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MECH 321 – 321 – Lab Lab XI-X EXPERIMENT 3 – 3 – FRACTURE FRACTURE TOUGHNESS TESTING TEST ING OF ALUMINUM 11/2/2016 Kevin Nguyen (6944434) Calvin Ngai (27042221) Corey Levy (7072023) Ernest Toka (26698301)
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OBJECTIVE The objective of this lab is to fracture fatigued an d non-fatigued samples of aluminum and determine the load and stress intensity at fracture, the plane stress or strain, and determine the plastic zone size. The fracture toughness of the aluminum samples will be characterized and measured.
INTRODUCTION As materials experience stress and strain, there exists a possibility of a crack to form. While a small crack may not seem like such a big deal in a large structure, it can cause the structure to fracture below its normal loads. Understanding the strengths of materials when a crack is present is very important for engineers. In an idealized situation, a uniform material of infinite extent which contains a semiinfinite horizontal crack in it is being pulled apart by a stress acting in the y direction σy. In this scenario, the stress concentration near the crack m ay be analytically determined if the material is allowed to deform in only a linear elastic fashion and if the crack tip is assumed to be sharp by using the formula: σy =
K √ 2πx
(1)
where K, the stress intensity, is proportional to the uniform tension being a pplied to the material. The real situation is much more complicated than the idealized situation. In metals, plastic yielding occurs to redistribute the stresses, and in other materials there are other types of deformations such as micro-cracking that occur, so it is not possible to have the material being pulled apart in a linear fashion. If the plastic zone is small compared to the specimen size, the stress intensity, K, also known as the region of K dominance is valid from equation (1) and can be used to characterize the strength of the stress field around the crack.
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The resistance to fracture can be characterized by the stress intensity at fracture K C, called the fracture toughness. When a specimen with a small crack is pulled apart, the plastic zone will undergo Poisson contraction, which relieves the stresses in the z direction. This plane stress acts only in the x-y plane, so the large x and y stresses near zero and the shear stress on the 45 ° plane is at a maximum.
For the experiment, a 1 inch and 1.5 inch non-fatigued 6061-T6 aluminum sample is used alongside a 1.0 and 2 inch fatigued specimen. The non-fatigued samples contain a notch while the fatigued samples have the tip of the notch being true cracks which have been produced from repeated loading on the samples. An electro-mechanical, uniaxial tensile machine is used to deform the samples until complete fracture occurs. The machine reads the force applied to the specimen and the displacement of the crosshead. The machine also measures the crack opening, and the results are monitored onto the computer.
PROCEDURE Four samples of 6061-T6 aluminum will be provided, each containing a notch. Two of those specimen will have nominal thickness of 1 inch and 1.5 inch. The other two specimen will have a nominal thickness of 1 inch and 2 inch, but has been fatigued by repeated loading. Using a caliper, measure the height and width (to the hole centers) of each sample. Afterwards, measure the thickness of the samples using the micrometer. The specimen will be mounted in the tensile machine and the load is applied through two half-inch diameter dowel pins. A computer program will record the necessary data, such as the load applied. Continue to apply the load until fracture occurs, splitting the sample in half. Repeat the process for the other samples, making adjustments when mounting the specimen when necessary. Measure the total crack length, a1, of each specimen and sketch the fracture.
