checked and residual stresses of gear

L χ

Preamp A

Preamp B

Delay line

Depth from surface, mm 1

2

3

Residual stress, kpsi

A

B

Diffracted x-rays

0

D

Center wire (anode) Detector gas

C 0

Cathode

10

E −10 −20

Residual stress, k/mm2

20

0

X-ray tube η Incidence x-rays

η

2θ°

−20

−40

Crystal grain 0

0.08 0.04 Depth from surface, in.

Influence of specimen size on the distribution of residual stress. A: 12.7 mm diam, AISI 8610 steel, TCD ⳱ 1.524 mm, tempered at 148.9 C. B: 19.1 mm diam, AISI 8610 steel, TCD ⳱ 1.524 mm, tempered at 148.9 C. C: 25.4 mm diam, AISI 8610 steel, TCD ⳱ 1.524 mm, tempered at 148.9 C. D: 6.35 mm diam, AISI 8610 steel, TCD ⳱ 1.27 mm, tempered at 190.6 C. E: 38.1 mm diam, AISI 8610 steel, TCD ⳱ 1.02 mm, tempered at 148.9 C. A–D, source: Ref 3; E, source: Ref 2

Ψ

TA = Dχ, TB = D(L − χ)

0.12

TA − TB = D(L −2χ) d

Fig. 4

Principle of detector used in x-ray stress measurement by PSPC system. Delay time per unit: Dns /mm; time to produce output at A: TA; at B: TB; TB ⳮ TA position v. h, x-ray angle; v, distance from edge of counter end; g, reflection angle of x-ray; L, length of counter; D, delay time (n s/mm); d, lattice space of the crystal grain. Source: Ref 10

Fig. 5

440 / Residual Stress Formation During Manufacturing Processes ference results from reproducibility of heat treatment condition. The variation of treatment condition of the induction-hardened gear is more stable than in the carburizing process, where many gears are hung or mounted on a tray and quenched in oil at once. The cooling condition of each gear differs depending on position in the tray, and also the cooling rate at the foot of gear tooth is slower than at the tooth tip, reducing transformation speed and resulting in the increases of the formation of nonmartensite phases at the surface. The variation in average value and range of group A is smaller than that of group B. Average value and variation range of group B varies much more widely and seems to indicate that the variation of quenching condition of B group was not the same for each gear. Residual Stress of Gas-Carburized and Direct-Quenched Gears. An average residual stress was measured on production gears made of JIS SCr 420 of module 3. Gears were heat treated in a continuous gas-carburizing furnace with gas atmosphere using the boost-and-diffuse method, in which surface carbon content before

itself are measured on limited samples. Measurement of residual stresses of gears takes a long time, and a lot of laboratory work is necessary; therefore, quality control of gear strength needs precise process control of key factors. Bending fatigue strength of gear teeth depends on hardness, case depth, and magnitude of compressive residual stresses at the tooth root portion. Measurement of residual stress at this point is not easy because of limited space and round root shape, and the measured value is not as accurate as measured stresses on flat testpieces or other open faces. Surface residual stress of production gears varies more than that of simple shape test samples heat treated in precisely controlled conditions. Residual Stress Variation at Tooth Root Surface of Induction-Hardened and Carburized Gears. Table 2 shows the variation in residual stress measured at the foot of gear teeth of induction-hardened gears and carburized-andhardened gears. Compressive residual stresses produced in induction-hardened gears are higher than that of carburized gears, and their variation is smaller than that of carburized gears. This dif-

quenching is controlled to about 0.9% C and directly quenched in hot oil of 130 C. The residual stress level was 24.8 Ⳳ 4.25 kg/mm2 in compression, which is quite an agreeable result compared with that of other testpieces carburized and quenched in same furnace. Axial Stress Distribution Estimated in Carburized Gear during Quenching (Ref 11). Figure 8 shows the details of generation of axial stress distribution estimated by calculation of a carburized gear during quenching. In the early stages, the contour areas of equal stress were almost unaffected by the surface profile. Later, a zone of high compressive stress distribution occurred in the central subsurface portion of the teeth. Such high stress has a large influence on transformation plasticity and determines distortion, sometimes resulting in cracking. During cooling, stress distribution changes are caused by shrinkage and expansion by transformation to martensite. The state of stress distribution is estimated by a simulation model, as shown in Fig. 8. However, in actual quenching, the cooling speeds at the tooth tip and tooth foot differ extensively, and vapor generation accel-

20

SCM 420

600 50 HRC (513 HV) 500

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

−10 −20 S O H

−30 −40

300

0

0.5

1.0

1.5

2.0

Depth from surface, mm

S15CK

(a) TCD

20 10

−10 Residual stress, kg/mm2

0

400


Carbon content, %

ECD

Hardness, HV (5)

700


10 800

−20

SCM 420

−30

0 −10 −20

−40

−40

S O H

−30

0

0.5

1.0

1.5

2.0

Depth from surface, mm −50

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

20

Depth from surface, mm Carbon gradient, hardness, and residual stress variation produced in carburized specimens. Steel: SCM 420 (Jominy hardenability 1⁄2 in. ⳱ 34.8 HRC), rotating beam bending fatigue test specimen; 9 mm diam. Carburizing process: 920 C, 0.9% CP for 5 h. Quenched from 880 C in JIS-1-1 cold oil (35–50 C) and tempered at 160 C for 2 h (7.2 ks). Carbon concentration is measured in S15CK straight carbon steel 25 mm diam specimen. ECD ⳱ 1.22 mm, surface ⳱ 824 HV (10), core ⳱ 468 HV (10). CP, carbon potential of gas carburizing atmosphere. Source: Ref 9

Fig. 6

(b) Distribution of residual stress produced in carburized plate and cylinder rod. Steel: JIS SCM 420 (Jominy hardenability 1⁄2 in. ⳱ 26.5 HRC), Test piece size: (a) 20 by 10 by 200 mm, (b) 14 mm diam by 200 mm. Carburizing process: 920 C for 5 h, quenched from 880 C in JIS 2-1 hot oil (135 C). S, still hot oil; O, mild agitation; H, fast agitation.

Fig. 7

Residual Stresses during Gear Manufacture / 441 erates this difference. It is important to prevent slow cooling at tooth foot portion to reduce the introduction of surface soft layer and tensile residual stresses.

reported comparing different types of steels and heat treatment methods. However, the chemical contents and related properties of steels, even in one type or grade, has considerable influence on carburized-and-hardened steels as explained in this section.

Influence of Steel Grade and Hardenability on Residual Stress

Influence of Steel Grade

Case depth, core hardness, residual stress, and distortion vary depending on chemical composition of steels, hardenability, and processing variables even if parts are heat treated in the same manner. Those characteristics have profound effects on strength and durability of casehardened components. Much research has been

The steel grade, in relation to its hardenability, directly and indirectly influences surface and core hardness and hardness profile through the transformation characteristics of the steel. Along with the steel grade as investigated in the past, the hardenability of steels such as Jominy hardenability also has profound influence on the

Table 1 Surface residual stress and total area in compressive stress introduced in carburized plate and rod

JIS SCM 420, Jominy hardenability (1⁄2 in.) ⳱ 26.5 HRC, carburized at 920 C, in continuous carburizing furnace and quenched in hot oil (135 C) Agitation Stress/area

Still oil

Slow agitation

Fast agitation

Plate Surface residual stress, kg/mm2 Compressive area, %

ⳮ32, ⳮ33 100

ⳮ21, ⳮ32 113.6

ⳮ36, ⳮ45 133.6

Cylinder rod Surface residual stress, kg/mm2 Compressive area, %

ⳮ32, ⳮ28 100

ⳮ24, ⳮ17 102.4

ⳮ28, ⳮ22 106.8

Table 2

Residual stress measured at the tooth foot surface of carburized gears

JIS SCr 420, carburized in continuous gas-carburizing furnace and tempered at 160 C for 2 h Residual stress of sample, kg/mm2 Heat treatment

A-1

A-2

A-3

B-1

B-2

B-3

ⳮ33.8 Ⳳ2.8

ⳮ42.7 Ⳳ2.4

ⳮ31.3 Ⳳ1.6

ⳮ40.0 Ⳳ5.6

ⳮ32.7 Ⳳ8.8

ⳮ32.8 Ⳳ4.4

Carburized and oil quenched Average ⳮ30.0 Deviation Ⳳ3.1

ⳮ15.4 Ⳳ2.3

ⳮ12.4 Ⳳ1.4

ⳮ0.2 Ⳳ5.0

ⳮ19.5 Ⳳ17.2

ⳮ27.1 Ⳳ5.4

Induction hardened Average Deviation

Measured at three positions of the foot of one gear. Average stress value Ⳳr (in kg/mm2). A and B, heat treated in different lots. 1–3 show different portions.

−900 σz = 200 MPa

0

100 0 −100

0 0 0

−600 −300

300 300

0 −300 −600 −300 −300

−900 −600

−600

0 0

−900 −300

0 300

300

600 900

t=3s

Fig. 8

30 s

60 s

600

˚

Estimated axial stress distribution in carburized gear (SNC815) during quenching. Source: Ref 12

hardness pattern resulting in fluctuation of residual stress profile and distortion. Generally, the higher the hardenability of steel, the larger the distortion. On the other hand, the surface residual stress and residual stress profiles produced by carburizing-and-hardening processes are complicated, and there seems to be no simple proportional relation between hardenability and residual stresses. Residual stress distribution of two different grade steels with same alloying elements are compared in Fig. 9 (Ref 2), which shows a higher-carbon smaller-diameter AISI 8620 sample with higher surface residual stresses compared with the other two larger AISI 8617 samples. This result indicates the influence of core hardness or strength. Surface residual stresses of surface carbon content of 0.95 % C are lowest compared with the other two samples. In particular, the surface residual stress of deepest case depth is the lowest compared with thinner case depth, which seems to be caused by a larger volume percentage of retained austenite. Areas in compressive stress increase as case depth increases; however, the residual stress profile of 12.7 mm diam 8620 specimen is a little different from that of the other two 19.05 mm diam 8617 samples, where the area in compressive stress increases with increasing case depth. The differences of three residual distributions indicates the influence of core hardness, case depth, and specimen size. Figure 10 shows the influence of steel grade on residual stress (Ref 3). When surface compressive stress of higher hardenability AISI 8640 is lower than that of AISI 8620, the depth in compressive residual stresses is deeper than that of 8620. Similar to Fig. 9 the difference of residual stress distribution in Fig. 10 suggests the influence of steel hardenability on residual stress. The impact strength of carburized-andhardened steels simply decreases as the case depth and core hardness increase. However, fatigue strength of carburized-and-hardened steels is influenced by hardenability of steel in relation with the hardness profile and microstructure produced during the carburizing-and-hardening operation. Influence of steel hardenability on residual stress distribution is partly shown in Fig. 9 and 10.

Influence of Hardenability Variation of a Steel Grade Influence of Steel Hardenability on Core Hardness and Case Depth. Steel hardenability is controlled by keeping the content of alloying elements within a specified limit. However, standard specifications of steels have a range, and this affects the variation of resulting hardenability of steel. Thus it is quite difficult to produce exactly the same impact and fatigue strength, distortion, and residual stresses even under the same heat treat conditions. The variation of steel hardenability due to variation of chemical content investigated on a

442 / Residual Stress Formation During Manufacturing Processes the core has a direct influence on the distribution of residual stresses and distortion in relation with transformation plasticity at higher temperature, where the surrounding matrix is soft and under large temperature difference between surface and core. Influence of core hardness (core strength) on fatigue strength investigated using the rotary bending fatigue test is shown in Fig. 12 (Ref 9). Variation in endurance limit reaches maximum when the core hardness of a beam specimen is around 430 to 450 HV. In the lower core hardness zone, a large percentage of fracture starts from the inner side of hardened case, called fisheye fracture. By increasing the core hardness or case depth, fisheye fracture disappears and endurance limit increases. In the higher core hardness zone, endurance limit seems to decrease when carburizing time exceeds 5 h in this fatigue test condition. Besides the important contribution of core hardness, the influence of case depth also has a profound influence on fatigue strength, which is explained later in this article. The fatigue test results of rotating beam evaluated in relation to core strength has a peak near 140 to 150 kg/mm2, which coincides with the fatigue test results of module 3 gears as shown in Fig. 13 (Ref 1, 13). Influence of Core Hardness on Residual Stress. Steel hardenability has direct influence on core hardness and indirect influence on surface

residual stress and distribution. However, little difference is observed in surface hardness and residual stress where the carbon concentration at the surface layer of longer carburizing time tends to increase retained austenite and to reduce hardness and compressive residual stresses. High hardness case produced by the carburizing-andquenching operation introduces compressive residual stresses in the surface layer, which increase as case depth increases; however, the highest residual stresses are in the same level.

Influence of Carburizing Processes Influence of Carburizing and Quenching The profiles of residual stresses and maximum peak values vary depending on miscellaneous 20

10 A Residual stress, kg/mm2

Table 3 Chemical composition and hardenability of five lots of chromium-molybdenum steel JIS SCM 415, 420H

Lot

A B C D E

C

Si

Mn

P

S

Cr

Mo

(1⁄2 in.), HRC

0.13 0.17 0.21 0.23 0.23

0.26 0.28 0.20 0.33 0.35

0.80 0.75 0.80 0.79 0.82

0.013 0.014 0.016 0.014 0.013

0.011 0.011 0.013 0.009 0.014

1.03 1.04 1.11 1.06 1.11

0.21 0.20 0.19 0.19 0.28

20.0 25.7 29.1 34.8 40.1

0

A

2

3

30

1

2

−20

−30

−30 −40

−60 0

0.04 0.08


−10

Fig. 9

30

−10 −20

−30

−30 −40

−60 0

0.12

Depth from surface, in. (a)


0

0

0.04 0.08

0

1

2

3 10

0.12

0

0

−10 −20

−30

−30 −40

−60 0

Depth from surface, in. (b)

3.0

Residual stresses produced in gas-carburized and oil-quenched 6.5 mm diam rods made from AISI 8620 (curve A) and AISI 8640 (curve B) steel. Source: Ref 3

10 Residual stress, kg/mm2


0

0

2.0

1.0

Fig. 10

3

10

0



1


30


0

B

−20

−40

Source: Ref 6


−10

−30

Jominy hardenability

Composition, %

B

0

0.04 0.08


JIS SCM 420 chromium-molybdenum casehardening steel grade of different melting lot is shown in Table 3. Case depth and core hardness of higher-hardenability steel increase even when they are carburized and hardened in the same conditions, as shown in Fig. 11. However, the surface hardness is not influenced by hardenability of steel produced under a controlled carburizing atmosphere (Ref 6). Influence of Steel Hardenability on Fatigue Limit and Residual Stresses. Generally, the residual stress at the surface layer of carburized-and-hardened steel is compressive due to the larger expansion caused by transformation to martensite at the near-surface highercarbon layer that balances out the already transformed subsurface lower-carbon concentration region. Even though the amount of expansion by transformation is reduced to some extent due to transformation plasticity, still the carburized case introduces compressive stresses at the surface layer and tensile stresses at the inner side of the high-carbon hard case. The compressive residual stresses introduced in the outer carburized layer are caused by the timing of transformation at the last part of quenching balancing to strength of core. The core strength is related to the steel hardenability, and the timing of transformation to low-carbon martensite proceeds earlier than that of highcarbon case. This preliminary transformation of

0.12

Depth from surface, in. (c)

Influence of steel grade and case depth on residual stress profile. (a) 12.7 mm ( ⁄2 in.) diam; AISI 8620; surface 0.80% C; ECD ⳱ 0.76, 1.27, 2.54 mm. (b) 19.05 mm (3⁄4 in.) diam; AISI 8617; surface 0.95% C; ECD ⳱ 0.76, 1.40, 2.29 mm. (c) 19.05 mm (3⁄4 in.) diam; AISI 8617; surface 0.70% C; ECD ⳱ 0.76, 1.52, 2.54 mm. Source: Ref 2 1

Residual Stresses during Gear Manufacture / 443

70 Carburizing time, h 2.5 5.0 8.0 20.0 150 200

60 100

Core strength, kg/mm2

800

Fig. 12 Relation between core hardness and endurance limit of 9 mm diam rotating beam fatigue test. JIS SCM 420, carburized in muffled gas-carburizing furnace at 920 C for selected duration and quenched directly in JIS 1-1-1 cold oil (45–60 C), and tempered at 160 C for 2 h. Source: Ref 9

700

500


1

2

20 Residual stress, kpsi

Endurance limit, kg/mm2

80

The control of residual stress profile is not easy even if the carburizing-and-hardening operation is the same and is influenced by steel lots. Difficulty of control of residual stresses is shown by two gears processed to same specifications, but from different but acceptable heats of 43BV14 steels in Fig. 16. Residual stress distribution of lot C is much lower, and surface residual stress is in tension if shot peening is not provided. Residual stress distribution of lot D is much better even before shot peening. Residual stresses at the surface are increased by postquench shot peening to the same level and depth of about 0.13 to 0.25 mm (0.005–0.01 in.) and resulted from work hardening and stressing by the impact of blasted shots. Figure 17 shows the two extremes in residual stress distribution found in 40 production gears of various specifications and steels. Residual stress distribution of A (large gear of approximately 3 pitch AISI 4320 reheat quenched and shot peened) is very poor, and residual stress at the surface layer is tensile before shot peening. Residual stress of B (medium gear of approximately 10 pitch marquenched and not peened) is highly compressive. The carburizing process specification including carburizing and quenching should be well standardized so as not to produce type A distribution.

10 0

0

−10

−20

−20

−40

−30

−60

−40 −50

−80

−60

1.2

−70

400

2.0

1.0

20

25

30

35

40

Hardenability (Jominy 1 / 2 in.), HRC

Fig. 11 Influence of steel hardenability on effective case depth, core hardness, and surface hardness of carburized-and-hardened gears. Carburizing temperature at 920 C with carburizing atmosphere of 0.9% C potential for 2.5, 5, 8, and 20 h, quenched in JIS-1-1 cold oil, held at 40–60 C with agitation and tempered at 160 C for 2 h. ECD: A cycle, 1.4 mm; B cycle, 1.2 mm; C cycle, 1.0 mm. Source: Ref 6

1.0

60 Carbon ccontent, %

A cycle B cycle C cycle

300

0

3


sidual stresses of the pack-carburized specimens. The influence of steel grade and quench methods on three-dimensional residual stresses are compared in Fig. 15. Three quench media—10% saltwater, water, and oil—are compared on a pack-carburized specimen. Surface carbon concentration is about 1.0% C and produced about 10 to 16% retained austenite in an oil-quenched specimen. However, the longer carburizing time seems to introduce a greater percentage of retained austenite and reduces hardness. The longitudinal and tangential residual stress near the surface differs where a saltwater quench produces highest residual stresses, and an oil quench seems to produce the lowest residual stress. Saltwater quench for AISI 1020 (JIS S20C) and water quench for AISI 5120 (JIS SCr420) can produce higher surface residual stresses compared with that of oil quench, as shown in Fig. 15 (Ref 14).

Fatigue bending strength, kg/mm2

Case depth, mm

Core hardness, HV

Surface hardness, HV

processing factors and steel properties. Even when a certain number of parts are heat treated in the same condition or batch, it is quite difficult to get the same residual stress magnitude and profile, for it is almost impossible to completely control every factor of carburizing and quenching in the same manner. Figure 14 compares the distribution of residual stresses introduced in AISI 8620 steel by different carburizing-and-quenching methods. A pack-carburized testpiece has very high carbon content (1.2% C) compared with that of gas carburizing (0.8% C) and salt-bath carburizing (0.5% C). Residual stresses produced in packcarburized specimens differ depending on quench methods. Where water quenching produces deeper and larger compressive residual stresses compared with that of oil-quenched specimen, even the carbon gradient is the same. Residual stresses near the surface of both packcarburized specimens drop sharply because of a high-carbon layer with a large volume of retained austenite. The difference in carburizing methods such as liquid and gas methods produce different carbon distribution, and the resulting distributions of residual stresses differ as observed in Fig. 14 (Ref 2). Salt-bath carburizing has a very thin case and low carbon gradient; however, the case hardenability of salt-bath carburizing is improved by nitrogen diffused during the carburizing process and then the near-surface residual stresses drop. Also, residual stresses of gas-carburized specimens have a mild drop of near-surface residual stresses compared to the re-

40

0.8 0.6 0.4 0.2 0

20 50

100

150

200

−0.2 50

Core strength, kg/mm2 Influence of core strength on fatigue strength of carburized-and-hardened gears. Fatigue limit of gears of different core strength. Nonalloyed and alloyed case-hardened steels. Modulus ⳱ 3. Source: Ref 1, 13

Fig. 13

Pack carburized, water quenched Pack carburized, oil quenched Gas carburized, oil quenched Liquid carburized, oil quenched

0.02 0.04 0.06 0.08 0.10 0.12 Depth from surface, in.

Comparison of residual stresses produced in AISI 8620 steel 38.1 mm diam rods by different carburizing-and-quenching methods. Pack-carburized and reheat quenched in water or oil, and gas or liquid carburized and oil quenched. Source: Ref 2

Fig. 14

444 / Residual Stress Formation During Manufacturing Processes Water quenched SCr 420 Residual stress, kg/mm2

0

–40

D = 0.3 mm 80

60 40 20 Sectional area, mm2

0

10% Salt water quenched 1020

40

–40

D = 0.3 mm 80

60

40

20

–40

D = 0.3 mm

40

0

–80

0

–80



40

–80


Influence of Carbon Potential During Carburizing

Oil quenched SCr 420

40

0

80

60 40 Sectional area, mm2

20

0

Water quenched AISI 1020

0

–40

D = 0.3 mm –80

80

Sectional area, mm2

60

40

20

0

Sectional area, mm2

Residual stress distribution produced in AISI 1020 (JIS S10C) and AISI 5120 (JIS SCr 420) test specimen. Specimen: 11.3 mm diam, 80 mm long. Pack-carburized (surface carbon: 1.0% C) and furnace cooled. Reheated up to 880 C and quenched in 10% saltwater (20 C), water (20 C), and 40 C oil. Case depth D is distance from surface to the point of 0.6% C. Source: Ref 14

Fig. 15


0.5

1.0

1.5

2.0

2.5

3.0

30 20

0

−10 −20 −20

−30 D

−40


10 C

−10

Compression


Tension

10 10

−30

−50 −40

−60 −70 0

0.010

0.030

0.050

0.070

0.090

0.110

0.130

Depth from surface, in. Two gears processed to the same specifications made from different but acceptable heats of steels. C and D: Different heats of 43BV14 steel gears processed in the same schedule. Open circles, total case depth; closed circles, effective case depth (50 HRC). Source: Ref 15

Fig. 16

Precise control of carburizing cycle is very important for producing quality components with optimal distribution of carbon and residual stress and for minimizing carburizing time by the boost-and-diffuse control method (Ref 16). Carbon Potential Control of Carburizing Processes. Usually, the carburizing process is controlled by carbon potential by measurement of dew point, methane (CH4), carbon dioxide (CO2), or oxygen sensor, and various other gas elements contained in carburizing atmosphere in recent gas-carburizing processes. Compared with pack-carburizing and salt-bath-carburizing processes, gas-carburizing processes are more stable by the application of such gas analysis and control methods. However, throughout the carburizing operation the carbon potential of the used gas atmosphere varies depending on carrier gas carbon potential, enriching gas types and flow volume, total surface area of works, and furnace design and construction materials. The specificationes usually designated in part drawings are case depth, surface hardness, and core hardness. There are various control methods to get a designated case depth, for example, the selection of steel grades, carbon potential in a time frame, and quench media. Vacuum or reduced-pressure carburizing methods are becoming popular, but have difficulty in carbon potential control due to the lack of an appropriate carbon sensor. Therefore, the establishment of carburizing control methods has been dependent on trial and error. The boost-and-diffuse carburizing method is popular, but the development of appropriate control measures for vacuum and reduced pressure carburizing is requested. Alloying elements such as nickel and carbon concentration above the eutectic percentage increases retained austenite in carburized case. Therefore, carbon potential during carburizing should be carefully controlled to prevent excessive retained austenite in carburized gears. Figure 18 shows the influence of carbon content on hardness distribution by two different carbon potential atmospheres. The hardness and carbon distribution treated in higher 0.9% C potential has lower hardness due to a larger amount of retained austenite and deeper carbon diffusion, while that of 0.7% C potential hardness is higher in surface layer to the depth of 1 mm but carbon distribution is lower than in the former condition. Careful carbon potential control is very important for deep-case treatment to prevent excessive retained austenite, and optimal control of diffusion process is the key to fabricating quality products. Relation between Carburizing Time, Carbon Potential, and Residual Stress. Carbon potential control is important not only for hardness and residual stresses, but also for reducing treating time. Boost-and-diffuse carburizing methods have been widely applied since the late 1950s (Ref 16). The influence of carbon potential con-

Carbon content, %

800

800

700

B

A SCM 420, 9 mm ø

C

600

600 500

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

10

700

Hardness, HV(5)

1.7 kg/mm2. Similar results were reported when quench oil temperature was raised from 50 to 270 C, and the most significant increase is attained above 200 C (Ref 18). However, influence of quenching media such as hot or cold oil, salt-bath, and water-base polymer solution is not simply defined. Not only the types of quench media but their viscosity, heat transfer coefficient, Leidenfrost point, and flow speed change corresponding to the solution temperature. Influence of Tempering on Residual Stresses. Carburized-and-hardened components are usually tempered at low temperatures (130– 190 C) for about 1.5 to 2 h to prevent the chipping or cracking often observed in grinding

400

B A

S15CK, 25 mm ø

300

C

A

0 C

0 Residual stress, kg/mm2


trol on carbon distribution and their relation with residual stresses is shown in Fig. 19. In spite of large differences in carbon potential during carburizing and carburizing time where that of shortest method is less than half of the longest, the case depth and distribution of compressive residual stresses differ only slightly. The variation of residual stress is within 10 kg/mm2, and the total depth of compressive layer is similar. Additionally, the endurance limit of shortest cycle A is 6 to 7% higher than that of B and C. It means optimizing the carburizing method by controlling carbon potential is very important not only for the improvement of durability, but is also effective for improving processing efficiency and manufacturing cost. The profiles of longitudinal residual stresses produced in carburized-and-hardened steel differ from each other depending on case depth, as shown in Fig. 20. The surface compressive residual stress of ECD 0.8 mm is highest and decreases as case depth increases, while the compressive residual stress zone expands inward as case depth increases. Influence of Quenching Oil on Residual Stress. Quench methods influence the residual stress state. Surface residual stress produced in 9 mm diam rotating beam bending fatigue specimens quenched in hot and cold oils are compared. The surface compressive residual stresses in the carburized fatigue specimen made of JIS SCM 420 increase as the quench oil temperature is raised from 30 to 135 C. Surface residual stresses of specimens carburized and quenched in 30 C oil was 39.7 Ⳳ 0.7 kg/mm2 and that of specimens quenched in 130 C oil was 46.0 Ⳳ

Hardness, HV(5)


−10 −20 Carbon potential 0.9% C 0.7% C

−30 −40

0

1.0

2.0

3.0

−10

−20

SCM 420, 9 mm ø

−30 B −40

0

0.4

4.0

0.8

1.0

1.4

1.8


Depth from surface, mm Influence of carbon potential on longitudinal residual stress distribution produced in AISI 8617 19 mm diam specimen carburized and quenched directly in oil. Source: Ref 3

Fig. 18

Surface residual stress of test specimen in relation to effective case depth. Material: JIS SCM 420. 0.9 mm diam rotating beam fatigue testpieces. Carburizing condition in three different carbon potential histories: A, 1.2–0.9% C/6 h; B, 0.9% C/constant 8 h; C, 0.6– 0.9% C/13 h. Source: Ref 17

Fig. 19


0.5

1.0

1.5

2.0

2.5

30

3.0 10

10 Tension

0

0

−20 −20

−30 −40

−30

B −50

−40

−60 −70 0

0.010

0.030

0.050

0.070

0.090

0.110

0.130


−10


10 −10

Compression


20 A

0 −10

−20

−30 0.8 mm 1.3 mm 2.0 mm

−40

−50

0

Depth from surface, in. Extremes in residual stress distributions found among 40 production gears of various modules and heats made of the same steel. Open circles, total case depth; closed circles, effective case depth (50 HRC). A, large gear (approximately 3 pitch) AISI 4320 reheat, quenched and shot peened; B, medium gear (approximately 10 pitch) marquenched, no peening. Source: Ref 15

Fig. 17

1.0

2.0

3.0

Depth from surface, mm Influence of case depth on residual stress distribution produced in 6.5 mm diam cylinder rod made from AISI 8620 carburized and directly quenched in oil. Source: Ref 3

Fig. 20

446 / Residual Stress Formation During Manufacturing Processes operations. Tempering after quenching at 160 C reduces residual stresses about 1 to 2 kg/mm2 and reduces the volume of retained austenite. Reduction of surface residual stresses measured at each of the surfaces of 12 by 35 by 80 mm plates and 20 mm diam rods are shown in Table 4. Tempering temperature has considerable influence on the decrease of residual stress and the increase of temperature resulting in a larger decrease of residual stress. Tempering after quenching at 165 C reduced a compressive residual stress produced in AISI 4130 and 1526 about 50 to 60 MPa in both steels (Ref 18). However, the influence of temperature depends on tempering methods such as type and construction of furnace corresponding to the heat capacity, temperature control system, and measuring methods of holding time, which is explained in a later section.

Influence of Carburizing Time and Case Depth on Fatigue Strength The influence of case depth on fatigue properties has been investigated for about a half cenTable 4

tury, and various conclusions were drawn. However, Fig. 21 shows a clear relationship between ECD and endurance limit investigated by 9.00 mm diam rotating beam bending fatigue tests. The approximate value of the optimal ECD for the 9 mm diam specimen is 1 to 1.2 mm. Endurance limits of shallow ECD and low core hardness specimen are low due to subsurface fracture and by increasing case depth or core hardness fatigue strength. Even though the carburized case is strengthened, the core to case boundary often originates a fracture, which propagates outward leading to a breakage called fisheye fracture. By increasing case depth, the distribution of materials strength inside the specimen increases, and all fracture starts from the surface. The strength of the surface becomes the key factor, and damage such as grainboundary oxidation, nonmartensite phases at the surface, and retained austenite reduce the endurance limit. By increasing case depth or core hardness, fatigue strength can be increased. However, the peak ECD becomes deeper as the core hardness increases, and there seems to be a possibility of obtaining higher endurance limit

Surface compressive residual stresses in relation to effective case depth

JIS SCM 420, Jominy hardenability (1⁄2 in.) ⳱ 25.0. Plate 13 by 35 by 80 mm long and rod 20 mm diam by 80 mm long. Gas-carburizing temperature: 920 C with carburizing atmosphere of 0.9% C potential for 2.5, 5, 8, and 20 h, quenched from 860 C in JIS-1-1 cold oil held at 35–50 C with agitation and tempered at 160 C for 2h Residual compressive stress, kg/mm2 Average Effective case depth, mm

0.2 0.5 1.0 2.0 Average

Plate

Rod

As carburized

Tempered

As carburized

Tempered

As carburized

Tempered

30.3 28.9 34.7 29.8 30.9

27.0 30.9 30.3 30.0 29.6

30.8–32.0 27.8–29.5 34.5–37.5 30.0–33.3 32.0

23.9–29.5 27.0–33.5 31.0–34.3 29.5–33.5 30.2

26.5–32.8 27.8–33.0 32.3–35.5 20.8–33.0 29.8

26.3–29.0 29.0–33.0 28.2–32.3 27.3–31.8 29.1

Jominy hardenability (1/ 2 in.) 20.0 HRC 29.1 HRC 25.7 HRC 40.1 HRC

0

Surface residual stress, kg/mm2

Endurance limit, kg/mm2

80 −10

−20 B C

−30 D

E

−40

F −50

0

0.5

1.0

1.5

2.0

2.5

Effective case depth, mm 60

0

0.5

1.0

1.5

2.0

2.5

3.0

Effective case depth, mm Influence of effective case depth on endurance limit. Material: JIS SCM 420 9 mm diam fatigue test specimen carburized at 920 C, quenched in cold oil and tempered at 160 C. Source: Ref 6

Fig. 21

Relation between effective case depth and surface residual stresses produced in carburizedand-hardened steel. A: 10 by 10 mm, Jominy hardenability 1 1 ( ⁄2 in.) (J- ⁄2) ⳱ 14 HRC; B: 10 by 10 mm, J-1⁄2 ⳱ 22 HRC; C: 20 mm diam, J-1⁄2 ⳱ 25 HRC; D: 10 by 35 mm, J-1⁄2 ⳱ 25 HRC; E: 10 by 10 mm, J-1⁄2 ⳱ 20 HRC; F: 10 by 10 mm, J-1⁄2 ⳱ 35 HRC. Source: Ref 6

Fig. 22

Influence of Case Depth on Residual Stress The goal of the carburizing process is to produce high hardness case and also give high compressive residual stresses in the hardened case. The influence of case depth on fatigue strength is also related to the influence on residual stress. Figure 22 shows the influence of ECD on surface residual stresses, indicating the peak of the residual stresses is around an ECD of 1.0 to 1.5 mm, where the highest endurance limit exists. The figure also shows another important point that the optimal ECD and residual stresses are influenced by core hardness, and by increasing core hardness the surface compressive residual stresses increase higher than that of lower core hardness peak. The region over the peak of case depth influence turns negative because of grainboundary oxidation and retained austenite. Fatigue durability of testpieces or parts with stress concentration becomes a little different from that of unnotched specimens. It is related to the balance of applied stress and distribution of materials strength leading to the shift of optimal case depth. Carburized components such as gears have stress concentration at the tooth foot portion, and the relation between ECD and endurance limit differs from the results observed in Fig. 22. However, the basic factors related to the influence of case depth, residual stress, and grain-boundary oxidation play the key role as explained in a later section.

Influence of Microstructure on Residual Stress and Fatigue Strength Influence of Retained Austenite on Residual Stress and Strength of Carburized Steels

A

70

by a combination with higher-hardenability steels.

The distribution of carbon has an important influence on fatigue strength and the profile of residual stresses and is controlled by the carburizing condition. In particular, the variation of carbon potential in relation to operating temperature is the key to designed strength and durability. Microstructural changes introduced by carburizing and quenching vary depending on carbon gradient and quench severity, in relation to alloy elements. The carbon content of the surface layer decides the percentage of high-carbon martensite and retained austenite changes and affects wear properties and strength of carburized products. Retained Austenite in Carburized-andHardened Case. Generally, carburized-andhardened case contains 20 to 35% retained austenite phase that has considerable influence on the fatigue properties of carburized steels. Retained austenite at the surface layer due to high carbon content reduces compressive residual stresses as shown in Fig. 23. Therefore, car-


Influence of Tempering and Cryogenic Treatment on Retained Austenite

Carbon content (estimated)

10

25

0

Residual stress

−10

20 Retained austenite

15

−20

10

−30

5

−40

0

−50 60

0

10

20

30

40

50

0 −10 −20


10 Residual stress, kpsi

Retained austenite, vol.%

30

−30

Depth from surface, in. (a) Depth from surface, mm 0.5 1.0 1.5

0 60

20 SAE 1118

10

Residual stress

40

0

−10

30

Carbon content

20

−10

−20

−30

10 Retained austenite

0

−20

0


10


Retained austenite, vol.%

50

0

10

20

30

40

50

−40 60

−30

Depth from surface, in. (b) Relation among carbon gradient, retained austenite, and residual stress produced in carburized-and-hardened steels. (a) AISI 8620. (b) AISI 1118. Source: Ref 4

Fig. 23

Low-Temperature Tempering and Retained Austenite. Usually, carburized parts are tempered at about 150 to 190 C to prevent problems such as chipping or cracking in the finish machining process. Tempering at this temperature range after carburizing and hardening reduces hardness, residual stresses, and retained austenite depending on temperature and holding time. Figure 25 shows the decrease of residual stress by tempering at each temperature. Retained austenite also decreases by tempering at higher temperatures. Cryogenic (Subzero) Treatment. Retained austenite transforms to martensite by subzero or cryogenic treatment, cooling down to deep freezing temperature and increasing martensite volume and residual stresses. Retained austenite volume at the surface is lower than that of subsurface results from nonmartensite anomaly layers. Austenite volume increases by polishing away a few microns of the surface anomaly layer. From the surface to a depth of 10 to 30 lm, the retained austenite volume decreases to less than half. Although the retained austenite volume is governed by the carburizing and quenching conditions the values listed in Table 5 seem to be in the generally acceptable range. The volume of retained austenite changes by tempering and subzero treatment as shown in Table 5. The carburized-and-hardened and tempered conditions retained almost the same level of austenite volume (Ⳳ10%). Cryogenic treatment reduces retained austenite, and the volume decreases as treatment temperature is lowered. Tempering after cryogenic treatment is important, for there is a possibility of introducing microdefects caused by forced transformation by very-low-temperature subzero treatment. Microextrusion is often observed at the grain boundary, caused by transformed martensite and

Distance below surface, in. 40

0

0.010

0.020

0.030

0.040

0.050

Direct quench Single reheat Double reheat

35 30 Retained austenite, %

SAE 8620

reducing fatigue life. Tempering after subzero treatment has no observable effects on retained austenite volume and hardness. Influence of Rolling, Shotblasting, and Stress Loading. Excessive retained austenite is hazardous for fatigue strength and wear resistance. Retained austenite transforms to martensite by repeated loading such as rolling and improves load-carrying capacity under rolling fatigue applications (Ref 20). For this purpose,

25 20 15 10 5 0 0

0.25

0.50

0.75

1.0

1.25

Distance below surface, mm Profile of retained austenite in carburized-andhardened steel produced by different quench methods. Retained austenite, measured by x-ray diffraction, as a function of distance from the surface of an AISI 8620 steel carburized at 925 C. The single and double reheats were accomplished by heating to 845 and 790 C, respectively. Source: Ref 19

Fig. 24

Retained austenite, %

Depth from surface, mm 0.5 1.0 1.5

0

sensing methods is improving the reliability and reproducibility of carburizing processes. Figure 23 shows distribution of residual stresses, carbon gradient, and retained austenite of two carburized-and-hardened steels. The distance from surface to the peak of residual stresses is influenced by the volume of retained austenite. Increase of retained austenite decreases hardness and residual stresses by reduction of transformation to martensite that accompanies expansion and increases the compressive residual stress (Ref 4). Retained austenite transforms to martensite or other phases by succeeding tempering, cold working, or stressing, which is explained in a later section. Figure 24 compares the distribution of retained austenite, measured by x-ray diffraction, resulting from different quenching methods. Direct or single reheat quench after carburizing produces more retained austenite, while double reheat and quench operations can reduce the amount of retained austenite to some extent.

