International Journal of Fatigue 22 (2000) 717–726 www.elsevier.com/locate/ijfatigue
Fatigue analysis of autofrettaged pressure vessels with radial holes Seung-Kee Koh Department of Mechanical Engineering, Kunsan National University, Kunsan, Chonbuk, 573-701, South Korea
Received 20 October 1999; received in revised form 23 March 2000; accepted 23 March 2000
Abstract
Fatiguee analysis has been performed Fatigu performed to predict the fatigu fatiguee life of an autofr autofrettaged ettaged pressure pressure vessel containing containing radial holes subject subjected ed to cyclic internal pressure of 200 MPa. Finite element analyses were used to calculate the residual and operating stress distributions of the pressure vessel due to the autofrettage process and pulsating internal pressure, respectively. Numerical stress concentration factor fac torss at the hol holee of the aut autofr ofrett ettaged aged pressure pressure vess vessel el sub subject jected ed to int intern ernal al pre pressur ssuree wer weree appr approxi oximat mately ely 3. Fat Fatigu iguee dam damages ages,, including the mean stress effects, were evaluated using the local stresses and local strains determined from the elastic–plastic finite element analysis. An increase in the amount of overstrain by the autofrettage process moved the fatigue cracking location from the inner radius towards a mid-wall, and extended the fatigue life. Predicted fatigue life of a 50% autofrettaged pressure vessel with radial holes increased by 45%, compar compared ed to that of the unautof unautofretta rettaged ged pressure vessel. The level of autofrettage autofrettage did not significantly significantly influence the failure location and fatigue life of the pressure vessel for more than 50% autofrettage level. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Autofrettaged pressure vessel; Finite element analysis; Fatigue crack initiation; Mean stress; Fatigue damage
1. Introd Introduction uction
In a pre pressu ssure re ves vessel sel sub subjec jected ted to a cyc cyclic lic int intern ernal al pressure, fatigue cracks initiate and grow from the inside surface, at which the largest tensile stress occurs. Therefore, to counteract the large tensile tangential stress at the inside surfa surface, ce, an autof autofrettag rettagee proce process ss which produces compressive tangential residual stresses near the bore of the pressure vessel has been commonly used [1]. The com compre pressi ssive ve tan tangen gentia tiall res residu idual al str stress esses es nea nearr the inside ins ide sur surfac facee due to the aut autofr ofrett ettage age pro proces cesss ret retard ard crack formation and growth. However, the presence of struct str uctura urall dis discon contin tinuit uities ies whi which ch are nec necess essary ary for the engineering purposes of the pressure vessel, significantly change the stress distributions of the pressure vessel and reduce the fatigue life of the pressure vessel due to the stress concentration concentration.. For the auto autofrettag frettaged ed press pressure ure vessel, the structural discontinuities at the outside surface have been reported as critic critical al locati locations ons of early fracture, resu re sult ltin ing g in sh shor orte tene ned d fa fati tigu guee li life fe co comp mpar ared ed to th thee unautofrettaged pressure vessel [2]. This can be ascribed to the high magnitude of tensile tangential stresses and
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plastic deformation at the discontinuities from the combination of residual stresses by autofrettage, operating stresses stress es by inter internal nal press pressure, ure, and stress concentration concentration.. Recently, several fracture mechanics-based fatigue life analyses have been performed for autofrettaged pressure with various types of discontinuities [3–5], resulting in good descriptions of measured fatigue life. The objective of this study is to evaluate the low-cycle fatigue life of the autofrettaged pressure vessel with radial hol holes es sub subjec jected ted to cyc cyclic lic int intern ernal al pre pressu ssure re usi using ng a local strain approach. Elastic–plastic finite element stress analyses were performed in order to calculate the local stress and local strain distributions near the radial hole. The effects of autofrettage on the critical locations of fatigue cracking and the fatigue life of the pressure vessell we se were re fo foun und d us usin ing g da dama mage ge pa para rame mete ters rs,, wh whic ich h accounted for the mean stresses induced by the autofrettagee pro tag proces cess. s. Eve Even n tho though ugh dir direct ect com compar pariso isons ns of pre pre-dicted and measured fatigue lives were not made in this study due to the considerable cost and time required for full-scale tests, the fatigue analysis was expected to provide useful information for the design of the autofrettaged pressure vessel under the pulsating high internal pressure.