DATA SHEET FRACTURE TOUGHNESS TESTING OF ALUMINUM 6061-T6 ALUMINUM MATERIAL PROPERTIES
1'' NF
1.5'' NF
1'' F
2'' F
σ0 [MPa]
276
276
276
276
h [mm]
31.69
31.80
31.69
25.99
w [mm]
51.13
50.88
51.13
50.81
t [mm]
25.39
38.31
25.39
51.96
ai [mm]
22.86
22.86
26.72
27.11
DETERMINING LOAD AT FRACTURE
1'' NF
1.5'' NF
1'' F
2'' F
INITIAL SLOPE M
41714
64045
33915
70980
DATA SHEET FRACTURE TOUGHNESS TESTING OF ALUMINUM 6061-T6 ALUMINUM MATERIAL PROPERTIES
1'' NF
1.5'' NF
1'' F
2'' F
σ0 [MPa]
276
276
276
276
h [mm]
31.69
31.80
31.69
25.99
w [mm]
51.13
50.88
51.13
50.81
t [mm]
25.39
38.31
25.39
51.96
ai [mm]
22.86
22.86
26.72
27.11
DETERMINING LOAD AT FRACTURE
1'' NF
1.5'' NF
1'' F
2'' F
INITIAL SLOPE MT
41714
64045
33915
70980
M5 = 95%MT
39628
60843
32219
67431
P5(M5) [N]
30410
47238
16925
35651
PMAX [N]
39955
62770
18300
38376
PQ [N]
30410
47268
16941
35651
DETERMINING STRESS INTENSITY AT FRACTURE
1'' NF
1.5'' NF
1'' F
2'' F
α = ai/w [-]
0.447
0.449
0.523
0.534
K Q [MPa*mm1/2]
1811.78
1892.06
1549.64
1714.36
K Q [MPa*m1/2]
57.29
59.83
49.00
54.21
DETERMINING PLANE STRESS OR PLAIN STRAIN
1'' NF
1.5'' NF
1'' F
2'' F
2.5(K Q/σ0)2 [m]
0.11
0.12
0.08
0.10
2.5(K Q/σ0)2 [mm]
107.73
117.49
78.81
96.46
NO
NO
NO
NO
< ai ?
NO
NO
NO
NO
< w-ai ?
NO
NO
NO
NO
NO
NO
NO
NO
PMAX/PQ [-]
1.31
1.33
1.08
1.08
PMAX/PQ < 1.1 ?
NO
NO
YES
YES
PLANE STRESS OR STRAIN
STRESS
STRESS
STRESS
STRESS
DETERMINING PLASTIC ZONE
1'' NF
1.5'' NF
1'' F
2'' F
r O [m]
0.00457
0.00499
0.00334
0.00409
r O [mm]
4.57
4.99
3.34
4.09
4*r O [mm]
18.29
19.95
13.38
16.37
< ai ?
YES
YES
YES
YES
< w-ai ?
YES
YES
YES
YES
YES
YES
YES
YES
K C [MPa*m1/2]
57.29
59.83
49.00
54.21
RESULTS 2. According to the calculations, all of the 6061-T6 samples indicate to be under plane stress. Therefore, K 1C is non applicable in this experiment. Precisely, the K Q condition showed that the relation between the factor K Q and PMAX and the dimensions of the specimen did not satisfy the test, and so the sample is under plane stress. Furthermore, since 4*r O gave us positive answers, we can approximate K Q to K C. The values for K C are : 1” specimen non-fatigued :
57.29 MPa*m1/2
1.5 “ specimen non-fatigued : 59.83 MPa*m1/2 1’’ specimen fatigued :
49.00 MPa*m1/2
2’’ specimen fatigued :
54.21 MPa*m1/2
3. With values ranging from 49 to almost 60 MPa*m1/2 , this particular material shows some serious mechanical properties, considering that materials such as medium carbon steel averages 51 MPa*m1/2 , and high strength steels can vary from 50 up to 154 MPa*m1/2. And if we would compare to other aluminum alloys, the highest spotted is at 44 MPa*m1/2, and it is the 7475. (data provided by efunda.com cited in the reference)
4. All the fractures occurred at plain stress. The fractures occurring at the edges of the sample and which are along the 45 degree plane represent plain strain. In our case, the fracture never fractured at the 45 degree plane, which means that it is a mixed fracture.
5. MATERIAL STEEL 4340 MARAGING STEEL ALUMINUM 7075-T6
YIELD STRENGTH, 2 σYS [N/mm ] 1470
TENSILE STRENGTH, 2 σUTS [N/mm ] 1820
KIC [N/mm3/2]
KIC CALCULATED
1500
1945
aCR [mm] 0.594
1730
1850
2900
2290
1.604
500
560
1040
662
2.470
Fracture occurs when the tested value for K C is less than the materials original K IC, because under the specified conditions, the material is less resistant to notch or crack fracture. Therefore : Steel 4340 will resist fracture since 1945 > 1500. Maraging Steel will fracture since 2290 < 2900. Aluminum 7075-T6 will fracture since 662 < 1040
The critical defect at stress 2/3 of yield strength occurs at : Steel 4340 :
0.594 mm
Maraging Steel :
1.604 mm
Aluminum 7075-T6 : 2.470 mm
=
:
SAMPLE CALCULATIONS
mT : initial slope of elastic line : draw a line tangent line on the displacement-load graph on the linear portion m5 : 95% * mT = 0.95*64584 [N] = 61354 [N] Pmax : highest value for load
Non dimensional crack length
= = 250.2.8868 = 0.449
Stress Intensity Calculation Example with the 1.5” inch specimen
= (√ )0.8664.64 13.32 14.72 5.6 [12.] 14.720.449 = .√ .5.60.4049.8664. 6 4∗0. 4 4913. 3 20. 4 49 +.. −.