40 Untempered

30

Tempered

20 0 0

50

100 150 200 250 Quenchant temperature, °C

300

(a) Retained austenite, %

bon potential control during the carburizing process is very important to get quality products. Alloy elements added to case-hardening steels such as nickel, chromium, and manganese increase retained austenite; therefore, surface carbon content should be carefully controlled in carburizing alloyed steels containing nickel, manganese, and chromium. Compared with pack carburizing and salt-bath carburizing, the recent technology in gascarburizing processes are much more stable, and carbon potential control is easy via the use of various sensors. However, periodic maintenance of the oxygen sensor is very important to prevent excess or shortage of carbon potential due to the deterioration of any controlling sensors. Therefore, the recent trend toward the use of multi-

40 Untempered 30 Tempered 20 0 0

50

100 150 200 250 Quenchant temperature, °C

300

(b) Influence of quench oil temperature and tempering on residual stresses. Variation in surface retained austenite content of untempered and tempered carburized (a) AISI 4130 steel, and (b) AISI 1526 steel for various quenchant temperatures. Source: Ref 18

Fig. 25

448 / Residual Stress Formation During Manufacturing Processes Table 5

Influence of tempering and subzero treatment on volume of retained austenite

JIS SCM 420, gas carburized at 920 C, quenched from 850 C in cold oil of 35–50 C, tempered at 160 C for 2h Retained austenite (a), vol% Treatment

At carburized surface

At 10 lm, etched

At 30 lm, etched

14.7 16.5 10.6 6.7

21.8 18.5 18.6 11.0

9.15 10.7 11.3 6.7

Carburized-and-hardened surface Tempered Subzero, 25 C, treated Subzero, 75 C, treated (a) Reliability range: vol% Ⳳ 10%

40

30 Shot blasted

20

Shot peened (45 HRC, 55 m/s) Hard shot peened (53 HRC, 90 m/s)

10

0 0

100

50

150

Depth from surface, mm Change of retained austenite content by hard shot peening investigated on carbonitrided steel. 20 to 50 vol% of austenite retained at surface layer of carbonitrided steel. Retained austenite volume decreases by shot peening, depending on shot peening condition. Hard shot peening is more effective for reducing retained austenite than traditional shot peening. Source: Ref 21

Maximum residual stresses after shot peening, kg/mm2

Fig. 26

Influence of Grain-Boundary Oxidation on Residual Stress and Fatigue Strength

−120 Hard shot peened (53 HRC, 90 m/s) (57 Hard shot peened (53 HRC, 90 m/s)

−100

Hard shot peened (53 HRC, 90 m/s) (45 −80 Traditional shot peening (45 HRC, 55 m/s)

−60

Shot Shotblasted blast −40

Carburizing time, (t ), h

0

10

20

30

Volume change of retained austenite by shot peening, %

Relation between volume of change of retained austenite and maximum residual stress produced by shot peening of carbonitrided steel. Retained austenite before shot peening was 32 vol% at the point of measurement 25 lm from surface. Shot hardness and shot speed are as indicated. Hardness of shot is indicated by HRC values. Source: Ref 21

Fig. 27

Variations of surface hardness and volume of retained austenite of carburized-and-hardened steels are related to the steel type and grainboundary oxidation. The formation of nonmartensite phases—such as bainite, troostite, or pearlite phases at the grain boundary in the surface layer—directly results in decrease of hardness and compressive residual stress. Grain-boundary oxidation accompanying traditional carburizing processes is caused by reaction of the steel surface with the carburizing atmosphere containing carbon monoxide. The grain-boundary oxidation itself and the associated introduction of surface anomalies such as nonmartensite phases are closely related, but the basic phenomena are different from each other (Ref 22–24). Grain-Boundary Oxidation. During carburizing in an atmosphere containing carbon monoxide, gas grain-boundary oxidation progresses simultaneously with carburizing by metal gas reaction caused by dissociation of carbon mon-

30

Depth of anomaly, µm

Retained austenite, vol %

As quenched

30 to 40% of retained austenite is selected in special components used for rolling fatigue applications. Retained austenite transforms by mechanical stressing such as rolling and shot peening, causing stress-induced transformation into martensite. The stress loading that accompanies rolling fatigue or bend loading during mechanical operation also assists transformation of austenite. The shot peening process is effective to increase hardness, reduce retained austenite, and improve fatigue durability (Ref 11). Figure 26 shows the volume change of retained austenite by shot peening using different hardness shots. Retained austenite of the as-quenched condition can be reduced by various shot peening methods, and a great decrease is observed by hard peening. Figure 27 shows the relation among hardness increment results from shot peening blasted on various levels of retained austenite. It shows that the hardness increase results from transformation of retained austenite to martensite accelerated by shot impact. The depth of hardness increase caused by shot peening reaches down to nearly 200 lm by the hardest peening condition (Ref 21).

oxide. Also, the amount of carbon monoxide has a direct relation to the degree of grain-boundary oxidation (Ref 25), and as carburizing time or concentration of carbon monoxide increases, the depth of grain-boundary oxidation increases. Grain-boundary oxidation decreases the hardenability of near-surface grain boundary and reduces the volume of transformation into martensite and reduces surface hardness and compressive residual stresses. Therefore, grainboundary oxidation affects the fatigue property of carburized steel directly by reducing hardness and compressive residual stress and indirectly weakens grain-boundary strength to some extent. The depth of oxidation increases as carburizing time increases, as shown in Fig. 28. However, the depth of grain-boundary oxidation varies by condition. Etched microstructure shows a deeper anomaly than that of an unetched microstructure. Diffusion depth of oxygen investigated by electron probe microanalysis is much deeper than that observed by optical microscopy. Formation of Nonmartensite Phases. Depth of grain-boundary oxidation measured on nonetched and etched microstructures differs as shown in Fig. 29. Alloying elements such as chromium, silicon, and manganese are oxidized rather easily by the reaction with carbon monoxide in carburizing atmosphere (for example, Ref 22–25). Those alloy elements move to the grain boundary where oxygen is supplied from atmosphere through the grain boundary and forms metallic oxides. The depth of oxygen diffusion is far deeper than that measured by optical microscopy observing nonmartensite phases such as upper bainite, troostite, or pearlite. The transformation from austenite to nonmartensite phases is caused

0

1

2

4

9

6

16

25

20

10 SCM 420 cold oil

No etching 10% nital

SCr 420 cold oil


SCr 420 hot oil


0 0

1

2

3

4

5

t Relation between carburizing time and depth of grain-boundary oxidation. Material: JIS SCM 420, SCr 420 steels, gas carburized at 920 C in 0.9% C atmosphere for various times. Quenched from 860 C in hot and cold oil. Grain-boundary oxidation measured aspolished and etched with nital 10%. Source: Ref 26

Fig. 28

Residual Stresses during Gear Manufacture / 449 by reduced hardenability resulting from a decrease in alloy elements from austenite grains. This phenomenon is accelerated by a poor cooling rate caused by delayed quenching operation, prolonged vapor blanket stage during quench, and poor quench power. The hardenability of grain boundary of surface layer to obtain martensite can be recovered by the addition of other alloying elements such as nickel, molybdenum, boron, and nitrogen or by maintaining sufficient carbon higher than eutectic content in austenite. In addition to the influence of grain-boundary oxidation, the case hardenability of the surface layer is related to the surface carbon concentration and has considerable influence on the case hardenability. However, the influence of grainboundary oxidation is overstated because of lack of knowledge on the difference of oxidation itself and nonmartensite formation related to poor cooling speed or quench operation. In a comparison of the influence of quench media, hot oil quench produces a more nonmartensitic structure than do cold oil quench and salt quench. In the early vapor blanket stage in quenching, the cooling speed is slow and the low hardenability surface with reduced alloy elements tends to produce the nonmartensite phases rather easily. Influence of Nonmartensite Phases on Residual Stress. The compressive residual stress produced in carburized-and-hardened case decreases if the surface layer has nonmartensite phases or excessive retained austenite; the surface residual stresses are lost and turn to tension in an extreme case. Therefore, grain-boundary oxidation, the associated formation of nonmartensite, and excessive residual austenite result from excessive high-carbon content should be prevented by appropriate processing specification (Ref 28). Removal of the nonmartensite layer can improve residual stress distribution and results in improvement of fatigue durability. Figure 28 shows how to eliminate negative effects of the nonmartensite layer. It is clear that shot peening can easily eliminate the influence of grain-boundary oxida-

tion and works better than removal of the layer by chemical etching or grinding. The influence of nonmartensite phases is easily eliminated by various methods as shown in Fig. 30 and 31. However, shot peening and hard peening processes directly shot on as a carburized-and-hardened surface give the best result, as observed in the figures. Recently, various gears have applied hard or double peening to improve fatigue strength of carburized gears. Optimization of shot peening conditions such as size, shape, and hardness of shots, shot peening machine, and its operating speed and combination with those of the double peening condition is being investigated, and further progress is anticipated.

Benefit and Change of Compressive Residual Stress after Heat Treatment The particular benefit of carburizing is the introduction of high hardness case and introduction of compressive residual stresses. The compressive residual stresses produced in the hardened case counteract the applied stresses and improve bending fatigue strength. As the necessity of improving the performance of carburized parts emerges, much effort has been devoted to developing quick measuring methods, modeling, and simulation technologies to understand and increase compressive residual stresses. The benefit of compressive residual stresses in addition to the fatigue strength of the hardened surface layer is that longitudinal compressive stresses increase the endurance limit about 10% of the residual stress (Fig. 32) (Ref 1, 30).

Changing Residual Stress by Aging and Tempering Aging. Residual stress decreases by aging and by tempering, as internal stresses are released by aging effects that precipitate over saturated carbon and other elements from martensite phases.

Aging effects proceed gradually and reduce residual stresses as shown in Fig. 33; the change of residual stress distribution due to aging is different depending on steel grade. As observed in Fig. 33(a), straight carbon steel loses residual stress more easily than does nickel and chromium alloy steel (Fig. 33b). Tempering. Similar to aging phenomena, tempering also reduces residual stress as observed in Fig. 34 and 35. The reduction of residual stress resulting from tempering differs depending on factors such as steel grade and state of carbon gradient in relation to microstructures and tempering condition, as observed in Fig. 34 (Ref 3). The decrease in compressive stress influences distribution, and the stress peak disappears at tempering at temperatures higher than 200 C.

Changing Residual Stress Profile by Repeated Stressing Residual stress decreases during fatigue (repeated) loading. However, compressive residual Limited time life strength, kg/mm2 × 106 J- 1/ 2 = 20 HRC J- 1/ 2 = 40 HRC

A B C D

90

100

110

120

J − 1/ 2 , Jominy hardenability (1/ 2 in.) Influence of posthardening finishing method on rotating beam bending fatigue life. Surface: 0.9% C. 920 C for 8 h. Cold oil quench: 860 C. J-1⁄2, Jominy hardenability (1⁄2 in.). A: as-carburized and quenched; B: carburized, quenched, and shotblasted; C: carburized, quenched, and chemically etched; D: carburized, quenched, etched, and shotblasted. Source: Ref 26

Fig. 30

(c) (a)

(b)

Microstructures of grain-boundary anomalies. (a) AISI 8620 steel, gas carburized at 955 C. Specimen shows grain-boundary anomaly to a depth of approximately 0.02 mm. 1% nital. 750⳯. (b) AISI 4118 steel, gas carburized at 955 C. Grain-boundary anomaly to a depth of approximately 0.02 mm. As polished. 750⳯. (c) AISI 8822 steel, gas carburized 15 h at 925 C, reheated to 840 C, and held 40 min, oil quenched, and tempered 2 h at 150 C. Bainite-pearlite mixture near the surface is visible because of the lighter etching. 2% picral. 500⳯. Source: Ref 27

Fig. 29


(a)

(b)

(+1.4%)

(c)

(+10%)

(d)

(+12%)

(+25%) (+47%)

(e)

50

100

Rotate bending fatigue strength, kg/mm2 Comparison of various finishing methods to eliminate problems caused by surface anomalies. (a) Basic process SCM 420 carburizing. Traditional carburizing as the base data. (b) Carburizing and NH3 addition. Ammonium gas addition at the final stage of carburizing. (c) Vacuum carburizing. (d) Alloying. Experimental steel with Ni-0.2%, reduce Si to 1⁄2 of standard steel. Mo increased. (e) Electrochemical etching and shot peening compared by fatigue test. Source: Ref 29 Improvement of endurance limit, kg/mm2

Fig. 31

Fig. 32

6

5

4

3

2 1 0

−30 −40 −20 Axial residual stresses, kg/mm2

stresses do not disappear completely, even after fatigue failure. The process of stress decrease is not simple, and reduction and partial increase is observed until fatigue failure. Changing Surface Residual Stress by Repeated Stressing. The change of surface residual stress investigated by rotating beam fatigue test samples made of JIS SCM 420 is shown in Fig. 36 (Ref 5). The surface compressive residual stresses decrease at first and then turn to increase at around 0.5 million cycles, then turn to decrease again after a million cycles. The point of fatigue failure does not correspond to the upand-down trend of residual stresses (Ref 5). The process of reducing surface residual stress differs by testpieces as decrease, increase and decrease again until final failure. The data indicated in Fig. 37 show amplitude of repeated stress. Occasionally, some fatigue failure occurs during the increase stage of surface residual stress that results from partial irregular distribution of the residual stress measured at the portion near the fracture face. Changing Residual Stress Distribution by Repeated Stressing. The decrease of residual stresses is not only a phenomenon that occurs at the surface, but the decrease of compressive residual stress is also observed as the change of residual stress distribution as shown in Fig. 38 and 39. Figure 38 shows the process of reducing residual stresses at several layers in a fatigue testpiece made of nickel-chromium casehardening steel (SNC21: 0.13C, 2.16Ni, 0.38Cr). Near the surface, the change or decrease of residual stresses is clear, but change at the inner core is not so large and is rather simple compared with the surface changes (Ref 31). The progress of relaxation of compressive residual stress by repeated stressing is clear in residual stress distribution as shown in Fig. 39. The decrease of area in compressive stress by fatigue is compared with the residual stress distribution pro-

duced in the same lot of carburizing and hardening as shown in Fig. 6. The change in the surface residual stresses does not directly correspond to the change in distribution of residual stresses shown in Fig. 37. The change of residual stress distribution is not simple, and their wavy distribution patterns have no characteristic tendency. The general trend in decrease of residual stresses is in Table 6, where the total area in compressive stresses decreases as stress cycle increases, even when the cyclic stress level is lower than that of high-stress short-life test condition (Ref 5). The reduction of area in compressive stress is compared with that of average distribution of three carburizedand-hardened samples shown in Fig. 6.

Influence of Residual Stress and Grain-Boundary Oxidation on Gear Strength Case depth influences the endurance limit and fatigue lifetime of gear teeth as shown in Fig. 40. When the endurance limit exhibits double peak, the first peak exists at very thin case depth and second peak at about 1.0 mm ECD. This tendency is different from unnotched rotating beam fatigue test results; however, the case depth of the second peak is similar to that of rotating beam bending fatigue test as shown in Fig. 21. The same tendency is observed in impact bending fatigue test results of carburized notched square bar (Ref 25). Carburized-and-hardened case gives high hardness, strength, and compressive residual stress and contributes to the improvement of fatigue durability, while the static and impact strength deteriorate. The compressive residual stresses possess an independent feature that has the highest value when certain case depth is obtained at the surface layer, as shown in Fig. 22.

Improvement in bending fatigue life by surface residual stresses. Source: Ref 30

10 10

0

20 1 day 3 days 1 week 15 days 23 days 1 month after quenching

30

40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fig. 33

−20

1 day 1 week 15 days 23 days 1 month after quenching

−30 −40

0.8

Depth from surface, mm (a)

−10

0.1

0.2

0.3

0.4

0.5

0.6


10



0 0

−10

−20

−40 0

Decrease of residual stress distribution due to aging. (a) AISI 1015 (S15CK) carbon steel. (b) AISI 8620 (JISSNC21) nickel-chromium steel. Source: Ref 31

1.0

2.0

3.0


Depth from surface, mm (b)

As quench 150 °C for 1 h 190 °C for 1 h

−30

Influence of tempering on longitudinal residual stress of gas-carburized AISI 8617 steel. Gas carburized and directly oil quenched AISI 8617 19 mm cylinder rod. Source: Ref 3

Fig. 34


Influence of Residual Stresses Produced by Hard Shot Peening

Table 6 Decrease of area in compressive residual stress by fatigue test in relation to nominal stress and repeated cycles

General strengthening effects of compressive residual stress are well known, as shown in Fig. 32. The important influence of residual stresses have been reevaluated and investigated intensively (Ref 21, 29, 33–38). Figure 41 shows the relation between compressive residual stress introduced by intensive peening methods and fatigue strength investigated via control of compressive residual stress profile and simulation of their effects on fatigue strength (Ref 35).

Testpiece No.

Nominal stress, kg/mm2

Average of 3 1 2 3

Stress cycles, N

Area in compression, %

Before fatigue test 86.6 2.6 ⳯ 106 78.2 4.6 ⳯ 106 74.1 1.0 ⳯ 107

100 ⳮ4.8 ⳮ15.1 ⳮ21.2

Source: Ref 5

Posthardening Shotblast Finish In mass production, transmission gears are blast cleaned to eliminate adhered soot and/or color resulting from the dissociation of quench oils. Shotblasting and peening increase compressive residual stresses. However, general shotblasting equipment cannot introduce the uniform arc height and coverage necessary to improve surface fatigue durability. By appropriate control of blasting condition to attain uniform coverage and arc height, shotblasting can increase fatigue durability of production gears by increasing surface compressive residual stresses, although the durability is far less than that attained by shot peening and hard peening. The details of shot peening and hard peening operations are explained later in this article. For example, compressive residual stresses of production gears that were 0.1 Ⳳ 6 kg/mm2 can be improved up to 30 kg/mm2. If the condition is controlled in an optimal level, it can increase surface residual stresses up to 48 Ⳳ 5 kg/mm2 in compression even by traditional shotblasting machines. It is very important to notice

−40 Surface residual stress, kg/mm2

The depth of grain-boundary oxidation increases as carburizing time is elongated, as shown in Fig. 28, and their influence on fatigue strength increases too. These two main factors combine and result in a complicated influence on fatigue properties. Apparently, although grain-boundary oxidation has deleterious effects, the importance of residual stress is more profound and should be taken into account when designing gear durability. Figure 40 shows the influence of residual stress and grain-boundary oxidation on gear tooth bending fatigue strength. The bending fatigue strength of a carburizedand-hardened gear tooth depends on the fatigue strength of gear tooth root where applied stresses concentrate. Fatigue strength of notched specimen or mechanical components has the highest peak at thin case depth zone as observed in Fig. 40. On the other hand, tooth contact areas have rolling fatigue strength in relation to contact pressure and Hertz shear stress, which means the tooth pitch area needs a thick case depth to withstand high rolling loads. Therefore, the design specification of ECD for gear teeth is not as simple as the optimal case depth for flat specimens. Specification of ECD should take the operation condition into account to satisfy application needs to guarantee total gear life against rolling fatigue and bending fatigue life. In addition to the fatigue strength given by carburizing and hardening, the influence of the postheat treatment process is increasing in importance. A part of postheat carburizing-and-hardening treatment, such as shotblasting, is explained earlier in this article; however, the recent hard peening technology has made great advancement and contributes to the improvement of load-carrying capacity of carburized-and-hardened gears. The following section explains the influence of recent shot peening technology.

x

77.7

78.8

x

−30 68.7

x

x

−20 73.3 86.3 x

−10

0 105

106 Number of cycles, N

107

Changes in surface residual stresses during fatigue. Gas carburized at 920 C for 5 h (18 ks) in 0.8% C atmosphere, quenched from 860 C in cold oil of 35 C , and tempered at 160 C for 2 h (7200 s). x, fracture point. Source: Ref 5

Fig. 36

10

0 40 Residual stress, kg/mm2

20

0

0 D = 0.3 mm As quenched

−20 Residual stress, kg/mm2


−40

Axial stress Tangential stress Radical stress

−80 40 20 0 −20

−60 40

D = 0.3 mm 250 °C C tempered tempered

−60 80

60

40

Sectional area, mm

20

As quenched After 2.15 × 104 cycles After 9.27 × 104 cycles After 6.05 × 105 cycles After 2.82 × 106 cycles After 1.15 × 107 cycles

−30

0 −20 D = 0.3 mm 300 °C C tempered tempered

−60 20

0

−80 100

80

60

40

−40 20

0

0.1

0.2

0.3

0.4

0.5

0.6


0

Sectional area, mm

Change of residual stress distribution by tempering. Pack carburized, oil quenched from 880 C, and tempered at each temperature for 2 h. Surface carbon 1.0% C, retained austenite 9–16.5%, case depth (0.6% C) ⳱ 0.3 mm, TCD ⳱ 0.9 mm. JIS SCr 420 steel, 11.3 mm diam by 80 mm. Source: Ref 32

Fig. 35

−20

−40

−40

−80 100

D = 0.3 mm 180 °C C tempered tempered

−40

−10

Change in residual stresses due to repeated stressing. Materials: SNC21, pack carburized for 2 h at 900 C, annealed, reheated up to 750 C, and quenched in cold oil of 15 C and tempered at 150 C for 30 min. Stress amplitude: 40 kg/mm2. Source: Ref 31

Fig. 37


Contribution of Residual Stresses Introduced by Hard Shot Peening Bending fatigue durability of carburized gears is improved by surface compressive stresses introduced by hard shot peening. The influence of compressive residual stress introduced by shot

From surface: 0.01 mm 0.1 mm 0.2 mm 0.3 mm

−30

−20

−10

106

rW ⳱ 0.931rR Ⳮ 0.275

700

700

600

600

−10

500 400 300

0.4

Micro hardness, HV (500 g)

800

Carbon content, %

800


Micro hardness, HV (500 g)

Fig. 38 Change in residual stresses due to repeated stressing. Materials: SNC21, pack carburized for 2 h at 900 C, annealed, reheated up to 750 C, and quenched into cold oil of 15 C and tempered at 150 C for 30 min. Stress amplitude: 40 kg/mm2. Source: Ref 31

0.6

0.2 0 After 107 After 4.6 × 106

−20

After 2.6 × 106

−30 Initial

−40 0

0.4

0.8

1.2

1.6

2.0

Distance from surface, mm Changes in residual stress distribution due to fatigue. Materials and test conditions are the same as that of Fig. 6 and 37. Source: Ref 5

Fig. 39

800 As carburized, hardened, and tempered

700 600 500 400

(Eq 1)

107

Number of cycles

0.8

900

where rW is the endurance limit (MPa) and rR is the peak compressive stress (MPa).

Carburizing time, h 0

0

1

2

3

4

B

5

−50

−30

10

Carburized, hardened, tempered, and shotblasted

A

20

−10

200 0 Carburized, As carburized, hardened, hardened, tempered, and andshotblasted tempered

−10 −20 −30 −40

sCarburized, carburized,hardened, hardened, tempered, and and tempered shotblasted

−50 −60

0

0.5

1.0

1.5

2.0


Fig. 41

Change of hardness and residual stress distribution by shotblasting. Source: Ref 11

70 2.0 105

60

Fatigue strength, GPa

105

Distortion is an irreversible dimensional change in the component during heat treatment. From a metallurgical standpoint, there are thermally induced distortion, transformationinduced distortion, and distortion induced by both principal causes. In many cases, uneven cooling often causes distortion corresponding to any of the three principal causes. Dimensional change means change in both shape and size. It is not easy to solve the distortion problems confronting the heat treater and heat treat industries on a daily basis. Changes in straightness or warpage of shafts are reversible by applying stress in the elastic range or during tempering, for size and shape are not reversible by applied stresses.

300

2.82 × 1046


9.27 × 104 0 104

1.15 × 1047

The conclusive result proved by a linear relationship between maximum compressive residual stress and bending fatigue strength of gear tooth leads to Eq 1 (Ref 35). This result fits well with that of Fig. 42 concluded from various materials and heat treatment.

Distortion of Carburized-andHardened Steels

Residual stresses, kg/mm2

6.05 × 1045

maximum values of compressive residual stress introduced by shot peening and bending fatigue strength of gears. ● Shot peening was investigated on shot size and shape, materials, peening machine, shot speed, arc height, coverage, and the interrelationship among those factors, and these were simulated to give optimal results. ● The maximum compressive residual stress does not depend simply on the shot peening condition, but also on the relative effects of retained austenite before peening. Retained austenite volume is increased by carbonitriding or by increase of carbon content in relation to other alloying elements such as nickel or molybdenum.

Grain-boundary oxidation, µm

2.15 × 104

● Linear relationship is concluded between

Nominal bending stress, 105 Pa


−40

peening on bending fatigue strength of module 2.55 gears was studied—using JIS SCr 420 and experimental steels to analyze retained austenite effects, taking various shot peening conditions into account and using statistical analysis—and led to the following conclusive results (Ref 35):

Hardness, HV

those accomplishments that can almost eliminate the negative effect of surface anomalies due to intergranular oxidation (Ref 28).

5 × 105

50

40 Endurance limit

30

0

0.5 1.0 1.5 2.0 Effective case depth, mm

1.8

1.6

1.4

Calculated Fatigue test

2.5

Fig. 40 Influence of residual stress and grain-boundary oxidation on gear tooth fatigue strength, tested hydraulic pulsating machine. Module 3 JIS SCr 420 gears are gas carburized at 920 C and quenched to JIS 1-1-1 cold oil, and tempered at 160 C for 2 h. Source: Ref 26

1.2 1.0

Fig. 42 Ref 35

1.2 1.4 1.6 1.8 Peak compressive stresses, GPa

2.0

Relation between compressive residual stress (rR) and fatigue strength (rW). See Eq 1. Source:


Maximum pitch error, µm

Recent advancement in modeling and simulation to estimate hardness, microstructure, and stresses is offering new ways to understand the mechanism of distortion and appropriate measures to reduce distortion problems. Transformation plasticity influences distortion at the higher-temperature region, where the temperature difference influences the expansion due to transformation, and at the lower-temperature region where the region transformation at the final stage is affected by surrounding stress field. Depending on the type of heat treatment, causes of distortion are different, and the solution to dis-

+

tortion problems vary. However, by the application of appropriate countermeasures in jigging and quenching methods, many distortion problems can be minimized.

Types of Distortion Distortion can be classified into several categories, such as geometrical change as warpage, twisting, bending, waving, expansion or shrinkage, and nonsymmetrical dimensional change. Shape and small size changes such as gear tooth profiles and changes in lead angles also quite common phenomena that always raise problems. Distortion related to gears are classified into three basic categories: ● Body distortion in the form of warpage ● Twisting introduced in body shape itself ● Body shape distorted out of concentricity

Spec. limit

The most serious complicated distortions include tooth shape change on lead angle, tooth contour shape as pressure angle, teeth width and height balance, and pitch errors, which affect gear noise, vibration, and tooth fatigue life. These types of distortion have a profound influence on tooth contact, fatigue durability, local wear and scuffing problems, and contact noise.

0

Change of pitch error, µm

+

Examples of Methods to Reduce Distortion 0 20 25 30 35 40 Jominy (1/ 2 in, HRC)

(a)

S M L Quench oil

C B A Carburizing cycle

Gear distortion is affected by various factors such as steel grade, hardenability, grain growth during carburizing, and quench methods. Most automotive gears are carburized in continuous gas-carburizing furnaces and quenched into cold or hot oil. Recent new technologies applying vacuum or reduced-pressure carburizing furnaces use a pressurized gas quench system and the differences of the cooling media from the traditional process necessitate new cooling technologies. Influence of Steel Hardenability on Distortion. The following paragraphs discuss the

Fastener hole

Pitch error

(b) Influence of steel hardenability, quench oil flow, and case depth on distortion of hypoid ring gears. Gas carburized at 920 C and press quenched with cold oil. (a) Maximum pitch error and change of pitch error in relation to steel hardenability (Jominy, 1⁄2 in.) quench oil flow volume, and effective case depth. (b) Radial distribution of pitch error in relation to fastener hole placement. Press quench oil flow is adjusted from minimum (S), regular (M), and about 1.5⳯ volume (L) compared with regular flow volume. Approximate effective case depth is A, 1.1 mm; B, 0.9 mm; C, 0.7 mm. Source: Ref 39

Fig. 43

Change of overball diameter, µm

100

80 φ110 mm 60

40

20

HT = carburizing (920 °C) and semihot oil quenching (90 °C)

0 0

24

26

28

30

32

Jominy (1/ 2 in.) HRC Influence of steel hardenability of SCr 420, on over ball diameter of module 2.8 carburizedand-hardened transmission spur gears. Source: Ref 40

Fig. 44

influence of steel hardenability on the distortion of differential ring gears and its affect on the over ball diameter (OBD) of transmission gears. Distortion of Differential Ring Gears (Ref 39). Differential ring gears have been press quenched to prevent warpage caused by uneven geometry, for example, when one side has a gear tooth and the other side is flat but has many fastener holes. However, even with press quenching, distortion of ring gear causes many problems. Most of the distortion types resulting from quenching are flatness, taper, inner diameter, ellipticity, pitch error, and tooth angle and pressure angle. The pitch error of a ring gear increases with increasing steel hardenability, as shown in Fig. 43. It also affected by gear design with regard to placement of fastener holes. The decrease of thickness behind the gear tooth increases hardness, causes deflection of gear teeth, and increases pitch error. Oil flow rate also has considerable influence, and pitch error increases with increasing the volume of oil flow. Even with press quenching, the minimum volume of oil flow exceeds the level of oil flow necessary to quench small ring gears used for popular passenger vehicles. Distortion increases as hardenability increases. Observations show that a quench method appropriate for small ring gears is hot oil quench with a rather high cooling rate. As ring gears have gear teeth on one side and cooling severity of the tooth side and the fastener hole side differ very much, it is important to prevent overcooling of gear tooth side. Therefore, application of a hot oil jig quench is recommended for small-pitch hypoid ring gears. Distortion Affecting OBD of Transmission Gear (Ref 40). Steel hardenability has a profound influence on heat treatment distortion. Generally, the higher the hardenability of steel, the larger the core hardness and distortion increase. The average variation of steel hardenability indicated by Jominy (1⁄2 in.) value has a hardness of about 15 to 20 HRC if appropriate chemical composition control is not provided. Therefore, the control or selection of steel hardenability is important to reduce lot-by-lot scatter of distortion. The same influence is observed in many components, especially on gears having high core hardness and ring gears that have a fastener hole behind the gear teeth. The distortion indicated in Fig. 44 is JIS SCr 420 (chromium case-hardening steel), and the hardenability is Jominy 1⁄2 in. HRC. Transmission gear of module 2.8 are carburized at 920 C and quenched into semihot oil of 90 C (Ref 40). Influence of Machining Condition on Distortion (Ref 40). Residual stress resulting from previous machining has profound effects on distortion, and as shaved thickness increases, distortion such as OBD and its variations also increases (Fig. 45). Such effects may result from difference of machinability, tool sharpness, and also by other machining conditions. Therefore, the process control for stable quality production even before heat treatment should be carefully maintained.

454 / Residual Stress Formation During Manufacturing Processes Influence of Setting Methods Jig Design for Gears (Ref 40). Jig design to set components is very important to reduce part shape distortion. Usually, gears are stacked or hung on several layers of holding shafts depending on the size and shape of components. The influence of gear-setting methods on lead error and pitch error is compared to minimize distortion due to the difference of lower side and upper side of gear flange. A vertical holding method can reduce the difference of cooling speed at both sides of the gear flange and seems to reduce gear tooth distortion (Fig. 46) (Ref 40). Improvement of Ratchet Gear Roundness by Jig Design Change (Ref 41). Distortion of ratchet gear made from straight carbon plate was corrected by a special jig design developed for the parts. The hole diameter varies depending on the fine blanking direction and the cooling condition after carbonitriding. The distortion of shaft hole diameter (12.06 Ⳳ 0.01 mm) of carbonitrided (900 C) hot-rolled plate (5 mm thick) results in additional reamer finishing to maintain

80 φ54

OBD error, µm

Input shaft

60

tight fit. The first design to hold 15 ratchet plates could not maintain roundness and necessitated additional reamer finishes. This type of hole distortion, called out-of-roundness (OOR) can be corrected by changing the design of holding jigs. Reducing the cooling speed by using the type C jig shown in Fig. 47 successfully reduces the OOR and contributed to the elimination of reamer finish after treatment. Change in distribution of jig mass near the assembly hole results in extensive improvement of hole roundness and completely eliminated rejection.

Direct Hot Quench of Hypoid Gear (Ref 40) Hypoid ring gears have been using press quench methods for more than 60 years. The elimination of press quench enables reduction of production cost via the improvement in production efficiency. A stacking jig using a vertical stacking shaft with massive base plate enables direct hot oil quench of ring gears. This stacking jig enabled the reduction of setting work as observed from direct automatic gear-mounting methods after machining compared to gear setting and removing with each spacer jig gear. The repeated quenching of the jig distorted the massive base (Fig. 48) and necessitated periodic re-

grinding to keep flatness of quenched gears in specification (Ref 40).

Influence of Quenching Media and Cooling Condition on Distortion Ultrahigh Temperature Oil Quenching of Ball Bearing Race (Ref 42). Generally, saltbath quenching can produce minimum distortion products compared with oil quench. The oilquench temperature is usually lower than that of salt bath. However, new oil usable at 210 C enables the reduction of distortion to a level almost the same as salt-bath quenching, as shown in Fig. 49. Compared with distortion results from quenching in the traditional temperature of 80 C, each of the ultrahigh temperature oil and salt kept at 210 C reduced distortion to almost the same level (Ref 42). Influence of Quenching Oils on Distortion of Steering Sector Shaft. Quench severity of quenching oil has profound effects on case depth, core hardness, and distortion of carburized components. Figure 50 shows the relation between the H value (quench severity index) and core hardness, case depth, and distortion, respectively, of a carburized shaft. The shaft has gear teeth on one limited portion, which accelerates local cooling faster than on the other side

356

40

20

A jig

x-y diameter after carburizing and quenching B jig

C jig

A jig

B jig

C jig

As fine boring 0 60

80

100

120

140

160

180

200

Shaved thickness, µm

Fig. 45

0.5

Influence of shaving thickness on over ball diameter. Source: Ref 40

φ = 12.06 mm

0.3 0.2

φ120

y′

0.1 0

x′

Lead error, µm

A 60 50

B

Drive face

40

Coaster face Out-of-roundness spec = ± 0.01 mm

30

Upper limit

20

0.01

10 0 A

Pitch error, µm

C

B

C

−0.01

80 60

−0.02

Lower limit

−0.03

40

−0.04

20 0 0

Fig. 46

A

B

−0.05

C

Influence of setting jig design in gear tooth distortion. Source: Ref 40

Fig. 47

Influence of holding jig design on ratchet gear distortion. Hot-rolled plate gas carbonitrided at 900 C and quenched in cold oil. Source: Ref 41

Residual Stresses during Gear Manufacture / 455 Distortion Control by Control of Vapor Blanket Stage. By controlling quench chamber pressure, the vaporizing character of oil changes and the cooling power of quench oil can be adjusted to get better results (Fig. 51) (Ref 43, 44).

With quenching after vacuum heat treatment, the cooling power of the quenching oil does not fit the necessary cooling speed to increase hardness and reduce distortion. By changing the quench chamber pressure from 500 to 100 torr, distor-

450 Core hardness, HV

and causes bending of straight shaft. Figure 50 shows the relation between case depth and core hardness as almost linear as the H value increases, resulting in deeper case depth and higher core hardness, while the relation between H value and distortion is nonlinear, as observed in Fig. 50. Some oils increase distortion, and other oils can reduce distortion even if their H value is high. The characteristic feature of the best oil that enables distortion reduction is a long vapor blanket stage; this seems to reduce overcooling of the gear tooth portion. A similar phenomenon (Fig. 51) enables the control of vapor blanket stage of oil quench by the adjusting quench chamber pressure (Ref 41).

400

TP

350 300

Flatness, µm

100

Ring gear

80 60 40

Effective case depth, mm

120

1.0

Shaft warpage, 1/100 mm

250

15

0.9 0.8 0.7 0.6 0.5

20 0 0

1

2 3 4 5 6 Jig usage, months

7

8 Stacking jig base

Fig. 48 Influence of base jig distortion on flatness of ring gears. Jig: second generation; eight gears stacked, no spacer. DHR gear: SCM 420H (Cr-Mo casehardening steel, Jominy 1⁄2 in. controlled. Heat treatment: carburized and hot oil direct quenched (130 C). Source: Ref 40

x−

10

R

5

0

0.06

0.08

15

0.12

0.14

0.1

10

0.4

Agitator pump pressure, kg/mm2

Relation between H value of quenching oil and ECD, core hardness, and distortion, respectively. Gas carburized at 920 C and quenched from 850 C in cold oil JIS SCr 420 shaft. Warpage is measured at center of shaft. TP, test piece; R, range of variation; x, average value. Source: Ref 41

Fig. 50

5 Top Middle Lower

(a) 200 Nonagitation Agitation

150

1 atom 130 °C

900

Top

800

Middle

700 Lower Top part cooled fast

600 500

100

0

50 0 Sample 2 (80 °C)

Sample 4 (210 °C)

Salt (210 °C)

(b)

Fig. 49 Influence of quenching media on distortion of helical transmission gears. (a) Cylindrical distortion. (b) Elliptical distortion. Source: Ref 42

Fig. 51

Temperature, °C

Salt (210 °C)

20 40 60 80 Cooling rate, °C/s

100

Top Middle Lower

0.2 atom 160 °C oil

900 800

Lower

700

Top Middle

600

Uniform vapor blanket

500 0

20 40 60 80 100 Cooling rate, °C/s

10 Lead error, µm

Sample 4 (210 °C)

Temperature, °C

0

Pressure angle, µm

Cylindrical distortion, µm

Nonagitation Agitation

20

Sample 2 (80 °C)

Elliptical distortion, µm

0.1 H value,cm−2

25

500

−10

760

600 400 Pressure, torr

200

0 −15 −30

760

600 400 Pressure, torr

Reduction of distortion by adjustment of quench chamber pressure. Source: Ref 44, 45

200

456 / Residual Stress Formation During Manufacturing Processes tion of bearing steel parts was reduced and hardness was also improved (Fig. 52) (Ref 43). Similar pressure-control quenching is applied to carburizing of automotive gears. The distortion in pressure angle and helical angle becomes smallest at 100 torr as shown in Fig. 51.

Distortion Control by Plug Quenching Roundness and taper distortions of ringshaped products can be corrected by plug quenching. This method enables precise control of diameter and roundness by putting a prepared plug inside the ring work before quenching and dip or supply cooling media in a way similar to the press quench machine. Mesh-belt-type continuous reheating furnace or induction reheating can be fit with plug quench station, and the plug is pulled out of work after quenching (Ref 41).

Ways to Reduce Distortion by Various Measures

ables understanding of the effects of cooling on distribution of temperature, pressure, microstructure, and progress of transformation. In quenching carburized components, the early stage of about 30 s after dipping the outer portion of core materials just inside of carburized case starts to transform. The influence that high compressive pressure caused by cooling from the outer austenite shell has on transformation plays a very important role in distortion. Under high compressive stress, transformation starts from the outer noncarburized core portion and is affected by the pressure and direction of new martensite phase expansion to the direction to reduce pressure. After 50 to 60 s from immersion and following cooling, the outer-carburized case reaches the transformation start temperature under the restriction of transformed core, and the influence of transformation plasticity plays another role on transformation of high-carbon case and affects residual stresses and distortion (Ref 46).

Depending on component shape and size, design and materials such as shafts, flanged gears, sector shaft, weld products, and pressed sheet, quenching or cooling methods are selected to reduce distortion. Also, the cooling process should not only be simple, but various cooling stages should be designed for distortion reduction. Such cooling methods as quick-slow-quick quenching, immersion time quench, delayed quench, and many other methods can be used for reduction of distortion. In the future, technology to reduce distortion should be established with the computer-simulation technology to understand the cooling and transformation processes that may open better routes to minimizing distortion.