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S.-K. Koh / International Journal of Fatigue 22 (2000) 717–726
2. Finite element analysis of autofrettaged pressure vessels with radial holes
Fatigue analysis of the autofrettaged pressure vessel with radial holes subjected to cyclic internal pressure loading requires a thorough understanding of the stress distributions in the pressure vessel. A three-dimensional finite element analysis was performed to find the stress and strain distributions of the autofrettaged pressure vessel with radial holes. Fig. 1 shows the autofrettaged pressure vessel containing 10 equally spaced holes, which penetrate the wall of the pressure vessel radially at an angle of 90 °. In Fig. 1, a, b, and W are the inside and outside radii, and the wall thickness of the pressure vessel, respectively, and d is the diameter of the radial hole in the pressure vessel. The wall ratio, b / a, of the pressure vessel was 1.53, and the diameter ratio of the radial hole to the pressure vessel, d /2a, was 0.043. Three sources of loadings from the autofrettage, the internal pressure on the pressure vessel, and the internal pressure on the radial hole were considered.
(1)
s ys
b2
r2
r 2
2b2 b2−a2
1
Fig. 1.
a2
r2−b2 r ln 2
2b
a
,
for
rr b
for
T r
(2)
A thermal stress analysis of the pressure vessel with the temperature gradient in Eq. (2) yields the tangential stresses as [7],
r2b2 r ln 2
2b
r
a E
T a−T r
2(1−n)ln( r / a)
for
a2
T a−T r
,
1
for a r r
b2
r2
r 2
2b2 b2−a2 2b
a2
r2−b2 r ln 2
a
(3) ,
rr b
From a comparison of Eqs. (1) and (3), the autofrettage residual stresses can be simulated by imposing a thermal loading satisfying the following relation:
b2 r2−b2 r r2b2 r 1 ln ln , b2−a2 r 2 a r 2b2 2b2
for a r r
T a−T r r ln for a r r ln( r / a) a
b2 r2−b2 r s q 1 ln 2(1−n)ln( r / a) b2−a2 r 2 2b2 a
The smooth pressure vessel prior to the introduction of radial holes was overstrained by autofrettage pressure in order to induce the compressive tangential residual stresses near the inside surface. If the plastic deformation is extended to a radius of r during the autofrettage process, then the tangential residual stresses due to autofrettage are derived using the Tresca yield criterion and elastic–perfectly plastic material behavior [6], s qs ys
T
T a−
a E
2.1. Stress distributions of smooth pressure vessel
a2
where s ys is the yield strength of the material, and r is the elastic–plastic radius of the autofrettaged pressure vessel. The percentage of plastically deformed wall thickness of the pressure vessel during the autofrettage process was defined as the level of autofrettage or overstrain (%OS). If a thermal loading of T a and T r is imposed on the surfaces at r =a and r, respectively, then the temperature distribution can be obtained as,
rr b
s ys
a E
T a−T r
2(1−n)ln( r / a)
where
a is
(4)
the coefficient of thermal expansion, and E
Configuration of autofrettaged pressure vessel with radial holes ( a=77.5 mm, b=118.2 mm, W =40.7 mm, d =6.65 mm).
S.-K. Koh / International Journal of Fatigue 22 (2000) 717–726
and n are Young’s modulus and Poisson’s ratio, respectively. Stresses due to internal pressure are given by the wellknown Lame equations [7], s q
Pia2
b2−a2
1
b2
(5)
r 2
2.2. Elastic stress analysis of autofrettaged pressure vessel with radial holes
Fig. 2 shows the finite element model of the pressure vessel containing a radial hole meshed with three-dimensional eight-noded brick elements. Due to the symmetry of the pressure vessel, only one-fortieth of the total geometry was considered in the finite element model with appropriate boundary conditions. The mesh was refined until the convergence of the solution was reached. Total numbers of nodes and elements of the model were 7440 and 6300, respectively. The same internal pressure of 200 MPa was imposed on both surfaces of the pressure vessel and the radial hole. The plane strain condition was applied by constraining the axial deformation of the long open-ended thick-walled pressure vessel [6]. The autofrettage residual stresses were simulated by imposing thermal loading from Eq. (4). Inside temperatures of 286.5 and 158.2 °C for 100 and 50%OS, respectively, were applied along with T r=0°C. Yield strength of 1170 MPa, Young’s modulus of 200 GPa, thermal expansion coefficient of 12.24 ×10 6 / °C, and Poisson’s ratio of 0.29 were used. The ANSYS finite element program was employed to perform the thermal and stress analyses [8]. Nominal tangential stress distributions along the
Fig. 2. Finite element model of thick-walled pressure vessel with radial holes.
