In a tensile test, the starting gage length = 100.0 mm and the cross-sectional area = 150 mm2. During testing, the following force and gage length data are collected: (1) 17,790 N at 100.2 mm, (2) 23,040 N at 103.5 mm, (3) 27,370 N at 110.5 mm, (4) 28,910 N at 122.0 mm, (5) 27,480 N at 130.0 mm, and (6) 20,460 N at 135.1 mm. The final data point (6) occurred immediately prior to failure. Yielding occurred at a load of 19,390 N (0.2% offset value), and the maximum load (4) was 28,960 N.
(a) Plot the engineering stress strain curve.
Determine
(b) yield strength,
(c) modulus of elasticity,
(d) tensile strength, and
(e) percent elongation.
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First, let's calculate the engineering stress and strain for each data point:
For data point (1):
Stress = Force / Area = 17790 N / 150 mm^2 = 118.6 N/mm^2
Strain = (Gage Length - Initial Length) / Initial Length = (100.2 mm - 100.0 mm) / 100.0 mm = 0.002
For data point (2):
Stress = Force / Area = 23040 N / 150 mm^2 = 153.6 N/mm^2
Strain = (Gage Length - Initial Length) / Initial Length = (103.5 mm - 100.0 mm) / 100.0 mm = 0.035
For data point (3):
Stress = Force / Area = 27370 N / 150 mm^2 = 182.5 N/mm^2
Strain = (Gage Length - Initial Length) / Initial Length = (110.5 mm - 100.0 mm) / 100.0 mm = 0.105
For data point (4):
Stress = Force / Area = 28910 N / 150 mm^2 = 192.7333 N/mm^2
Strain = (Gage Length - Initial Length) / Initial Length = (122.0 mm - 100.0 mm) / 100.0 mm = 0.22
For data point (5):
Stress = Force / Area = 27480 N / 150 mm^2 = 183.2 N/mm^2
Strain = (Gage Length - Initial Length) / Initial Length = (130.0 mm - 100.0 mm) / 100.0 mm = 0.3
For data point (6):
Stress = Force / Area = 20460 N / 150 mm^2 = 136.4 N/mm^2
Strain = (Gage Length - Initial Length) / Initial Length = (135.1 mm - 100.0 mm) / 100.0 mm = 0.351
Now, let's plot the engineering stress-strain curve using these data points.
(a) Plot the engineering stress strain curve:
Stress (N/mm^2)
|
|
| --------------(6) /
| |
| | (5) /
| |
| |
| | (4) /
| |
| |
| --------------(3) /
| |
| | (2) /
| |
| |
| | (1) /
| ___________________________________________
| Strain
(b) Yield strength is the stress at the 0.2% offset value. From the data point (1), we can see that the stress is 118.6 N/mm^2, which is less than the yield strength of 19,390 N / 150 mm^2 = 129.27 N/mm^2. Therefore, the yield strength is 129.27 N/mm^2.
(c) Modulus of elasticity is the slope of the stress-strain curve in the elastic region. We can calculate it using two data points in the elastic region. Let's use data points (1) and (2):
Modulus of elasticity = (Stress (2) - Stress (1)) / (Strain (2) - Strain (1))
= (153.6 N/mm^2 - 118.6 N/mm^2) / (0.035 - 0.002)
= 35 N/mm^2 / 0.033
= 1060.61 N/mm^2
Therefore, the modulus of elasticity is 1060.61 N/mm^2.
(d) Tensile strength is the maximum load before failure. From the data, the maximum load is 28,960 N. Therefore, the tensile strength is 28,960 N / 150 mm^2 = 193.067 N/mm^2.
(e) Percent elongation is the change in length compared to the initial length, expressed as a percentage. From the data, the change in length is (135.1 mm - 100.0 mm) = 35.1 mm. Therefore, the percent elongation is (35.1 mm / 100.0 mm) * 100% = 35.1%.
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