Figure 53 shows the difference of ring distortion (outer diameter, 75 mm; inner diameter, 25 mm; and thickness, 10 mm) comparing calculated results with and without transformation plasticity. Simulation results of distortion estimated for carburized-and-hardened ring showed large differences in diameter change and distortion of ring body. The simulated results show that outer and inner diameter without transformation plasticity expand, and the final shape of the cut section becomes like a hand drum. On the other hand, simulated results with transformation plasticity shrink both the inner and outer diameter, and shape of cut section expands and becomes drum shape. The simulation results of the same specimen for estimating quenching and tempering are also shown in Fig. 53. The distortion in diameter change simulated with and without transformation plasticity is quite similar to that of a carburized-and-hardened ring, while that of changes in cut section does not differ as much as that observed in carburized case. Simu-

With transformation plasticity Without transformation plasticity Initial shape Experimental

Carburized quenching

Normal quenching

t = 10 s t = 60 s t = 2400 s

Influence of Transformation Plasticity Recent advancement in computer simulation has enabled the analysis of progress of cooling, internal stress, and transformation timing (Ref 12, 46). Distortion of heat treated steel can be analyzed by watching intermittent steps of quenching by computer simulation, and this en-

No. of works

500 torr

250 torr





Carburized quenching

Normal quenching

100 torr

20

10

0 0.01 0.03 0.05 0.07 0.01 0.03 0.05

0.01 0.03 0.05

Distortion, mm

Fig. 52 Ref 43

Distortion of SUJ 2 part quenched under different pressures. Hardness, 66 HRC. Source:

Influence of transformation plasticity on distortion. (a) Simulated distortion during quenching and measured data after quenching. (b) Comparison of the simulated results depending on the effect of transformation plasticity. Dimension is enlarged 100⳯, and central axis is on left. Source: Ref 46

Fig. 53

Residual Stresses during Gear Manufacture / 457 lation technologies should be improved further to get satisfactory results through the improvement of model and validation efforts and construction of the necessary database, but even at this stage it can contribute greatly to understanding and improving heat treatment conditions for reduction of distortion. REFERENCES 1. H. Sigwart, Influence of Residual Stresses on the Fatigue Limit, Proc. Int. Conf. Fatigue of Metals, American Society of Mechanical Engineers, 1954, p 272–281 2. J.E. Campbell and H.O. McIntire, The Iron Age, Nov 1953, p 102–103 3. W.S. Coleman and M. Simpson, Residual Stresses in Carburized Steels, Fatigue Durability of Carburized Steel, American Society for Metals, 1957, p 33 4. D.P. Koistinen, The Distribution of Residual Stresses in Carburized Cases and Their Origin, Trans. ASM, Vol 50, 1958, p 92–97 5. K. Funatani, Change of Residual Stress of Case Hardened Steel by Fatigue, X-Ray Materials Strength, Symposium of Society of Materials Science, Japan, Nov 1967 6. K. Funatani and F. Noda, The Influence of Residual Stress on the Fatigue Strength of Carburized Hardened Steels, J. Soc. Mater. Sci. Jpn., Vol 17 (No. 183), 1968, p 1124– 1128 7. K. Hammer, Untersuchungen zum Zusammenhang zwischen Biegewechselfestigkeit und Eigen-spannungsverteilung einsatzgehaerteter stahle, Ha¨rt-Tech. Mitt., Vol 22 (No. 2), 1967, p 161–162 8. G. Parrish and G.S. Harper, Production Gas Carburizing, Pergamon Press, 1985 9. K. Funatani and H. Nakamura, Influence of Case Depth and Core Strength to the Fatigue Strength of Carburized Steels, Toyota Eng., Vol 17 (No. 4), 1966, p 293–301 10. “PSPC/MSF System,” Rigaku Catalog 11. K. Funatani and F. Noda, Residual Stresses and Fatigue Durability of Carburized Steel, Symposium on X-Ray Study of Material Strength, Society of Materials Science, Japan, 1–2 Nov 1968, p 115–120 12. T. Yamaguchi, Z.G. Wang, and T. Inoue, Proc. 27th Japan Congress on Materials Research, 1984, p 147; Mater. Sci. Technol., Vol 1, 1985, p 872–876 13. M. Ulrich and H. Glaubitz, Stand der Induktionshaertung von ZahnraedernFestgkeit- und Verschleissverhalten, Z. Verein Deutscher Ingenieure, Vol 91 (No. 22), 1949, p 577–583 14. M. Motoyama and H. Horisawa, “Residual Stress Measurements in Case-Hardened Steels,” SAE 710281, Society of Automotive Engineers, 1971 15. R.L. Mattson, Fatigue, Residual Stresses and Surface Cold Working, Proc. Int. Conf.

Fatigue of Metals, American Society of Mechanical Engineers, 1956, p 593–603 16. I. Niimi, Speed Up Carburizing by Controlling Gas Atmosphere in Gas Carburizing, Toyota Eng., Vol 13 (No. 4), 1962, p 339– 350 17. K. Funatani, Key Features in Carburizing and Carbonitriding, Proc. Carburizing and Nitriding with Atmosphere, American Society for Metals, 1995, p 255–260 18. M.M. Shea, Influence of Quenchant Temperature on the Surface Residual Stress and Impact Fracture of Carburized Steel, J. Heat Treat., Vol 3 (No. 1), June 1983, p 38–47 19. C.A. Apple and G. Krauss, Microcracking and Fatigue in a Carburized Steel, Metall Trans., Vol 4, 1973, p 1195–1200 20. C. Razim, Ueber den Einfluss von Restaustenit auf das Festigkeitsverhalten einsatzgehaerteter Probe-koerper bei schwingender Beanspruchung, Ha¨rt-Tech. Mitt., Vol 23 (No. 1), 1968, p 1–8 21. Y. Kojima, N. Miwa, M. Suzawa, K. Nishimura, and Y. Arimi, “Carbonitriding and Hard Shot Peening for High-Strength Gears,” Technical Report No. 5, Mazda, 1987, p 165–173 22. A. Hultgren and E. Hagglund, Carbide and Oxide in Surface Zone of Carburized Alloy Steels, Trans. ASM, Vol 39, 1947, p 820– 842 23 J.J. Kary, Nonmetallic Grain Boundary Material in Carburized Cases, Met. Prog., 1948, p 218–222 24. S. Gunnarson, Structure Anomalies in the Surface Zone of Gas-Carburized, Case Hardened Steel, Metal Treat. Drop Forging, June 1963, p 219–229 25. M. Ichihara and S. Kakuwa, Study on the Abnormal Surface Structure in GasCarburized Steel, J. Jpn. Inst. Met., Vol 30 (No. 3), 1966, p 307–312 26. K. Funatani, Einfluss von einsatzgaehaertungstiefe und Kernhaerte auf die Biegedauerfestigkeit von aufgekohlten Zahnraedern, Ha¨rt-Tech. Mitt. Vol 25 (No. 2), 1970 27. Case Hardening of Steel, Metallography and Microstructures, Vol 9, ASM Handbook, American Society for Metals, 1987, p 222 28. K. Funatani, “The Influence of Post Carburizing Processes on Fatigue Strength,” No. 61, Fall Conf., Japan Institute of Metals, Oct 1967 29. S. Hisamatsu and T. Kanazawa, Improvement of Carburized Gear Strength by Shot Peening, J. SAEJ, Vol 41 (No. 7), 1987, p 722–728 30. H. Buehler and H. Buchgholtz, Longitudinal Residual Compressive Stresses and Fatigue Strength, Mitt. Forsch., Vol 3, 1933, p 235 31. S. Taira and H. Murakami, Change of Residual Stress by Aging and Repeated Stresses, J. Mater. Test., Vol 7 (No. 62), 1958, p 591

32. S. Motoyama and S. Yonetani, Residual Study Committee Report, 1 Feb 1970, Japan Society for Mechanical Engineering 33. D.P. Townsend and E.V. Zaretsky, “Effect of Shot Peening on Surface Fatigue Life of Carburized and Hardened AISI 9310 Spur Gears,” NASA Technical Paper 2047, National Aeronautics and Space Administration, 1982 34. M.D. Lawrenz, Shot Peening and Its Effect on Gearing, SAE 841090, SAE Trans., 1984, p 57–67 35. H. Aihara, M. Ogino, M. Mitsubayashi, H. Inagaki, and K. Ogawa, The Strengthening of Gears by Shot Peening, No. 921125, Proc. Spring Conf., Society of Automotive Engineers, Japan, 1992, p 69–71 36. M. Mitsubayashi, T. Miyata, and H. Aihara, Phenomenal Analysis of Shot Peening: Analysis of Fatigue Strength by Fracture Mechanics for Shot-Peened Steel, JSAE No. 9430040, JSAE Rev., Vol 15, 1994, p 67– 71 37. K. Ogawa and T. Asano, Theoretical Prediction of Residual Stress Produced by Shot Peening and Experimental Verification for Carburized Steel, Mater. Sci. Res. Int., Vol 6 (No. 1), 2000, p 55–62 38. M. Mitsubayashi, M. Ohnishi, and H. Aihara, Improvement of Pitting Strength by Combined Shot Peening for Transmission Gears, Toyota Tech. Rev., Vol 50 (No. 1), 2000, p 106 39. K. Funatani, The Effect of Hardenability of Steels on Distortion of Differential Gears, Toyota Tech. Rev., Vol 18 (No. 1), 1966, p 11–18 40. A. Takahashi, T. Morishima, and H. Yamada, Quality Control in Heat Treatment, J. Jpn. Soc. Heat Treat., Vol 30 (No. 6), 1990, p 301–308 41. K. Funatani, The Trends and Tasks of Modeling and Simulation for Heat Treatment Processes, First Int. Conf. Thermal Process Modeling (Shanghai), March 2000, Intl Fed. for Heat Treatment and Surface Eng. 42. E. Nakamura, H. Uchida, and S. Koyama, The Improvement of Distortion by HighTemperature Oil Quenching, 2nd Intl Conf., Quenching and the Control of Distortion, ASM International, Nov 1996 43. M. Sugiyama, H. Iwata, and M. Uchigaito, Controlling Oil Surface Pressure in Vacuum Oil Quenching, Heat Treat., July 1987 44. M. Ogino, State and Future of Materials and Heat Treatment of Toyota Motor Corp. Automobile and Heat Treatment, Proc. for Symp. of Japan Society of Industrial Furnaces, Feb 1995, p 20 45. S. Asada and M. Ogino, Reduced Pressure Quenching Oil and Distortion, 2nd Intl Conf., Quenching and the Control of Distortion, ASM International, 1996 46. S. Yamanaka, T. Sakanoue, and S. Yoshii, Influence of Transformation Plasticity on the Distortion of Carburized Quenching Process of Cr-Mo Steel Ring, J. Jpn. Soc. Mater. Sci., Vol 48 (No. 7), 1999, p 733– 739



Metric Conversion Guide This Section is intended as a guide for expressing weights and measures in the Syste`me International d’Unite´s (SI). The purpose of SI units, developed and maintained by the General Conference of Weights and Measures, is to provide a basis for worldwide standardization of units and measure. For more information on metric conversions, the reader should consult the following references: ● “Standard for Metric Practice,” E 380, Annual Book of ASTM Stan-

dards, American Society for Testing and Materials, 1916 Race Street, Philadelphia, PA 19103 ● “Metric Practice,” ANSI/IEEE 268–1982, American National Standards Institute, 1430 Broadway, New York, NY 10018

● The International System of Units, SP 330, 1986, National Institute

of Standards and Technology. Order from Superintendent of Documents, U.S. Government Printing Office, Washington, DC 204029325 ● Metric Editorial Guide, 4th ed. (revised), 1985, American National Metric Council, 1010 Vermont Avenue NW, Suite 1000, Washington, DC 20005-4960 ● ASME Orientation and Guide for Use of SI (Metric) Units, ASME Guide SI 1, 9th ed., 1982, The American Society of Mechanical Engineers, 345 East 47th Street, New York, NY 10017

460 / Metric Conversion Guide

Metric Conversion Guide / 461


Metric Conversion Guide / 463




Index

A ABAQUS computer program .. 21, 155, 202, 303, 425 ABAQUS/Explicit software program, to model rail steel residual stresses ....... 433 ABAQUS/Standard software program, to model rail steel residual stresses ....... 433 ABB ................................................11 Abel’s kernel ................................... 128 Abrasive-jet drilling .......................... 123 Abrasive jet machining (AJM) ............. 111 Ac3 ............................................... 189 Acoustic emission ...................... 13, 14(F) crack growth in low-alloy steel .............75 evaluating residual stresses in P/M products ................................. 413 measuring kinetics of stress-corrosion cracking ...................................80 for studying delayed fracture in steels .....77 Activation enthalpy ................... 56, 57, 58 Activation enthalpy for residual stress relaxation .......................... 56, 58(F) Activation enthalpy of self-diffusion ........58 Active-part corrosion (APC) main gas-pipe line steels .....................82 mechanism .....................................79 Additional light deformation drawing ............................... 146(F) Adhesion, effect of thermal treatment on coatings .................................. 16(F) Admixed powder .......................... 400(F) Ae1, carbon and alloying element effects ...................................... 200 Ae3, carbon and alloying element effects ...................................... 200 Aging and distortion ................................ 172 effect on residual stress of carburized steels .......................... 449, 450(F) Agitation .............. 258, 259(F), 274, 279(F) effect of heat transfer ...... 271–273, 274(F), 275(F), 276(F), 277(F) effect on quench oils ............. 264, 268(F) effect on residual stress and distortion .......... 275–277(F), 283(F), 284(F), 285(F, T) Agitation rate .............. 262, 266(F), 267(F) of aqueous polymer quenchants ......... 264, 269(F) Aggregates of impurities .................... 260

Ain calibration coefficient .....................12 Aircraft coupling rods, shot peening effect on fatigue life ...............................20(T) Aircraft engines, P/M parts ................. 398 Aircraft Material Specifications (AMS), specific types AMS-S-131 65, Almen strip system .... 349, 350(F) 2770, quench media selection ............. 257 Air drying ...................................... 412 Airey’s stress function u(x, y) .............. 106 Air quenching ....... 257, 259(T), 260, 264(F) Alkaline-earth elements, addition effect on stress-corrosion cracking ..................81 Alkaline solutions, and stress-corrosion cracking ......................................79 Alligatoring .................................... 147 Alloying Mo ⴐ 0.5% Si, rotate bending fatigue strength ....................... 450(F) Alloying Ni ⴐ 2% Si, rotate bending fatigue strength ................................ 450(F) Alloy steel reactor pressure vessel, inhomogeneous residual stress investigated ..................... 136–137(F) Alloy steels cryogenic cooling ........................... 331 dimensional instability ................. 337(F) martensitic transformation ....... 332, 333(F) nitriding ....................................... 212 plasma nitriding ............................. 210 quenching materials ......................... 312 residual stresses due to turning ....... 109(F) time of intension cooling calculation ....................322–323(T) Almen block(s) with the strip .......... 349(F) Almen intensity ..................................19 Almen strip ......... 91, 96, 151, 152, 351, 352 controlling shot peening intensity .... 349(F) development of .............................. 345 monitoring degree of shot peening ........91, 93(F) system ............................... 349, 350(F) types ....................................... 349(F) Alpha ferrite (ferrite-martensite), first-order residual stress parameters ........... 335(T) Alternating bending fatigue ..................48 Alternating bending tests .........64(F), 65(F) Alternating magnetic fields, for inducing residual stress relaxation ..................54 Alumina grinding wheel ..................... 150 Aluminothermic (termite) welding, of rail steel .................................... 434(F)

Aluminum alloying effect on hydrogen embrittlement of steel ....................................83 alloying element effect on crack growth ..80 as alloying element to help obtain fine grain at heating ............................... 325 density .................................... 367(T) effect on transition temperature .........76(T) first-order residual stress parameters 335(T) heat capacity in liquid .................. 367(T) heat capacity in solid ................... 367(T) initial temperature ....................... 367(T) latent heat ................................ 367(T) mechanical properties .................. 367(T) melting temperature ..................... 367(T) plasticity loss after hydrogenation ......76(T) Poisson’s ratio ........................... 367(T) resistance to hydrogen embrittlement ..76(T) thermal conductivity in liquid ......... 367(T) thermal conductivity in solid .......... 367(T) thermal expansion coefficients ........ 367(T) thermal properties ....................... 367(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Young’s modulus ....................... 367(T) Aluminum alloys modulus of elasticity .....................96(T) Poisson’s ratio .............................96(T) residual stresses in castings with solidification time ................. 362(F) shear modulus .............................96(T) Aluminum alloys, specific types 2014-T6 residual stress of soft metallic material .......................... 346(F) 7010-T76 material library screen printout .... 352(F) 7075 casting speed .......................... 378(T) density ................................. 378(T) dilation due to solidification ........ 378(T) gradient of liquidus time ............ 378(T) gradient of solidus line .............. 378(T) hardening coefficient ................ 378(T) heat conductivity ..................... 378(T) initial yield stress .................... 378(T) latent heat due to solidification .... 378(T) liquidus temperature ................. 378(T) pipe and mold of centrifugal casting ..................380, 382–383, 384(F), 385(F), 386(F)



466 / Index

Aluminum alloys (continued) Poisson’s ratio ........................ 378(T) solidus temperature .................. 378(T) specific heat ........................... 378(T) thermal expansion coefficient ...... 378(T) viscosity ............................... 378(T) Young’s modulus .................... 378(T) Aluminum-magnesium alloys, macro and micro residual stress relaxation ..........55 Aluminum nitride (AlN) ............... 209, 325 effect on transition temperature .........76(T) influence on residual stress ............ 214(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Aluminum oxide coating .................... 118 Aluminum-silicon alloys, permanent mold casting ..................................... 369 American Standard of Testing Materials (ASTM) test methods, specific types D6200, cooling-curve analysis ............ 266 E 837–92 hole-drilling method ....... 123(T) Amorphous materials ........................ 400 Anharmonic property of the solid ........ 113 Anisotropic transformation strain modeling of 7–9(F) and transformation plasticity ............. 7(F) Annealing eliminating residual stresses ............... 144 factors affecting ...............................54 hardened or machined materials ........ 55(F) inducing residual stress relaxation ..................... 54–60(F,T) before nitriding .............................. 209 P/M parts .........................406, 407, 408 soft, and distortion ...... 153, 154(F), 155(F) temperature .....................................56 time ......................................... 54, 56 Annealing twinning, shape change ........ 5(T) Anodizing ....................................... 118 ANSYS software program ............ 127, 202 Antimony alloying effect on hydrogen embrittlement of steel .................................. 83, 84 alloying element effect on crack growth ..80 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Antioxidants, in quench oils .......... 263, 264 Approximation method ..................... 334 Aqueous acid solutions, and stress-corrosion cracking ......................................79 Aqueous polymer quenchants ....... 257, 264, 268(F), 269(F), 314–316, 319–320, 323–324, 326–327 Aqueous polymer quenching ........ 269, 270, 272–277(F), 279(F), 280(F), 283(F), 285(F,T) computer simulation of steel cylinder ... 289, 291(F) Ar1 ............................................. 91(F) Ar3 ............................................. 91(F)

ARBITRARY computer modeling program ................................... 429 Arbitrary cut-out indicator method ..............................132–133 Arc height ...................................... 349 Arc welding .................................... 405 Area reduction ...... 144(F), 145, 146, 147(F) Argon, as quenchant ................ 261, 265(F) Armco iron, nitriding ......................... 212 Armor-iron, delayed fracture ..................74 Arsenic, alloying element effect on crack growth .......................................80 Associated ammonia furnace atmosphere, composition ........................... 404(T) Associated methanol furnace atmosphere, composition ........................... 404(T) Asymmetry of axle components ..... 159–161, 163(F,T), 164(F) and distortion of components ............ 165, 167(F,T), 168(F) Atmosphere composition of constituents ........... 404(T) gas velocity differences and distortion ... 184 hot pressing .................................. 408 oxygen-containing, and carbon fibre composite materials ................... 184 requirements for sintering .............. 404(T) sintering ......................402–403, 404(T) Atmosphere control, and distortion ..................256–257, 259(T) Atomization of molten metal ............... 399 Auger spectroscopy, to study brittle fracture in hydrogen embrittlement in steel ......79 Austempering .. 252–253, 257, 261–263, 280, 281, 417 Austenite anisothermal decomposition ..... 200–202(F) atomic volume in ferrous alloys ...... 250(T) electronic states of .......................... 3, 4 expansion coefficient ...................... 4(F) heat capacity and magnetic properties ........................... 3–4(F) homogenization with induction hardening ..................... 233–234(F) nitrocarburizing of, deformation tendency ............................ 170(T) in schematic representation of relative transformation of mild steel plate ................................... 91(F) thermal expansion coefficient ............ 7(F) transformation products .............4(F), 5(F) transformation to acicular lower bainite, volumetric change ................. 250(T) transformation to feathered upper bainite volumetric change ................. 250(T) transformation to martensite at cryogenic temperatures ................. 331, 332(F) transformation to martensite volumetric change .............................. 250(T) Austenite grain growth ...................... 325 Austenite grain size ........................... 325 Austenite transformation after carburizing and carbonitriding ...... 189 during hardening processes, computation of .............................. 200–202(F) Austenitic stainless steels .................... 110

abrasive jet machining ...................... 111 residual stresses due to grinding ...... 109(F) strain hardening ............................. 109 Austenitic steels floccules not observed ........................73 residual stress vs. temperature ........... 7(F) shot peening of chemical process vessels ........................ 354, 356(T) Austenitic steels, specific types X 2 CrNiMoN 22–5-3 (1.4462) stress-corrosion cracking test results ............................ 356(T) X 6 CrNiTi 17–12–2 (1.4571) stress-corrosion cracking test results ............................ 356(T) X 6 CrNiTi 18–10 (1.4541) stress-corrosion cracking test results ............................ 356(T) Austenitizing ................................... 407 of high-speed steels ......................... 337 high-temperature ..............................81 of low-alloy steels ...................... 337(T) supercarburized high-speed steels .... 337(T) two-stage .......................................81 Austenitizing temperature ....77, 248(F), 251 and volume changes .............. 252, 254(F) Autofrettaged tube, crack propagation .. 35(F) Autofrettaging process, and crack propagation 35(T) Autofretting ......................................12 Automated stress mapping ................. 100 Automobiles, ferrous P/M parts ............ 398 Automotive gears, carburization of ........ 453 Avrami approach ......... 56, 57, 59(F), 60(T) parameters ............................. 56, 58(F) Avrami equation .............................. 217 Avrami kinetic law ........................... 201 Axial internal residual stresses from induction hardening ............. 234–235(F), 236(T) Axial residual stresses, after induction hardening .............................. 240(F) Axial stresses .. 144(F), 145, 146, 147, 148(F), 149 for bearing ring .......................... 317(F) residual stress distribution in radial direction at t⳱8.32 s using a plane-strain assumption ......................... 368(F) residual stress variation in the axial direction at t⳱8.3202 s with a traction-free top surface .............................. 368(F) semicontinuous casting distribution ..... 378, 380(F) specimen heating ........................ 313(F) thermal stress history with a plane-strain assumption ......................... 368(F) thermal stress history with a traction-free top surface .......................... 369(F) Axle components asymmetry of ... 159–161, 163(F,T), 164(F) distortion ........ 159–161, 163(F,T), 164(F) quenching of ............................. 174(F)

B Back stress ........................... 299, 300(F) Backstress tensor, of rail steel .............. 432


Bain distortion ................................. 332 Bainite ................................ 4(F), 250(T) deformation systems associated with transformations ....................... 5(T) in schematic representation of relative transformation of mild steel plate .......................................... 91(F) shape change ................................ 5(T) transformation-start temperature, stress effects on ...........................6(F)(T) Bainite habit plane, volume fraction of, tensile load effects ................7–8, 9(F) Bainitic steel, residual stress vs. temperature ............................... 7(F) Ball Kondratiev form factor, K, ............ 323(T) quenching and heating computational and experimental results ...... 321–323(F,T) Ball-bearing steels cryogenic cooling ........................... 340 dimensional stability of French specimens .................339(F), 340(F) Ball screw, distortion of ............ 166, 168(F) Banded segregation of carbide, and quenching distortion ........... 168, 169(F) Barkhausen noise analysis (BNA) ........ 112, 114–115, 156(F) Bars drawing ................................... 141(F) hollow cylinder, rotationally symmetric stresses, measurement ................ 106 solid cylinder, with/without rotationally symmetric stresses, measurement ... 105 Basquin relation ............................ 30, 34 Batch quench system ............... 258, 259(F) Bauer-Heyn method .......................... 102 for destructive residual-stress measurement ....................... 102(T) Bauschinger effect ...... 62, 66, 142–143, 299 in rail steel ......................... 431, 432(F) Bauschinger-induced work-softening .......66 Beam stress ..................................92–93 Bearing rings deformation prediction during hardening .................. 317–320(F,T) distortion ........................... 152–155(F) ovality after hardening ........... 153, 155(F) quenching in a hardening press ....... 185(F) quenching process and hardening .................. 315–317(F,T) residual stresses and conicity .......... 319(T) service life .................................... 319 surface layer removal and service life ... 319 Beilby layer .................................... 214 Bending ............................... 151, 154(F) mechanical, thermal, or structural origins of residual stress ........................13(T) modeling and measurement of residual stresses ........................ 154–156(F) with superimposed tension ................ 143 Bending deflection, asymmetrical components 165, 167(F,T), 168(F) Bending fatigue ................................ 189 crack initiation and residual stresses ... 34(F) increased by shot peening .......... 198–199, 201(F)

Bending fatigue crack initiation, types ..................................197–198 Bending fatigue limit, in medium-strength steel ..............................49(F), 50(F) Bending fatigue resistance of carburized steels ......................... 195 and residual stresses of carburized steels ..............................197–198 Bending fatigue strength deep rolling effect ......................... 37(F) of gear teeth, grain-boundary oxidation effect ....................450–451, 452(F) gear wheels ............................... 244(F) grinding effect ............................. 37(F) of induction-hardened gear teeth and machine parts ................ 243–244(F) and milling residual stress influence ......................... 36–37(F) milling vs. grinding of steels ................38 roughness effect on surface of low-strength steels .................................. 39(F) shot peening with grinding, S-N curves and residual stress effect ........... 37–38(F) vs. surface hardness in low-strength steel ................................... 40(F) Bending fatigue testing, quenched-andtempered steels in seawater ........... 34(F) Bending moment .....91–92, 93, 94(F), 95(F), 143(F), 145 symbol and units of .......................93(T) Bending of sheet .... 142(F), 143(F), 144–145 Bending out (d) ...................... 152, 154(F) Bend testing ..........................64(F), 65(F) Bent-beam stress corrosion test, specimen preparation practices ..................... 110 Biaxial residual-stress state, determination of .................................... 96–97(F) Biaxial stress analysis ........................ 122 Bidimensional dislocation networks ...... 342 Bielastic bands ........................... 129, 131 piecewise-homogeneous, residual stress determination .......................... 131 Biharmonic differential equation .......... 106 Bimetallic bands, edge cracking ........ 129(F) Bimetallic materials (bimetals) inhomogeneous residual stress fields ................................ 137(F) used in power installation shells with corrosion-proof surfacing ............ 129 Bin calibration coefficient .....................12 Binder bonded powder ............ 399, 400(F) Binders .................................... 399, 401 Binder systems, for metal-injection molding .................................... 412 Biot criterion ................................... 322 Biot number ........265, 282, 314(F), 316, 323 circular residual stresses compared to generalized value ............ 314–315(F) generalized ................... 322, 323, 324(T) usual ..................................... 314, 315 Birefringence shear wave ................................... 114 texture-induced .............................. 114 Birefringent gages ............................ 109 Birefringent methods ........................ 110 Blank manufacturing methods ... 167–169(F) Blasting ......................................... 150


Index / 467 Blind hole drilling ................. 99, 110–111 Blisters ....................................... 72, 83 Blowpipe positioning, in induction hardening .................................. 220 Blue tempering ..................................91 Bodner inelastic constitutive equations .. 372 Bodner’s model ...................... 373, 374(F) Body-centered cubic (bcc) materials, residual stresses ..................................... 333 Boiling film ..................................... 314 Bolt, distortion of .......................... 181(F) Boost-and-diffuse carburizing method .. 189, 190(F), 440, 444 Boreholes, for quenching after induction hardening .................................. 232 Boriding, deformation tendency ......... 170(T) Boring, mechanical, thermal, or structural origins of residual stress ..............13(T) Boron alloying effect on grain-boundary oxidation ................................ 449 alloying element effect on crack growth ..80 content effect on shrinkage and sintered density .................................. 404 Boronizing, deformation tendency ...... 170(T) Bosch, Robert ....................................11 Boundary-value problems for twodimensional elasticity theory ........ 127, 128, 129 Bowing ............................................91 Bragg angles ............................... 112(F) Bragg reflection ............................... 120 indices of ..................................... 120 Bragg’s Law ............................. 113, 333 Brass first-order residual stress parameters 335(T) third-order residual stresses ...... 334–335(F) Brass 4–6, first-order residual stress ......................... 335(T) Brass 7–3, first-order residual stress parameters ........... 335(T) Brazing ...................... 393(T), 394–396(F) finite element analysis for modeling residual stresses .................. 394, 395, 396(F) mechanical, thermal, or structural origins of residual stress ........................13(T) metal-ceramic compounds ....... 394–395(F) parameters influencing complex residual stress state ........................394–395 P/M parts ...............................405–406 shrinkage of joints ................ 394(F), 395 tensile residual stresses and thickness ratio ............394(F), 395(F) thermal expansion coefficients and their differences .................394(F), 395(F) thickness ratio influence for ceramic and steel .........394(F), 395(F) tungsten carbide-carbon cemented carbide with steel ..................... 395–396(F) tungsten carbide-cobalt with steel ....... 394, 395(F) Brine, as quenchant ...........264–265, 270(F) Brine quenching, ..............264–265, 270(F) British Aerospace ...............................11



468 / Index

Brittle coatings ................................ 110 Brittle fracture, carburized steels ........... 196 Bubbles ............................................72 Buckling ..........................................27 Built-up crack method .................128–129 Bushings eccentric cylinder, distortion ..159, 161(F,T) plug quenched ......................... 257 Butt curl ........................................ 363

C CAD. See Computer-aided design. Calcium alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ..80 Calcium chloride, as quenchant ............ 326 Calibration coefficients ........................12 Cam springs, shot peening effect on fatigue life ........................................20(T) Canning ......................................... 404 Cantilever beam bending test ........ 102, 119 Carbide coagulation, and nitriding ......... 209 Carbide precipitation and nitriding ................................. 209 of P/M tool steels ........................... 408 Carbide segregation .................... 168, 260 Carbon alloying element effect on crack growth ..80 composition requirements for powder forged parts ................................. 411(T) content effect in nitrided compound layer ..................................... 213 content effect on cracking propensity ... 254, 256(T) content effect on cylinder distortion .... 159, 163(F) content effect on quench cracking ....... 279, 286(F) content effect on residual stresses and distortion ..................... 249, 250(F) content effect on shrinkage and sintered density .................................. 404 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Carbonate-bicarbonate earth solutions, pH media for gas pipe line steels ............82 Carbonate solutions, and stress-corrosion cracking ......................................79 Carbon atoms, effect on micro residual stresses in hardened steels ................63 Carbon diffusion model ........... 199, 202(F) Carbon distribution in steel, and stresscorrosion cracking .........................80 Carbon fibre composite (CFC), not used with oxygen-containing atmospheres ........ 184 Carbon fiber/epoxy composites, incremental hole-drilling method for residual stress evaluation .......................... 12, 14(F)

Carbon gradient, of carburized-and-hardened steels ................................... 437(F) Carbonitrided steels, cryogenic cooling .. 340 Carbonitriding ......... 189, 190–191(F), 407, 408(F) of gears ................................... 454(F) increasing retained austenite volume and maximum compressive residual stresses .................................. 452 introducing compressive residual stress 437 process temperatures ..................190–191 temperature differences and distortion ... 184 Carbon-manganese steel, stress relief and yield strength ................... 251, 254(F) Carbon monoxide, and carburizing steel process ..................................... 448 Carbon potential .............................. 407 and carburizing, influence during ...................... 444–446(F,T) control in carburized steels ...... 446–447(F) effect on carburized-and-hardened steels .................................... 438 Carbon profile ................................. 193 after boost/diffuse carburizing ........ 203(F) after carburizing of 15CD4 steel cylinder ................. 203, 204(F) Carbon steels aging effect on carburized steel .......... 449, 450(F) austempering ................................. 281 carbonitriding ............................ 191(F) case hardening ........................... 438(F) cold plastic deformation ......................79 composition .............................. 407(T) for gear wheel, induction hardened, computer simulation ....... 296, 306(F), 307–309(F) hydrogen embrittlement .................. 76(F) quenching ...... 275, 281(F), 282(F), 284(F), 285(F) quenching, agitation effect ...... 276, 283(F), 284(F), 285(F) quenching of disk and cylinder computer simulation ......... 288–289(F), 290(F), 291(F) for ring, induction hardened and carburized quenched 303(F), 304(F), 305–307(F) stress-corrosion cracking ................... 110 tight scale formation .............. 255, 258(F) unalloyed, carburized CCT diagram ..........192–193, 194(F) Carbonyl iron process, decomposition of ......................... 400 Carbonyl process ............................. 412 Carburization .................. 407, 408(F), 418 atmosphere influence ....................... 402 of P/M parts ....................... 406, 407(F) Carburized-and-hardened steels carbon gradient, hardness, and residual stress ................ 437–438(F), 439(F) distortion ........................... 452–457(F) residual stress distribution ....... 437–438(F) Carburized bushing, quenching and thermal stresses ........................ 320–321(F,T) Carburized case ............................. 92(F) Carburized parts .................... 196, 199(F)

Carburized products, hardening methods .......................... 189, 190(F) Carburized steels. See also Carburized-andhardened steels, Carburizing. aging effect on residual stresses ......... 449, 450(F) bending fatigue resistance .... 195, 197–198 contact fatigue resistance .................. 198 cryogenic cooling ........................... 340 induction hardening of cylinder, model ......... 203–204, 205(F), 206(F) quenching temperature effect on mold hole distortion ........................... 171(T) repeated loading effect on residual stresses ........ 449–450, 451(F), 452(F) repeated stressing effect on residual stresses ........ 449–450, 451(F), 452(F) retained austenite influence ...... 446–447(F) tangential stresses of cylinder during quenching, model ........... 202, 203(F) tempering effect on residual stresses .... 449, 450(F), 451(F) tempering evaluation by x-ray diffraction .............................. 112 Carburizing. See also Carburized-andhardened steels, Carburized steels. .... 189 carbon potential influence ..... 444–446(F,T) compressive residual stresses from ....... 437 compressive stress development ........ 92(F) diffusion process computation .. 199, 202(F) distortion tendency ...... 176(T), 178–179(F) duration effect on fatigue strength of steels ................................. 446 heating device distances .................... 184 heat-transfer model ...................199–200 and nitriding, compared .................... 209 phenomenological coupling (thermal, metallurgical, and mechanical interactions) .................. 199, 201(F) pre-cooling quenching ...................... 177 rotate bending fatigue strength ........ 450(F) techniques .................................... 189 temperature differences and distortion ... 184 temperature field computation .......199–200 transformations and stress evolution ........... 191–194(F), 195(F), 196(F), 197 (F) Carburizing and NH 3 addition, rotate bending fatigue strength ......... 450(F) Carburizing and quenching, variation influence on residual stresses .............. 442–444(F), 445(F) Carburizing at low temperature, deformation tendency ............................... 170(T) Carburizing-quenching process of chromium-molybdenum steel ring, distortion computer simulation ..... 290, 292(F) of cylinder, computer simulation ........ 296, 302(F), 305 deformation tendency ................... 170(T) of ring, computer simulation ... 296, 303(F), 304(F), 305–307(F) simulation of ...........................285–286 Case depth ...................................... 407 of carburization ........................178–179


in carburized gears, residual stresses .... 441, 442(F) and carburized steel residual stress ... 445(F) and fatigue strength of carburized steels ................................ 446(F) heat treatment effect on residual stress distribution ............................. 194 after induction hardening rollers ..... 239(T), 240(F) influence on residual stresses of carburized steels ................................ 446(F) unevenness and distortion potential ...... 184 Case hardening ........................... 12, 211 compressive stresses from ...................90 and crack initiation ...........................29 mechanical, thermal, or structural origins of residual stress ........................13(T) P/M parts ............................... 406, 407 Case-hardening depths, influence on residual stresses ........................... 194, 197(F) C.A.S.E. process .... 350–351, 352(T), 353(F), 354(F) Case thickness, defined ....................... 194 Casting ............... 99, 361–370(F,T), 400(F) air-gap width ............. 365(F), 366(F), 369 axial, hoop, and radial stresses of solidification ................. 368–369(F) continuous .................................... 370 defects due to porosity formed from shrinkage ............................... 370 distortion ..................................... 361 elastic-plastic deformation regimes in solidifying material ......... 361–362(F) elastoplastic behavior ....................... 363 elastoviscoplastic behavior ................ 363 ferrostatic pressure effects ................. 370 finite-element analysis for modeling ................... 364–369(F,T) finite-element analysis of defects ......... 363 hysteresis loop of stress ................ 375(F) ingot ........................................... 370 interdendritic voids ......................... 370 locking problems ............................ 369 mechanical, thermal, or structural origins of residual stress ........................13(T) mixed-section, uneven, cooling causing constraints .......................... 361(F) permanent mold, of aluminum-silicon alloys .................................... 369 production of residual stress ..... 362–364(F) residual porosity ............................. 363 shrinkage defect location and size determination .......................... 370 single-component heavy-section .......... 361 static ........................................... 370 stress concentration regions predicted 367(F) thermal stress-generated defects, dollar loss ...................................... 361 Castings boundary condition of heat transfer and thermal radiation ...................... 375 creep ...................................... 373(F) distortion factors contributing to ....167–168 L-shaped, shrinkage cavity prediction ... 370 strain rate effect on hardening coefficient .......................... 373(F)

stress related to creep strain in a logarithmic scale ................................. 373(F) tension testing ............................... 373 T-shaped, shrinkage cavity prediction ... 370 yield stress ............................... 373(F) Casting speed, of aluminum alloy ...... 378(T) Cast iron roller burnishing effect on fatigue strength ................. 19, 20(F) spray forming ..........................412–413 Cast steels, stress-corrosion cracking .........81 Catalytic debinding ........................... 412 Catastrophic fracture ..........................90 Cathode polarization method ........... 73, 74 Cauchy (C) distribution ..................... 334 Cauchy method ................................ 122 Caustic quenching ............264–265, 270(F) Caustic soda, as quenchant ..264–265, 270(F) Cavity of concave dies, distortion of ...... 165, 168(F) Cementation steel, induction hardening .............................. 244(F) Cemented carbides, in brazed joint with steel .....................395(F), 396(F) Cementite ....................................... 249 atomic volume in ferrous alloys ...... 250(T) Cementite plates, shape change ............ 5(T) CEN. See European Committee for Standardization. Center of gravity method ................... 122 Centrifugal atomization ........... 400(F), 414 Centrifugal casting ..................... 167, 168 products formed ............................. 380 and residual stress formation ... 379–383(F), 384(F), 385(F), 386(F) Ceracon (CERAmic CONsolidation) process .................................... 409 Ceramic coatings ................................12 Ceramic shot, hardness range ............... 349 Cerium alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ..80 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack .........................76(T) Chaboche’s multiple component plasticity model ............................ 432(F), 433 Characteristics data file format ............ 304 Characteristic x-ray radiation, of first-order residual stresses of metallic materials .................... 335(T) Charging basket, and distortion .. 172, 173(F) Chasing, mechanical, thermal, or structural origins of residual stress ..............13(T) Chemical driving forces ........................ 8 limits affected by temperature ............ 6(F) Chemical etching .............................. 439 Chemically Assisted Surface Engineering (C.A.S.E.) process ...... 350–351, 352(T), 353(F), 354(F) Chemical polishing ........................... 109 Chemical species flow .............. 362, 363(F) Chemical strain-measurement methods .. 110