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thickness ( A A in Fig. 2) away from the radial hole, compared to the stresses near the hole ( B B in Fig. 2), are obtained from the elastic finite element analysis as shown in Fig. 3. As the amount of overstrain increased, the magnitude of compressive residual stresses near the inside surface of the pressure vessel increased. The finite element solutions of the nominal tangential stresses along the thickness for each loading case were in very close agreement with the theoretical solutions in Eqs. (1) and (5). The difference between finite element and theoretical solutions was less than 2%. Stress concentration due to the introduction of radial holes increases the magnitude of the elastic stresses along the holes, as shown in Fig. 3, depending on the types of loadings. The increasing level of autofrettage amplified not only the magnitude of compressive residual stresses near the inside surface of the pressure vessel, but also the tensile residual stresses near the outside surface, which might be susceptible to fatigue cracking due to high tensile mean stresses in cyclic loading. The numerical stress concentration factors of the 0, 50 and 100% autofrettaged pressure vessels subjected to internal pressure were 3.02, 3.13 and 3.01, respectively. These were close to the stress concentration factor of the hole in an infinite plate, due to the relatively small diameter of the radial holes in the pressure vessel. Locations of fatigue crack initiation in the pressure vessel with different levels of autofrettage were not clearly identified by the elastic stress analysis, since the variations of stress and strain along the radial hole were complex. 2.3. Elastic–plastic stress analysis of pressure vessel with radial holes
In this paper, the pressure vessel containing the residual stress due to the autofrettage process is sub jected to the cyclic internal pressure. Therefore, the cyclic loading on the pressure vessel is not fully-reversed and mean stress, defined as s m=(s max+s min)/2, does exist. The maximum and minimum stresses in the cyclic loading correspond to the stresses of the pressure vessel subjected to internal pressure loading superimposed on the autofrettage loading and autofrettage loading alone, respectively. In order to obtain the local deformation of the autofrettaged pressure vessel in the vicinity of radial holes, an elastic–plastic finite element analysis was performed. The same mesh and boundary conditions used in the elastic analysis were adopted in the elastic–plastic analysis. THe kinematic strain hardening rule and von Mises yield criterion were employed in the elastic–plastic finite element analysis. Since the pressure vessel was under cyclic loading, a cyclic stress–strain relationship determined from the strain-controlled fatigue testing should be used in the analysis. Therefore, the range of cyclic stress (or strain) was obtained from the maximum and mini-
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Fig. 3.
Nominal and elastic tangential stress distributions along a hole of pressure vessel for each loading case.
mum stresses (or strains) by using the elastic–plastic finite element analysis with cyclic stress–strain relations. Monotonic and cyclic properties of the ASTM A723 pressure vessel steel in Table 1 have been obtained in previous work [9], and the cyclic stress–strain curve can be represented as
s s e E K
1/ n
(6)
Fig. 4 shows contours of the equivalent stress, defined in Eq. (7), for the pressure vessel subjected to a combined loading of autofrettage overstrain and internal pressure of 200 MPa. ¯ s
1 [(s 1−s 2)2+(s 2−s 3)2+(s 3−s 1)2] 2
(7)
A steep gradient in the vicinity of the radial hole due to the stress concentration can be observed in Fig. 4. Maximum equivalent stress occurred near the inner wall of the pressure vessel for the unautofrettaged case of 0%OS. However, the location of maximum equivalent Table 1 Monotonic and cyclic properties of cylinder steel Young’s modulus, E (MPa) Ultimate tensile strength, s n (MPa) 0.2% offset yield strength, s ys (MPa) Elongation, %EL Reduction in area, %RA Fracture strength, s f (MPa) Fracture strain, ef Hardness, HRC Cyclic strength exponent, n Cyclic strength hardening coefficient, K (MPa) 0.2% offset cyclic yield strength, s ys (MPa)
197 1264 1112 15.5 46 1807 0.617 43 0.083 1704 1014
stress moved towards the outside wall of the pressure vessel as the amount of overstrains increased. Fig. 5 shows the equivalent stress distributions along the radial hole of the autofrettaged pressure vessel subjected to internal pressure. Four levels of overstrain, i.e. 25, 50, 75 and 100%OS, were considered. In Fig. 5, the autofrettage process considerably decreases the equivalent stress near the inner surface of the pressure vessel, even though the effect seems less pronounced at the high levels of overstrain. A continuous increase in equivalent stress near the outside surface of the pressure vessel was observed as the level of overstrains increased. Fig. 6 shows contours of the equivalent plastic strain, defined in Eq. (8), for typical %OS, compared to those for unautofrettaged case.