= 57.29 [MPa*m1/2]
Test for plane stress
1892. 0 6 [ ∗ ] 2.5∗() = 2.5 ∗ 276 = 0.12 = 117.49
The test gives us less than t = 38.31 mm, a i = 22.86 mm , w-ai = 22.02 mm and h = 31.80 mm. The test has failed for plain strain. Next test will validate for plane stress.
/ 59. 8 2 ∗ ( ) ( ) 276 = 3 = 3 = 0.00499 = 4.99 4r O is less than t, a i, w-ai and h, therefore, plane stress is validated.
K C can be approximated by K Q.
Report question a) : example with steel 4340
= √ = 23 √ = 23 1470 ∗1.12∗√ ∗1 = 1945 // where σ = 2σ(YS)/3
Report question b) : critical defect size, an ex ample with steel 4340 :
From the above equation, solve for a :
/ / = 23 = 23 1500 ∗1470 ∗1. 1 2 = 0.594
DISCUSSION
As expected, the fatigued and non-fatigued samples gave different results during the crack propagation. While observing the surface o f the cracked samples, it can be easily seen that the fatigued blocks have a small and smooth region emanating from the cracked area. This region is not present on the non-fatigued samples, however. Furthermore, the thickness of the samples also had an effect on the results. Thinner samples experience what is known a Type I curve. Otherwise known as plane stress fracture, this type of curve h as a curved break and is tearing dominant. When thickness increases, Type III will occur. Also kno wn as plane strain fracture, it has a sharp break and its cleavage is dominant. Finally, Type II curve is a mix of Type I and Type III and it shall curve down before its slope increases until the sample fractures.
If we would compare the values for K C obtained in the laboratory and the ones from literature, we quickly observe that there is a major gap. The obtained values for 6061-T6 range from 49-60 MPa*m1/2 while its commercial value (reference cited : asm.matweb.com) gives fracture toughness of 29 MPa*m1/2. Note one cannot directly K C and K IC. However closely related, the values of 49 - 60 and 29 is a rapport of almost 2, therefore the presence of errors occurring during the experiment are present, without doubt. In addition, it is doubtful that no aluminum alloy from the list (efunda.com) comes close to our 6061-T6. Let us hypothesize about the possible errors in the next paragraph.
There are a few possible sources of error when p erforming the experience. Most importantly, the positioning of the sample in the testing machine, without taking into account its precision. The positioning could potentially give incorrect values for loads and could also perform undesired types of forces of the sample material. Second, the measurements of the sample materials. The dimensioning is a great source of potential error since values for K Q directly depend on the geometry of the unit sample. If the experiment has to be performed again, an thorough inspection of the calibration of the machine (Instron tensile machine) shall be done and more precise instructions regarding dimensions shall be given.
CONCLUSION
In material science, fracture toughness is a mechanical propert y of any engineering material that describes its ability to resist fracture when a crack is present. And since the is no perfect material (without crack), the fracture toughness is a very important property which can be used to predict at which load and for which geometry a material will fail.
The purpose of a fracture toughness test is to measure the magnitude of a material’s resistance to the presence of a flaw in terms of the load required to cause brittle or ductile crack extension in a standard specimen containing a fatigued pre-existing crack. The result is expressed is terms of toughness parameter, K IC.
Using the fracture toughness value and fracture mechanics, engineers are able to establish allowable stress values to specific structures for safety purposes.
REFERENCES : Callister Jr., W.D., Materials Science and Engineering : An Introduction, 6 th Ed, John Wiley Concordia Laboratory Manual Internet Resources : http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6 http://www.efunda.com/formulae/solid_mechanics/fracture_mechanics/fm_lefm_Kc_Matl.cfm