Index / 469 Chemical vapor deposition (CVD) ...25, 118, 120 deformation tendency ................... 170(T) mechanical, thermal, or structural origins of residual stress ........................13(T) Chemical vapor deposition (CVD) coatings ................................ 11, 12 Chen method, for destructive residual-stress measurement .......................... 102(T) Chills, in L-shaped and T-shaped castings with shrinkage defects ......................... 370 Chip formation, in milling .................. 150 Chip-removal methods .................. 109(F) Chrome plating ..................................12 Chromic steels, floccules present .............73 Chromium alloying element effect on crack growth ..80 effect on transition temperature .........76(T) first-order residual stress parameters ....335(T) increasing retained austenite in casehardening steels ....................... 447 for low-alloy P/M steel powders ......... 399 oxidation in carburizing atmosphere ..... 448 plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Chromium-alloyed steels, nitriding ........ 216 Chromium carbides ....................403–404 in high-speed steels after cryogenic cooling ..................340–341(F), 343 Chromium-manganese steels floccules present ...............................73 nitriding ....................................... 212 Chromium, (max), composition requirements for powder forged parts ............. 411(T) Chromium-molybdenum steels hardenability effect on core hardness and case depth .......... 441–442(T), 443(F) nitriding ....................................... 212 ring distortion, carburized-quenched, computer simulation ........ 290, 292(F) for ring, induction hardened and carburized quenched .... 303(F), 304(F), 305–307(F) Chromium-molybdenum-nickel steels, induction hardening .................. 244(F) Chromium-molybdenum-vanadium steels, nitriding ................................ 212(T) Chromium nickel (cementation) steels, induction hardening .................. 244(F) Chromium-nickel steels, floccules present .......................................73 Chromium-nickel-tungsten steels, floccules present ............................73 Chromium nitrides .............. 209, 403–404 Chromium nitride (CrN), influence on residual stress ......................... 214(T) Chromium nitride (Cr 2N), influence on residual stress .................. 214(T) Chromium-silicon spring wire, residual stress distribution after shot peening .. 91, 94(F) Chromium steels, cryogenic cooling ....... 340 Circular hole drilling method ........ 130, 133 Circumferential hoop stress ......... 94, 95(F) Circumferential (hoop) stress in tube, formula for calculating residual stress .................................... 95(F), 96(T)



470 / Index

Circumferential stress for bearing ring .......................... 317(F) from specimen heating ................. 313(F) Circumferential stress in tube from net opening displacement X, formula for calculating residual stress .............96(T) Cladding, crack-indicator method for determining inhomogeneous residual stress fields ........... 136–137(F) Clamping, and distortion ..................... 166 Clausius-Duhem inequality ................. 298 Clay-coating method .........278(F), 281–282 quenching, and quench cracking ......... 278, 286(T) Climb ..............................................58 Coagulation phenomenon ......... 342(F), 343 Coalescence ......................................15 Coatings brittle .......................................... 110 compressive stress at elevated temperature ............................. 118 compressive stresses ........................ 118 and quenching, effects on ........ 273, 278(F) stress determination in ........ 118–124(F,T) tensile stress at elevated temperature ..... 118 Coating separation ........................... 118 Cobalt alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ..80 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Cobalt-chromium-aluminum-yttrium coating ..................................... 118 Cobalt-free superhigh speed steels composition .............................. 406(T) designation ............................... 406(T) hardness .................................. 406(T) Weq ........................................ 406(T) Coefficient K, of first-order residual stresses of metallic materials .................... 335(T) Coefficient of linear expansion, of bearing ring being hardened .................. 318(F) Coefficient of thermal expansion .......... 427 Coffin-Mason relation .........................30 Coherent-optical interference methods ..................................... 134–136(F) Cold cracks .......................................73 Cold die pressing, in P/M processing .....397(F) Cold-die quenching ........................... 281 Cold forging .................................... 141 Cold forming (working) definition ..................................... 141 steel ................................. 147–148(F) Cold injection molding, in powder metallurgy processing ............................. 397(F) Cold isostatic pressing ................. 402, 404 in powder metallurgy process ......... 397(F) Cold oil quenching ................. 449, 453(F) Cold-rolled steel ............................... 111 Cold-rolled steel sheet stampings, distortion of ................................. 168–169(F)

Cold rolling .............................. 141, 419 and distortion ...... 152, 153, 154(F), 155(F) in powder metallurgy processing ..... 397(F) Cold-shortness threshold, antimony and tin alloying effects .............................83 Cold sintering .................................. 402 Cold slip casting, in powder metallurgy processing ............................. 397(F) Collectors. See Pores. Compaction, in powder metallurgy processing ............................. 397(F) Compaction cycle ......................... 401(F) Compatibility equations of ............ 105, 106 Compliance method ............................91 Component design, and distortion ... 252–253, 255(F), 256(F) Compressive hoop stress ......................95 Compressive residual stresses ... 193, 196(F), 211, 216 area decrease by fatigue test, repeated stressing ...................... 450, 451(T) in carburized steels after heat treatment ...... 449–450(F), 451(F) after induction hardening .................. 239 induction hardening of gear tooth .... 242(F) induction hardening of machine parts .... 243 in spring steel ..................................27 Compressive residual stress zone ....194–195 Compressive shrinking stresses ............ 193 Compressive stresses increase by shot peening ...198–199, 200(F) induction hardening ............... 232–242(F) Compressive thermal stresses, from welding ................ 392, 393(F), 394(F) Computational fluid dynamics (CED) .... 258 Computer-aided design (CAD) ............ 413 Computer-aided engineering (CAE) systems ..............................302–303 HEARTS ........... 296, 301(F), 302–304(F) Computer-controlled robotics system, fiveaxis for lasershot peening ............. 355 Computer modeling ......................... 100 Computer-numerical-controlled (CNC) servohydraulic multiplaten powder press ............................... 410, 411 Computer programs. See also Computer simulation. modeling ...................................... 202 Computer simulation ........................ 202 of carburizing-quenching process ...285–286 chromium-molybdenum steel ring distortion carburized-quenched ........ 290, 292(F) of cylinder, carburized ..... 296, 302(F), 305 discrepancies of calculated models with measured amounts .......... 204–206(F) of gear wheel, dual frequency induction hardened ...... 296, 306(F), 307–309(F) heat-transfer coefficients modeling ....... 268 for jet-hardening and fog-quenching process .................................. 174 of quenching a carbon steel disk and cylinder ... 288–289(F), 290(F), 291(F) rail steel roller straightening ..... 432–434(F) of residual stresses/distortion of scanning induction hardened cylinder ........ 290, 293(F), 294(F)

of ring, induction hardened and carburized quenched ...........296, 303(F), 304(F), 305–307(F) software for residual-stress measurement ........................... 113 stress/strain prediction in case-hardened parts ........................... 199, 201(F) warpage of steel shafts .....289–290, 291(F) Concurrent engineering .......................11 residual stress-integrated design and other sectors connected ............... 24(F), 25 Conductance-time curves ................... 269 Conformal mapping functions ............. 132 Consistency relation held during creep loading .................................... 302 Constantinescu and Ballard method ..... 105 Construction, and distortion potential ..... 183 Contact fatigue ............. 150, 196, 215–216 carburized steels ............................. 196 Contact fatigue resistance, and residual stresses of carburized steels ............ 198 Contact length ................................. 143 Contamination, of quenchants ............. 259 Continuous casting and crack initiation in gas main pipes .....82 finite-element method formulation .......................376–377 Continuous casting by twin-roll method, residual stress formation ......... 383–385, 386(F), 387(F), 388(F), 389(F) Continuous cooling ................. 191–193(F) Continuous cooling curves, superposition of .......................... 249 Continuous-cooling-transformation (CCT) diagrams ........................ 248–249(F) of carburized steels ........ 191–192, 193(F), 196(F) cooling austenite transformation for steel .........................45, 314(F) of supercooled austenite .................... 320 Continuous gas-carburizing furnaces, to carburize automotive gears ............. 453 Continuous weight functions ............... 127 Continuum approach ........................ 415 Contour hardening ........................... 241 Control/analysis condition data file format ..................................... 304 Convection-cooling stage ....... 268, 269, 270, 271, 274 Convection heat transfer, area of .......... 312 Convective heat transfer (cooling) (CONV) ......................... 258, 261(F) Converters ...................................... 221 Cooling ................................... 89–90(F) circumferential stresses at characteristic points versus time ................. 314(F) effect on distortion of components ............... 172–177(F,T) residual stresses experimental vs. calculated values ............................... 314(F) temperature field changes ........ 313–314(F) and thermal stress buildup relieved ......... 7 without transformation ........... 250, 252(F) with transformation ........ 250–251, 252(F), 253(F) Cooling acceleration effect ........ 273, 278(F)


Cooling atomic reactors, stress-corrosion cracking of steel ............................81 Cooling characteristics, effect on residual stress and distortion from quenching 275–278, 281(F), 282(F), 283(F), 284(F), 285(F),T) 286(T) Cooling condition, effect on distortion of gears .......................... 454–456(F) Cooling curve ........... 192, 193, 196(F), 259, 262(F), 265–271(F), 272(F) agitation effect ..................... 271, 274(F) water temperature effect ............... 270(F) Cooling curve analysis ..........265–267, 268, 270(F), 271(F) Cooling-curve tests ..................... 265, 274 Cooling factor ................................. 322 Copper alloying addition effect on sintering ..... 402 alloying effect on P/M structural steels ..........................406–407(T) alloying element effect on crack growth ....................................80 composition requirements for powder forged parts ........................ 411(T) effect on transition temperature .........76(T) first-order residual stress parameters 335(T) modulus of elasticity .....................96(T) plasticity loss after hydrogenation ......76(T) Poisson’s ratio .............................96(T) quenching .......................... 273, 279(F) resistance to hydrogen embrittlement ..76(T) shear modulus .............................96(T) time up to fracture ........................76(T) work of propagation of a ductile crack 76(T) Copper-infiltrated steels, composition ........................... 407(T) Copper infiltration, cost, relative ....... 413(F) Copper-nickel, first-order residual stress parameters ............................. 335(T) Copper steels, composition .............. 407(T) Copper-zinc alloys, macro and micro residual stress relaxation ............................55 Core hardness, effect on residual stress of carburized-and-hardened steels ......... 442 Correction in stress c(Z1) ................... 108 Corrosion, nitrided surfaces ................. 215 Corrosion fatigue ............................. 100 resistance improved by shot peening ..... 354 Corrosion pittings, and crack initiation in seawater .....................................34 Cost in Euro for production 1. 4462 (X 2 CrNiMoN 22–5-3) cost comparison of 5000L vessel .. 356(F) 1. 4539 cost comparison of 5000L vessel .. 356(F) 1. 4541 (X 6 CrNiTi 18–10) cost comparison of 5000 L vessel 356(F) 1. 4571 (X 6 CrNiTi 17–12–2) cost comparison of 5000L vessel .. 356(F) Crack arrest ...... 35, 47, 48, 49(F), 50(F), 52 and deep rolling ...................... 49–50(F) and shot peening .................. 353, 354(F) in steels .........................................75 Crack growth equation ........................29 Crack growth rate ..............................29 Crack-indicator method ................. 137(F)

Crack initiation ...............27, 28, 33–34(F) carburized steels .............196–197, 199(F) at notch root, and crack arrest ..........47–48 quenched-and-tempered steel in seawater ........................... 34(F) in steels .........................................75 Crack propagation ................... 16, 27, 28 carburized steels .......................196–197 in high-strength steels ............... 48–49(F) medium-strength steels ................... 49(F) residual stresses influence ........... 34–36(F) Crack propagation rate (velocity), work hardening effect and residual stresses ........................ 35(F) Crack tip plastic zone ..........................28 Crack-tip state ................................. 131 Crack-Nicholson method .................... 376 Crankshafts induction hardening and grinding ....................... 244–246(F) roller burnishing effect on fatigue strength .......................... 19, 20(F) shot peening effect on fatigue life ......20(T) C-ray stress corrosion test specimens, practices for making and using ........ 110 Creep ............ 4, 58–59, 60(F), 68, 213, 251 in casting models ............................ 364 high-temperature ..............................60 modeling distortion of bearing rings ..... 155 thermally controlled ........................ 216 Creep constitutive equation ................ 302 Creep function ................................. 302 Creep-hardening parameter ................ 302 Creep-resistant austenitic steel, stress relief and yield strength .............. 251, 254(F) Creep strain ..............................301–302 in strip continuous casting by twin-roll method .................................. 384 Creep strain limit ................. 58–59, 60(F) Creep strain rate ........................ 302, 374 C-ring test ............................... 91, 94(F) Critical compressive loading stress ................................ 61–62(F) Critical loading amplitude, cyclic deformation .................................66 Critical stress intensity factor ................30 Critical temperature of brittleness ..........76 Cross correlation method ................... 122 Crossland criterion ........................ 17, 19 Cross slip .........................................58 Cryogenic cooling ................ 331–344(F,T) carbide formation ................. 340–341(F) influence on dimensional stability of steels ...........336–339(F,T), 340(F) influence on residual stresses of steels ... 336 influence on structure and substructure of steels .................... 339–343(F,T) of low-alloy steels ...................... 337(T) purpose ....................................... 331 residual stresses evaluated after ........................ 333–336(F,T) residual stresses induced ...... 331–336(F,T) and retained austenite in carburized steels .......................... 447, 448(T) steels ................................ 331, 332(F) supercarburized high-speed steels .... 337(T) thermal range ................................ 331


Index / 471 Crystallites ..................................... 333 Crystal structure .................249(F), 250(F) Cube, Kondratiev form factor, K ........ 323(T) Cubic boron nitride (CBN) grinding wheel ....................................... 150 Cups, deep drawing ....... 147(F), 148–149(T) Curie temperature ............................... 3 Curie transition temperature .... 203, 205(F) Current surface stresses, vs. time ..... 315(F) Cut-out indicator method .............132–133 Cutting .......................................... 150 and distortion .......................... 155, 166 Cyclic bending tests, and residual stress relaxation ........................... 66, 67(F) Cyclic creep ............................ 63–64, 66 Cyclic deformation .................... 28–29(F) for inducing residual stress relaxation ....54, 63–68(F,T) residual stresses influence ........... 31–33(F) residual stress relaxation ......... 63–68(F,T) Cyclic hardening ................................27 Cyclic hardening material ....................20 Cyclic loading ........................22(F), 23(F) and fatigue life ...........................20–21 Cyclic plasticity in low-strength steels ................ 39–40(F) in medium-strength steels ....................41 Cyclic softening ................ 27, 31(F), 32(F) Cyclic softening material ......................20 Cyclic stress-strain curve, of plain carbon steels ................................ 28–29(F) Cyclic surface yield strength ........ 66, 68(T) Cyclic work softening ............ 63–64(F), 66 Cyclic yield strength, and fatigue behavior ................................. 32(F) Cylinders (cylindrical components) of carbon steel, quenched, computer simulation .......... 288–289(F), 291(F) computer simulation of metallothermo-mechanics during quenching .............. 296, 302(F), 305 destructive residual-stress measurement procedures .......................... 102(T) eccentric hollow, distortion of .. 165, 166(F) heat treatment distortion ...... 159, 162(F,T), 163(F), 164(T) hollow distortion ..... 161–165(F,T), 166(F), 167(F) hollow with different cross sections, distortion of .................. 165, 167(F) quenching and heating computational and experimental results ...... 321–323(F,T) residual stresses/distortion in scanning induction hardening .................. 290, 293(F), 294(F) solid, residual stress measurement ........ 108

D DAM. See Discrete atom method. Damage parameters ............................45 Dang Van criterion .................... 17(F), 19 Dang Van diagram ......................... 18(F) DANTE (Deformation Control Technology, Inc.), software program ..............95–96



472 / Index

Data processing procedure, accuracy evaluation ............................. 129(F) Debinding ................................. 412, 419 Debye specific heat function ............. 3, 335 Debye temperature ..................3, 335, 336 Decarbonization ............................... 278 Decarburization .........................254–256 atmosphere influence ....................... 402 and distortion ..........................255–256 Decohesion .......................................78 Decreasing plasticity under tension .........72 Deep cooling ................................... 195 Deep drawing ........................ 141–142(F) cups ....................... 147(F), 148–149(T) Deep freezing process, and distortion ...... 178 Deep rolling ......................................55 and crack arrest ....................... 49–50(F) and cyclic deformation behavior ............33 and fatigue strength ...........................52 generating compressive macro residual stresses ....................................54 microcrack initiation in medium-strength steels ......................................42 residual stress influence on cyclic deformation behavior .......31(F), 32(F) S-N curves and bending fatigue strength ...................... 38(F) S-N curves and residual stresses effect ........................ 37(F) Deflection formula derivation ....... 93, 95(F) Deflection methods ........... 89–98(F,T), 120 to determine residual stress in coating ............................118–119 Deflection of Almen strip ......................91 Deformation. See also Distortion. adiabatic ......................................... 3 characteristics of different modes ........ 5(T) interaction with time, temperature and microstructure ........................ 3(F) plastic ............................................ 5 Deformation-induced transformation ......... 198–199, 200(F), 201(F) Deformation zone and drawing .................................. 145 shape of ....................................... 143 Deformed material, interplanar spacings and residual stresses .......................... 333 DEFORM-HT (SFTC Company), computer program ....... 289–290, 291(F), 302–303 Delayed fracture ................................72 in steels ............................. 73–79(F,T) Delayed quench ............................... 456 Dendrite arm spacing, of metal powders/ substrates for atomization techniques ............................. 400(F) Densification process ......................... 408 Density of aluminum alloy ...................... 378(T) and expansion coefficient .......... 3(T), 4(F) Densmix powders, warm compacted ....... 413 Deviatoric stress ...................288, 297, 299 Deviatoric stress tensor ................ 202, 288 DHR. See Direct hot quench. Diamond-like carbon (DLC) coating .......25 Diamond pyramid hardness test .......... 223 Diamonds, artificial, high-speed steel dies for growing, service life ..................... 326

Die pressing .................................... 404 Differential equation of heat conductivity ........................ 312 Diffraction angle .............................. 333 of first-order residual stresses of metallic materials ............................ 335(T) Diffraction line ................................ 342 physical width of .................. 334, 335(F) Diffractogram ........................... 333, 334 Diffractometers to measure residual stresses in coatings portable ................................. 122 Diffusion, during carburizing ...... 199, 202(F) Diffusion-alloyed powder ................... 399 Diffusion coefficient of carbon ... 199, 202(F) Diffusion-controlled dislocation creep ......60 Diffusion creep ............................. 54, 58 Diffusion equation for carbon content ........................... 298 for carbon content during carburizing ... 285 Diffusion zone .....................211, 214, 215 Dilatational component .................. 6(F), 7 Dilation due to solidification, of aluminum alloy .................................... 378(T) Dimensional stability ...........................16 of high-alloy tool steels ................ 343(F) of steels, cryogenic cooling influence ..........336–339(F,T), 340(F) Dimensional tolerance limits ............... 186 Direct chill (DC) casting ...............363–364 finite-element analysis predictions of defects ............................363–364 Direct hot quench (DHR), of hypoid gear ...................... 454, 455(F) Direct-metal deposition ...................... 419 Direct metal laser sintering (DMLS) ..... 413 Direct method ................................. 334 Direct quenching .............................. 189 Direct stretching (plastic deformation), after shot peening .................... 151, 153(F) Dirty steels ..................................... 254 Discrete atom method (DAM) .............. 419 Disk, of carbon steel, quenched, computer simulation ...................... 288–289(F), 290(F), 291(F) Disk deflection method ...................... 120 Disk deflection test ........................ 119(F) Dislocation and crack initiation ......................33–34 in quenched surface layer .................. 326 Dislocation arrangement, and thermally induced stresses from annealing .........58 Dislocation-core diffusion-controlled climb by edge dislocations ......................58 Dislocation creep ........................... 54, 58 Dislocation density ...................... 342, 343 of high-alloy tool steels ................ 343(F) Dislocation movement .........................57 Dislocation pinning ........................66–67 Dislocation slip .............................54–68 stable obstacles to .............................59 Dispersion hardening, niobium alloying effect ....................................... 325 Dispersoids ..................................... 414 Displacement rate vector ..............376–377 Displacement vector, of invariant-plane strain .......................................... 5

Disruption cracks ...............................72 Dissection .........................................89 Dissociated ammonia hydrogen atmosphere ............................... 403 Distance from neutral axis, symbol and units of ...................................93(T) Distortion See also Deformation. .............27 asymmetrical components .... 165, 167(F,T), 168(F) asymmetry increasing tendency for component .............................. 159 and atmosphere control .....256–257, 259(T) ball screw ........................... 166, 168(F) of bearing ring after quenching ................. 315–317(F,T) of bearing rings, prediction during hardening ......... 317–320(F,T) bolt ........................................ 181(F) carbon content effect ............. 249, 250(F) of carbon steel from quenching .......... 275, 281(F), 282(F), 283(F), 284(F), 285(F) of carburized-and-hardened steels .......................... 452–457(F) of carburized bushing due to high-rate quenching ................. 320–321(F,T) of carburized workpiece ............... 176(T), 178–179(F) castings .......................... 167–168, 361 causes ......................................... 453 cavity of concave dies ............ 165, 168(F) of chromium-molybdenum steel ring, carburized-quenched, computer simulation .................... 290, 291(F) clamping apparatus choice ................. 166 cold-rolled steel sheet stampings ..................... 168–169(F) and component design ........... 252–253(F), 255(F), 256(F) component design as control method ...................278–279 cooling process and equipment ................. 172–177(F,T) and decarburization ...................255–256 and deep freezing ........................... 178 definition ..................................... 452 of eccentric cylinder bushing ..159, 161(F,T) as effect of process equipment design ......................... 183–186(F) elastic chuck ....................... 166, 168(F) after final shaping .............. 151–157(F,T) forgings ....................................... 168 of gears ...... 176(T), 179, 253, 255, 256(F), 307(F), 309, 441–442 generating process equipment .......183–185 gravity causing .......... 178(F), 179–180(F) heating rate and uniformity factors ...............170–171 heat treating procedure influence .. 165–166, 168(F), 169–172(F,T), 173(F) by heat treatment of component shapes ......... 159–161(F,T), 162(F,T), 163(F), 164(F) high-speed gear wheel ............ 166, 169(F) hob ......................................170–171 hot-rolled steels .............................. 168 hypoeutectoid steels ........................ 168


after induction hardening ....... 238–239(F), 242(F), 243 influences of heating rules ....... 171(F), 172 of Japanese sword steel ....308(F), 309–310 loading methods contributing to ......178(F), 179–182(F,T) of machine parts ............................. 221 machining process influence ........ 165–166, 168(F), 169(F), 254, 256(F) measurement ................................. 438 metallurgical sources during reheating and quenching ..............251–252, 254(F) methods to reduce ..............453(F), 454(F) minimized by press and plug quenching dies ...................................... 281 of nitrided workpiece ....................... 179 at notch, with quenching ......... 253, 256(F) one-dimensional ............................. 260 out-of-roundness ........................ 454(F) and overheating, localized ...........256–257 pinion shafts ....................... 255, 257(F) plug quenching for control of ............. 456 prediction, after quenching ...... 284–293(F) quench ..................................259–260 quenchant effect on ............ 174–175(F,T) quench chamber pressure control of vapor blanket stage ................. 455–456(F) and quenching ..................... 252, 255(F) quenching, agitation effect ...... 276, 283(F), 284(F), 285(F) from quenching, cooling characteristics effects ........ 275–278, 281(F), 282(F), 283(F), 284(F), 285(F,T), 286(T) quenching media effect on gears ........................... 454–456(F) and quench press machines ... 181–182(F,T) and quench severity ...................279–280 of rail steel ......................... 424–435(F) ratchet gear roundness improved by jig design ............................... 454(F) reduction and prevention in quenched parts ..................................... 323 reduction in quenched parts ............... 328 reduction measures for gears .............. 456 and retained austenite content ... 257, 259(T) of ring ............... 303(F), 305(F), 306, 307 of scanning induction hardened steel cylinder, computer simulation ...... 290, 293(F), 294(F) setting method influence ............... 454(F) shape ....................................259–260 of shaped components .........159–161(F,T), 162(F,T), 163(F), 164(F) size ............................................ 260 and stabilization ............................. 178 steel grade selection as control method ......... 278, 279, 286(F) steel hardenability influence ........... 453(F) of steering sector shaft ........... 454–455(F) stop ring ............................ 180(F), 181 and tempering .........177–178(F), 283–284, 287(F) transformation plasticity influence ...................... 456–457(F) two-dimensional ............................. 260 types ........................................... 452 and welding ......................391 to 394(F)

in welds .................................... 7(F,T) zero value fixed by heat transfer intensification .......................... 328 DistSIMR (heat treatment simulation code) ....................................... 155 DMLS. See Direct metal laser sintering. Domfer process ................................ 399 Double-action tooling system .........401–402 Double-exposure technique (DET) .. 112, 135 Double-hard peening, to improve fatigue strength .................................... 437 Double peening ................................ 449 Double-press/double-sinter, cost, relative ................................. 413(F) Downcut milling, residual stresses generated ................................ 36(F) Drawing .................................... 99, 141 advantages .................................... 142 bars ........................................ 141(F) contact length ................................ 143 deformation zone geometry ................ 143 for inducing residual stress relaxation .....54 mean thickness or diameter ................ 143 residual stresses ............................. 143 rod ......................... 143(F), 145–146(F) tube .................................. 145–146(F) wire ............................141, 145–146(F) Drilling .................................... 109, 150 and distortion potential ..................... 183 mechanical, thermal, or structural origins of residual stress ........................13(T) Driving rods, shot peening effect on fatigue life ........................................20(T) Dry bag tooling ................................ 402 Dual shot peening ............................. 347 Ductile-brittle transition temperature, alloying elements effects ..................82 Dummy gage ................................. 110 Duplex surface treatments, carburizing and induction heating and quenching ....... 203–204, 205(F), 206(F) Durability, of high-speed steels ... 343–344(F) Durability till complete failure ...............80 Dyescan fluorescent tracer liquids, for inspecting shot peening coverage ...... 349 Dynamic deformation ........................ 335 DYNA2D (computer program) .. 156–157(F)

E Eddy currents, and induction hardening ..................... 242–243, 246 Edge dislocations ........................... 58, 71 Edge effect .........271, 273–274, 276, 279(F), 280(F), 283(F) EDM. See Electric discharge machining. Effective case depth (ECD) ................. 437 and carburized steel residual stresses .............................. 445(F) and fatigue strength of carburized steels ................................ 446(F) of gear teeth, grain-boundary oxidation effect .......................... 451, 452(F)


Index / 473 of scanning induction hardened cylinder, computer simulation ....... 290, 293(F), 294(F) Effective diffusion coefficient .................71 Effective stress intensity range (DKeff) .............................. 35–36(F) and crack propagation rates with welding .................... 35–36(F) quantitative determination ...................36 Eight-noded quadratic isoparametric elements, in casting thermal model ... 364 Elastic chuck, distortion of ........ 166, 168(F) Elastic compression, regime in simple slab casting ................................. 362(F) Elastic constants ....................... 95, 96(T) Elastic crack tip, as mechanical driving force coefficient ................................ 6(T) Elastic distortion .............................. 333 Elastic modulus .................................. 3 of bearing ring being hardened ....... 318(F) effect on residual stress development in steels ................................ 3(T) Elastic-plastic time-independent model, semicontinuous casting calculated stress distribution ............... 378, 381(F) Elastic recovery, after straightening ....... 151, 154(F) Elastic residual strains (Ee) ...................54 Elastic strain ... 101, 111–112, 113, 125, 285, 298–299, 373 Elastic strain component .................... 217 Elastic strain rate ....................... 202, 312 Elastic stress-strain relation of the mixture .................................... 298 Elastic tension, regime in simple slab casting ................................. 362(F) Elastic theory ....................................12 Elastic theory problem solution for regions with the wedge cutouts ................ 130 Elastic-viscoplastic constitutive model ... 378 semicontinuous casting calculated stress distribution ................... 378, 381(F) Elastic-viscoplastic solids .................... 372 Elastic-viscoplastic stress-strain matrix .. 376 Elastoplastic behavior ....................... 363 Elasto-plastic rolling contact, of rail steel ...................... 434–435(F) Elastoviscoplastic behavior ................. 363 Elastoviscoplastic constitutive equation .. 363 Elastoviscoplastic stress model ............. 364 finite-element analysis ...................... 365 Electrical conductance ............. 259, 262(F) measurement ....................... 269, 273(F) Electrical discharge machining ..............91 Electrically activated pressure sintering ................................... 408 Electrical-resistance strain gages ... 101, 102, 103, 104 for strain measurement ............... 109, 110 Electric discharge machining (EDM) ..... 147 Electrochemical etching, rotate bending fatigue strength ....................... 450(F) Electrochemical metal corrosion ............82 Electrodischarge machining ................ 405 Electrodischarge milling (EDM) ........... 109 Electroless deposition ........................ 118



474 / Index

Electrolytic etching method, to measure residual stresses .......................... 146 Electrolytic polishing ......................... 109 Electromagnetic-acoustic transducers ......91 Electromagnetic (EM) casting, finite-element analysis predictions of defects ......... 363 Electron beam, mechanical, thermal, or structural origins of residual stress .......................13(T) Electron beam hardening ................... 220 Electron beam heating-quenching, deformation tendency ................ 170(T) Electron beam welding ...................... 405 of maraging steel ..................... 60–61(F) Electronic digital speckle interferometry .........130, 132, 135, 136 Electronic packaging ...........................25 Electronic specific heat coefficient ........... 3 Electron probe micro-analysis (EPMA), to calculate time-dependent distribution of diffused carbon content in rings ...304(F), 306 Electroplating ............................ 118, 120 mechanical, thermal, or structural origins of residual stress ........................13(T) Electropolishing .................. 104–105, 109 combined with x-ray diffraction .......... 109 Electroslag heating (ESH) tundish process .......................... 405 Enameling ........................................12 End effect ............. 252, 255(F), 276, 283(F) Endothermal heat of solution ................70 Endothermic furnace atmosphere ......... 403 composition .............................. 404(T) Endothermic nitrogen-base atmosphere ............................... 407 Endothermic nitrogen/methanol atmosphere ............................... 407 Endurance limit ........................ 28, 30(F) of carburized-and-hardened steels, 442, 443(F) case depth influence in carburized steels ................................ 446(F) hard shot peening effect on carburized gears ................................. 452(F) Endurance ratio .................................17 ENSPED program in Europe ................25 Enthalpy ........................................... 4 Entropy ............................................ 4 Epsilon carbides ............................... 342 e-carbonitrides ................................ 213 e-nitrides ........................................ 213 Equilibrium equations of ............................ 105, 106 of loading mean stresses vs. residual stresses ....................................28 Equivalent creep strain ................ 288, 374 Equivalent loading stress .....................62 Equivalent octahedral stress .................21 Equivalent stress .............. 144(F), 145, 146 ERRI. See European Rail Research Institute. Eta (g) carbides ............................... 342 Etching .......................................... 439 Euler backward method ..................... 304 Euler’s equation ............................... 127 European Aeronautic, Defense and Space (EADS) ......................................11

European Committee for Standardization (CEN), draft standard, residual stress measurement of rail steel ........... 431(F) European Network of Surface and Prestress Engineering and Design (ENSPED) ..11 European Rail Research Institute (ERRI) .................................... 431 report on rail steel residual stresses ...... 431 Eutectoid, transformation-start temperature stress effects on .......................... 6(T) Eutectoid tool steels, distortion of ....171–172 Exfoliation ...................................... 215 Exothermic gas atmosphere ................ 403 Expansion coefficient, and density .... 3(T), 4(F) Explosion welding, to apply cladding to nuclear reactor casing ............... 137(F) Explosive forming ............................ 402 Explosive Newtonian wetting ..... 259, 263(F) Explosive-type wetting ............. 259, 262(F) Extensometer .................................. 102 Extrusion ....... 141, 142(F), 146–147(F), 399 advantages .................................... 142 contact length ................................ 143 deformation zone geometry ................ 143 mean thickness or diameter ................ 143 mechanical, thermal, or structural origins of residual stress ........................13(T) open-die ............................ 146–147(F) in powder metallurgy processing ..... 397(F) of rods .................................... 147(F)

F Fabrication, residual stress introduction ...... 7 Face-centered cubic (fcc) materials, residual stresses ..................................... 333 Facing, residual stresses on stainless steels ........................ 109(F) Failure modes, castings .................. 361(F) Fatigue ..............................100, 150, 152 carburized gears and shot peening effect .......... 353, 356(F) crack initiation ........................ 33–34(F) crack propagation .................... 34–36(F) critical layer thickness approach for steel ............................... 18(F) cyclic deformation in steels ........ 28–29(F) cyclic plastic deformation ....................27 cyclic softening of plain carbon steels ......................... 29(F) determined by residual stress interaction with cyclic loading stresses ............28 local fatigue strength ................ 45–47(F) macrocrack propagation in steels ..................28–29(F), 30(F) mechanisms of residual stress formation ..27 microcrack initiation in steels ...... 28(F), 29 modeling residual stress influence ......................... 43–50(F) nitrided steel .................... 214–216(F,T) phase-hardening mechanism .................29 quenched-and-tempered steels .......... 29(F) residual stress alterations of behavior leading to ...........................................27 residual stress on steel surface taken into account ................................ 18(F)

residual stress stability .......................27 of steels ................................ 28–31(F) unstable crack propagation and failure in steels .................................. 28(F) Fatigue cracking and shot peening application .... 353, 354(F) and subzero cooling ........................ 195 Fatigue damage parameters .............30–31 Fatigue ductility coefficient ...................30 Fatigue ductility exponent ....................30 Fatigue failure, from repeated stressing in carburized steels ................ 450, 451(F) Fatigue life .................................. 19, 28 calculation while taking residual stresses into account ................................ 21(F) of cold-formed products .................... 144 deep rolling effect ......................... 37(F) distribution of ..................................22 grinding effect ........................ 37–38(F) heat treatment effect on carburized steels .......................... 449, 450(F) of high-strength steel after shot peening and grinding .......................... 38–39(F) increase for mechanical components from shot peening .............................20 prediction calculations affected by residual stress ............................. 16–19(F) prediction of .................. 22, 23(F), 24(F) of shot-peened steel, Dang Van criterion ............................... 18(F) shot peening effect on stainless steel .......16 Fatigue life distribution .......................21 Fatigue limit hardenability influence on carburized-andhardened steels .............. 442, 443(F) in high-strength steels ............... 48(F), 49 of medium-strength steels ....................49 nitrided layer ................................. 216 Fatigue notch factor of high-strength steels ........................51 of low-strength steel ..........................51 of medium-strength steel .....................51 Fatigue slip bands ..................... 28(F), 29 Fatigue strength ..................... 14–15(F,T) of carburized-and-hardened steels ........ 441 case depth effect on carburized steels ................... 446(F) gears with induction hardened flanks ..............................241–242 of gear teeth, grain-boundary oxidation effect ....................450–451, 452(F) of gear wheels, and tangential residual stresses .................................. 238 of induction-hardened machine parts ........................... 243–244(F) of induction-hardened steel ................ 224 after induction hardening ............ 239, 246 prediction taking residual stress into account ....................................24 residual stress effect ................. 16–19(F) surface finish and strain hardening effects ................................. 19(F) Fatigue strength coefficient ...................30 Fatigue strength diagrams ................ 30(F) Fatigue strength exponent ....................30 Fatigue testing


carburized steels ................... 195, 199(F) induction-hardened steels .............. 244(F) FATIGUE3D (computer program) .... 21, 22 Ferric carbide (Fe 3C), dissolving, influence on residual stress .................. 214(T) Ferric nitride (Fe 4N), influence on residual stress ................................ 214(T) Ferrite acicular ...................................... 4(F) acicular, shape change ..................... 5(T) acicular, transformation-start temperature, stress effects on ....................... 6(F) allotriomorphic ............................. 4(F) allotriomorphic, shape change ........... 5(T) atomic volume in ferrous alloys ...... 250(T) expansion coefficient ...................... 4(F) heat capacity and magnetic properties ........................... 3–4(F) idiomorphic ................................. 4(F) idiomorphic, shape change ............... 5(T) massive ...................................... 4(F) nitrocarburizing of, deformation tendency ............. 170(T) in schematic representation of relative transformation of mild steel plate ............................. 91(F) thermal expansion coefficient ............ 7(F) Widmansta¨tten .............................. 4(F) Widmansta¨tten, deformation systems associated with transformations .... 5(T) Widmansta¨tten, shape change ............ 5(T) Widmansta¨tten, transformation-start temperature, stress effects on ....... 6(F) Ferrite, allotriomorphic, shape change 5(T) Ferrite, idiomorphic, shape change ...... 5(T) Ferrite, nitrocarburizing of, deformation tendency ............................... 170(T) Ferrite, Widmansta¨tten, deformation systems associated with transformations .................. 5(T) Ferrite, Widmansta¨tten, shape change .. 5(T) Ferrite, Widmansta¨tten, transformation-start temperature stress effects on ...........6(F) Ferrite, 0. 1N, influence on residual stress ..................... 214(T) Ferrite-pearlite steels Barkhausen noise analysis for stress measurement ........................... 114 hydrogen embrittlement ......................72 hydrogen states ................................72 Ferrite ⴐ carbides, atomic volume in ferrous alloys ......................... 250(T) Ferritic steels, floccules not observed ........73 Ferrochrome ................................... 399 Ferromagnetics, for inducing residual stress relaxation ....................................54 Ferromanganese .............................. 399 Fiat .................................................11 Fick’s second law ............................. 199 Film-boiling (FB) process ........ 258–260(F), 261(F), 262(F), 264–265, 268, 269, 270–271, 312 Film cooling .......................... 258, 260(F) Final instability effect ..........................30 Final part shaping asymmetry influence .. 165, 167(F,T), 168(F)

auxiliary equipment effects and loading methods ...........178(F), 179–182(F,T) axle components ......... 159–161, 163(F,T), 164(F) blank manufacturing methods ... 167–169(F) cavity of concave dies ............ 165, 168(F) chemical heat treatment ............... 176(T), 178–179(F) cooling process and equipment influence ................... 172–177(F,T) cutting ......................................... 166 cylinders ...... 159, 162(F,T), 163(F), 164(T) cylinders, hollow ..... 161–165(F,T), 166(F), 167(F) factors and relationships between heat treatment and distortion .... 159, 160(F) heat treating procedure influence .. 165–166, 168(F), 169–172(F,T), 173(F) heat treatment distortion ......159–161(F,T), 162(F,T), 163(F), 164(F) machining process influence ........ 165–166, 168(F), 169(F) screw ................................ 161, 164(F) stress relieving ............................... 166 Final shaping distortion after .................. 151–157(F,T) prior to heat treatment ......... 150–158(F,T) Final steady-state temperature (Ta) ....... 367 Finding coefficients ........................... 130 Fine-grain steels ............................... 325 Finishing, in powder metallurgy processing ............................. 397(F) Finite cylinder, height: z, Kondratiev form factor, K ............................... 323(T) Finite-difference two-stage Crank-Nicolson predictor-corrector method ........... 364 Finite-element method (FEM), (finiteelement analysis) ........................ 144 for brazing, residual stress prediction ... 394, 395, 396(F) to calculate residual stresses after shot peening ................................. 151 calculation of time variation of internal stresses ......................234, 235, 236 of casting defects ............................ 363 casting elastoviscoplastic stress model .. 365 for casting modeling ........... 364–369(F,T) centrifugal casting modeling ....... 379, 380, 383(F) determining stabilized residual stress after fatigue loading ...........................19 formulation for unsteady-state casting ... 376 heat-flow problem in casting .............. 364 measuring distortion of ring ..... 290, 292(F) modeling bending .............. 155, 156–157 modeling elasto-plastic rolling contact of rail steel ........................... 434–435(F) modeling phase transformations ... 296, 300, 301(F), 302, 303, 306(F), 307(F), 309 modeling relaxation behavior of multiaxial macro residual stresses ........ 62–63(F) for modeling roller straightening ...432–433 modeling straightening ........... 156–157(F) predicting distortion and residual stress after quenching .................... 284, 288(F) predicting relaxation of residual stresses ..11 quench-crack formation .................... 313