¯ p e
2 p p2 p p2 p p2 [(e1−e2) +(e2−e3) +(e3−e1) ] 9
(8)
As the %OS increases, the localized plastic deformation at the hole increases and the location of maximum equivalent plastic strain moves toward the outside surface of the pressure vessel as shown in Fig. 6. The maximum values of equivalent plastic strain for 0, 50 and 100%OS were 0.0045, 0.0042 and 0.0102, respectively. It should be noted that the magnitudes and distributions of the equivalent stress and plastic strain near the radial hole depend on the variables such as wall ratio ( b / a), diameter ratio (d / a), autofrettage level (%OS), and internal pressure of the pressure vessel. An elastic–plastic analysis of a pressure vessel with one radial hole under monotonic internal pressurization by Chaaban and Barake [10] showed that the amount of plastic deformation near the hole increased, as the diameter ratio and autofrettage level increased and the wall ratio decreased. The ranges of cyclic stress and strain near the radial hole in the pressure vessel subjected to the pulsating
S.-K. Koh / International Journal of Fatigue 22 (2000) 717–726
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internal pressure were determined by unloading the internal pressure using a stabilized hysteresis loop curve, which was modeled as twice the cyclic stress–strain curve in Eq. (6). Fig. 7 shows the variations of maximum and minimum strains along the radial hole of the autofrettaged pressure vessel, which is subjected to the cyclic internal pressure loading of 200 MPa. Even though the autofrettage process alleviated the large tensile stress at the inside surface of the pressure vessel by inducing the compressive residual stress, the strain amplitude due to cyclic internal pressure was the highest at the inside surface. The maximum strain amplitude near the inside surface was 0.0037 with cyclic plasticity, but the cyclic 0.2 was essentially straining for the region of ( r a)/ W elastic. Depending on the autofrettage level, the strain ratio, emin / emax, along the hole varied from 0 to 0.65 for 0.2, resulting in considerable tensile mean (r a)/ W strains and mean stresses during cyclic loading. Therefore, it was expected that the cyclic plastic deformation and high tensile mean stress were dominant damaging factors in the inside and outside surfaces of the pressure vessel, respectively.
3. Fatigue life prediction of autofrettaged pressure vessel with radial holes 3.1. Low-cycle fatigue damage and mean stress parameters
The finite element stress analysis showed the high stress concentration at the region along the radial hole, which was susceptible to fatigue cracking due to the localized plastic deformation and high tensile mean stresses. Fatigue life of the autofrettaged pressure vessel containing radial holes subjected to pulsating internal pressure can be defined as the sum of the crack initiation life at the critical location and the subsequent crack growth life. In this study, however, the cycles to crack initiation was considered as the fatigue life of the pressure vessel for a conservative evaluation. Fatigue life from the fully reversed strain-controlled test is mathematically modeled by Basquin and Manson as [11], e
2 Fig. 4. Equivalent stress contours of 0% (a), 50% (b) and 100% (c) autofrettaged pressure vessels with radial holes subjected to internal pressure.
s f
(2 N f )bef (2 N f )c
E
(9)
where low-cycle fatigue properties of the ASTM A723 pressure vessel steel are listed in Table 2, determined by using smooth cylindrical uniaxial specimens [9]. It is known that the low-cycle fatigue damage is significantly influenced by the mean stress. Autofrettage residual stresses play the role of mean stress and thus influence the fatigue life of the pressure vessel. In order to take the mean stress into account, damage parameters from
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Fig. 5.
Equivalent stress distributions along a hole of autofrettaged pressure vessel subjected to internal pressure.
