Chapter 5, Problem 30P

In a typical tension test a dog-bone shaped specimen is pulled in a machine. During the test, the force F needed to pull the specimen and the length L of a gauge section are measured. This data is used for plotting a stress-strain diagram of the material. Two definitions, engineering and true, exist for stress and strain. The engineering stress s_eand strain ?_eare defined by ${\sigma }_e=\frac{F}{A_0}$ and ${ϵ}_e=\frac{L-L_0}{L_0}$ , where L₀and A₀are the initial gauge length and the initial cross-sectional area of the specimen, respectively. The true stress s_tand strain ?_tare defined by ${\sigma }_t=\frac{F}{A_0}\frac{L}{L_0}$ and ${ϵ}_t=\ln \frac{L}{L_0}$ .

The following are measurements of force and gauge length from a tension test with an aluminum specimen. The specimen has a round cross section with a radius of 0.25 in. (before the test). The initial gauge length is 0.5 in. Use the data to calculate and generate the engineering and true stress- strain curves, both on the same plot. Label the axes and use a legend to identify the curves.

Units: When the force is measured in pounds (lb) and the area is calculated in in.2, the unit of the stress is psi (pounds per square inch).

F (lb)	0	4,390	7,250	10,780	11,710	12,520	12,800	13,340
L (in.)	0.5	0.50146	0.50226	0.50344	0.50423	0.50577	0.50693	0.51138
F (lb)	13,740	13,820	13,850	13,910	13,990	14,020	14,130
L (in.)	0.52006	0.52169	0.52362	0.52614	0.53406	0.54018	0.56466