Index / 475 quenching of carbon steel disk and cylinder ........ 288–289(F), 290(F) quenching simulation for carburized bushing ......... 320321(F,T) rail steel deformation by residual stresses .............................. 424(F) residual stress distribution modeling ... 14(F) semicontinuous casting numerical calculation for temperature ........................ 377 for simulating particulate, compaction .. 413, 416, 417, 419 for simulating thermomechanical problems in casting .........................374–375 software programs .......................... 202 solidification modeling ..................... 372 for straightening, Swedish steel industry research project ........................ 156 stress/strain prediction in case-hardened parts ........................... 199, 201(F) for strip continuous casting by twin-roll method model ........ 383–385, 386(F), 387(F), 388(F), 389(F) thermoplasticity of carburized bushing .. 320 through-thickness temperature variation of plate ........................... 223–224(F) unsteady-state heat-conduction problem of carburized bushing .................... 320 warpage prediction of steel shafts with keyway ..................289–290, 291(F) Finite plate, dimensions of sizes: L1, L2, L3, Kondratiev form factor, K ............. 323(T) Fisheye fracture ......................... 442, 446 Fishtailing ............................... 89(F), 93 Fixture hardening ............................ 185 Fixtures and distortion ...................... 172, 173(F) for hardening of ring-shaped bodies .....186(F) Flame cutting .................................. 109 Flame hardening .............................. 220 Flame heating-surface quenching, deformation tendency ................ 170(F) Flat rolling ..................................... 143 Flocculation .................................72–73 prevention in steels ...........................73 Floccules ................................. 72–73(F) prevention of formation in steels ...........73 Flow rule for plastic strain rate .....299–300 Flow speed, of quenching media and carburizing ................................ 445 Flow stress ...................................... 299 Fluid-flow analysis, for solidification modeling, benefits listed ............ 363(F) Fluidity coefficient ............................ 366 Fluidized-bed quenching .......... 263, 267(F) Foaming, of quenchants ...................... 259 Fog quenching ................................. 282 equipment .................................... 174 Foreman equation, crack propagation taking mean stresses into account ................35 FORGE (software program) ............... 202 Forging ..... 99, 109, 141–142, 148–149(F,T), 399 advantages .................................... 142 mechanical, thermal, or structural origins of residual stress ........................13(T) in powder metallurgy processing ..... 397(F) process conditions ....................... 148(T)



476 / Index

Forging (continued) workpiece geometry .................... 148(T) Forging reduction ratio ...................... 254 Forgings cylindrical steel neutron diffraction methods ................................. 113 distortion ..................................... 168 steel rocket case, neutron diffraction methods ................................. 113 Forming ............................ 141–149(F,T) bending ............. 142(F), 143(F), 144–145 deep drawing ............ 141–142(F), 147(F), 148–149(T) and distortion potential ..................... 183 drawing ... 141(F), 142, 143(F), 145–146(F) electric discharge machining .............. 147 extrusion ...... 141, 142(F), 143, 146–147(F) forging ...............141–142, 148–149(F,T) press braking ....................... 147–148(F) pressing .................................141–142 rolling ............ 141, 142, 143, 146–148(F) Forward solution ................................91 Fourier coefficients ........................... 334 Fourier law ............................... 199, 375 Fourier number ............................... 321 generalized ................................... 322 Fourier’s heat conduction law ............. 298 Fredholm integral equation, method of the first type ......................... 126–128(F) Fredholm integral equation (computation experiment) residual stress determination .................. 126, 127(F) Free quenching ................................ 257 French specimens ...... 338(F), 339(F), 340(F) French Technical Center for Mechanical Industry (CETIM) .............. 15, 16, 17 Fretting corrosion ...................... 215, 216 Fretting fatigue, shot peening to promote resistance .................................. 354 Friction ............................................16 Fringe effect .................................... 134 Function smoothness measure ............. 127 Furnace hardening, carbon content limits ................................... 256(T) Furnaces atmosphere-hardening ...................... 257 austenitizing ............................155–156 batch-type .................................... 402 belt ............................................ 257 combustion-heated, and distortion ........ 172 continuous, and distortion ................. 172 continuous gas-carburizing ................ 440 continuous mesh-belt sintering ........ 402(F) design and operation to control heat treating problems ................................ 257 direct-fired gas ............................... 255 distortion of bearing rings ...........155–156 hardening ..................................... 257 heat irradiating areas in ratio to the size of the batch ................................ 184 for hot isostatic compaction ........... 409(F) insulation ..................................... 184 muffle-type continuous production ... 402(F) passing-type, and distortion ............... 172 pit-type and distortion potential ........... 184 pusher ......................................... 402 roller hearth .................................. 402 shaker hearth ................................. 257

sintering .................. 402–403(F), 404(T) vacuum ....................................... 402 vacuum, and distortion potential .......... 184 walking-beam ................................ 402 zones ...................................... 404(T)

G Galerkin method .............................. 364 Galerkin type formulation .................. 376 Galvanic corrosion, stainless steel P/M parts ..................................403–404 Galvanopairs, in stress-corrosion cracking ......................................79 Gamma ferrite (austenitic), first-order residual stress parameters ........... 335(T) Gas atomization ............... 400(F), 412, 414 Gas blending ................................... 261 Gas carburizing ........ 189, 190, 194, 197(F), 443(F), 450(F), 451(F), 453(F) carbon potential control .................... 444 diffusion ............................ 199, 202(F) and retained austenite content ............. 447 Gas dissolution in metal melt .............. 400 Gaseous nitrocarburizing ............... 215(F) Gas jet and fog jet cooling equipment ...................... 172, 174(F) Gas lances ...................................... 184 Gas-pipe lines steels, stress-corrosion cracking ............................. 81–82(F) Gas quenching ...... 256(T), 257, 261, 265(F), 266(F), 271 distortion minimizing ....................... 185 equipment .......................... 172–174(F) high-pressure ....................... 172–174(F) Gas turbine components, shot peening and distortion .................................. 156 Gauss (G) distribution ....................... 334 Gaussian method .............................. 122 Gauss’s theorem ........................ 375, 376 Gear box, shot peening effect on fatigue life ........................................20(T) Gears automotive ............................... 453(F) automotive, pressure-control quenching .................... 455–456(F) carburized, and shot peening effect on fatigue ......................... 353, 356(F) carburized, axial stress distribution during quenching .................... 440–441(F) carburized, shotblasting and peening ....................... 451–452(F) carburized variation of residual stresses ........................ 439, 440(F) case hardening, transformations and stress evolution model ... 202–203(F), 204(F) differential ring .......................... 453(F) distortion ..... 253, 255, 256(F), 307(F), 309 distortion after carburizing and quenching .................... 176(T), 179 dual-frequency induction hardening, computer simulation ....... 296, 306(F), 307–309(F) gas-carburized and direct-quenched, residual stress .................................... 440

grain-boundary oxidation effect on fatigue strength .................450–451, 452(F) hypoid ring ............................... 453(F) hypoid ring, direct hot quench (DHR) ......................... 454, 455(F) induction-hardened and carburized residual stresses ........................ 440, 441(T) loading methods ................179(F), 180(F) manufacture of .................. 437–457(F,T) quenched in quench press machine .................... 181–182(F,T) quenching .................................... 257 ratchet ..................................... 454(F) residual stresses in ............. 439–441(F,T) ring .................................. 255, 256(F) setting methods effect on distortion .. 454(F) shot peening and C.A.S.E. process ...... 350, 351, 352(T), 354(F) shot peening application ......... 353, 355(F) steel grade and hardenability influence ..........441–442(F,T), 443(F) stress profile .............................. 354(F) transmission spur ........................ 453(F) Gears, modulus, mⴔ5 to 8 mm, advantages ................................ 327(T) former steel and process ............... 327(T) new steel and process .................. 327(T) Gear wheels bending fatigue strength when induction hardened ............................ 244(F) dual-frequency induction hardening, computer simulation ....... 296, 306(F), 307–309(F) fatigue strength after induction hardening ..................... 243–244(F) induction hardening ........ 226, 227–231(F), 236–239(F), 241–242(F) shot peening ...........................347–348 shot peening effect on fatigue life ......20(T) temperature variations during cooling after induction hardening ......... 230–231(F) Generatrix ...................................... 318 Gerber parabola ............................ 30(F) Germanium, alloying element effect on crack growth .......................................80 German steels. See Steels, series and classes: 1023, 1045, C80, and CK01. Gibbs free energy .......................297–298 Glassy alloys ................................... 400 Glide ...............................................58 Gliding, irreversible .............................29 Global momentum balance in combined domain .................................... 375 Glow discharge spectroscopy ............... 216 Goodman approximation .. 30(F), 43, 44, 45, 48, 49, 50, 51 Goodman endurance diagrams .... 14–15, 17 Goodman relationship .................... 16, 17 Grade, influence on steel gear stresses ...............441–442(F,T), 443(F) Gradient of liquidus line, of aluminum alloy .................................... 378(T) Gradient of solidus line, of aluminum alloy .................................... 378(T) Grain boundaries, and crack initiation ................................33–34 Grain-boundary glide ..........................58


Grain-boundary oxidation in carburized-and-hardened steels ....... 438, 448–449(F), 450(F) of carburized steels ......................... 446 effect on fatigue strength of gear teeth 450–451, 452(F) Grain-boundary sliding .......................54 Grain growth, and sintering ................. 402 Grain refinement .............................. 189 Grain size, and stress-corrosion cracking resistance ....................................81 Grain slips ........................................15 GRANTAS (Komatsu Company) computer program ................................... 303 Gravity line method .......................... 122 Gray iron residual stresses in castings with solidification time ................. 362(F) three-bar frame casting model ............. 362 Green density .................................. 401 Greenwood-Johnson transformation ..... 320 Grids, as distortion sources ............184–185 Grinding 55, 57(F), 101, 109, 150(F), 151(F) carburized steels ................... 198, 199(F) costs dependent on overmeasures knowledge .............................. 183 and distortion .......................... 152, 156 drifting ................... ................... 198 effect on local fatigue strength and crack arrest, with shot peening ........... 48(F) factors causing residual stresses .......... 150 and induction hardening ...220, 244–246(F) mechanical, thermal, or structural origins of residual stress ........................13(T) with milling and shot peening, S-N curves and residual stress effect ...... 37–38(F) power ..................................... 150(F) and quenching in a hardening press ...... 185 residual stresses in austenitic stainless steels ..................... 109(F) S-N curves and residual stress effect in highstrength steel .................... 38–39(F) S-N curves and residual stresses effect ................37(F), 38(F) wheels ......................................... 150 Grossman factor .......................... 176(T) Grossman n number (H value) .. 257, 259(T), 262, 265 definition ..................................... 265 Grossman Quench Severity factor ........ 174 Gunnert method ........................ 102, 103 for destructive residual-stress measurement ....................... 102(T) Gun splat atomization ................... 400(F) Gyaku-sori (reverse bending), of Japanese sword ............................. 309–310(F)

H Habit plane ........................................ 5 of invariant-plane strain ....................... 5 Habit plane indices ....................... 5(T), 6 Haigh diagram, (fatigue strength) .........14, 17(F), 30(F), 43–45(F), 47–48, 52 Half-width values ........................... 61(F)

Hammer peening ................................12 mechanical, thermal, or structural origins of residual stress ........................13(T) Hamon (border of martensite structure), of Japanese sword ................. 308(F), 309 Hardenability effect on fatigue limit and residual stresses ........................ 442, 443(F) grade variation effect on carburized gears ........................ 441–442(F,T) influence on gear stresses .....441–442(F,T), 443(F) Hardenable steel, tempering ...... 284, 287(F) Hardened steels, micro residual stresses ....63 Hardened surface layer depth ............. 327 Hardening of carburized components ........ 189, 190(F) and distortion ............ 153, 154(F), 155(F) mathematical model ........................ 315 quench-crack formation prediction .................. 315–317(F,T) of ring-form workpieces ............... 186(F) thermal stress state calculation ............ 315 Hardening coefficient (H⬘) ........ 300(F), 301 of aluminum alloy ...................... 378(T) Hardening function ........................... 300 Hardening modulus, of bearing ring being hardened ............................... 318(F) Hardening parameter ........................ 299 Hardening regimes ........................... 327 Hardening residual stress state ............ 191 Hardening rule ................................ 299 Hard layer, optimal depth, and maximum compressive surface stresses ....... 315(F) Hardness and bending fatigue strength in low-strength steel ................................... 40(F) of carburized-and-hardened steels .... 437(F) carburized and induction-hardened steel cylinder ....................... 203, 205(F) Hard shot peening austenite transformation in carburized steels .......................... 448(F), 449 of carburized steels ............... 451–152(F) Harmonic analysis method ....... 334–335(F) Hatched temperature range, after induction hardening ........................ 240–241(F) Head-hardening, of rail steel ............ 428(F) HEARTS (HEAt tReaTment Simulation computer program) ... 202, 288–289(F), 290–294(F), 296, 301–304(F), 306(F), 308 Heat-affected zone (HAZ) and crack propagation rates .............. 35(F) of induction-hardened and carburized steel cylinder ............. 204, 205(F), 206(F) induction hardening and residual stresses distribution ............................. 245 and shrinkage due to temperature distribution ............. 391(F), 392, 394 Heat capacity ........................... 3–4, 288 Heat conduction ............................... 288 Heat-conduction analysis ..............303–304 Heat-conduction equation ............ 284–285, 297–298 finite element formula of ................... 376 Heat conductivity


Index / 477 of aluminum alloy ...................... 378(T) differential equation of ..................... 312 Heat-flow analysis, for solidification modeling, benefits listed ............ 363(F) Heat flux ............267, 288, 376, 377, 378(F) in rail steel ......................... 425–426(F) Heating factor ................................. 322 Heat-resistant and superhigh-speed steels containing 5–12% Co and 2–6.5% V composition .............................. 406(T) designation ............................... 406(T) hardness .................................. 406(T) Weq ....................................... 406(T) Heat transfer, boundary conditions on outer surface ..................................... 285 Heat-transfer coefficient .. 264, 323, 375, 377, 378(F) aluminum alloy pipe centrifugal casting 380–382 in casting ........................... 365, 366(F) definition ..................................... 265 determination of ...............................23 estimation techniques ..........267–268, 269, 271(F), 274(F) nickel-chromium alloy pipe centrifugal casting ........ 380, 382, 383(F), 384(F) of quenching media, and carburizing .... 445 quenching of carbon steel disk and cylinder computer simulation .............. 289(F) and quenching process modeling ......... 319 Heat-transfer-coefficient curve ...............23 Heat-transfer intensification ................ 312 Heat transfer rates ................. 257, 259(T) Heat treatment ................................ 109 as cause of residual stress ....................12 distortion caused by procedure ..... 165–166, 168(F), 169–172(F,T), 173(F) distortion of component shapes ................ 159–161(F,T), 162(F,T), 163(F), 164(F) and distortion potential ..................... 183 effect on residual stress distribution .. 194–196, 197(F), 198(F), 199(F) effect on residual stress of plasma-sprayed coatings ............................... 16(F) to eliminate residual stresses .............. 144 media influences on distortion ........ 171(T) modeling of transformation and stress evolution processes ................... 202 in powder metallurgy processing ..... 397(F) of powder metallurgy steel parts ........................... 417–418(F) of sintered P/M steel components ............... 406–408(F,T) variant A ...... 331, 332(F), 337(F,T), 342(T) variant B ...331, 332(F), 337(F,T), 338(F,T), 339, 342(F,T), 343(F), 351(T) variant C ........331, 332(F), 337(T), 342(F), 343(F) variant D ..... 331, 332(F), 337(F), 338(F,T), 339–340, 341(F,T), 342(F,T), 343(F) variant E ..... 331, 332(F), 341(T), 342(F,T), 343 variant F .........331, 332(F), 342(F), 343(F) variant G ...331, 332(F), 338(F,T), 339–340, 341,(F,T) 342(F,T), 343(F) variant H .. 331, 332(F), 339, 340(F) 341(T), 342(T)



478 / Index

Heat treatment (continued) variant ␽ ........ 331, 332(F), 341(T), 342(T) variant K ............ 331, 332(F), 339, 341(T) variant L ............................ 331, 332(F) variant M ........... 331, 332(F), 339, 341(T) variant I ................................... 339(F) variant II .........................339(F), 340(F) variant III ........................339(F), 340(F) variant IV ........................339(F), 340(F) variant V .........................339(F), 340(F) HEAt tReaTment Simulation program (HEARTS) ............... 202, 288–289(F), 290–294(F), 296, 301–304(F), 306(F), 308 Helical springs, shot peening effect on fatigue life ........................................20(T) Helium, as quenchant ............... 261, 265(F) Hertzian pressure, and microcrack initiation in steels ......................................29 Hertzian pressure formation ..... 151, 153(F) Hertz’s compression ...................... 346(F) Heteromodulus materials ................... 129 Hexagonal close-packed (hcp) materials, residual stresses .......................... 333 High-alloy austenitic steels, stress-corrosion cracking ......................................80 High-alloy steels cryogenic cooling ........................... 331 delayed failure ............................78–79 quenching temperature effect on mold hole distortion ........................... 171(T) High-alloy tool steels. See also High-speed steels. cryogenic cooling .... 339, 340(F), 341(F,T), 342(F,T), 343(F) dimensional stability .................... 343(F) dislocation density ...................... 343(F) retained austenite .................. 343(F), 344 High-carbon alloy steels, hardening steelquenching method, arbitrarily hard matrix ................................ 327 High-carbon low-alloy steels, quenching temperature effect on mold hole distortion ........................ 171(T) High-carbon steel dimensional variation with time ......... 257, 259(T) quenching temperature effect on mold hole distortion ........................... 171(T) High cycle fatigue ...............................16 carburized steels ............................. 196 of high-strength steels ........................46 High-energy-rate compaction .............. 402 High-frequency quenching .................. 169 High-pressure consolidation, at ambient temperature ................................ 402 High-pressure gas quenching .... 172–174(F) High-speed gear wheel, distortion of ..... 166, 169(F) High-speed steels. See also High-alloy tool steels. cryogenic cooling ................. 331, 332(F) cryogenic cooling effect on microstresses ....................... 336(F) cryogenic cooling twice repeated ........ 339, 340(F) cryogenic heat treatment and dimensional stability ........................... 338(F,T)

distortion after straightening ........... 156(F) durability ........................... 343–344(F) flocculation not observed ....................73 heat treatment variants ........... 331, 332(F) inclusion control in P/M processing ..... 405 microstress evaluation and calculation .. 334, 335(F) retained austenite decomposition at 823 to 973 K ...................... 337–339(F,T) High-strength materials, thermal fundamentals of making ..........327–328 High-strength spring steel, crack initiation ..............................34 High-strength steels delayed fracture ................. 74(F), 76–77 effective stress intensity factor range .. 48(F) Haigh diagram model of residual stress sensitivity influence ................. 44(F) local fatigue strength ................ 46–47(F) macro residual stress effect ..................27 macro residual stress effect on fatigue strength .......................... 50–51(F) S-N curves and residual stress effect ................38–39(F), 42–43(F) stress-corrosion cracking ............ 79–82(F) High-strength structural steel, crack propagation .............................. 35(F) High-temperature sintering ................ 399 High-temperature thermo-mechanical processing ..................................81 High-velocity oxygen fuel (HVOF), mechanical, thermal, or structural origins of residual stress .......................13(T) Hob, distortion of ........................170–171 Hoganas reduction process ................. 399 Hole-drilling strain gage, to measure residual stresses in coatings ....................... 118 Hole-drilling strain-gage technique, to calculate elastic-viscoplastic stresses ..................... 377, 378, 381(F) Hole-drilling technique .... 99, 100, 110–111, 144 applied to rail steel .......................... 430 for evaluating brazed joint of steel and cemented carbide ...................... 395 for measuring residual stresses ..122–124(T) Holographic interferometry ... 130, 131, 133, 136 Holographic speckle-interferometry ...... 132 Homologous annealing temperature .... 55(F) Hooke’s law ........... 202, 298, 333, 334, 373 Hooke’s law of elasticity .................... 113 Hoop stress ..............91, 92(F), 96(F), 97(F) residual stress distribution in radial direction at t⳱8.32 s using a plane-strain assumption ......................... 368(F) residual stress variation in the axial direction at t⳱8.3202 s with a traction-free top surface .............................. 368(F) thermal stress history with a plane-strain assumption ......................... 368(F) thermal stress history with a traction-free top surface .............................. 369(F) Hot consolidation ............................. 414 Hot die pressing, in powder metallurgy processing ............................. 397(F) Hot extrusion ............................ 404, 410 Hot isostatic compaction .......... 408–409(F)

Hot isostatic pressing (HIP) ... 399, 402, 404, 408–409(F), 417 in powder metallurgy processing ..... 397(F) Hot oil jig quench ............................. 453 Hot oil quenching .................257, 449, 453 Hot pressing ........................399, 417, 420 P/M parts ........................... 408–409(F) Hot pressureless sintering, in powder metallurgy processing ............... 397(F) Hot-rolled steels, and distortion ............. 168 Hot rolling ........................................90 and distortion ............ 153, 155(F), 156(T) in powder metallurgy processing ..... 397(F) Hot spraying, in powder metallurgy processing ............................. 397(F) Hull plate steel, residual stress investigations ............................. 136 Hydro Aluminum ...............................11 Hydrogen alloying element effect on crack growth ..80 atomic ...................................... 78, 81 desorbent amount over the period of holding ................................77 diffusive-mobile .......................... 78, 79 diffusive-mobile source in quenched steel structure ..................................77 influence on crack propagation .............71 ionized ..........................................78 lattice solubility ...............................77 as quenchant ....................... 261, 265(F) solubility in steel ..............................71 states in steel ..............................71–72 Hydrogenation ............................... 74(F) Hydrogen corrosion ............................72 Hydrogen diffusion, in iron, pure annealing ................................ 71(F) Hydrogen embrittlement ......... 70, 100, 256 alloying effect on steels .................82–84 alloying elements influence ..............76(T) aspects of theory ..............................72 carbide-forming elements effects ......82–83 carbide-non-forming elements ..............83 external .........................................75 ferrite-pearlite steels ..........................72 and hydrogen-induced corrosion cracking ...................................79 impurities effects ..............................83 impurity elements effects on steels ....82–84 internal ..........................................75 martensitic steels ..............................72 mild steels ......................................83 types of .........................................72 Hydrogen furnace atmosphere, composition ........................... 404(T) Hydrogen-induced corrosion cracking (HISCC) ....................................79 main gas-pipe line steels .....................82 Hydrogen-induced stress cracking ........ 110 Hydrogen solubility in iron ....................................... 70(F) in steel ..........................................70 Hydrogen stress cracking .....................83 Hydrogen sulfide, effect on stress-corrosion cracking of steels ...........................81 Hydrogen-sulfide cracking ....................83 Hydrogen traps ..................................71 Hydrostatic pressure


effect on transformation kinetics ... 249, 250, 251(F) maximum .......................................17 mean ............................................17 Hydrostatic stresses ... 6, 379, 380(F), 381(F) Hydro-sulfide ....................................70 Hypereutectoid tool steels, distortion of .........................171–172 Hypoeutectoid 0.43% carbon steel, induction hardening-temperature cycle variations .............................. 223(F) Hypoeutectoid steel distortion of ............................ 168, 171 hot rolling and air cooling .......... 89, 91(F) Hysteresis loops .................................32

I I-DEAS computer program ................ 304 Immersion cooling ........ 258, 260(F), 261(F) Immersion quenching, after induction hardening .................................. 232 Immersion time quench ..................... 456 Impact bending fatigue test, fatigue limit and life of carburized notched bar .......... 450 Impact strength, of carburized-and-hardened gears .............................. 441, 442(F) Impregnation resins .......................... 406 Inclusions, crack initiation in steels ..........29 Incremental hole-drilling method ..... 11, 12, 13(F), 18 Incremental isotropy ......................... 374 Incubation period of crack growth in steels ........... 74, 75, 77 of hydrogen embrittlement .............. 74, 75 Indicator crack method .....128–132(F), 134 Induction, mechanical, thermal, or structural origins of residual stress ..............13(T) Induction-hardened steels, contact fatigue ............................ 198 Induction hardening .............. 220–247(F), 407–408 advantages over other procedures ....... 220, 221–222 applications .................................. 220 to attain compressive residual stress ..... 437 austenization and residual stresses .... 245(F) carbon content limits ................... 256(T) of carburized steel cylinder model ......... 203–204, 205(F), 206(F) case depths ................................... 220 case hardnesses .............................. 220 characteristics ...................... 221–222(F) compressive stresses .............. 232–233(F) contour hardening ........................... 241 current frequencies .......................... 223 dual-frequency ........... 226, 227(F), 228(F) dual-frequency distortion ........ 238–239(F) dual-frequency gear tooth hardness profiles .............................. 229(F) dual-frequency gear wheel computer simulation .... 296, 306(F), 307–309(F) dual-frequency martensite volume fractions simulated ..................228(F), 229(F)

dual-frequency of gear wheels ........... 226, 227(F), 228(F) dual-frequency, tangential residual stresses .............................. 238(F) dual-frequency temperature distributions ........ 227, 228(F), 229(F) electromagnetic analysis ......... 226, 227(F) electrothermomechanical model .......... 226 and finish grinding ................ 224–246(F) flame hardening ............................. 220 gear wheel, computer simulation ........ 296, 306(F), 307–309(F) generator frequency ............... 222(F), 223 grinding ....................................... 220 hardness of surface, roller specimen ....239(F) homogeneous austenitization temperature ............................. 227 induction heat treatment .................... 221 Langeot’s method of mathematical modeling with quenching .................... 225(F) machine parts ................................ 220 magnetic field relation to thermomechanical state of workpiece material ...... 226(F) martensite distribution and hardness 240(F) martensite volume-fraction distribution ......................... 231(F) mass of specimen effect on heating time ............................ 224–225(F) materials used ................................ 220 metallothermomechanical analysis ...... 226, 227(F) metallothermomechanical model ......... 226 numerical calculation flow chart ......... 226, 227(F) parameters of system ....................... 222 power/frequency regions of heat treatment applications ........................ 221(F) and quenching ......................... 227, 228 quenching systems ................ 231–232(F) quenching temperature distributions .................. 230–231(F) of ring computer simulation .... 296, 303(F), 304(F), 305–307(F) scan hardening ........................... 241(F) scanning ...................................... 220 shape distortion .................... 238–239(F) shot hardening ............................... 241 single-frequency, distortion ...... 238–239(F) single-frequency, gear tooth hardness profiles .............................. 229(F) single-frequency, gear wheels .. 226, 227(F), 228(F), 229(F) single-frequency, martensite volume fractions simulated .......228(F), 229(F) single-frequency, tangential residual stresses .............................. 238(F) single-frequency, temperature distributions ........ 227, 228(F), 229(F) single-shot .... 220, 222, 223, 225(F), 233(F) single-shot, time-temperature variations at various high-frequency generation .................... 240–241(F) techniques for machine parts .............. 220 temperature cycle variations of surface and core considering enthalpy of phase transformations .............. 223, 224(F)


Index / 479 temperature distributions during cooling process ........................ 230–231(F) time/temperature dependence ... 222–231(F) time/temperature variations in scan hardening at various speeds and HF generation power .................. 241(F) time variation of residual stresses in a material .................... 232–242(F,T) time variation of stresses in a material .................. 232–242(F,T) tooth-by-tooth ...................... 253, 256(F) tooth gap hardening ......................... 241 volume changes after ....................... 222 volume changes and distortion, gear teeth ........................... 242(F) water jet quenching ............... 241, 242(F) Induction heating—surface quenching, deformation tendency ................ 170(T) Industrial heat treatment temperature, cryogenic cooling influence on steels ................................... 336 Inelastic strain rate ...............202, 302, 373 Infiltration ...................................... 405 in powder metallurgy processing ..... 397(F) Infinite cylinder ........................... 323(T) Infinite plate, thickness of 2R, Kondratiev form factor, K ......................... 323(T) Inhomogeneous diffusion equation ........ 217 Inhomogeneous microstresses, in coatings ................................. 118 Inhomogeneous residual stress fields, determination methods ........ 125–137(F) Initial incompatible strain .................. 125 Initial method .................................. 377 Initial strain .................................... 125 Initial yield stress, of aluminum alloy .................................... 378(T) Injection molding .......................400–401 Inspection plan, for quality assurance ......13, 14(F) Institute for Strength Problems/Engineering Thermophysics Institute, National Academy of Sciences of Ukraine, software flow chart ................... 313(F) Insulation, nonuniformity as cause of distortion .................................. 184 Integral equation kernel ..................... 126 Intensive cooling .... 312, 316, 317, 319(F), 320 advantages .................................... 317 effect on distortion of quenched parts ...............................323–324 Intensive jet cooling .................... 327, 328 Intensive quenching .......................... 282 Interaction energies ........................ 8, 71 Interatomic bonds, stress-corrosion cracking role ...........................................80 Interfacial wetting, kinematics .............. 258 Interference fringe .. 120, 135–136(F), 137(F) patterns ............................. 119–120(F) Interferencial-optical methods ............. 132 Interferometer ................................. 135 high sensitivity moire´ ........................12 Interferometry .....................110, 119, 120 Intergranular effects ......................... 260 Intergranular fatigue crack initiation .... 197 Intergranular fracture ....................... 196



480 / Index

Intermediate file format ..................... 304 Intermetallic materials ................. 25, 400 Internal cracking ................... 193, 196(F) Internal deflection method of shot peening ................................ 348(F) Internet Web site ............................. 100 Interplanar spacing ................ 333, 334(F) nonhomogeneity degree .................... 334 Interrupted quenching .................280–281 definition ..................................... 280 Intracoating spallation ....................... 118 Invariant-plane strain (IPS) ......... 4, 5(T), 6 and bainite growth ..........................7–8 Inverse heat conduction problem solution .................................... 268 Inverse residual stress problem ......125–126 Inverse solution .................................91 Inverters ........................................ 221 Inv-Probe-2D computer program ........ 268, 289(F) Ion implantation, deformation tendency ............................... 170(T) Ion implantation enhanced vapor phase deposition, deformation tendency ............................... 170(T) Iron. See also Pure Iron. alloying addition effect on sintering ..... 402 composition requirements for powder forged parts ................................. 411(T) nitrogen concentration ............ 216(F), 217 Iron-aluminum-carbon alloy, nitriding residual stresses .......................... 217 Iron-carbon-chromium-manganese steels, delayed fracture ........................ 77(F) Iron-carbon-chromium-manganese-silicon steels delayed fracture ........................... 77(F) stress-corrosion cracking ................. 81(F) Iron-carbon-chromium-nickel-manganese steel, stress-corrosion cracking ....... 81(F) Iron-carbon-chromium-nickel-molybdenum steel manganese sulfides causing corrosion ........81 stress-corrosion cracking .....................81 Iron-carbon-chromium-silicon steel, delayed fracture ................................... 76(F) Iron-carbon-manganese-nickel-molybdenum steel, stress-corrosion cracking ...........81 Iron-carbon-manganese-silicon-nickel steel, stress-corrosion cracking ..................81 Iron-carbon-manganese-silicon-nickelvanadium steel, stress-corrosion cracking .................................. 82(F) Iron-carbon-manganese-silicon steel, stresscorrosion cracking ..................... 82(F) Iron-carbon-manganese-silicon-vanadiumniobium steel, stress-corrosion cracking ............................. 81–82(F) Iron-carbon-manganese-silicon-vanadium steel, stress-corrosion cracking .. 81–82(F) Iron-carbon-nickel-chromium-manganesesilicon steel delayed fracture ..........................76–77 stress-corrosion cracking ............ 80–81(F) stress-corrosion cracking in sodium chloride solution ...................................80

Iron-carbon-nickel-chromium-molybdenumsilicon steel, stress-corrosion cracking ......................................81 Iron-carbon-nickel-chromium-molybdenum steel, stress-corrosion cracking ...........81 Iron-carbon-nickel-chromium-molybdenumvanadium steel, stress-corrosion cracking ......................................81 Iron-chromium alloys, nitrogen concentration .................... 216(F), 217 Iron-chromium-aluminum yttrium coating ..................................... 118 Iron-chromium-nickel-molybdenumaluminum-titanium steel, delayed failure ...................................78–79 Iron-copper steels, composition ........ 407(T) Iron-copper system, liquid-phase sintering ................................... 416 Iron micropowders ........................... 400 Iron-nickel-cobalt-molybdenum-titanium steel, delayed fracture ................. 77(F) Iron-nickel-molybdenum-tungsten-titanium steel, delayed fracture ................77–78 Iron-nickel powder, P/M processing ...... 402 Iron-nickel steels, composition ......... 407(T) Iron-nickel-tungsten-molybdenum-titanium steel, delayed fracture ............ 77–78(F) Iron nitrides .............................. 209, 216 Iron powder, production of .................. 399 Isochronal lines ................................ 192 Isochronous curves, mechanical properties dependencies on temperature .......... 313, 314(F) Isolines for temperature, for bearing ring (317(F) Isoparametric elements ...................... 364 ISO test methods ISO 9950, cooling-curve analysis ....................... 266–270(F) Isothermal cooling in the air ............... 328 Isothermal nitriding .......................... 170 Isothermal quenching and distortion ............................ 177(F) tanks ........................................... 172 Isothermal transformation ........ 331, 332(F) Isothermal transformation (IT) diagrams. See also Time-temperature transformation diagrams. ........ 248(F), 249, 250, 251(F) Isotherm fields ............................. 317(F) of bearing ring ........................... 317(F) Isotherms, temperature distributions during induction heating of gear teeth .....230(F), 231(F) Isotropic function theory .................... 298 Isotropic-hardening hypothesis .. 299(F), 301 Isotropic strain ................................ 298 Iteration method .............................. 268

J J2-flow theory of von Mises ................. 431 Jakibatsuchi (Japanese clay mixture) ............... 307(F), 308(F), 309

Japanese Industrial Standard (JIS) steels. See Steels, series and classes, JIS numbers. Japanese Industrial Standard (JIS) test methods, JIS K 2242 cooling-curve analysis ......266–267, 271(F) Japanese swords ........................281–282 distortion .....................308(F), 309–310 quenched, computer simulation of metallothermo-mechanics ...... 96, 304, 307(F), 308(F), 309–310(F) Japan Heat Treatment Society, Quench Cracking Working Group .. 227, 285(F) Jet cooling ...................................... 314 Jet-hardening and fog-quenching equipment ...................... 172, 174(F) Jet shot peening, optimal peening angle ................................... 348(F) J-intergal, resistance to crack growth ........80 Johanssen method ........................ 106(F) for destructive residual-stress measurement ....................... 102(T) modification of ........................108–109 Johnson-Mehl relation, modified .... 288, 297 Joining ............................. 391–396(F,T) P/M components ......................405–406 Jominy hardenability, influence on gear stresses ............... 441–442(FT), 443(F) Joule heating effect ........................... 225

K Kakuno criterion ................................17 Kernel ........................................... 147 Kernels of integral operators ......... 126, 127 Keyslot, effect on hollow cylinder distortion after quenching ................. 165, 166(F) Kinematic hardening equations ........... 432 hypothesis .......................... 299–300(F) Kinetic diagrams of cracking ............ 74(F) Kinetics of transformations .................... 3 Kirkendall effects ............................. 416 Koistinen-Marburger law, ............201–202 Kolosov-Muskhelishvili’s relations (potentials) ............................... 132 Kondratie´v form coefficient ................ 315 Kondratie´v form factor ............ 322, 323(T) analytical calculation of, functions for ................................... 323(T) Kondratie´v number .....322, 323, 324(T) 328

L Laboratory of Mechanical Systems Engineering (LASMIS) ..................22 design tool on fatigue ................... 20, 21 k stress singularity ........................... 131 Lance method of shot peening ......... 348(F) Lanthanum, alloying element effect on crack growth .......................................80 Lapping ......................................... 278 Large-modulus gears, m ⴔ 10 to 14 mm advantages ................................ 327(T)


former steel and process ............... 327(T) new steel and process .................. 327(T) Laser cladding three-dimensional printing ................................... 413 Laser cutting ................................... 109 Laser hardening ............................... 220 applications .................................. 220 Laser heat treatment, deformation tendency ............................... 170(T) Laser shock treatment .........................25 mechanical, thermal, or structural origins of residual stress ........................13(T) Laser shot peening ...........354–355, 357(F) Laser sintering ................................ 413 Laser spraying, mechanical, thermal, or structural origins of residual stress ..13(T) Latent heat due to solidification, of aluminum alloy ....................... 378(T) Latent heat of transformation ................ 3 Lathe turning ............................ 101, 109 Lathe martensite .............................. 254 Lattice parameter, of first-order residual stresses of metallic materials ....... 335(T) Lead alloying element effect on crack growth ..80 as quenchant ................................. 261 error ....................................... 454(F) Lean exothermic furnace atmosphere, composition ........................... 404(T) Least-square method ................... 107, 108 Ledeburite ...................................... 168 in induction-hardened and ground microstructure ......................... 245 Lehrer phase diagram ....................... 209 Leidenfrost point, of quenching media and carburizing ........................... 445 Leidenfrost Temperature, definition ..................................... 258 Length of curved beam symbol and units of .......................93(T) Lever rule ................................ 376, 377 Life cycle simulation with residual stress consideration ..........................11–12 Lift height ........................................91 Linear absorption coefficient ............... 121 Linear elastic fracture mechanics ...... 29, 30 Linear mixture rule .......................... 200 Linear shrinkage (LS) (isotropic) for molded dimension to sintered part dimension ................................. 419 Liquid carburizing ................. 190, 443(F) Liquid flow velocity ......... 271–273, 274(F), 275(F), 276(F), 277(F) Liquid-phase sintering ................. 416, 417 Liquid tracer system, to inspect shot peening coverage control .......................... 348 Liquidus temperature, of aluminum alloy .................................... 378(T) List image file format ........................ 304 Loading, and distortion ............ 255, 256(F), Loading mean stresses, and residual stresses compared ...............................27–28 Loading methods, and distortion .......178(F), 179–182(F,T) Loading pattern, and distortion .. 171(F), 172, 173(F)