Morrow, SWT and strain energy density were considered in the fatigue life evaluation. The Morrow equation can be obtained from a modification of the elastic strain-life term in Eq. (9) by introducing the mean stress, s m [12]. e
2
s f −s m (2 N f) bef (2 N f) c
(10)
E
A mean stress parameter proposed by Smith et al. [13] is expressed in the following form: s maxeaC (2 N f )g
(11)
where s max and a are maximum local stress and local strain amplitude, respectively, at the critical location such as the radial hole in the autofrettaged pressure vessel. The coefficient, C and exponent, g in Eq. (11) for the material were determined as 95.1 MPa and 0.3571 from the fully reversed strain-controlled tests, respectively, and a good correlation with the nonzero mean strain tests was obtained in the previous work [9]. The damage parameter using strain energy density, , can be represented for a uniaxial cyclic loading as [14], 2(1−n)(2K ) 1+n
−
W pW e+
1/ n
(s )
1+n n
(12)
1 2 s maxu N a f C u 2 E
where
W p
is the plastic strain energy per cycle, and W is the positive or tensile elastic strain energy per cycle. In the uniaxial cyclic loading, W p is the area of the hysteresis loop, and W e =s 2max /2 E if s min0 and s 2 /2 E if s min0. Mean stress effects are considered in the tensile elastic strain energy term. Material constants, 3 u and a were determined as 550.4 MJ/m and 0.6098, respectively, for the ASTM A723 steel from the fully e+
+
reversed uniaxial fatigue tests. A material constant, C u defined as the energy value corresponding to the fatigue limit of the material, was neglected for the low-cycle fatigue lifetime prediction of the pressure vessel in this study. 3.2. Fatigue life prediction
Fatigue crack initiation life of the pressure vessel was estimated using the local strain approach by incorporating the low-cycle fatigue properties of the material and the finite element stress analysis. Fatigue damage parameters accounting for the mean stress effects were considered in the fatigue life prediction. Effects of multiaxial stress state near the radial holes of the pressure vessel were taken into account by using equivalent stress and strain in the fatigue analysis. Fatigue damage along the hole of the autofrettaged pressure vessel can be effectively evaluated by using the elastic–plastic finite element analysis. Fatigue damages using Morrow, SWT and strain energy parameters at various overstrain levels are calculated along the hole as shown in Figs. 8–10, respectively. For the unautofrettaged pressure vessel, the largest fatigue damage occurred at the inner radius of the pressure vessel. As the level of autofrettage increased, the location of the largest fatigue damage moved toward the mid-wall of the pressure vessel due to the autofrettage residual stresses. It is observed in Figs. 8 and 9 that the fatigue damage calculated by using Morrow and SWT parameters reaches the maximum at r =89.9 mm, i.e. about 0.3W away from the inner surface of the pressure vessel, and the fatigue damage at the critical location is of similar magnitude, regardless of the autofrettage level if higher than 50%OS. This implies that a high level of autofrettage does not always assure an improved fatigue life of the pressure vessel containing radial holes, and
S.-K. Koh / International Journal of Fatigue 22 (2000) 717–726
Fig. 6. Equivalent plastic strain contours of 0% (a), 50% (b) and 100% (c) autofrettaged pressure vessels with radial holes subjected to internal pressure.
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there may exist an optimum level of autofrettage. When the strain energy parameter is used for the damage evaluation, the location of the highest fatigue damage moves to the outside surface of the pressure vessel as the autofrettage level increases as shown in Fig. 10. This was attributed to the continuous increase in the maximum and mean stresses at the outside surface as the autofrettage level increased, resulting in the increased elastic strain energy density. In Figs. 8 and 9, a localized cracking at the inside surface of the unautofrettaged pressure vessel is expected due to the highly concentrated fatigue damage. However, for the overstrain level higher than 50%OS, the uniformly distributed fatigue damages along the hole, except for the inside surface, indicate a broad cracking region across the thickness. Therefore, to some extent the autofrettage may extend the fatigue life of the pressure vessel with radial holes by preventing the localized damage at the inside surface. An autofrettage level of approximately 50%OS seemed to be the optimum for the fatigue life improvement of the pressure vessel with radial holes subjected to pulsating internal pressure of 200 MPa considered in this study. It should be mentioned that the optimum level of autofrettage might vary, depending on the wall ratio, diameter ratio, and magnitude of internal pressure. Fig. 11 shows the predicted fatigue lives of the pressure vessels based on the calculated fatigue damages, as shown in Figs. 8–10. The fatigue life defined as the cycles to crack initiation was evaluated at the critical location of the largest damage along the hole in the pressure vessel. Predicted fatigue life ranged from 2290 to 4899 cycles depending on %OS. When the Morrow and SWT damage parameters were used for the life prediction, a 45% increase in fatigue life by 50% autofrettage was obtained, and noticeable life improvement was not found for the autofrettage level higher than 50%OS. Decrease in fatigue life at the high %OS for the strain energy parameter in Fig. 11 is attributed to the damage from the large elastic strain energy component caused by the high residual stresses near the outside surface. A direct comparison of the predicted fatigue life with the experimentally measured life of the autofrettaged pressure vessel with radial holes was not possible, since the experiments using the pressure vessel with the same dimensions in the open literature were not available. However, Underwood et al. [5] measured the fatigue life of the pressure vessel with radial holes, whose geometry and internal pressure were comparable to the one used in this study. The experimentally observed locations of crack initiation and crack shapes by Underwood et al. were fairly similar to the predictions by damage distribution curves in Figs. 8 and 9 in this study. Fracture surfaces from the fatigue test revealed that the fatigue cracking occurred at the localized inside surface region for the unautofrettaged pressure vessel and the broad
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Fig. 7.
