Question

A Grade 2 Titanium tension test specimen has a diameter of 12.60 mm and a gage length of 50 mm. In a test to fracture, load and deformation data obtained during the test are given in the accompanying table. Plot the stress strain relationship then, determine the following: (a) the modulus of elasticity. (b) the proportional limit. (c) the yield strength (0.20% offset). (d) the ultimate strength. (e) the fracture stress. (f) the true fracture stress if the final diameter of the specimen at the location of the fracture was 9.77 mm. (g) %elongation of specimen at failure (h) %reduction in area at failure Load (kN) 0.00 4.49 8.84 13.29 17.57 22.10 26.46 30.84 35.18 39.70 43.95 48.44 Change in Length (mm) 0.000 0.017 0.032 0.050 0.064 0.085 0.103 0.123 0.144 0.171 0.201 0.241 Load (kN) 52.74 56.95 60.76 63.96 66.61 68.26 69.08 69.41 69.39 69.25 68.82 68.35 68.17 Change in Length (mm) 0.314 0.480 0.840 1.334 1.908 2.562 3.217 3.938 4.666 5.292 6.023 6.731 fracture

Answer 1

Load	Change in Length	area= 3.148/4*12.60^2	Stress	Strain
kN	mm	mm^2	Mpa
0	0	124.6898124	0	0
4.49	0.017	124.6898124	36.00936	0.00034
8.84	0.032	124.6898124	70.89593	0.00064
13.29	0.05	124.6898124	106.5845	0.001
17.57	0.064	124.6898124	140.9097	0.00128
22.1	0.085	124.6898124	177.2398	0.0017
26.46	0.103	124.6898124	212.2066	0.00206
30.84	0.123	124.6898124	247.3338	0.00246
35.18	0.144	124.6898124	282.1401	0.00288
39.7	0.171	124.6898124	318.3901	0.00342
43.95	0.201	124.6898124	352.4747	0.00402
48.44	0.241	124.6898124	388.484	0.00482
52.74	0.314	124.6898124	422.9696	0.00628
56.95	0.48	124.6898124	456.7334	0.0096
60.76	0.84	124.6898124	487.2892	0.0168
63.96	1.334	124.6898124	512.9529	0.02668
66.61	1.908	124.6898124	534.2056	0.03816
68.26	2.562	124.6898124	547.4385	0.05124
69.08	3.217	124.6898124	554.0148	0.06434
69.41	3.938	124.6898124	556.6614	0.07876
69.39	4.666	124.6898124	556.501	0.09332
69.25	5.292	124.6898124	555.3782	0.10584
68.82	6.023	124.6898124	551.9296	0.12046
68.35	6.731	124.6898124	548.1603	0.13462
68.17	fracture	124.6898124	546.7167

Stress vs Strain Stress, MPa -Strain 0 0.01 0.02 0.03 0.04 0.05 0.06 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.07 0.08 Strain

a). Modulus of elasticity- E= slope of stress strain curve at 50% of peak that is at 228.33 MPa

considered point

212.2066	0.00206
247.3338	0.00246

E = (247.33-212.20)/(0.00246-0.00206)

E = 87.817 GPa

b) Proportion Limit

when stress reaches to 388.484 MPa, stress strain curve behave as nonlinear and that point is proportion limit.

hence proportion limit is 388.484 MPa

c).Yield Strength at 0.002 strain

to measure accurate yiels strength draw 0.002 offset like this

Stress vs Strain uuuung Stress, MPa HEHHENNNNNWwwww. 0000000000000000000000000000000 Strain 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068 0.07 0.072 0.074 0.076 0.078 0.08 0.082 0.084 0.086 0.088 0.09 0.092 0.094 0.096 0.098 0.1 0.102 0.104 0.106 0.108 0.11 0.112 0.114 0.116 0.118 0.12 0.122 0.124 0.126 0.128 0.13 0.132 0.134 0.136 0.138 0.14 0.142 Strain

Stress vs Strain esw Osons -Strain g 0 0.02 0.04 0.06 0.1 0.12 0.14 0.16 0.08 Strain

Yield strength is 430 MPa( mesured from aove figure

d) Ultimate strength is maximum peak stress of stress strain curve

i.e. fu = 556.66 MPa

As per HOMEWORKLIB POLICY 1st four part is done for rest of the parts you have to ask again and please upvote if you got yyour answer.. thank you!!11