Loading stresses, and residual stress relaxation ....................................59 Local fatigue strength and crack initiation ...........................34 high-strength steels .................. 46–47(F) medium-strength steels ................... 47(F) Locally effective fatigue strength, calculation of .............................................45 Local quenching, deformation tendency ............................... 170(T) Logarithmic creep law ....................63–64 Longitudinal compressive stresses, effect on bending fatigue life in carburized steels ............................. 449, 450(F) Longitudinal electricity modulus material ................................... 334 Longitudinal residual stresses .......... 93–94, 95(F), 146 of carburized-and-hardened steels .... 437(F) of Japanese sword ................. 309–310(F) of rail steel .....427(F), 428(F), 429–430(F), 431(F), 434(F) Longitudinal stress in plate, formula for calculating residual stress .... 95(F), 96(T) Longitudinal stress in solid bar where r is radius of bar, formula for calculating residual stress .................. 95(F), 96(T) Longitudinal stress in thin-walled tubing ............................... 94, 95(F) formula for calculating residual stress ......................... 95(F), 96(T) Lorentz (L) distribution ..................... 334 modified method ............................ 122 Low-alloyed pipe steels, hydrogen embrittlement resistance ..................76 Low-alloy high-strength steels, stresscorrosion cracking ....................... 110 Low-alloy plasma-nitrided steels, residual stress modeling ........................... 216 Low-alloy steels austempering ................................. 281 austenitizing .............................. 337(T) carbonitriding ............................ 191(F) composition .............................. 407(T) crack growth shown by acoustic emission ..................................75 cryogenic cooling ................. 331, 337(T) cyclic deformation behavior .................28 metal-injection molding .................... 412 modulus of elasticity .....................96(T) nitriding ....................................... 209 Poisson’s ratio .............................96(T) quenching ................................ 337(T) shear modulus .............................96(T) stress-corrosion cracking ............ 79–82(F) stress relief and yield strength .. 251, 254(F) tempering ................................. 337(T) tempering effect on ultrasonic velocity .. 114 Vickers hardness ........................ 337(T) Low-alloy structural steel, nitriding ... 210(F) Low-angle diffraction methods ............ 439 Low-carbon ferritic steels, Barkhausen noise analysis for stress measurement ........ 114 Low-carbon steel delayed fracture ...............................74 nitriding ................................... 209(F)


Index / 481 quenching temperature effect on mold hole distortion ........................... 171(T) Low-cycle fatigue(LCF) carburized steels ............................. 196 cyclic deformation behavior of shot peening and deep rolling on plain carbon steel .............................. 31(F), 32 effect on bending fatigue strength of medium strength steel ..................41 of high-strength steels ........................46 Lower bainite ........................ 250(T), 257 Low-strength steel macro residual stress effect ..................27 macro residual stress effect on fatigue strength .......................... 50–51(F) S-N curves and residual stress effect ................36–37(F), 39–40(F) LS-DYNA 3D (software program) ........ 363 Lubrication, effect modeled for casting ... 364 Lu¨ders bands ....................................28 Lumped-heat-capacity method (computer program) ........... 267, 268, 269, 271(F), 274(F), 279(F) LUMP-PROB (computer program) ..... 268, 289(F)

M Machine driving system, and distortion ... 172 Machine parts, induction-hardened stress profiles in the loaded state .... 242–243(F) Machining ................................... 19, 99 and distortion ...................... 254, 256(F) distortion caused by process ........ 165–166, 168(F), 169(F) and distortion potential ..................... 183 effect on distortion of gears ..... 453, 454(F) P/M parts ............................... 405, 406 in powder metallurgy processing ..... 397(F) Mackenzie and Bowles notation, for deformation matrix describing shape deformation .................................. 8 Macroresidual stress ...........................45 and annealing ......................... 54–55(F) relaxation in notch root .................. 33(F) state .............................................27 vs. fatigue strength ........................ 50(F) Macroscopic residual stress ..12, 331, 332(F) Macrosegregation, reduced by rapid solidification .............................. 400 Macrostresses (first-order residual stresses) 89, 143, 145, 215, 331, 332(F), 333–334, 335(T) calculation of ................................ 217 carburizing and carbonitriding ............ 189 in coatings .................................... 118 definition ..................................... 125 and hydrogen embrittlement .................72 residual or tensile, in carburized steels .. 197 Magee’s rule, modified ....................... 288 MAGNA (computer program) ... 306(F), 308 Magnetic Barkhausen noise, .. 112, 114–115 Magnetic domain temperature ......... 225(F) Magnetic-flux concentrator ................. 222 Magnetic measurement methods ............25 Magnetic methods ............... 13, 14(F), 109



482 / Index

Magnetic permeability, and induction heating ..................................... 226 Magnetic transformation temperature .. 223, 225, 226–227 Magnetomechanical acoustic emission (MAE) ..................................... 115 Magniflux inspection ......................... 256 Mandrels, and quenching in a hardening press .............................. 185–186(F) Manganese alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ............................... 80, 81 composition requirements for powder forged parts ................................. 411(T) effect on transition temperature .........76(T) and flocculation susceptibility of steels ....73 increasing retained austenite in casehardening steels ....................... 447 for low-alloy P/M steel powders ......... 399 oxidation in carburizing atmosphere ..... 448 plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Manganese sulfides ........................ 72, 76 effect on hydrogen embrittlement of steels ...................................83 effect on iron-carbon-chromium-nickelmolybdenum steel .......................81 Manson-Coffin relationship ..................45 Manual on Shot Peening (1952) SAE publication ............................... 345 Maraging steels crack growth mechanism in delayed failure ................................. 78(F) delayed fracture .......................... 75, 78 high-strength, delayed fracture of ..........77 hydrogen states ................................72 stress-corrosion cracking .....................81 welding of ............................. 60–61(F) MARC (software program) .... 202, 363–364 Marquenching. See also Martempering. ........... 261–263, 266(T), 280–281, 287(F) and distortion .................. 176(T), 177(F) modified ............................ 281, 287(F) Martempering. See also Marquenching. ........... 261–263, 266(T), 280–281, 287(F), 417 Martensite ..................................... 4(F) atomic volume in ferrous alloys ...... 250(T) contact fatigue effect ....................... 198 deformation systems associated with transformations ....................... 5(T) formation, causing compressive residual stresses .................................. 150 formation during hardening processes .. 200, 201–202 hardening from grinding power ........... 150 in induction-hardened and carburized steel cylinder ....... 203–204, 205(F), 206(F) after induction hardening .............. 240(F) in schematic representation of relative transformation of mild steel plate ................................... 91(F)

shape change ................................ 5(T) transformation affected by stress ..... 297(F) transformation-start temperature, stress effects on ............................ 6(F,T) transformation through sinter-hardening process .................................. 408 volume fraction after induction hardening ........................... 228(F) volume fraction after water quenching of disk .................................. 289(F) volume-fraction distribution after induction hardening ........................... 231(F) volume fraction in induction hardened gear wheel ................ 306(F), 307(F), 309 volume fraction in quenched Japanese sword ................ 308(F), 309–310(F) Martensite finish (Mf) temperature .. 251, 260, 263(F), 332, 333 Martensite formation, in bearing ring hardening study .............. 314–317(F,T) Martensite start (Ms) temperature ...... 248, 249, 250(F), 260, 263(F), 332 carbon and alloying element effects ...... 200 of carburized steels ...................191–192 and quench cracking ....... 279, 281, 286(F), 287(F) and quenching in a hardening press ...... 186 after induction hardening and grinding .. 245 Martensitic hardening .........................99 Martensitic steels hydrogen embrittlement ......................72 hydrogen states ................................72 residual stress vs. temperature ........... 7(F) Martensitic transformation ............. 314(F) alloy steel ........................... 332, 333(F) mixed theory ................................. 332 stress theory .................................. 332 thermal theory ............................... 332 tool steel ............................ 332, 333(F) total energy exchange ...................... 332 Martin’s process ................................70 Mass effect ..................................... 274 Material removal ............................. 109 Maximum shearing .............................17 Maximum static pressure .....................21 MC carbides ............................. 404, 405 M6C carbides ............................. 404, 405 Mean stress .............................30(F), 297 Mean stress sensitivity ....................45–46 of medium-strength steel .....................51 Measured deflection, symbol and units of .........................................93(T) Measurement destructive procedures ......... 101–110(F,T) destructive residual-stress procedures .......................... 102(T) elastic strain .................................. 101 generic destructive stress-relief procedure ............................... 101 indentation methods ........................ 111 isolation of gaged element ................. 101 material-removal methods ................. 109 nature of residual stresses ..........99(F), 100 need for ....................................... 100 nondestructive procedures ...........111–115 post-stress relaxation ....................... 101 of residual stress .................. 438–439(F)

sectioning ..................................... 109 semidestructive procedures .......... 110, 111 spot annealing ............................... 111 strain-measurement methods ........109–110 strain-measurement technique ............. 101 stress-field condition assumptions ............... 101–109(F,T) Mechanical alloying .......... 400, 414(F), 419 Mechanical alloying of Japanese sword steel ........................................ 309 Mechanical chip-removal processes ...... 109 and isolation of gaged element ............ 101 Mechanical deflection ........................ 124 to measure residual stresses in coatings .............................. 118 Mechanical driving force ................. 6(F,T) limits affected by temperature ............ 6(F) Mechanical gages, for strain measurements ....................... 109, 110 Mechanical-gaging technique .............. 102 Mechanical strength of material, residual stress effect ...................... 14–16(F,T) Mechanical stresses ........................... 332 Mechanical twinning ............................ 4 characteristics ............................... 5(T) shape change ................................ 5(T) Mechanisms of transformations .............. 3 Medium-carbon low-alloy steel, quenching temperature effect on mold hole distortion ........................ 171(T) Medium-carbon steels quenching temperature effect on mold hole distortion .......................... (171(T) residual stresses due to milling ...... (109(F) tempering ........................... 284, 287(F) Medium-strength steels bending fatigue limit .........................50 bending fatigue strength vs. residual stress .................................. 43(F) crack propagation .................... 48–49(F) Haigh diagram model of residual stress influence ......................... 44–45(F) local fatigue strength ..................... 47(F) macro residual stress effect on fatigue strength .......................... 50–51(F) relaxed residual stress sensitivity and mean stress sensitivity of bending fatigue strength ............................... 45(F) S-N curves and residual stress effect ................37–38(F), 40–42(F) Melting, and distortion potential ............ 183 Melting temperature (Tm) .............. 54, 367 Melt penetration .............................. 416 Melt pressure, in casting ........... 368–369(F) Mesnager-Sachs boring-out technique ... 102 for destructive residual-stress measurement ....................... 102(T) Metal infiltration, residual stresses ......... 419 Metal-injection molding (MIM) .... 399, 400, 412(F) residual stresses ............................. 419 Metallic cementation, deformation tendency ............................... 170(T) Metallic mold casting ........................ 167 Metallothermomechanical theory ............................ 284–288(F) Metallo-thermo-mechanics


application to quenching ......... 296–310(F) parameters in schematic diagram ..... 296(F) Metal-matrix composites ............ 11, 12, 25 Metal-oxide semiconductors ................ 118 Metal powder production, in powder metallurgy processing ............... 397(F) Metal welding ....................................70 Metastable alloys .............................. 400 Michelson interferometer ................... 135 Microalloying, to preserve fine-grain austenite ................................... 325 Microcarbides ................................. 339 Microcracking ......................... 32, 33, 70 of carburized steels ...................196–197 of gas main pipes .............................82 in low-strength steels ......................................41 in maraging steels .............................75 propagation in medium-strength steels .................................41–42 in steel ..........................................71 Microcreep .................................. 59, 60 Microdefects, and cryogenic treatment .. 447 Micro distortion quenching ................. 171 Microextrusion, and cryogenic treatment ................................. 447 Microhammering .......................325–326 Microlamination .............................. 419 Micronotches, crack initiation enhanced by shot peening ................................34 Micro plastic strains (ep) ......................54 Micropores, hydrogen accumulation in steel .......................................72 Micro-quasi-chips ...............................73 Micro residual stress cyclic deformation .......................67–68 uniaxial deformation for relaxation .........63 Micro residual stress state ............... 27, 55 Microsegregation of prealloyed powder ....................... 402 reduced by rapid solidification ............ 400 Microstrains ...... 112, 331, 332(F), 335–336 Microstresses (second-order residual stresses) .......77, 89, 112, 114, 125, 143, 331, 332(F), 334 in coatings .................................... 118 definition ..................................... 125 and hydrogen embrittlement .................72 residual .........................................19 of steels, cryogenic cooling influences ........................... 336(F) Microstructural evolution analysis ..............................303–304 Microstructure influence on residual stress and carburized steel strength ..... 446–449(F,T) 450(F) interaction with time, temperature and deformation ........................... 3(F) of powder metallurgy processed steels ..............................419–420 transformations ....................... 3–6(F,T) Microstylus profilometry .................... 119 Microstylus traces ........................ 120(F) Microvoids ..................................... 339 Mikus diagram ............................ 337(F) Milam system ............................351–352 Mild steels

cold drawing ............. 147(F), 148–149(T) hydrogen embrittlement ......................83 Military specifications, MIL-S-13165 shot peening ................................. 345 Miller indices .............................. 334(F) Miller indices of the diffraction planes hkl, of first-order residual stresses of metallic materials ............................... 335(T) Milling ...........55, 57(F), 101, 109, 150–151, 152(F), 414 and distortion ................................ 152 and distortion potential ..................... 183 down-cut ......................150–151, 152(F) effect on fatigue behavior of high-strength steels ......................................43 face-milling ..................150–151, 152(F) with grinding, S-N curves and residual stresses effect ...........37–38(F), 39(F) and local fatigue strength ....................47 mechanical, thermal, or structural origins of residual stress ........................13(T) and P/M processing .................. 400, 414 residual stresses effect on S-N curves ............................ 36–37(F) residual stresses in medium-carbon steels ................................ 109(F) up-cut .........................150–151, 152(F) Mineral oils, for quenching ............319–320 Mises criteria .......................... 6, 17, 155 von Mises equivalent stress ................. 374 Mises-type yield function .................... 288 von Mises flow criterion ............. 6, 17, 155 von Mises J2-flow theory .................... 431 von Mises yield function ........299, 301, 302 Mixing, in powder metallurgy processing ............................. 397(F) Mixture rule ................................... 284 Mixture theory ................................ 379 MJS. See Multiphase jet solidification. Mode I crack, crack propagation rate ........36 Modeling.See also Computer simulation, Finite-element method. ....................25 residual stress field ................ 199–206(F) Modified Bessel functions of the first type .................................. 132 Modified Lorentzian method ............... 122 Modified Struve functions .................. 132 Moire´ interferometry ..........................12 Mold shrinkage factor ....................... 419 Molten metal quenching .........261, 271, 275 Molten-salt baths. See also Salt-bath quenching. as quenchant ...........................261–262 Molybdenum alloying effect on grain-boundary oxidation ................................ 449 alloying effect on P/M structure steels ..........................406–407(T) alloying element effect on crack growth ..80 effect on sintering of stainless steels ..... 404 effect on transition temperature .........76(T) and flocculation susceptibility of steels ....73 for low-alloy P/M steel powders ......... 399 plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T)


Index / 483 Molybdenum carbides, in high-speed steels after cryogenic cooling ..340–341(F), 343 Molybdenum (max), composition requirements for powder forged parts .................................... 411(T) Molybdenum nitrides ........................ 209 Moment of inertia .........................91–92 symbol and units of .......................93(T) Moore and Evans method .................. 105 for destructive residual-stress measurement ....................... 102(T) Mosaic blocks ............. 71, 342(F), 343, 344 Multiangle technique ......................... 112 Multimaterials ...................................11 inducing residual stress ......................24 Multiphase jet solidification (MJS) ....... 413 Multiple-motion die-set process ........... 401 Multiroll straightening .................. 146(F) Mushy zone .................... 362, 375, 376(F) centrifugal casting ........... 379, 382, 383(F) cooling water discharge effect .. 379, 381(F) Muskhelishvili equation of the elastic theory ...................................... 132

N NACTRAN software program ............. 127 Nanocrystalline materials ................... 400 National Center for Manufacturing Sciences (NCMS) ................................... 202 Navy C-ring test ........................ 91, 94(F) Near-net-shape components ................ 404 Neél temperature ................................ 3 Net opening (x) ..................................95 Net opening deflection method ..... 95–96(F), 97(F) Net opening displacement, simulation of residual stress effects .........96(F), 97(F) Net-shape powder compaction ............. 415 Net-shape products .............. 398–399, 418 Neutron bombardment, for inducing residual stress relaxation ............................54 Neutron diffraction (ND) .....11, 12, 109, 144 to evaluate brazed joint of steel and tungsten carbide-carbon cemented carbide ........................ 395–396(F) to evaluate residual stresses after grinding ............................. 151(F) to evaluate residual stresses in P/M processing .............................. 413 to evaluate steel/tungsten carbide-cobalt brazed compounds ................ 395(F) to measure actual crystal dimension ................. 111–112, 113 to study rail steel residual stresses ........ 431 Neutron radiation method .................. 438 Neutron scattering method ................. 431 Neutron stress analysis, brazed metallic components and ceramic-metal joints ................................. 395, 396 Newtonian wetting .................. 259, 263(F) Newton-Raphson method .......131, 288, 377 Newton’s iteration method .................. 304 Newton’s law of heat transfer .............. 200



484 / Index

Nickel alloying effect on grain-boundary oxidation ................................ 449 alloying effect on hydrogen embrittlement of steel .......................................83 alloying effect on P/M structural steels ..........................406–407(T) alloying element effect on crack growth ..80 effect on transition temperature .........76(T) first-order residual stress parameters 335(T) increasing retained austenite in casehardening steels ....................... 447 for low-alloy P/M steel powders ......... 399 plasticity loss after hydrogenation ......76(T) quenching, surface oxidation effect ..... 273, 277(F) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Nickel-base superalloys, specific types Inconel 600, as ISO probe for computer simulation .......................... 289(F) Inconel 600, as quench temperature probe .................... 266, 267, 270(F) Inconel 718, lasershot peening .. 355, 357(F) Inconel 718, shot peening ....... 355, 357(F) Inconel 718, shot-peened gas turbine components and distortion ........... 156 Inconel 718, turning .............. 151, 153(F) Nickel-chromium alloy case-hardening ........................... 438(F) centrifugal casting of pipe .......... 380, 382, 383(F), 384(F) Nickel-chromium-aluminum yttrium coating ..................................... 118 Nickel-chromium steel aging effect on carburized steel .......... 449, 450(F) repeated stressing effect in carburized steel ........................... 450, 452(F) for ring, induction hardened and carburized quenched .... 303(F), 304(F), 305–307(F) Nickel-containing steels tight scale formation .............. 255, 258(F) Nickel (max), composition requirements for powder forged parts .................. 411(T) Nickel plating ....................................12 Nickel steels composition .............................. 407(T) Niobium alloying effect in steels dispersion hardening ............................... 325 alloying element effect on crack growth ..80 critical amount in steel for affecting recrystallization and energy of activation ............................... 325 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack 76(T) Niobium nitride (NbN) ...................... 209 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T)

work of propagation of a ductile crack ..................................76(T) Nitrate solutions and stress-corrosion cracking ................79 Nitriding .......................12, 209–219, 407 alloy steels ................................... 212 Armco iron ................................... 212 and carburizing, compared ................. 209 C45 steel ..................................... 212 chromium-alloyed steels ................... 216 chromium-manganese steels ............... 212 chromium-molybdenum steels ............ 212 chromium-molybdenum-vanadium steels ................................ 212(T) compound layer residual stresses ..................... 211–213(F,T) computer modeling ............ 211–214(F,T) deformation tendency ................... 170(T) diffusion layer of residual stresses ............................213–214 and distortion of surface layer ............ 172 distortion tendency ................ 179, 181(F) EN 19 steel ................................... 216 gaseous nitriding in NH3-N2-H2 mixtures ............................ 209(F) gaseous nitrocarburizing ............... 215(F) heating device distances .................... 184 low-alloyed steels ........................... 209 low-alloy structural steel ............... 210(F) low-carbon steel ......................... 209(F) mechanical, thermal, or structural origins of residual stress ........................13(T) modeling of residual stresses .... 216–218(F) nitrocarburizing (ferritic) ........ 209–210(F), 211(F) plain carbon steel ....................... 210(F) plasma nitriding ... 210–211(F), 215(F), 216 plasma nitrocarburizing ... 210–211, 212(F), 215(F) process temperature ......................... 209 residual stress influence on steel fatigue ...................... 214–216(F,T) salt bath nitrocarburizing ........ 210, 211(F), 215(F) short time, deformation tendency ..... 170(T) stainless steels ............................... 211 steel .............................. 214–216(F,T) structure of nitrided layers ....... 209–211(F) unalloyed steels .............................. 209 Nitrocarburizing ........................ 407, 408 and cyclic deformation behavior after deep rolling ................................. 31(F) deformation tendency ................... 170(T) and distortion of surface layer ............ 172 modeling of residual stresses .... 216–218(F) Nitrocarburizing of austenite, deformation tendency ............................... 170(T) Nitrocarburizing of ferrite ....... 209–210(F), 211(F) deformation tendency ................... 170(T) Nitrogen alloying effect on grain-boundary oxidation ................................ 449 alloying element effect on crack growth ..80 as quenchant ....................... 261, 265(F) Nitrogen furnace atmosphere, composition ........................... 404(T)

Nitrogen/helium, as quenchant ............. 261 Nodal point/element data file format ..... 304 Nonhomogeneity degree, of interplanar spacing ..................................... 334 Non-isothermal phase transformations, computation of .................. 200–202(F) Nonmartensite phases .............. 448–449(F) and residual stresses ...........449(F), 450(F) at surface ..................................... 446 Nonmeteallic impurities, ..... effect on stresscorrosion cracking .........................81 Nonmetallic stringers, and distortion ..... 255, 256, 258(T) Nonnegative continuous weight functions .................................. 127 Non-Newtonian wetting 259, 262(F), 263(F) Nonuniform quenching ................ 268, 280 Normalization ....................... 147(F), 254 Normalized steel, crack initiation .............34 Normalized stress gradient ...................36 Normalizing ......................................81 and distortion ...................... 154, 155(F) before nitriding .............................. 209 Norton’s creep equation ........... 217, 374(F) Norton’s law .............................. 60, 374 Notch, quenching and distortion ... 253, 256(F) Notching ........................... 125–126, 128 Notch line ....................................... 126 Notch root residual stresses .............. 32(F) Nucleate-boiling (NB) stage ...... 258, 260(F), 261(F), 269–271, 312, 314 Nuclear magnetic resonance imaging (NMR), to evaluate residual stresses in P/ M products ................................ 413 Nuclear power plant reactor casing, residual stresses in weld zone of bimetallic material ................................ 137(F) Number of cycles at a crack length, formula ......................................34 Number of cycles to crack initiation, residual stresses effect from mechanical surface treatments ...................................34 Numerical analysis, formulation of ........ 376 Numerical analysis algorithm .............. 377 Numerical analysis method incorporating solidification .............................. 372 Numerical analysis method of thermomechanical problems in casting 374–377(F) Numerical inverse methods ........... 268, 271

O OBD. See Over ball diameter. Octahedral shearing ............................17 Octahedral shearing plane ....................17 Oil cooling ...................................... 315 Oil impregnation ........................ 405, 406 Oil quenching ....... 263–264, 267(F), 268(F), 269, 272–273(F), 275, 277(F), 282(F), 316 of carburized testpieces and gears ....... 439, 440(F) edge effect .......... 273–274, 279(F), 280(F) steering sector shaft ............... 454–455(F)


tanks ........................................... 172 ultrahigh temperature ............. 454, 455(F) Oils. See Oil quenching. (X)-diffractometer ............................ 121 One-angle technique (SET) ............. 112(F) One-phase convection heat transfer ..... 312, 314 OOR. See Out-of-roundness. Open-hearth process ...........................70 Operator kernel of Fredholm integral equation of the first type ...................................... 126 of Volterra integral equation .............. 126 Optical gages ............................. 109, 110 Optical-geometrical methods, to measure strains and displacements fields in area of crack indicator ............................ 130 Optical interferometry methods ......................... 134–136(F) Optically sensitive coating method ........ 132 Optically sensitive coatings ................. 133 ORE Committee .............................. 431 ORE Report .............................. 431(F) Organic matrix composites ...................12 Orikaeshi ........................................ 309 Oscillating stress .............................. 345 Oscillators ...................................... 221 Ostergren damage parameter ...... 30–31, 45 Out-of-phase hardening ..................... 432 Out-of-roundness (OOR) .......418(F), 454(F) Over ball diameter (OBD) ........ 453, 454(F) Overheating, localized, and distortion ............................256–257 Overload-induced compressive residual stresses ......................................35 Overload ratio ............................... 35(F) Overpeening effects .......................... 347 Oxide-dispersion-strengthened iron-base alloys ....................................... 414 Oxides, role in stress-corrosion cracking .....81 Oxide scale ..255, 258(F), 273, 277(F), 278(F) and quench cracking .......... 278(F), 286(T) Oxygen alloying element effect on crack growth ..80 composition requirements for powder forged parts ................................. 411(T) effect on gaseous nitrocarburizing .... 214(F)

P Pack carburizing ..........189, 443(F), 444(F), 451(F) carbon potential control .................... 444 and retained austenite content ............. 447 Parabola method .............................. 122 Parallelepiped, quenching and heating computational and experimental results ......................... 321–323(F,T) Paris equation ...............................29,30 describing crack propagation ...........34–35 Partial damage, for inducing residual stress relaxation ....................................54 Partially alloyed powder ................ 400(F) Patch test ....................................... 369 Patel and Cohen’s method ..................... 8

Patenting ........................................ 261 PA-TRAN computer program ............. 304 PCD. See Pitch circle diameter. Peak shift method ..........................12–13 Pearlite ................................... 4(F), 448 atomic volume in ferrous alloys ...... 250(T) in carburized cases .......................... 189 in schematic representation of relative transformation of mild steel plate ................................... 91(F) shape change ................................ 5(T) transformation to austenite, volumetric change .............................. 250(T) volume fraction in quenched Japanese sword ................ 308(F), 309–310(F) volume fraction of .......................... 297 Pearson VII method .......................... 122 Peen forming ................... 151, 347, 348(F) Peening, fatigue ..................................27 Peening-induced microstructural workhardening effect ............... 62–63(F,T) Peenscan process .......... 349–350(F), 351(F) Peenstress (computer program) ......91, 350, 352(F), 353(F) Penetration depth ............................. 121 Persistent slip bands (PSBs) ........ 28(F), 29, 33–34 Perzyna’s constitutive model, modification for semicontinuous casting ............. 377 Perzyna’s inelastic constitutive equations .................................. 372 Perzyna’s viscoplastic constitutive relationship, modified .................. 385 Perzyna’s viscoplastic model on excess stress theory ............................ 373–374(F) temperature-dependent viscosity variation ............................ 374(F) pH, effect on main gas-pipe line steels corrosion .....................................82 Phase transformations due to welding ........... 392–393(F), 394(F) and fatigue .....................................27 finite-element method for modeling ..... 296, 300, 301(F), 302, 303, 306(F), 307(F), 309 during heat treating .. 248–251(F,T), 252(F), 253(F), 254(F) material movements ..................251–252 volume changes ................... 252, 254(F) Phonons ............................................ 3 Phosphate solutions, and stress-corrosion cracking ......................................79 Phosphorus alloying addition effect on sintering ..... 402 alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ..80 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Phosphorus (max), composition requirements for powder forged parts ............. 411(T) Photoelastic coating method ... 127, 128, 130, 131, 133–134(F), 135, 136(F), 137


Index / 485 Photoelastic coatings ...........................91 thickness selection .......................... 134 Photoelasticity, to evaluate residual stresses in P/M products ............................. 413 Photoelastic technique ....................... 110 Photographs, to measure surface wetting .... 269 Photometer parameter ....................... 334 Physical vapor deposition (PVD) .....25, 118, 119, 120, 121 coatings .................................... 11, 12 deformation tendency ................... 170(T) mechanical, thermal, or structural origins of residual stress ........................13(T) Pickel method .................................. 106 Piecewise-homogeneous materials, peculiarities in study of ....... 130(F), 131 Pinion shafts, distortion ............ 255, 257(F) Pinned dislocations ........................66–67 Pinning ............................................55 Pipe weldment residual stresses ............. 100(T) weldments .................................... 102 Pipe steels, stress-corrosion cracking .........81 Pisarenko-Lebedev criterion ...312, 317, 328 as failure criterion during hardening ..... 315 Piston ring, tempering and distortion ..177(F), 178 Pitch circle diameter (PCD) ..........308–309 Pitch error .........................453(F), 454(F) Pitting ........................................... 215 Plain carbon steels crack initiation .................................34 cryogenic cooling ........................... 331 cyclic deformation behavior ....... 28–29(F), 31(F), 32 modulus of elasticity .....................96(T) nitriding ................................... 210(F) Poisson’s ratio .............................96(T) residual stress relaxation produced by annealing ........................ 54–55(F) shear modulus .............................96(T) Plain carbon tool steels, cryogenic cooling ..................................... 340 Plane-strain fracture toughness .... 74(F), 80 Plane-strain stress analysis, with von Mises yield criterion for casting ............... 366 Planing .......................................... 150 PLASMA (plasma-nitriding computer program, simulation) .................. 216 Plasma carburizing ........................... 189 Plasma cutting ................................. 109 Plasma nitriding ... 210–211(F), 215(F), 216, 407 stainless steels ............................... 211 Plasma-nitriding simulation program (PLASMA) ............................... 216 Plasma nitrocarburizing ... 210–211, 212(F), 215(F) Plasma-sprayed coatings ................. 11, 25 Plasma spraying ............................. 16(F) mechanical, thermal, or structural origins of residual stress ........................13(T) Plastic Ball Grid Array (PBGA) package .....................................12 Plastic compression, regime in simple slab casting ................................. 362(F)



486 / Index

Plastic deformation ........... 4–5(F,T), 19, 27 and cyclic softening ...................... 32(F) nonhomogeneous ..............................12 of rail steel ......................... 431–432(F) Plastic flow, nonhomogeneous ................12 Plastic flow theory ............................ 315 with kinematic strengthening .............. 315 Plastic (inelastic) strain ...................... 299 Plasticity ........................................... 3 Plasticity-creep interaction condition .... 302 Plasticity theory equations .................. 312 Plasticizing ..................................... 220 Plastic potential, of casting .................. 365 Plastic potential theory ...................... 300 Plastic strain rate ...... 202, 286, 299–300(F), 302, 312 Plastic stretching of immediate workpiece surface ................................. 346(F) Plastic tension, regime in simple slab casting ................................. 362(F) Plastification ................................... 230 after induction hardening and grinding .. 245 of subsurface after induction hardening .... 239 Plate carburized, residual stresses .... 439, 440(F), 441(T) destructive residual-stress measurement procedures .......................... 102(T) flat, biaxial stresses measurement ..106–108 flat, residual stress measurement .......... 108 flat, shear stress measurement ............. 106 piecewise-homogeneous, residual stress close to edges .......................... 129 quenching and heating computational and experimental results ...... 321–323(F,T) residual-stress distributions ............ 107(F) residual stress in inner regions, determination of ............. 128–129(F) steel, plastically deformed, neutron diffraction methods ................... 113 stress profile from Peenstress software ............................. 353(F) thick, stress measurement .................. 106 through-thickness temperature variation ...................... 223, 224(F) welded, shot peening effect on residual stress .......................... 354, 356(F) Plate weldments, stress measurement ...... 106 Plating, of P/M parts ......................... 406 Plug quenching ..............257, 280, 281, 456 Poisson contraction .............................92 Poisson’s ratio .................................... 3 of aluminum alloy ...................... 378(T) effect on residual stress development in steels ................................... 3(T) of first-order residual stresses of metallic materials ............................ 335(T) symbol and units of .......................93(T) Polarization curves, active-passive region of potentials ....................................79 Polishing ........................................ 405 Polyakov rules for quenching .... 260, 264(F) Polyalkylene glycol (PAG), as quenchant .... 264, 268(F), 276(F), 279(F), 283(F), 285(F,T) Polyethyloxazoline ............................ 264 Polymer additive ratio, effect on cooling rate after induction hardening ........... 232(F)

Polymer quenchants, aqueous. See Aqueous polymer quenchants; Aqueous polymer quenching. Polymers, aqueous solutions as quenchants. See Aqueous polymer quenchants; Aqueous polymer quenching. Polysodium acrylate .......................... 264 Polyvinylpyrrolidone ......................... 264 Pores (collectors) ................................72 Porosity in castings .................................... 370 of P/M parts ................................. 406 Portable optical method for strain measurement in destructive techniques ..................................25 Position-sensitive proportional counter (PSPC) method ...................... 439(F) Position-sensitive proportional detector (PSPD) ................................ 439(F) Positive-pole figure analysis ................ 439 Positron lifetime measurements ........... 416 Post-processing file format .................. 304 Postsintering, and metal-injection molding .................................... 412 Powder forging ................... 410–411(F,T) cost, relative ............................. 413(F) Powder metallurgy iron, composition ........................... 407(T) Powder-metallurgy (P/M) processing advantages .............................. 397, 398 applications ............................397–398 automotive applications .................... 398 classes of components ...................... 401 compaction in rigid dies ......... 401–402(F) dendrite arm spacing .................... 400(F) density distribution ......................... 415 double-action tooling system ........401–402 ferrous P/M parts ................. 398–399(F) heat treatment of steel parts ..... 417–418(F) hot pressing ........................ 408–409(F) interparticle cohesion ....................... 415 isostatic compaction ........................ 402 lubricants ..................................... 400 market value ................................. 397 metal-injection molding ................ 412(F) metals processed ............................ 397 microstructural development and properties .........................419–420 mixing and blending ..................400–401 nonsintered areas ............................ 420 operations sequence ..................... 397(F) powder characteristics ............ 399–401(F) powder forging ................. 410–411(F,T) press-sinter manufacturing process ... 398(F) production capacity ......................... 397 production of powder ............. 399–400(F) products formed ............................. 397 rapid prototyping (RP) ..................... 413 residual stresses ................... 413–420(F) roll compaction .................... 409–410(F) simulations, particulate modeling ........ 413, 415–416, 417 sintering ......................... 402–408(F,T) spray forming ..........................412–413 structural steels, compositions ........ 407(T) superalloy weight in commercial jet aircraft engines .................................. 398

tool steel market ............................. 398 warm compaction ....................... 413(F) Power density .............................. 222(F) definition ..................................... 222 Prager model, of back stress rate .......... 299, 300(F) Prager’s consistency relation ............... 300 Prandtl-Reuss flow rule ..................... 301 Prealloyed powders ................. 399, 400(F) powder forging .............................. 410 sintering effect on microsegregation ..... 402 Pre-cooling quenching .................176–177 Prediction, residual stress field .... 199–206(F) Pre-heating to control distortion ...................155–156 and distortion ...................... 171–172(F) Pre-heat-treating, and distortion ............169–172(F,T), 173(F) Premixed powders, powder forging ........ 410 Press braking ........................ 147–148(F) Pressing ...................................141–142 applications .................................. 142 Press quench ................................... 454 Press quenching .............183, 280, 281, 453 system ............................... 253, 256(F) Press-sinter technique ....................... 397 Pressure-assisted sintering ............ 409, 417 Pressure casting ......................... 167, 168 Pressure rolling ..................... 151, 153(F) and distortion ................................ 152 Pre-straining .....................................19 Prestress engineering of structural materials (PESM or PRESMA) ....................25 Prestress processing ............................11 Primary gas porosity ...........................72 Primary microcreep ....................... 59, 60 Process equipment design ......... 183–186(F) Processing analysis ........................11–12 Processing modeling .......................11–12 Processing parameter optimization ....11–12 Production gears, residual stresses in ............................... 439–441(F,T) Profilometry .................................... 120 Programmable control units, storage of workpiece- and material-specific treatment parameters in a database ................ 186 Projection welding ............................ 405 Proportionality, coefficient ....................75 Protective films, rate of forming and stresscorrosion cracking .........................80 (w)-diffractometer ............................ 121 (w)-splitting .............................. 121, 122 PSPC. See Position-sensitive proportional counter method. PSPD. See Position-sensitive proportional detector. Pull cracking ............... 260, 263(F), 264(F) Pull stress ............................. 260, 263(F) Pure iron quenching, surface oxidation effect ..... 273, 277(F) specific heat capacity, as function of temperature ......................... 3–4(F) stress-corrosion cracking insensitivity .....79 Push cracking .............. 260, 263(F), 264(F) Push-pull fatigue testing ..........28, 63(F), 66


and cyclic deformation behavior ........ 33(F) Push stress ............................ 260, 263(F)

