Question

2. (70 pts) A cylindrical specimen of an alloy having a diameter of 12.8 mm and a gauge length of 50.800 mm is pulled in tension. The load-length data are recorded during the test and are tabulated below. After fracture, the diameter of the specimen near the fracture point was 9.5 mm. Load (N) 7,330 15,100 23,100 30,400 34,400 38,400 41,300 44.800 46,200 47,300 47,500 46,100 44,800 42,600 36,400 Length (mm) 50.800 50.851 50.902 50.952 51.003 51.054 51.308 51.816 52.832 53.848 54.864 55.880 56.896 57.658 58.420 59.182 Fracture - (20 pts) Use Excel or some other graphing software to plot the stress-strain curve. Do not draw the stress-strain curve by hand, which can affect the accuracy of your results. (10 pts each) Determine the following (draw lines or add labels on the graph if necessary): (a) The 0.2% offset yield strength (b) The tensile strength (c) Modulus of elasticity (d) Ductility in percent elongation (%EL) (e) Ductility in reduction in area (RA)

Answer 1

The following images provide the data points required to plot the graph. The stress is calculated by using the Load divided with the crossectional area. Similarly, Strain is calculated by a change in length per original length. Therefore Stress-Strain Curve is plotted using the same. An offset of 0.2% is plotted in the graph which is used to calculate 0.2% offset yield strength. Tensile Strength is the Maximum Strength under Stress-Strain Curve. Young's Modulus is the Slope of Longitudinal Stress by corresponding Strain. Ductility in terms of % change in length and % change in the area is also calculated.
Load (N) Length (mnr Original Length (nr Difference (m Crossection Area (n Stress (MPa) Strain Offset Offset Stress 50.8 50.8 128.6144 0 0.002 7330 50.851 50.8 0.051 128.6144 56.9920631 0.001003937 0.003 56.9921 15100 50.902 50.8 0.102 128.6144 117.405205 0.002007874 0.00401 117.405 23100 50.952 50.8 0.152 128.6144 179.6066381 0.002992126 0.00499 179.607 30400 51.003 50.8 0.203 128.6144 236.3654459 0.003996063 0.006 236.365 34400 51.054 50.8 0.254 128.6144 267.4661624 0.005 0.007 267.466 38400 51.308 50.8 0.508 128.6144 298.566879 0.01 0.012 554.173 41300 51.816 50.8 1.016 128.6144 321.1148985 0.02 0.022 44800 52.832 50.8 2.032 128.6144 348.3280255 0.04 0.042 46200 53.848 50.8 3.048 128.6144 359.2132763 0.06 0.062 47300 54.864 50.8 4.064 128.6144 367.7659733 0.08 0.082 47500 55.88 50.8 5.08 128.6144 369.3210092 0.1 0.102 46100 56.896 50.8 6.096 128.6144 358.4357584 0.12 0.122 44800 57.658 50.8 6.858 128.6144 348.3280255 0.135 0.137 42600 58.42 50.8 7.62 128.6144 331.2226314 0.15 0.152 36400 59.182 50.8 8.382 128.6144 283.0165207 0.165 0.167

002 004 006 0.08 01 0.12 0.14 0.16 0.18

SUMMARY OUTPUT Regression Statistics Multiple 0.99604 R Square 0.9921 Adjusted 0.99013 Standard 10.3313 Observat 6 ANOVA df Regressi Residual Total SSM S F gnificance F 1 53623.5 53623.5 502.398 2.3E-05 4 426.94 106.735 5 54050.4 Coefficientandard Err Stat Intercept -106.405 11.8985 -8.94276 X Variabl 55417.3 2472.42 22.4142 P-value Lower 95%Jpper 95%wer 95.0%pper 95.0% 0.00086 -139.441 -73.3699 - 139.441 -73.3699 2.3E-05 48552.8 62281.9 48552.8 62281.9

0.2% Offset Yield Strength Tensile Strength Young's Modulus/Modulus of Elasticity Ductility (%EL) Ductility (%RA) 288.02MPa 369.321MPa 55417.338MPa 16.39370079 44.91577148