Variations of strains along a hole of autofrettaged pressure vessel due to pulsating internal pressure.
Table 2 Low-cycle fatigue properties from fully reversed strain-controlled fatigue tests Fatigue strength coefficient, s f (MPa) Fatigue strength exponent, b Fatigue ductility coefficient, ef Fatigue ductility exponent, c
2717.5 0.1487 0.8195 0.9064
region along the radial hole for the fully autofrettaged pressure vessel, as predicted in this study. It was found that the strain energy density parameter overestimated the mean stress effects, thus requiring a modification of the elastic strain energy component for more accurate fatigue life evaluation. Measured fatigue lives including crack growth of the pressure vessels ranged from 3500
Fig. 8.
to 5000 cycles for 30–50%OS levels [5], which were in a similar range to the predicted fatigue lifetime in this analysis. 4. Summary and conclusions
Elastic and elastic–plastic stress analyses of an autofrettaged pressure vessel with radial holes were performed using the finite element method. Fatigue damages evaluated from the calculated local stresses and local strains were used for the fatigue lifetime prediction of the autofrettaged pressure vessel. Numerical stress concentration factors at the radial hole in the pressure vessels with different levels of autofrettage were approximately 3 due to the relatively small diameter of the hole. The elastic–plastic finite element
Damage distributions along a hole of autofrettaged pressure vessels using the Morrow parameter.
S.-K. Koh / International Journal of Fatigue 22 (2000) 717–726
Fig. 9.
Fig. 10.
Fig. 11.
Damage distributions along a hole of autofrettaged pressure vessels using the SWT parameter.
Damage distributions along a hole of autofrettaged pressure vessels using the strain energy parameter.
Predicted fatigue lives of autofrettaged pressure vessels with radial holes based on elastic–plastic finite element stress analysis.
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S.-K. Koh / International Journal of Fatigue 22 (2000) 717–726
stress analysis showed that the compressive residual stress by autofrettage considerably alleviated the large tensile stress near the inside surface of the pressure vessel. However, cyclic plasticity was observed near the inside surface due to the large strain amplitude caused by pulsating internal pressure. The cyclic straining along 0.2 was essentially the hole for the region of ( r a)/ W elastic with high mean strain and mean stress. The cyclic plastic deformation and high tensile mean stress were dominant damaging factors in the inside and outside surfaces of the pressure vessel, respectively. Due to the complex variations of stress and strain along the radial hole, the fatigue cracking locations of the autofrettaged pressure vessels were not clearly identified by the elastic stress analysis. However, damage distributions using elastic–plastic finite element stress analysis predicted that the locations of fatigue cracking moved from the inside surface to the mid-wall of the pressure vessel as the level of autofrettage increased. Contrary to the localized cracking for the unautofrettaged pressure vessel, the uniformly distributed damages along the hole implied a broad cracking region across the thickness. Predicted fatigue life evaluated at the critical location increased as the autofrettage level increased. The pressure vessel autofrettaged by 50% overstrain resulted in extended fatigue life by approximately 45%. However, no significant influence on the fatigue life of the pressure vessel with radial holes was observed for autofrettage level higher than 50% overstrain. Predicted fatigue life ranged from 2290 to 4899 cycles depending on the levels of autofrettage. The beneficial influence of autofrettage on the fatigue life of the pressure vessel with radial holes was not as remarkable as for the smooth pressure vessel, since the favorable compressive residual stress near the inside surface was removed by the cyclic plasticity due to the high stress concentration and the detrimental tensile residual stress near the outside surface of the pressure vessel was produced.
Acknowledgements
The author wishes to acknowledge the financial support of the Korea Research Foundation in the program year of 1998.
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