Q Quality assurance, inspection plan .. 13, 14(F) Quality control .............................11–12 of gear strength .............................. 440 Quantimet 720 quantitative microscope, with computer interface ....................... 341 Quantitative electronic microscopy, to identify and count microcarbides ...... 339 Quasi-spall .......................................76 Quasi-static surface yield strength in compression ....................... 66, 68(T) Quebec metal powder process ............. 399 Quenchants. See also Quenching; Quench severity; Quench uniformity. ......... 260–265(F,T), 266(F), 267(F), 268(F), 269(F), 270(F) agitation rate influence ................. 176(T) aqueous polymer ..257, 264, 268(F), 269(F), 272(F) brine ...........................264–265, 270(F) caustic soda ..................264–265, 270(F) circulation uniformity effect ............... 176 cooling rate and distortion compared ........................... 175(T) and distortion ................... 174–175(F,T) effect on quenching performance ........ 259, 262(T) factors influencing cooling intensity .... 174, 175(T) after induction hardening .................. 232 influence on distortions of C-style sample .............................. 175(T) influence on distortion trend of cavity of cold forging dies ............ 175, 176(T) intensively cooling .......................... 314 oils ... 263–264, 267(F), 268(F), 269, 272(F) selection, and cooling characteristics ... 275, 281(F), 282(F) selection, and distortion ..............279–280 selection effect ..... 269–270, 272(F), 274(F) temperature effect .......176, 268(F), 269(F), 270–271(F) uniformity ...... 258–259(F), 260(F), 261(F) vaporizable liquid ........................... 258 viscosity ...................................... 270 water ................ 264, 269, 270(F), 272(F) Quenchant solution circulation rate ...... 328 Quench cracking ... 253–256(F,T), 257, 259– 260, 263(F), 264(F), 285(F), 312 elimination by intensification of heat transfer at phase transformations ............. 328 prevention .................................... 323 probability of ............................ 313(F) and quench nonuniformity ................. 258 and surface roughness ......277–278, 286(T) techniques of steel quenching for prevention of .............................. 325, 326(F) Quench Cracking Working Group, Japan Heat Treatment Society ..... 277, 285(F) Quench distortion .......................259–260 Quenched-and-tempered steel bending fatigue tests in sea water ...... 34(F)

cyclic deformation ........................ 29(F) fatigue strength .......................... 244(F) local fatigue strength ..................... 47(F) Quenched steels, delayed fracture ........ 77(F) Quench embrittlement ....................... 196 Quenching. See also Air quenching; Aqueous polymer quenching; Brine quenching; Carburized quenching; Cold-die quenching; Direct quenching; Distortion; Fluidized-bed quenching; Fog quenching; Free quenching; Gas quenching; Hot oil quenching; Immersion quenching; Intensive quenching; Interrupted quenching; Marquenching; Martempering; Molten metal quenching; Nonuniform quenching; Oil quenching; Plug quenching; Pre-cooling quenching; Press quenching; Quenchants; Quench cracking; Quench distortion; Quench oils; Quench severity; Quench uniformity; Restraint quenching; Salt-bath quenching; Selective quenching; Spray quenching; Time quenching; Two-step quenching; Water quenching. ..... 99, 257–272(F,T), 273(F), 274(F), 275(F), 336 agitation effect .... 258, 259(F), 275–277(F), 283(F), 284(F), 285(F,T) boundary conditions selection for simulation .............................. 325 of carburized bushing .......... 320–321(F,T) of carburized cylinder, computer simulation .............. 296, 302(F), 305 carburized gear axial stresses .... 440–441(F) of case-hardened gear, model .. 202–203(F), 204(F) chloride solutions for tool steel punches ................................. 326 coating effects ..................... 273, 278(F) cooling characteristics effect on residual stress and distortion .. 275–278, 281(F), 282(F), 283(F), 284(F), 285(F,T), 286(T) dimensional changes ....... 252, 255(F), 274, 275, 282(F) direct or single reheat after carburizing, and retained austenite .................. 447(F) and distortion ...................... 252, 255(F) distortion, components 159, 161(T), 162(F) distortion, component with simple shape .......... 159–161(F,T), 162(F,T), 163(F), 164(F) distortion, metallurgical sources ... 251–252, 254(F) and distortion potential ...............184–185 distortion prediction .............. 284–293(F) double reheat and quench after carburizing, and retained austenite ............. 447(F) geometry effects ... 273–274, 279(F), 280(F) in hardening press, and distortion minimizing ................... 185–186(F) for inducing residual stress relaxation .....54 after induction hardening ....... 236–238(F), 241, 242(F), 246 for induction hardening .......... 231–232(F) from intercritical temperature interval .....81 of Japanese sword, computer simulation ....296, 304, 307(F), 308(F), 309–310(F)


Index / 487 kinetics of process .......................... 288 of low-alloy steels ...................... 337(T) material effect on distortion ........ 252–256, 257(F), 258(F,T) material effects .............. 274, 280(F), 312 mathematical modeling of process ....... 319 media, 449 media, influence of distortion of gears ........................... 454–456(F) media measurement and evaluation of power ........ 265–269, 270(F), 271(F), 272(F), 273(F) methods .................................280–282 methods, effect on carburized-and-hardened steel residual stresses ....... 443–444(F) methods, Ukraine Patent (No. 4448, Bulletin 6-I), 1994 ............................... 328 model of stress/strain prediction in casehardened parts ............... 199, 201(F) before nitriding .............................. 209 no phase transformation, mechanical, thermal, or structural origins of residual stress ..................................13(T) one-step ....................................... 319 Polyakov rules ..................... 260, 264(F) powder metallurgy processed parts ....... 407 quenchant and material properties effects ......................... 259, 262(T) quenchant choice and distortion .................. 174–175(F,T) residual stress prediction ......... 284–293(F) simple shape bodies, computational and experimental results ...... 321–323(F,T) simulation, inverse technique ...............23 steel chemical composition effect ........ 274 supercarburized high-speed steels .... 337(T) surface conditions effect ........ 273, 277(F), 278(F), 279(F) surface distortion comparison ......... 170(F) tank for immersion ................ 172, 173(F) temperature influence on distortion of mold hole .................................. 171(T) two-step ................. 312, 319(F), 320, 328 of carburized bushing .......... 320–321(F,T) workpiece size effects ..... 252, 255(F), 274, 275, 282(F) Quench oils .......... 263–264, 267(F), 268(F), 323–324 accelerated ......................... 264, 267(F) and carburized steel residual stresses .............................. 445(F) conventional ................................. 263 martempering ...................... 264, 268(F) MS-20 ...................................320–321 MZM-16 .................................. 318(F) quench chamber pressure control ........................ 455–456(F) quench severity index (H value) ..................... 454–455(F) vapor blanket stage ............... 455–456(F) Quench press machines, and distortion ..................... 181–182(F,T) Quench severity ........ 257, 259(T), 262, 265, 266(F), 269 of aqueous polymer quenchants .......... 264 definition ............................... 257, 265 and distortion ..........................279–280



488 / Index

Quench severity (continued) of gas quenching .................. 261, 266(F) water content effect ........ 262–263, 266(F), 267(F) Quench severity index (H value) of quenching oil .................. 454–455(F) Quench uniformity ...... 258–259(F), 260(F), 261(F), 266(F), 269 Quick-slow-quick quenching ............... 456

R Racking, and distortion ... 171(F), 172, 173(F) Radial forging .................... 148–149(F,T) Radial stress ......................... 144(F), 145 from induction hardening ........ 234, 235(F) residual stress distribution in radial direction at t ⳱ 8.32s rising a plane-strain assumption ......................... 368(F) residual stress variation in the axial direction at time t ⳱ 8.3202 s with a tractionfree top surface .................... 368(F) semicontinuous casting distribution ..... 378, 380(F) from specimen heating ................. 313(F) thermal stress history with a plane-strain assumption ......................... 368(F) thermal stress history with a traction-free top surface .............................. 369(F) Radiation, monochromatic, wavelength of ........................................... 113 Radiation thermometer, to measure temperature of centrifugal castings .... 382 Radius of curvature of beam on displaced section, symbol and units of .........93(T) Radius of round bar cross section, symbol and units of .............................93(T) Rail end problem ............................. 424 Railroad wheels, ultrasonic velocity measurement technique ................. 114 Rail steel cooling process .................... 424–430(F) cyclic plastic deformation ........ 431–432(F) distortion and residual stress formation ..................... 424–435(F) head-hardened ............................... 426 heat flux and cooling process ......... 425(F) moving/sliding on cooling bed ........... 429 production steps ......................... 424(F) rail end problem ............................. 428 roller straightening process ........ 424, 430– 434(F) in service ........................... 434–435(F) temperature influence ....................... 434 welding as cause of residual stresses .............................. 434(F) Rail steel stress tensor, decomposition into hydrostatic and deviatoric parts ........ 432 Railway tank cars, for transporting ammonia, shot peening effect on residual stress ............................. 354, 356(F) Ram force ...................................... 409 Rapid induction heating/intensive cooling ............................... 327, 328 Rapid omnidirectional compaction ....... 409 Rapid prototyping ...................... 399, 413

in powder metallurgy processing ..... 397(F) residual stresses ............................. 419 Rapid rewetting process ........... 259, 262(F) Rapid solidification ...............400, 412, 414 Rare-earth metals addition effect on stress-corrosion cracking ...................................81 alloying effect on hydrogen embrittlement of steel .......................................83 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack 76(T) Rate form of stress-strain relation .......................... 300–301(F) Rayleigh waves ................................ 114 Real hydrogen embrittlement ................73 Real-time visualization ................ 135, 399 Recovery mechanisms .........................58 Recrystallization .............................. 416 residual stress influence ..............419–420 and sintering ................................. 402 Recrystallization temperature, of ferritic steels .........................................54 Rectangular cross-section bar, destructive residual-stress measurement procedures ............................. 102(T) Redrawing ........................................60 Reduced-pressure carburizing carbon potential control .................... 444 furnace ........................................ 453 Reduction in area ............................. 146 Reduction of iron oxide ..................... 399 Reflection polariscope ........................ 110 Reflection polariscope “Photoelastic Inc.” ............ 136–137(F) Refrigeration treatments .................... 195 Regular conditions, theory of ............... 322 Regularization algorithm, when interpreting distribution containing random disturbance ...................... 127–128(F) Regularization methods .........126, 127, 318 Regularization parameter ␣ ................ 127 Reheating treatments ..................189–190 distortion, metallurgical sources ... 251–252, 254(F) Reheat temperatures ......................... 189 Repeated bending test ..................... 17(F) Repeated loading, effect on residual stresses of carburized steels ..... 449–450, 451(F), 452(F) Repeated stressing, effect on residual stresses of carburized steels ..... 449–450, 451(F), 452(F) Repeated tension test ....................... 17(F) Repressing ................................. 60, 410 in powder metallurgy processing ..... 397(F) Rerolling ..........................................60 Reserve strength factor, of bearing ring 317(F) Residual austenite ..............................81 Residual microstresses ....................... 335 Residual stresses admissible prediction of ............. 22–24(F) compressive macro ............................54

from cooling process, calculated vs. experimental ....................... 314(F) cumulated value at any point .............. 331 definition ............................... 143, 221 distribution, simulation models ........... 437 effect on fatigue strength ................ 19(F) first-order (macroscopic) ......... 331, 332(F) induction hardening ............ 232–242(F,T) and loading mean stresses compared ............................27–28 manufacturing implications ....90–91, 92(F), 93(F) measurement methods from deflection data ........................................91 origins of ..............................12–13(T) prediction, after quenching ...... 284–293(F) from quenching, cooling characteristics effects ........ 275–278, 281(F), 282(F), 283(F), 284(F), 285(F,T), 286(T) of scanning induction hardened cylinder, computer simulation ....... 290, 293(F), 294(F) second-order (microscopic) ...... 331, 332(F) state of .............................. 331, 333(F) third-order (ultramicroscopic) .. 331, 332(F), 335–336 types ................................. 331, 332(F) Residual stress field, modeling and prediction ........................ 199–206(F) Residual-stress-free condition, fatigue strength ......................................45 Residual stress relaxation phenomenon. See also Stress relaxation. .....................17 Residual stress restitution (inverse problem) ....................... 127 Residual stress sensitivity ................45–46 of medium-strength steel .....................51 Residual stress sensitivity factor (m) ........66 Resin impregnation ..................... 406, 418 Resintering, in powder metallurgy processing ............................. 397(F) Resistance sintering under pressure ...... 408 Resistance welding ............................ 405 Restart file format ............................ 304 Restraint fixturing ............................ 281 Restraint quenching .......................... 281 Restretching ......................................60 Retained austenite ......................336–337 in carburized gears ......... 441, 442(F), 443, 444(F), 446 in carburized plain carbon and low-alloy steels .......................... 194, 197(F) in carburized steels .................... 437, 438 in case region of carburized and hardened steels ....................195–196, 198(F) contact fatigue effect ....................... 198 decomposition in steels at 823–973 K ... 337 decreased by shot peening .......... 198–199, 200(F) and deep freezing ........................... 178 and distortion ...................... 257, 259(T) effect on carburized steel cylinder stresses, model ......................... 202, 203(F) effect on transgranular fatigue crack initiation ..........................197–198 factors affecting formation ................. 251 formation with austempering processes .. 257


as function of tempering temperature ... 251, 254(F) in heat treated P/M tool steel .......417–418 heat treatment effect on residual stress distribution ............................. 194 heat treatment variant effect in high-alloy tool steels ..................... 340, 341(T) of high-alloy tool steels .......... 343(F), 344 in high-speed steels ................... 338, 339 in induction-hardened and carburized steel cylinder ....... 203–204, 205(F), 206(F) influence on carburized steel residual stress and strength .................. 446–447(F) reduced by cryogenic cooling ............. 331 in reheated carburized parts ............... 190 and stabilization ............................. 178 and surface residual stresses ............... 449 tempering influence on distortion ..................... 177–178(F) transformation affecting volume during tempering ...............283–284, 287(F) transformation by mechanical stressing in carburized steels ............. 447–448(F) Reverse bending, of Japanese sword ............................. 309–310(F) Reverse impending method ................. 215 Rewetting, effect on carburized steels ...... 438 Rich exothermic furnace atmosphere, composition ........................... 404(T) Ridder method ................................ 129 Rigid-die compaction ........................ 415 Rimmed carbon steels, Barkhausen noise analysis for stress measurement ........ 114 Ring of chromium-molybdenum steel, carburizedquenched, computer simulation of distortion ..................... 290, 292(F) distortion ........... 303(F), 305(F), 306, 307 induction hardening and carburized quenching, computer simulation ... 296, 303(F), 304(F), 305–307(F) Ring coring ...............................110–111 Rings and races of bearings thicker than 12 mm advantages ................................ 327(T) former steel and process ............... 327(T) new steel and process .................. 327(T) Robert Bosch ....................................11 Rocker arm, shot peening effect on fatigue life ........................................20(T) Rods cylindrical, carburized, residual stresses .............. 439, 440(F), 441(T) destructive residual-stress measurement procedures .......................... 102(T) drawing ................... 143(F), 145–146(F) extrusion .................................. 147(F) Roll compaction ...............409–410(F), 414 friction role ................................... 409 and residual stresses ..................414–416 Roller burnishing .......................... 12, 19 effect on cast iron fatigue strength ........19, 20(F) to introduce residual compressive stress ...14 mechanical, thermal, or structural origins of residual stress ........................13(T)

Roller straightening ..........424, 430–434(F) simulation .......................... 432–434(F) Rolling ..... 99, 141, 146–147(F), 147–148(F), 399 advantages .................................... 142 deformation zone geometry ................ 143 mechanical, thermal, or structural origins of residual stress ........................13(T) in powder metallurgy processing ..... 397(F) screwplate, jig and fixture method for quench ........................ 159, 161(F) Rolling bearing steel, residual stress relaxation produced by annealing ................ 55(F) Rolling contact, elasto-plastic, of rail steel .............................. 434–435(F) Rolling-contact fagitue carburized parts .............................. 196 carburized steels ............................. 198 Rolling faces pulling ......................... 363 Romberg algorithm .......................... 129 Rosettes ....................................... 34(F) Rosenthal and Norton’s method ....... 103(F) for destructive residual-stress measurement ....................... 102(T) enhancement of .............................. 104 variation for determining triaxial residualstress condition of plate .............. 105 Rotary bending fatigue test ....... 442, 443(F) Rotating beam fatigue test ....... 446(F), 450, 451(F) unnotched gear teeth ........................ 450 Rotation velocity, of workpieces in induction heating ..................................... 232 Rough-condition temperature .............. 325 Roughness and bending fatigue strength of mediumstrength steels .......................41–42 effect on fatigue strength of high-strength steel .................................. 51, 52 effect on fatigue strength of mediumstrength steel .............................51 and quench cracking ........277–278, 286(T) of surface, and quenching ........ 273, 279(F) R ratio .............................................19 R ratio effect .....................................30 R6M5 punches ............................. 326(F) tool life in automatic forming machine ....................... 326, 327(T) Rupture strength ....................... 16–19(F) Ruud-Barrett Position-Sensitive Scintillation Detector ............................... 112(F)

S Sach’s method ................................. 148 Safety factor distribution of ..................................22 on fatigue ................................... 21(F) field of .............................. 313(F), 316 Sag, of rail steel section .................. 428(F) Salt bath carburizing .............. 189, 443(F) carbon potential control .................... 444 and retained austenite content ............. 447 Salt bath nitrocarburizing ....... 210, 211(F), 215(F)


Index / 489 Salt bath quenching ......... 261–263, 264(F), 266(T), 271, 275, 449, 454 with austempering ........................... 281 Sandblasting, as predecessor of shot peening .................................... 345 Sand casting ................................... 167 Sandwich-hologram method ................ 135 Saw curf width .............................94–95 Saw cutting .......................................91 Sawing ..................................... 101, 109 Scale formation. See Oxide scale. Scanning induction hardening, of cylinder, computer simulation of residual stresses/ distortion .............. 290, 293(F), 294(F) Scatter band ................................. 36(F) Scheil equation, to determine volume fraction of solid phase ............................. 375 Screw, distortion after quenching ....161, 164(T) Screw dislocations ..............................58 Sea water, quenched-and-tempered steel and crack initiation .......................... 34(F) Secondary ion mass-spectrometry, hydrogen ion behavior .................................78 Secondary porosity .............................72 Sectioning method ...................... 109, 424 to study rail steel residual stresses .... 431(F) Segregation effect, distribution coefficient representing .........................375–376 Selective laser sintering (SLS) ............. 413 Selective quenching .....................281–282 Self-agitation effect ........................... 271 Self-regulated thermal process ............. 328 Self-tempering ................................. 328 Semiconductor gages ......................... 110 Semicontinuous casting cooling water discharge and stress distributions .................. 379, 382(F) displacement mode ................ 378, 379(F) ingot radii, effect on stress distributions .................. 379, 382(F) ingot radii, isothermal lines for .... 379, 381(F) residual stress formation ........ 377–379(F), 380(F), 381(F), 382(F) speed of casting, and stress distributions .................. 379, 382(F) speed of casting, effect on stress distributions .................. 379, 382(F) speed of casting, isothermal lines for ... 379, 381(F) Semicontinuous direct-chill casting ....... 377 residual stress formation ........ 377–379(F), 380(F), 381(F), 382(F) Semiferritic steels, floccules not observed ..73 Sensors, for carbon potential control in gas carburizing ................................ 447 Service life, effect of quenching method ... 316 Servohydraulic test systems, computerized 28 Shafts shot peening effect on fatigue life ......20(T) warpage, computer simulation ..... 289–290, 291(F) Shape, influence on carburized steel residual stresses ........................... 438, 439(F) Shape-memory alloys ........................... 6 Shear component ......................... 6(F), 7 Shearography .................................. 110



490 / Index

Shear strains ...................................... 5 Shear wave birefringence ................... 114 Sheet bending of ....................142(F), 144–145 destructive residual-stress measurement procedures .......................... 102(T) Shell hardening ................................ 327 Shock laser treatment ..........................12 Shotblasting and austenite transformation in carburized steels .......................... 447–448(F) of carburized steels ............... 451–452(F) to improve fatigue strength ................ 437 Shot impact angle ............................. 348 Shot peening 12, 19(F), 55, 57(F), 61–63(F), 90 applications .... 352–354(F), 355(F), 356(F) area ............................................ 347 and austenite transformation in carburized steels .......................... 448(F), 449 automatic process .....................348–349 callouts ..........................................91 carburized steels .. 198–199, 200(F), 201(F), 451–452(F) C.A.S.E. process .. 350–351, 353(F), 354(F) ceramic shot .................................. 349 characterization and key data .... 346, 347(F) compressive stresses from .............. 90, 91 computer-controlled machine ... 350, 351(F) computer software program .... 350, 352(F), 353(F) coverage control inspection methods .... 349 crack initiation earlier in quenched-andtempered steel ....................... 34(F) and cyclic deformation behavior ........ 33(F) degree monitored by Almen strips ........91, 93(F) and distortion .......................... 152, 157 documentation by computer printout .... 350, 352(F) effectiveness in increasing fatigue life of mechanical parts ................ 19, 20(T) effect on bending fatigue strength in highstrength steels ................... 42–43(F) effect on fatigue life of stainless steel .....16 elementary processes ............. 345–346(F) and fatigue strength ......46(F), 47(F), 48(F), 49, 52 gas turbine components .................... 156 gear wheels .............................347–348 generating compressive macro residual stresses ....................................54 with grinding, S-N curves and residual stresses effect .......................37–39 hardness of material ..................346–347 hardness ranges of shot ..............348–349 historical development ..................... 345 impingement angle vs. intensity ...... 348(F) inspection methods for coverage control .................................. 349 intensity in proximity of edge layer ...... 348 to introduce residual compressive stress ...14 lasershot peening ............354–355, 357(F) mechanical, thermal, or structural origins of residual stress ........................13(T) media .............................348(F), 349(F) modeling capability ..... 350, 352(F), 353(F)

monitoring of process ........... 348–350(F), 351(F), 352(F) nonferritic materials, shot media used ... 349 numbers of cycles to crack initiation affected by ..........................................34 optimization of effects ..... 345, 350, 352(F), 353(F), 354(F) order of addressing parameters ............ 348 patents for machines ........................ 345 postquench for carburized gears ......... 443, 444(F) after powder forging ........................ 411 prior to heat treatment ...... 150, 151, 153(F) process parameters .......................... 350 prolonging life span under fatigue ........ 346 purposes ...................................... 345 residual stress advantages ........ 346, 347(F) residual stress distribution modeling ... 14(F) residual stresses having relatively large absolute value ...............54, 55, 56(F) residual stress influence on cyclic deformation behavior .......31(F), 32(F) rotate bending fatigue strength ........ 450(F) S-N curves and residual stress effect in medium-strength steel .............. 38(F) software path flow diagram ...... 350, 351(F) stress distributions ................ 346, 347(F) work hardening after process .............. 151 work-hardening effect in medium-strength steels .................................. 41(F) workpiece material and process parameters effect on residual compressive stresses ........................ 346, 347(F) Shot size ..................................... 347(F) Shot velocity ............................... 347(F) Shrinkage of brazed joints .................... 394(F), 395 welding residual stresses and temperature distribution ... 391(F), 392, 393(F), 394 Shrinkage factors ............................. 419 Shrinking-type residual stress distribution ..................... 193, 195(F) Siemens ...........................................11 Silicates, role in stress-corrosion cracking ...81 Silicon alloying addition effect on sintering ..... 402 alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ..80 effect on sintering of stainless steels ..... 404 effect on transition temperature .........76(T) first-order residual stress parameters 335(T) and flocculation susceptibility of steels ....73 oxidation in carburizing atmosphere ..... 448 plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Silicon (max), composition requirements for powder forged parts .................. 411(T) Silicon nitride (Si3N4) brazing residual stresses ................ 393(T) coating ........................................ 118 Silicon nitride ceramic, brazing ........394(F), 395(F) Silver (Ag)

brazing residual stresses ................ 393(T) first-order residual stress parameters 335(T) quenching, surface oxidation effect ..... 273, 277(F) Simple beam theory .............. 91–92, 94(F) Simple saw cutting .............................91 Simulations. See Computer simulations. Sines criterion ...................................17 Sine-square-psi technique ............. 112, 125 with CrK␣ radiation, to investigate residual stresses ....................................54 Single-exposure technique (SET) ...... 112(F) Single press and sinter, cost, relative .. 413(F) Single-stage carburizing ........... 189, 190(F) Singularity degree of k* stress ............. 131 Sintering ............... 400, 402–408(F,T), 414 atmospheres ..................402–403, 404(T) furnace condition for steel ............. 403(F) furnaces ................... 402–403(F), 404(T) high-temperature ............................ 403 iron-copper ................................... 403 iron-copper-carbon .......................... 403 iron graphite powder ........................ 403 phases and subphases ................... 404(T) in powder metallurgy processing ..... 397(F) residual stresses .......................416–417 sinter hardening ............................. 408 stainless steels ...............403–404, 405(F) tool steels .....................404–405, 406(T) treatment of P/M parts ........ 405–408(F,T) Size of specimen, effect on carburized steel residual stress ................... 438, 439(F) Sizing ..............................................90 in powder metallurgy processing ..... 397(F) Skin effect ............................ 220, 222(F) Slice depth, appropriate ...................... 108 Slip ............................................... 4, 5 crack initiation present ..................33–34 Slip band formation ........................ 28(F) Slip casting ..................................... 402 Slip deformation, characteristics ........... 5(T) Slip planes ...................................... 336 Slip systems ....................................... 6 Slitting ............... 91, 92(F), 94, 95(F), 96(F) axial ......................................... 96(F) point of ....................................... 131 Slow strain rate testing procedure (SSRT), for tests at constant load rate .............80 SLS. See Selective laser sintering. Slurry process, with roll compaction ...... 410 Small-base tensiometry ...................... 133 Smearing, in milling ....................150–151 Smith-Watson-Topper (SWT) parameter .................... 30–31, 45(F) Smoothing functional method ........ 127, 128 S-N curves .................................... 30(F) gas-carburized 4320 steel .............. 201(F) residual stress influence ............. 36–43(F) shot-peened vs. ground steel condition, cyclic deformation ............. 66, 67(F) S-N diagram .....................................30 slip band formation, microcrack formation and failure of carbon steel ......... 28(F) SNECMA .........................................11 Soft annealing, and distortion .... 153, 154(F), 155(F)


Soft magnetic materials, metal-injection molding .................................... 412 Solidification cylindrical body residual stress distribution ......................... 368(F) cylindrical body uniformly cooled ... 368(F) and distortion potential ..................... 183 kinetics of phase transformation ....375–376 Solidification kinetics ..................362–363 for solidification modeling, benefits listed ........................................ 363(F) Solidification modeling analysis methods available with their benefits ........................ 362, 363(F) architecture of a comprehensive system ......................... 362, 363(F) Solidification process, in steel ingots, mathematical models .................... 364 Solid quenching, deformation tendency ............................... 170(T) Solid solutions ................................. 400 Solid-state linear image sensor technique ................................. 418 Solid-state sintering ..............416, 417, 419 Solidus temperature (Tm) ......................54 of aluminum alloy ...................... 378(T) Solubility curve equation .....................70 Solvent extraction ............................. 412 Sori (complicated deformation) ............ 309 Spark sintering ................................ 408 Spatial distributions of residual stress, problems of determining ................ 128 Species flow analysis, for solidification modeling, benefits listed ............ 363(F) Specific heat capacity ........................ 312 of aluminum alloy ...................... 378(T) due to magnetism .............................. 3 effect on residual stress development in steels ................................... 3(T) of pure iron, as function of temperature ......................... 3–4(F) Speckle-correlation interferometry ...... 110, 133, 136(F) Speckle interferograms ............ 135, 136(F) Speckle interferometer ............. 135(F), 136 Speckle interferometry ...... 110, 133, 136(F) Speckle structures .................. 135, 136(F) Spheroidization ................................ 170 and nitriding ................................. 209 Spheroidize annealing .........................90 Spindles, shot peening effect on fatigue life ........................................20(T) Spline approximation ........................ 129 Sponge iron process .......................... 399 Spot annealing ................................. 111 Spot mode of x-ray beam method ......... 122 Spray deposition ........................412–413 Spray forming ...........................412–413 residual stresses ............................. 419 Spray hardening, and distortion .. 176(T), 177 Spray quenching .............................. 282 after induction hardening .................. 232 Springback effect ...........145, 401, 415, 416 Springback effect of rail steel .............. 430 Spring steel, compressive residual stresses .......................................27 Stabilization, and distortion ................. 178

Stabilized zirconia, P/M processed ........ 420 Stablein method, for destructive residualstress measurement .................. 102(T) Stacking faults ................................. 333 Stage I crack growth ...........................29 Stage II cracks ..................................29 Stainless steels cyclic deformation behavior ............. 32(F) metal-injection molding .................... 412 modulus of elasticity .....................96(T) nitriding ....................................... 211 P/M processing .............................. 399 Poisson’s ratio .............................96(T) quenching, agitation effect .......... 272–273, 277(F) quenching, surface oxidation effect ..... 273, 277(F) residual stresses due to facing ......... 109(F) for ring, induction hardened and carburized quenched .... 303(F), 304(F), 305–307(F) shear modulus .............................96(T) shot peening effect on fatigue life ..........16 sintering ......................403–404, 405(F) spray forming ..........................412–413 tension testing ............................... 373 tight scale formation .............. 255, 258(F) weldment residual stresses ............. 100(T) Stainless steels, series and classes AM-355. See S35500. S30303 (303L), corrosion resistance of P/M parts ................................. 405(F) S303LSC, corrosion resistance of P/M parts ................................. 405(F) S30400 (SUS 304) chemical composition ............... 372(T) crack initiation after mechanical surface treatments ......................... 33(F) cyclic deformation behavior after shot peening, and deep rolling ....... 32(F) fatigue crack propagation rates ....... 35(F) mechanical properties ............... 372(T) melting point .............................. 372 P/M processing .............. 399–400, 420 for ring, induction hardened and carburized quenched ...........303(F), 304(F), 305–307(F) strip continuous casting by twin-roll method ............................... 383 SWT parameter vs. number of cycles to failure .............................. 45(F) titanium nitride-coated, microstylus trace of residual stresses ............. 120(F) S30403 (304L) corrosion resistance of P/M parts ....405(F) P/M processing .....................399–400 S31600 P/M processing .....................399–400 sintering of powder metallurgy parts and corrosion resistance ................ 403 S31603 (316L) corrosion resistance of P/M parts ....405(F) P/M processing .....................399–400 sintering effect on corrosion resistance ............................ 404 S31700, P/M processing .............399–400 S31703 (317L), corrosion resistance of P/M parts ................................. 405(F)


Index / 491 S34700, P/M processing .............399–400 S35500 (AM-355), PVD titanium nitride coating .................................. 121 S41000, P/M processing .............399–400 S41003 (410L), P/M processing .......... 402 S44004 (440C), P/M processing ...399–400 S44600, P/M processing .............399–400 18–8, tight scale formation ...... 255, 258(F) SS-100, corrosion resistance of P/M parts ........................... 405(F) 22CR-5Ni-3Mo-0.015N-0.003C, balance Fe, hot extrusion ........................... 410 Fe-24Cr-8Ni, phase decomposition behavior of P/M powder ........................ 419 STAMP Process ............................... 409 Static loading, plasticity degree decrease ....75 Statistical process control (SPC), of powder forging ..................................... 411 Steady-state continuous casting, finiteelement method formulation ......376–377 Steam treatment, of P/M parts ...... 405, 406, 407 Steel ring, distortion prediction, carburizedquenching ....................... 290, 292(F) Steels cold forming ....................... 147–148(F) crack growth ...................................75 crack initiation .................................75 cryogenic cooling influence on dimensional stability ....... 331, 332, 336–339(F,T), 340(F) cryogenic cooling influence on residual stresses .................................. 336 cyclic behavior ............................ 22(F) cylindrical forgings, neutron diffraction methods ................................. 113 fatigue behavior ...................... 28–31(F) fatigue, Dang Van diagram .............. 18(F) grade, effect on residual stress ........ 438(F) grade, influence on gear stresses ............ 441–442(FT), 443(F) hydrogen states in ........................71–72 martensitic transformation of carburized surface ..................................... 5 nitriding .......................... 214–216(F,T) physical properties affecting residual stress development .......................... 3(T) plate, plastically deformed, neutron diffraction method .................... 113 P/M processed, heat treatment of .................. 417–418(F) production and distortion potential ....... 183 residual stress magnitudes and distributions ....................99(F), 100 rocket case forgings, neutron diffraction methods ................................. 113 shot-peened, fatigue life .................. 18(F) weldments, neutron diffraction methods for ....................................... 113 Steel shafts, warpage prediction, computer simulation .................289–290, 291(F) Steels, series and classes 0.18C-0.25Si-0.8Mn-0.5Cr-0.22Mo-0.62Ni, carburized cylinder tangential stresses during quenching, model ... 202, 203(F) 0.75Cr-3.05Ni (SNC815)



492 / Index

Steels, series and classes (continued) carburized gear axial stresses during quenching ....................... 441(F) gear application, model of case hardening and stresses from ........ 202–203(F), 204(F) for ring, induction hardened and carburized quenched ...........303(F), 304(F), 305–307(F) Cr12Mo, hollow cylinder distortion ...... 163 CrWMn, thermal straightening ............ 170 9CrSi, asymmetrical component distortion ......... 165, 167(F,T), 168(F) 15CrNi6, residual stress of hard metallic material ............................. 346(F) 15CrV6, volume changes during phase transformation ............... 252, 254(F) 17CrNiMo6, shot peening .......... 350, 351, 352(T), 354(F) 18CrNiMo5, residual stress of hard metallic material ............................. 346(F) 18Cr2Ni4W, gear wheel, distortion of ... 166 38CrMoAl, axle of boring lathe, distortion of ........................................ 166 50CrV4 residual stress of soft metallic material .......................... 346(F) stress peening ......................... 348(F) 9Mn2V, thermal straightening ............ 170 16MnCr5, carburized steel CCT diagram ....................... 192, 193(F) 26MnCr4, hardened and case-hardened plate ........................... 191, 192(F) 50MnCr5, carburized steel CCT diagram ....................... 192, 193(F) 90MnV8, volume changes during phase transformation ............... 252, 254(F) 90MoCrV8, fluidized-bed quenching ... 263, 267(F) 100MnCr5, carburized steel CCT diagram ....................... 192, 193(F) 20MoCr4, carburized cylinders and casehardening residual stress ... 195, 198(F) 1015 (CK15, S15CK) aging effect on carburized steel ....... 449, 450(F) case hardening ........................ 438(F) cold-rolled steel sheet stampings, distortion of ............... 168–169(F) distortion of carburized steel ........... 159 hollow cylinder distortion .............. 162 S-N curves and residual stresses effect, after deep rolling ................. 37(F) work-hardening effect on fatigue behavior ...............................40 1018 carbonitriding ......................... 191(F) carbonitriding and tempering .......... 191, 192(F) tempering carburized cases ......... 191(F) 1019, crack propagation rate and stress intensity in welded specimens ....................... 35–36(F) 1020 (JIS S20C) carburized and quenched ...... 443, 444(F) S-N diagram (Wo¨hler curves) for slip band formation, microcrack initiation, and failure .............................. 28(F)

1023 (CK22 German grade) cyclic stress-strain curve ......... 28–29(F) residual stress relaxation ..................59 residual stress relaxation produced by annealing .......................... 55(F) 1040, water quenching ...............253–254 1045 (CK45 German grade) brazed compound with tungsten carbidecobalt ............................. 395(F) brazing residual stresses ............. 393(T) brazing with ceramics compounds .............394(F), 395(F) bushing distortion, eccentric cylinder ..................159, 161(F,T) continuous-cooling-transformation diagram .................... 248–249(F) crack initiation .......................... 34(F) cyclic deformation behavior .......... 32(F) cyclic deformation behavior after deep rolling .............................. 31(F) cyclic deformation behavior in low-cycle fatigue regime ............... 31(F), 32 cyclic stress-strain curve ......... 28–29(F) distortion of cylinder ...... 162(T), 163(F) distortion of stop ring ......... 159, 161(F) eccentric hollow cylinder, distortion of ............... 165, 166(F) effective stress-intensity factor range ............................... 48(F) fatigue notch factor vs. surface residual stress .............. 40(F), 41(F), 42(F) grinding and macro residual stresses and half-width values ............ 55, 57(F) grinding and S-N curves influenced by residual stresses .................. 37(F) grinding-induced work softening ........42 Haigh diagram of bending fatigue strength of high-strength steel ............ 44(F) half-width values vs. annealing time, after shot peening ................. 55, 56(F) hollow cylinder distortion ....... 161, 162, 164(F), 165(F,T) induction hardening ............ 223–224(F) local fatigue strength ..........46(F), 47(F) macro residual stress and half-width values, shot peened and hardened ................. 55–56, 58(F) macro residual stress and half-width values, shot peened and normalized .............. 55–56, 58(F) macro residual stress and half-width values, shot peened and quenched and tempered ............ 55–56, 58(F) macro residual stress ratio vs. annealing time, after shot peening .... 55, 56(F) micro residual stresses, annealing temperature ............................55 milling and macro residual stresses and half-width values ............ 55, 57(F) quenched-and-tempered, effective stressintensity factor range ............ 49(F) quenched-and-tempered, local fatigue strength ............................ 47(F) quenched-and-tempered, shot peened, effective stress-intensity factor range ....................................... 49(F) quenching ....................... 275, 282(F)

relaxation of residual stresses after shot peening ............................ 33(F) residual stress relaxation, delayed .. 55(F), 59 residual stress relaxation produced by annealing .......................... 55(F) shot peened bending specimen and crack initiation ........................... 34(F) shot peening .......................... 347(F) shot peening and macro residual stresses and half-width values ....... 55, 57(F) shot peening effect on bending fatigue strength ....................... 42–43(F) S-N curves after grinding, residual stresses effect .......................38(F), 39(F) S-N curves and residual stresses effect from milling ................. 36–37(F) stop ring, distortion of ......... 180(F), 181 stress-controlled loaded in push-pull tests, cyclic deformation ............... 33(F) stress relief heat treatment effect on fatigue life and fatigue limit ........40 surface residual stress vs. number of cycles .............................. 40(F) SWT parameter vs. number of cycles to failure .............................. 45(F) time-temperature-transformation diagram .......................... 248(F) valve stem distortion ....160–161, 164(F) water quenching ....................253–254 1055 for cylinder scanning induction hardened, computer simulation .... 290, 293(F), 294(F) grinding .......................... 150, 151(F) 1070, Almen strip material ............ 349(F) 1080 austempering .............................. 281 crack initiation ..............................34 crack initiation and macro residual stresses .................................34 elastic chuck, distortion of .... 166, 168(F) hollow cylinder distortion .............. 162 1095, tight scale formation ...... 255, 258(F) 1118, residual stress distribution in carburized-and-hardened steel ... 447(F) 1137, water quenching ...............253–254 1141 quench cracking .......................... 254 water quenching ....................253–254 1144 quench cracking .......................... 254 water quenching ....................253–254 1340, quench cracking ..................... 254 1345, quench cracking ..................... 254 1526 quenching and tempering effects on residual stresses .......... 195, 198(F) tempering after quenching of carburized steels ................................. 446 tempering effect on residual stress ............................. 447(F) 1536 quench cracking .......................... 254 water quenching ....................253–254 1541 quench cracking .......................... 254 water quenching ....................253–254


4024, tempering carburized cases .... 191(F) 4118, grain-boundary anomaly, carburized steel ........................... 448, 449(F) 4130 quenching and tempering effects on residual stresses .......... 195, 198(F) tempering after quenching of carburized steels ................................. 446 tempering effect on residual stress ............................. 447(F) 4140 agitation rate effect on hardening ..... 262, 267(F) alternating bending tests and cyclic deformation .................. 66, 67(F) Bauschinger effect .........................62 brazed compound with cemented carbide tungsten-carbon ........... 395–396(F) cyclic deformation ..................... 29(F) cyclic deformation behavior ..28(F), 29(F) cyclic deformation behavior after shot peening ............................ 31(F) distortion of cylinder ................ 162(T) half-width vs. distance from surface under cyclic deformation ............... 67(F) induction hardening and grinding .................... 244–246(F) loading stress effect on shot peening macro residual stresses ..... 61, 62(F) loading stresses and macro residual stresses ............................. 61(F) macro and micro residual stress relaxation ..............................55 macro residual stresses at surface vs. number of cycles during alternating bending tests ..............64(F), 65(F) macro residual stresses in longitudinal direction vs. distance from surface ........................ 65, 66(F) macro residual stresses, measured and calculated ..................... 57, 60(F) macro residual stresses measured vs. modeled ....................... 62–63(F) peened and normalized, critical loading stresses for initiation of macro residual stress relaxation ..................... 62, 63(T) peened and quenched and tempered, critical loading stresses for initiation of macro residual stress relaxation .................................. 62, 63(T) peened condition, cyclic surface yield strength ....................... 66, 68(T) plastic strain rate vs. mean residual stress, shot peened ........................ 60(F) push-pull fatigue testing .............. 63(F) quench cracking .......................... 254 relaxation of half-widths and mean strains .................... 56–57, 59(F) shot peened and hardened, material properties of Avrami approach ...........................60(T) shot peened and normalized, macro residual stress ................ 61, 62(F) shot peened and normalized, material properties of Avrami approach ...........................60(T)

shot peened and normalized, ratio of halfwidth values .................. 62, 63(T) shot peened and quenched and tempered at 450 ⬚C, macro residual stresses ........................ 61, 62(F) shot peened and quenched and tempered at 650 ⬚C, macro residual stress .......................... 61, 62(F) shot peened and quenched and tempered, material properties of Avrami approach ...........................60(T) shot peened and quenched and tempered, ratio of half-width values .. 62, 63(T) shot-peened condition, quasi-static surface yield strength in compression .....66, 68(T) S-N curves, shot peened vs. ground condition ...................... 66, 67(F) strain aging effects on cyclic deformation and macro residual stresses ... 65–66, 67(F) thermal relaxation of macro residual stresses, quenched, tempered, and shot peened .............. 56–57, 59(F) total deformation and macro residual stress ............................... 61(F) unpeened and normalized, yield strength ratio ........................... 62, 63(T) unpeened and normalized, yield strengths ...................... 62, 63(T) unpeened and quenched and tempered, yield strength ratio .......... 62, 63(T) unpeened and quenched and tempered, yield strengths ............... 62, 63(T) volume diffusion-controlled dislocation creep in residual stress field ........57 warm-peened condition, cyclic surface yield strength ................ 66, 68(T) warm-peened condition, quasi-static surface yield strength in compression .................. 66, 68(T) 4142 induction hardening .................. 240(F) straightening of bars, distortion, and residual stresses ................ 156(T) 4150, quench cracking ..................... 254 4320 reheat quenched and shot-peened carburized gears .......... 443, 445(F) shot peening effect on carburized steel 198–199, 200(F), 201(F) 4337, crack propagation of autofrettaged tube .................................... 35(F) 5100, grinding ............................... 150 5115 crack arrest and bending fatigue limit ................................ 50(F) shot peening effect on S-N curves .. 38(F), 39(F) 5120 (JIS SCr 420) carburized and quenched ...... 443, 444(F) carburized gears, residual stresses at tooth foot surface ................ 440, 441(T) grain-boundary oxidation ........... 448(F) grain-boundary oxidation effect on gear tooth fatigue strength .......... 452(F)


Index / 493 hard shot peening effect on gear fatigue strength .............................. 452 hollow cylinder distortion .............. 163 steel hardenability effect on distortion of carburized steels ................ 453(F) tempering effect on carburized steel 449, 451(F) 5132, pressure rolling .................. 153(F) 5135 crack arrest .............................. 49(F) deep rolling effect on S-N curves and bending fatigue strength ........ 38(F) quench-crack formation ............. 313(F) 5140 C-ring test specimen distortions ... 175(F) hollow cylinder distortion ....... 161–162, 165(F) 52100 (100 Cr6, ShKh15) austenitizing temperature .........171–172 ball screw distortion of ........ 166, 168(F) bearing ring, prediction of deformation during hardening ...... 317–320(F,T) for bearing rings, distortion .. 152, 154(F), 155(F) bearing rings, quenching and residual stress distribution ................... 321 die service life after intense quenching 327(F) distortion of axle components ......... 160, 164(F) hollow cylinder distortion ....... 161, 162, 164(F) inner bearing ring 7515/02, hardened and water cooled ........... 315–317(F,T) quenching in a hardening press of bearing rings .............................. 185(F) residual stress relaxation produced by annealing .......................... 55(F) tempering effect ................ 251, 254(F) thermal straightening .................... 170 6150, crack initiation .........................34 8610, carburized-and-hardened, residual stresses .............................. 439(F) 8617 carbon potential effect in carburized and quenched gears ........... 444, 445(F) steel grade and case depth in carburized gears ........................ 441, 442(F) tempering effect on gas-carburized steel 449, 450(F) 8620 (JIS-SNC 21) aging effect on carburized steel ....... 449, 450(F) carbonitriding ......................... 191(F) carburizing and quenching variation effects ............................ 443(F) case-depth influence on carburized steels 445(F) grain-boundary anomaly, carburized steel 448, 449(F) repeated stressing of carburized steel ..................... 450, 451(F), 452(F) residual stress distribution in carburizedand-hardened steels ............ 447(F) retained austenite in carburized-andhardened steels ................. 447(F)



494 / Index

Steels, series and classes (continued) steel grade and case depth in carburized gears ........................ 441, 442(F) steel grade effect on carburized gears ........................ 441, 442(F) 8640, steel grade effect on carburized gears ........................... 441, 442(F) 8719, carburized and hardened ........ 190(F) 8822, grain-boundary anomaly, carburized steel ........................... 448, 449(F) 10100, hollow cylinder distortion ........ 162 10120, hollow cylinder distortion ........ 162 AZ 31, residual stress of soft metallic material ............................. 346(F) 43BV14, carburized and quenched with various heats ................. 443, 444(F) C15, case hardening .................... 438(F) C22, residual stress vs. distance from surface with different case-hardening depths ......................... 194, 197(F) C80 (German grade), cyclic stress-strain curve ............................. 28–29(F) 15CD4, induction hardening of carburized cylinder model ........ 203–204, 205(F), 206(F) CK01 (German grade), cyclic stress-strain curve ............................. 28–29(F) CK15. See 1015. CK22. See 1023. CK45. See 1045. 100Cr6. See 52100. EN9, nitriding ........................... 212(F) EN19, nitriding .............................. 216 EN-S355, crack propagation and welding residual stresses ..................... 35(F) FC0202, carburization of P/M parts .... 406, 407(F) JIS S20C. See 1019. JIS S38C, quenching and distortion ..... 284, 287(F) JIS S45C coated cylinders, quenching of ........................... 273, 278(F) cylinder quenched, computer simulation ............................... 289, 291(F) disk quenched, computer simulation ................ 288–289(F), 290(F), 291(F) for gear wheel, induction hardened, computer simulation .............. 296, 306(F), 307–309(F) induction hardening .................. 239(F) quenching ............. 275, 281(F), 282(F) quenching, agitation effect ... 276, 283(F), 284(F), 285(F,T) quenching, clay coating, effect on quench cracking .................... 278, 286(T) quenching, surface oxidation and quench cracking ................ 278(F), 286(T) quenching, surface texture and roughness and quench cracking tendency .. 278, 286(T) for ring, induction hardened and carburized quenched ...........303(F), 304(F), 305–307(F) selective quenching ......278(F), 281–282 steel shafts, warpage prediction by computer simulation ........ 289–290, 291(F)

surface finish effect on cooling curves ............................... 273, 279(F) JIS SCM420 case depth influence on endurance limit in carburized steel ................. 446(F) core hardness effect on fatigue strength (endurance limit) ......... 442, 443(F) grain-boundary oxidation ........... 448(F) hardenability effect on core hardness and case depth .................441–442(T) quenching oil influenced on carburized steel residual stresses .............. 445 repeated stressing effect in carburized steel ........................ 450, 451(F) JIS SCM 420H, distortion of gears ...... 454, 455(F) JIS SCM435 quenching ....................... 277, 285(T) quenching, clay coating effect on quench cracking .................... 278, 286(T) JIS SCM440 distortion .............................. 256(F) for ring, induction hardened and carburized quenched ...........303(F), 304(F), 305–307(F) JIS SCr 420. See 5120. JIS SK4 quenching ....................... 277, 285(T) quenching, clay coating, effect on quench cracking .................... 278, 286(T) quenching, surface oxidation and quench cracking .................... 278, 286(T) quenching, surface texture and roughness and quench cracking ..... 278, 286(T) JIS SNC 21. See 8620. JIS SNCM439, quenching and distortion 284, 287(F) K13NiCr12, case hardening ........... 438(F) MA956 mechanical alloying ...................... 414 microstructure and residual stresses .........................419–420 90MoCrV8, fluidized-bed quenching ... 263, 267(F) 60NCD11, dilatometer curves ...... 249–250, 251(F) S35, induction hardening .................. 229 S15CK. See 1015. S690QL1, crack propagation ............ 35(F) SF-Cu F20, residual stress of soft metallic material ............................. 346(F) ShKh15. See 52100. SS44, distortion after straightening ... 156(F) STE460 (P460N), welded plate, shot peening effect on residual stress .... 354, 356(F) Steel 14KhGSN2MA, carburized bushing having high-rate quenching ................. 320–321(F,T) Steel 35Kh2NgSM, austenite grain size effect .......................... 325, 326(F) Steel 40, austenite grain size effect ...... 325, 326(F) Steel 40Kh2NgSM, austenite grain size effect .......................... 325, 326(F) Steel ShKh15. See 52100. Steering sector shaft, distortion .. 454–455(F) Stefan-Boltzmann coefficient ............... 375

Step-by-step time-integration method .... 288 Step-quenching tanks ........................ 172 Stereolithography (SLA) .................... 413 Stick-slip effect ................................ 429 of supporting bar ............................ 429 Stiffness ......................................... 288 Stiffness equation ............................. 377 Stoney’s formula ..................119, 152, 157 Stop ring, distortion of ............. 180(F), 181 Straightening ...60, 90, 150, 151, 154(F), 220 of bars ......................................... 150 and distortion ...................... 156(T), 157 mechanical, thermal, or structural origins of residual stress ........................13(T) parallel-roll ......................... 156–157(F) Strain chemical measurement methods .......... 110 due to differential contraction ............. 362 due to volume change ...................... 217 measurement methods ................109–110 Strain aging effects, cyclic deformation ....65, 66, 67(F) Strain gages ......................................91 to measure residual stress magnitude .... 238 Strain gage technique .................. 100, 438 Strain gaging/sectioning technique ... 103(F) Strain hardening ......................19(F), 109 effect on fatigue strength ................ 19(F) and P/M processing ........................ 416 in roll compaction ........................... 415 Strain-hardening parameter ......... 299, 300 Strain peening ................................. 151 Strain rates ...............................285–287 computation of ............................... 202 Strain rate tensor ............................. 202 Strain relaxation, measurement of ...........91 Strength-differential effect ....................61 Stress amplitude, and crack initiation .......34 Stress-concentration factor ................. 420 and bending fatigue strength ....... 36–37(F) Stress corrosion .......................... 16, 100 Stress-corrosion cracking (SCC) .....72, 110, 150, 152 active-part corrosion (APC) .................79 alkaline and acid solutions for failure ......79 alloying elements contribution ..............80 alloying elements effect on resistance to ..80 crack growth mechanism .....................79 crack initiation .................................79 crystal structure role .....................80–81 estimation of sensitivity to, criteria and methods for .........................79–80 high-strength steels .................. 79–82(F) hydrogen-induced corrosion cracking (HISCC) ..................................79 insensitivity of high-pure metals ............79 of low-alloy steels ................... 79–82(F) resistance by shot peening in chemical industry applications ........... 353–354, 356(F,T) selectivity of material relative to a corrosion medium ...................................79 steels for main gas-pipe lines ...... 81–82(F) test methods .................................. 110 thermal processing role .............. 80–81(F) Stress-corrosion hydrogen-induced cracking ................................... 110


Stress-corrosion testing, preparation of test specimens for weldments ............... 110 Stress-free interplanar spacing, for a coating ..................................... 122 Stress gradient ..18, 36(F), 37(F), 40, 51, 101, 111 at notch root ...................................36 Stress in a simple beam .......................92 Stress in material, symbol and units of ...................................93(T) Stress intensity coefficient, threshold value ............................... 73, 74, 75 Stress-intensity factor .....................29–30 for normal breakoff ......................... 128 for transverse shear ......................... 128 Stress-intensity factor range (Mode I) ................................29–30 Stress loading, and austenite transformation in carburized steels ....................447–448 Stress mapping ................................ 100 Stress measurement temperature ......... 118 Stress peening ....................... 345, 348(F) Stress profile, by Peenstress software .. 353(F) Stress raisers ............................. 401, 405 Stress-reconstruction procedure (series method) ................................... 108 Stress relaxation ......................... 17, 150 for changing or disappearing residual stresses ....................................28 induced by phase transformations in induction-hardened and carburized steel cylinder ....................... 204, 206(F) residual stress, prediction of ........ 22–23(F) resistance to ...................... 58–59, 60(F) and tempering ...................... 284, 287(F) uneven, and distortion resulting from .... 156 welding of maraging steel .......... 60–61(F) Stress relieving ..95, 110–111, 120, 224, 251, 254(F) for avoiding changes in dimensional stability ...................................16 castings ....................................... 168 dimensional stability influenced by ...... 339 and distortion ................................ 166 to eliminate residual stresses .............. 144 by tempering ....................... 284, 287(F) Stress risers .....254, 255, 256, 257, 260, 264, 278 Stress Scan 500 equipment ................. 156 Stress/strain analysis ..................303–304 Stress-strain constitutive relation .......................... 298–302(F) Stress-strain curves of castings ................................ 373(F) under strain rates for castings ......... 374(F) Stress-strain-induced transformation .... 296 Stress-strain state, computation of ................................. 313–315(F) Stress tensors .................................. 121 Stress-transient method .............. 57, 60(F) Stretch forming, and distortion ......... 169(F) Stretching, for inducing residual stress relaxation ....................................54 Strip, rolling of ............................ 147(F) Strip continuous casting by twin-roll method, residual stress formation ........... 383–385, 386(F), 387(F), 388(F), 389(F)

Structural dilatation ...................286–288 due to phase transformations, strain rates for ....................................... 312 due to transformation plasticity, strain rate for ....................................... 312 Structure stress, as cause of distortion ............159–161(F,T), 162(F) Subcritical annealing ......................... 254 Subgrains ....................................... 333 Subsonic gas atomization ............... 400(F) Subzero cooling, and residual stresses ..... 195 Sulfides as fracture origin sites ........................75 role in stress-corrosion cracking ............81 Sulfide stress cracking .........................83 Sulfur alloying effect on hydrogen embrittlement of steel .......................................83 alloying element effect on crack growth ..80 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Sulfur (max), composition requirements for powder forged parts .................. 411(T) Sunk tubes ................. 147(F), 148–149(T) Superalloys .......................................73 Supercarburized high-speed steels austenitizing .............................. 337(T) cryogenic cooling ....................... 337(T) quenching ................................ 337(T) tempering ................................. 337(T) Vickers hardness ........................ 337(T) Superhardening ............................... 328 Superplasticity, of bearing ring ............. 318 Superposed model of plasticity and creep ....................................... 302 Superposition model ............... 373, 374(F) Superstrengthening, by intensive quenching 326 Surface crack formation .................... 215 Surface integrity .............................. 221 Surface nanocrystallization ...................25 Surface oxidation ......... 273, 277(F), 278(F) Surface quenching with a phase change, mechanical, thermal, or structural origins of residual stress .......................13(T) Surface texture and quench cracking ........277–278, 286(T) and quenching ..................... 273, 279(F) Surface values ................................. 108 Surface wetting ................................ 258 Surface work hardening ..................... 198 Swell ............................................. 363 SYS-WELD (FRAMATOME Company) (computer program) ............. 202, 303

T Tamahagane (Japanese steel) ............... 309 Tangential internal residual stresses, from induction hardening ..235(F), 236, 238(F), 239(F)


Index / 495 Tangential stress .............. 144(F), 145, 146 semicontinuous casting distribution ..... 378, 380(F) Tank chain, shot peening effect on fatigue life ........................................20(T) Tatara system .................................. 309 Taylor’s expansion, for viscoplastic strain increment of element at Kth time step ......................................... 376 Taylor/von Mises criterion .................... 6 Temperature carburizing heat-transfer model .....199–200 cooling process changes .......... 313–314(F) effect on chemical and mechanical driving forces ................................... 6(F) effect on distortion in welds .............. 7(T) effect on rail steel residual stresses ....... 434 effect on specific heat capacity of pure iron .................................. 3–4(F) induction hardening of carburized steel cylinder ....................... 203, 205(F) interaction with deformation and microstructure ........................ 3(F) quenchant ....... 268(F), 269(F), 270–271(F) and residual stress level in nitriding ...... 214 rough-condition .............................. 325 semicontinuous casting profile .. 378, 379(F) Temperature-dependent yield function .. 286 Temperature factor, for third-order residual stresses ..................................... 235 Temperature field, nonsmoothness or unevenness ................ 322, 323, 324(T) Tempered martensite .................. 195, 336 after sinter hardening of P/M parts ...... 408 Temper embrittlement .........................76 Tempering ................282–284, 287(F), 336 carburized-and-hardened steels ..445–446(T) and carburizing procedures ...... 190, 191(F) dimensional variation and retained austenite content ........................ 251, 254(F) and distortion .. 154, 177–178(F), 283–284, 287(F) effect on crack toughness ........... 80–81(F) effect on residual stress distribution ..... 195, 198(F) effect on residual stress of carburized steels 449, 450(F), 451(F) for inducing residual stress relaxation .....54 of low-alloy steels ...................... 337(T) of marquenched steels ............ 280, 287(F) microstructural variation effect on volume changes ....................... 251, 253(F) niobium alloying effect .................... 325 before nitriding .............................. 209 P/M parts ........................... 407, 408(F) P/M steel parts ........................417–418 and retained austenite content in carburized steels ................................ 447(F) stages .......................... 251, 253(F), 283 stress relief ......................... 284, 287(F) supercarburized high-speed steels .... 337(T) transformation process prediction ........ 202 volume changes .............283–284, 287(F) Tensile applied stress ....................... 6(F) Tensile residual stresses ..... 193, 196(F), 211 and brazing ......................394(F), 395(F) from welding .......... 392(F), 393(F), 394(F) Tensile strength .................................16



496 / Index

Tension testing ...................... 251, 254(F) Termite welding, of rail steel ........... 434(F) Test methods, stress-corrosion cracking ... 110 Testpieces, carburized, variation of residual stresses ................. 439, 440(F), 441(T) Tetragonality degree ......................... 338 Tetragonal martensite ....................... 338 tempering of ................................. 224 Theory of regular conditions ............... 322 Thermal conductivity ..................... 3, 312 effect on residual stress development in steels ................................... 3(T) nonlinear equations ......................... 315 nonstationary, equation for ................ 312 Thermal convection and radiation, in carburizing ................................ 200 Thermal cycles, as description of surface heat treatment process ......................... 223 Thermal cycling, for inducing residual stress relaxation ....................................54 Thermal diffusivity coefficient ............. 322 Thermal expansion coefficient of aluminum alloy ...................... 378(T) differences affecting brazing residual stresses .....................394(F), 395(F) Thermal expansion mismatch ................12 Thermal expansivity ............................ 3 effect on residual stress development in steels ................................... 3(T) Thermal gradients, nonuniform ............ 332 Thermal growth ............................... 118 Thermal inversion in workpiece quenching ............................. 223(F) Thermal load .................................. 288 Thermally activated processes, for inducing residual stress relaxation ...... 54–60(F,T) Thermal oscillations, influence eliminated in microstrains ............................... 335 Thermal plasticity ............................ 313 Thermal radiation coefficient, for centrifugal casting pipe models ...................... 382 Thermal shocking, ............................ 156 Thermal shrinking stresses ................. 191 Thermal spraying ....................... 118, 120 mechanical, thermal, or structural origins of residual stress ........................13(T) Thermal straightening ....................... 170 Thermal strain .......................... 286, 298 Thermal strain rate .................... 202, 312 Thermal stress of carburized bushing due to high-rate quenching ................. 320–321(F,T) castings, segregation in ..................... 167 as cause of distortion ..........159–161(F,T), 162(F,T), 163(F), 164(F), 165 cooling with transformation ........ 250–251, 252(F), 253(F,T) nonuniform ................................... 260 and quench severity ......................... 257 Thermal-stress analysis, to evaluate residual stresses in P/M products ................ 420 Thermal surface treatment .......... 19, 20(F) Thermochemical surface treatment ........19, 20(F) Thermocouples ................................ 223 for measuring temperature on gear-wheel teeth, induction hardening ....... 230(F)

and temperature monitoring to control distortion ............................... 184 and time variation of temperature of gearwheel teeth in induction hardening ........................... 230(F) Thermodynamics ................................ 3 Thermoelasticity effect, on rail steel ....... 426 Thermokinetic diagram of the supercooled austenite transformations ............. 313 Thermomechanical analysis, for solidification modeling, benefits listed ............ 363(F) Thermomechanical state, during and after surface induction heating ............... 226 Thermomechanical theory .................. 372 Thermoplasticity, of carburized bushing with two-step quenching ......... 320–321(F,T) Theta-method .................................. 304 Thickness of beam/plate/tube wall, symbol and units of .............................93(T) Thin-slab casting process, residual stress formation ....... 383–385, 386(F), 387(F), 388(F), 389(F) Three-point bending ......................... 155 Three-time rule ................................ 109 Threshold (critical) stress-intensity factor (KISCC), ......................................80 Threshold effect .................................30 Threshold stress valve .........................80 Through-hardened steels, contact fatigue ...................................... 198 Through-hardening .......................... 316 P/M parts ..................................... 406 Through-thickness temperature, from induction hardening ............ 223–224(F) “Tight” scale formation ........... 255, 258(F) Tikhonov’s method ........................... 127 Time of carburizing and fatigue strength ....... 446 interaction with deformation and microstructure ........................ 3(F) and residual stress level in nitriding .. 214(F) Time discretization, in unsteady-state casting analysis .................................... 376 Time function of temperature change ........................... 321–322(F) Time of diffusion, and hydrogen critical concentration ................................75 Time quenching ......................... 280, 281 Time-temperature-transformation (TTT) diagrams ........... 191, 248(F), 249, 250, 251(F), 288, 297 computation of, during hardening processes ............................... 200 Time till a crack initiation ....................80 Tin alloying effect on hydrogen embrittlement of steel .................................. 83, 84 alloying element effect on crack growth ..80 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack 76(T) Tin-bismuth alloy, strip continuous casting by twin-roll method .......................... 383 Titanium

alloying effect on susceptibility to austenite grain growth ..................... 325, 328 alloying element effect on crack growth ..80 alloying influence on delayed fracture of steel ................................... 78(F) effect on transition temperature .........76(T) first-order residual stress parameters 335(T) modulus of elasticity .....................96(T) plasticity loss after hydrogenation ......76(T) Poisson’s ratio .............................96(T) resistance to hydrogen embrittlement ..76(T) shear modulus .............................96(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Titanium alloys, macro and micro residual stress relaxation ............................55 Titanium carbide coating ................... 118 Titanium hydrides, formation at grain boundaries ...................................78 Titanium nitride ....118, 119, 120(F), 122(F), 209 Titanium nitride coatings ............... 121(F) Tool gap hardening .......................... 241 Tool steels alloying addition effect on sintering ..... 402 contact wear resistance improved ......... 420 cryogenic cooling ............. 340(F), 341(T) heat treatments applied for dimensional stabilization .............. 338(F), 338(T) martensitic transformation ....... 332, 333(F) metal-injection molding .................... 412 P/M processed, applications ........404–405 P/M processed, heat treatment of ....... 408, 417–418(F) P/M processing .............................. 400 sintering ......................404–405, 406(T) spray forming ..........................412–413 Tool steels, series and classes ASP30 (P/M tool steel) out-of-roundness measurements ... 418(F) D2, spray forming ........................... 413 H13 direct-metal deposition .................. 419 rapid prototyping ......................... 413 spray forming ............................. 413 M2, out-of-roundness measurements ...................... 418(F) M20, high-speed steel for R6M5 punches ....................... 326(F), 327 T12, distortion ............................... 159 T15 microstructures of convertional vs. P/M processed ........................ 418(F) P/M processing .............................. 402 spray forming ................................ 413 Tool steel UHB Chipper ................. 156(F) Torque rods, shot peening effect on fatigue life ........................................20(T) Total case depth (TCD) ..................... 437 Total strain increment ....................... 217 Total strain rate .............285, 300, 312, 373 Total strain Wo¨hler curve ................ 30(F) Tracked and road vehicles, shot peening for improving vibratory fatigue properties .................................. 345 Traction-compression loading ..... 22, 23(F), 24(F)


Transformation eigenstrain, of rail steel ........................................ 427 Transformation induced plasticity (TRIP) ...................... 90(F), 427–428 Transformation plasticity ............3–6, 201, 249–250, 251(F), 286–288, 302(F), 304–307(F) and anisotropic strain ...................... 7(F) definition ..................................... 288 distortion of steel ring, computer simulation .................... 290, 292(F) of gears ............................. 456–457(F) Transformation plasticity coefficient for martensitic or pearlitic transformation .......................... 288 Transformation plasticity effect ........... 296 Transformation plasticity strain rate .... 202, 288 Transformation plastic strain .... 301(F), 302 Transformations deformation systems associated with ... 5(T) diffusionless, in metallo-thermo-mechanics ....... 297(F) diffusion-type, in metallo-thermo-mechanics ....... 297(F) displacive ..............................4–5(F), 9 characteristics ............................... 5(T) mechanical driving force ...................... 6 stress components interacting with volume change ..................................... 6 intervariant ...................................... 6 reconstructive ............................ 4–5(F) characteristics ............................... 5(T) stress components interacting with volume change ..................................... 6 shape change due to ....................... 5(T) stress-assisted, limits to ................... 6(F) stress-(or strain–) induced ................. 296 unconstrained, and shape changes ....... 5(F) under influence of a mild stress .............. 8 Transformation-start temperature ....... 6(F) Transformation stress ..........159–160, 161, 163(F,T), 164(F), 191 of carburized parts .......................... 178 castings, segregation in ..................... 167 as cause of distortion ....................... 165 cooling with transformation ........ 250–251, 252(F), 253(F,T) Transformation superplastic strain ....... 302 Transformation temperature range ...... 192 Transformation volume strain ................ 5 Transgranular fatigue crack initiation ... 197 Transgranular spell mechanism .............79 Trapezium method ........................... 129 Trapezoid method ............................ 304 Traps ......................................... 71, 72 for hydrogen ......................... 75, 76, 82 TRAST (software program) ................ 202 Trepanning ...............................110–111 Tresca criteria ...................................17 Tresca yield function ................... 299, 302 Treuting and Read method .............. 89, 96 for destructive residual-stress measurement ....................... 102(T) Triaxial compression, by simultaneous isostatic and uniaxial compression .... 402 Triaxial residual stress state, and crack propagation .............................. 35(F)

Triaxial stress analysis ...................... 122 Triaxial stress state without shear stress, of coatings ..............................120–121 Triaxial stress state with shear stress, of coatings .................................... 121 TRIP. See Transformation induced plasticity. TRIP (transformation) induced plasticity effect ..................................... 90(F) Troostite .................................. 438, 448 Truck leaf springs advantages ................................ 327(T) former steel and process ............... 327(T) new steel and process .................. 327(T) Tubes autofrettaged, and crack propagation ... 35(F) destructive residual-stress measurement procedures .......................... 102(T) drawing ............. 141, 142(F), 145–146(F) sunk, deep drawing ..... 147(F), 148–149(T) Tungsten effect on sintering of stainless steels ..... 404 and flocculation susceptibility of steels ....73 modulus of elasticity .....................96(T) Poisson’s ratio .............................96(T) shear modulus .............................96(T) Tungsten carbide-carbon cemented carbide in brazed joint with steel ......... 395–396(F) brazed compound with steel residual stresses .............................. 395(F) Tungsten carbide-cobalt coating ...........................123–124(T) thermal spraying ....................... 118, 123 Tungsten carbides first-order residual stress parameters 335(T) in high-speed steels after cryogenic cooling ..................340–341(F), 343 Tungsten inert gas welding (TIG) ..... 392(F) of maraging steel ..................... 60–61(F) Turning ............... 150–151, 152(F), 153(F) and distortion ................ 152, 155(F), 156 and distortion potential ..................... 183 mechanical, thermal, or structural origins of residual stress ........................13(T) residual stresses in alloy steels ........ 109(F) 12% chromium steel, thermally activated relaxation after shot peening .... 56, 59(F) Twin boundaries, and crack initiation ..33–34 Twinning ........................................... 5 Twin-roll method of strip continuous casting, residual stress formation .... 383– 385, 386(F), 387(F), 388(F), 389(F) Two-angle technique (DET) ................ 112 Two-dimensional finite difference method .................................... 268 Two-dimensional inverse method ......... 268 Two-stage boost/diffuse method of vacuum carburizing model .........203(F), 204(F) Two-stage nitriding ........................... 170 Two-step quenching ......... 176, 312, 319(F), 320–321(F,T), 328 Twyman-Green interferometry ..............12

U U-bend stress corrosion test, specimen making and using ........................ 110


Index / 497 UIC54E rail steel profile .........424, 428,429 Ultimate strength, of bearing ring being hardened ............................... 318(F) Ultrahigh temperature oil quenching, of ball bearing race ..................... 454, 455(F) Ultramicroscopic stresses (third-order residual stresses) ..331, 332(F), 335–336 Ultrasonic gas atomization, ....... 400(F), 414 Ultrasonic inspection, to evaluate residual stresses in P/M products ................ 413 Ultrasonic instrumentation ................. 100 Ultrasonic methods ........................... 109 Ultrasonic shot peening ........................25 Ultrasonic velocity ............... 112, 113–114 Ultrasound, ..........................13, 14(F), 25 Unalloyed steels, nitriding ................... 209 Undeformed material, interplanar spacings and residual stresses ..................... 333 Undercooling, of austenite .............331–332 Uniaxial compression, as mechanical driving force coefficient ......................... 6(T) Uniaxial deformation .............. 60–63(F,T) for inducing residual stress relaxation ....54, 60–63(F,T) Uniaxial loading, resistance to residual stress relaxation ........................... 61–62(F) Uniaxial stress .................................... 6 Uniaxial tension, as mechanical driving force coefficient ................................ 6(T) Unidirectional compaction .............. 401(F) Unified constitutive theory .................. 372 Uniform casting, .............................. 377 Universal joint shaft, shot peening effect on fatigue life ...............................20(T) Unsteady-state centrifugal casting finite-element method formulation ....... 376 and residual stress formation ... 379–383(F), 384(F), 385(F), 386(F) Upcut milling ................................ 39(F) producing residual stresses .............. 32(F) residual stresses generated ............... 36(F) Upper bainite .................. 250(T), 257, 448 Upsetting forging ............................. 410

V Vacuum atmosphere ......................... 403 Vacuum carburizing ......................... 189 carbon potential control .................... 444 furnace ........................................ 453 rotate bending fatigue strength ........ 450(F) Vacuum extraction ........................... 412 Vacuum quenching ........................... 172 Valve, shot peening effect on fatigue life ........................................20(T) Vanadium alloying element effect on crack growth ............................... 80, 81 effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T)



498 / Index

Vanadium carbides (VC) in high-speed steels after cryogenic cooling ..................340–341(F), 343 resistant to dissolution ................ 325, 328 temperature for full dissolution in 30 ⳯ 2 steel ..................................... 325 Vanadium nitrides (VN) effect on transition temperature .........76(T) plasticity loss after hydrogenation ......76(T) resistance to hydrogen embrittlement ..76(T) resistant to dissolution ................ 325, 328 temperature for full dissolution in 30 ⳯ 2 steel ..................................... 325 time up to fracture ........................76(T) work of propagation of a ductile crack ..................................76(T) Vapor blanket cooling stage ...258–259, 268, 269, 272(F), 273(F), 274, 439 Vapor blanket cooling stage of quenching oil ................................. 455–456(F) Vaporizing, effect on carburized steels .... 438 Variational principle ................... 127, 376 Variation of residual stresses in test pieces and gears ....................... 439, 440(F) Versailles project on Advanced Materials and Standards (VAMAS) ............. 413 Vertical semicontinuous direct-chill casting process ......377–379(F), 380(F), 381(F), 382(F) Vestergards asymptotic relationships .... 130 Vibration, for inducing residual stress relaxation ....................................54 Vibration compaction, ....................... 402 Vickers hardness decreasing as relative shrinkage increases during tempering .................. 338(F) of low-alloy steels ...................... 337(T) supercarburized high-speed steels .... 337(T) Video .....to measure surface wetting ..... 269 Virtual work principle ....................... 377 Viscoplastic flow laws ........................ 365 Viscoplasticity ................................. 302 unified theories of .....................373–374 Viscoplastic strain rate ..........202, 366, 374 Viscoplastic stress analysis .............. 366(F) Viscosity of aluminum alloy ...................... 378(T) of quenching media, and carburizing .... 445 Viscous cup fracture ...........................76 Viscous fluids .................................. 372 Voids, in castings .............................. 370 Volterra equation of the first type 126, 127, 128 Volterra integral equation .....126(F), 136(F) Volterra integral equation method ........ 133 design diagrams ......................... 126(F) Volvo ..............................................11

W Warm compaction .................. 399, 413(F) residual stresses ............................. 419 Warm compaction and sinter, cost, relative ................................. 413(F)

Warm-peening .................. 65(F), 66, 67(F) and cyclic deformation ...........64(F), 65(F) fatigue ...........................................27 Warpage, of steel shafts, computer simulation 289–290, 291(F) Wartisla ...........................................11 Water content effect in salt-bath quenching .... 262–263, 266(F), 267(F) as quenchant ..........262–264, 269–280(F), 282(F), 283(F), 284(F), 285(T), 286(T) Water atomization ............ 400(F), 412, 414 Water-based polymer quenching tanks .. 172 Water jet quenching of steels .............. 327 Water quenching ... 264, 269–280(F), 282(F), 283(F), 284(F), 285(F), 286(T) agitation effects .......................... 283(F) computer simulation ... 288–289(F), 290(F), 291(F) under pressure ......................... 315, 316 Wear .................................. 16, 150, 189 Wear-resistant high-speed steels containing 3–4% V composition .............................. 406(T) designation ............................... 406(T) hardness .................................. 406(T) Weq ........................................ 406(T) Welded assembly, crack propagation speed affected by residual stresses .......... 15(F) Welded joints fatigue strength and residual stress ..... 15(F) stress relief of .............................. 15(F) Welding ...........................................99 crack propagation and residual stresses ........................35(F), 36(F) and distortion ...................... 391–394(F) effect on rail steel residual stresses ... 434(F) longitudinal and transverse residual stresses on aluminum plate .......392(F), 394(F) macro residual stresses set up ...... 60–61(F) mechanical, thermal, or structural origins of residual stress ........................13(T) multipass ..................................... 392 phase transformations and residual stresses .............. 392–393(F), 394(F) P/M parts ..................................... 405 quenching processes and residual stresses ............................ 392, 394 repair .......................................... 392 shrinkage and impeded shrinkage due to temperature distribution ... 391(F), 392, 393(F), 394(F) tensile or compressive yield strength as function of temperature .... 393–394(F) tungsten inert gas ....................... 392(F) Weldments destructive residual-stress measurement procedures .......................... 102(T) distortion dependent on temperature of transformation ........................ 7(T) hydrogen-induced stress cracking ........ 110 pipe ............................................ 102 residual stresses measurements ...99, 100(T) Rosenthal and Norton’s method, variation of ............................. 105 shot peening effect on fatigue life ......20(T) shot peening effect on residual stress ... 354, 356(F)

steel, neutron diffraction weldments of .. 113 stress corrosion test specimen preparation ............................. 110 Wet bag tooling ............................... 402 Wetting, period of (tw), ............. 258, 261(F) Wetting front .................. 258, 260(F), 269 Wetting kinematics ........................... 259 measurement methods .. 269, 272(F), 273(F) Wetting process ........ 268, 269, 270, 272(F), 273(F) and quenchant selection .................... 275 Wetting time ............................. 259, 272 Wetting velocity .. .. 269, 270, 271–272, 274 Wicking ......................................... 412 Widmansta¨tten ferrite. See Ferrite, Widmansta¨tten. William’s functions ........................... 130 Wire drawing ..................141, 145–146(F) in powder metallurgy processing ..... 397(F) Wo¨hler diagram (S-N diagram) ..............30 Wo¨hler stress curves .................. 17, 30(F) for induction hardened, carburized, or quenched-and-tempered steels .. 244(F) for slip band formation, microcrack initiation, and failure ............... 28(F) Work hardening ................................55 and cyclic deformation behavior ........ 33(F) and deformation systems ...................... 6 effect on fatigue life in low-strength steel .......................................40 and fatigue strength ................. 27, 28, 52 parameter ............................... 299, 300 P/M parts ........................... 407, 408(F) Workpiece size, influence on residual stresses ........................... 195, 198(F) Work-softening processes, and fatigue .....27, 28(F) www.residualstress.com ..................... 100

X X-ray diffraction (XRD) ......99–101(F), 104, 124, 144, 146, 339, 438–439(F) brazed metal-ceramic compounds .... 395(F) for calculating longitudinal residual stresses in Japanese sword ........309(F), 310(F) combined with electropolishing ........... 109 for determining residual stress variations after induction hardening ............ 233 for evaluating brazed joint of steel and cemented carbide ...................... 395 for evaluating residual stresses after grinding ............................. 151(F) for evaluating residual stresses after straightening ........................... 156 for evaluating residual stresses in P/M products .....................413, 415, 418 of high-alloy tool steels .................... 342 for measuring actual crystal dimension ........................111–113 for measuring axial residual stresses ........................ 236(T), 238 for measuring compressive stresses in rail steel ..................................... 431


for measuring computerized quenching of cylinder ....................... 302(F), 305 for measuring initial residual stress distribution ........................... 22(F) for measuring plate weldment strain ..... 106 for measuring residual stress distribution after quenching and tempering ..... 284, 287(F) for measuring residual stress distribution in scanning induction hardened cylinder ....................... 290, 294(F) for measuring residual stresses ... 11–13, 18, 54, 211, 212(F), 217, 223 for measuring residual stresses in coatings ..............118, 120–122(F) for measuring residual stresses in quenched steel disk ..................... 289, 290(F) for measuring retained austenite distribution in carburized-and-hardened steels ................................ 447(F) X-ray diffraction profiles ..............351–352 X-ray diffractometer, miniature ........112(F), 113(F) X-ray diffractometry ......................... 333 X-ray electron spectroscopy, grain boundary embrittlement ...............................78

X-ray interference lines to determine micro residual stresses .......55 and micro residual stresses and cyclic deformation ..............................67 X-ray profile analysis, micro residual stresses relaxation behavior .........................63


Index / 499 of first-order residual stresses of metallic materials ............................ 335(T) symbol and units of .......................93(T) Yttrium oxide/partially stabilized zirconia coating ..................................... 118 Yuriev formulas ............................... 313

Z Y Yield function ..................299–300(F), 301 of casting process ........................... 365 Yield point ...................................... 317 Yield strength of austenite after welding ........ 393–394(F) of bearing ring being hardened ....... 318(F) effect on residual stress development in steels ................................... 3(T) temperature effect ................. 251, 254(F) Yield stress of casting process ........................... 365 in cold forming .............................. 148 Young’s modulus ................... 142(F), 145 of aluminum alloy ...................... 378(T)

ZDT. See Zero ductility temperature. Zener-Wert-Avrami function, time effect on residual stress relaxation ......... 56, 58(F) Zero ductility temperature (ZDT) ........ 363 Zero strength temperature (ZST) ......... 363 Ziegler model of back stress rate ............................... 299–300(F) Zinc, alloying element effect on crack growth .......................................80 Zirconium, alloying effect on susceptibility to austenite grain growth ............. 325, 328 Zirconium oxide (ZrO2) brazing ...........................394(F), 395(F) brazing residual stresses ................ 393(T) Zone segregation .............................. 168 ZST. See Zero strength temperatures.

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Handbook of Residual Stress and Steel Deformation

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