Chapter 5, Problem 28P

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 o and strain t are defined by ${\sigma }_e=\frac{F}{A_0}$ and ${\epsilon }_e=\frac{L-L_0}{L_0}$ , where L₀and A₀are the initial gauge length and the initial cross-sectional area of the specimen, respectively. The true stress ${\sigma }_t$ , and strain ${\epsilon }_t$ are defined by ${\sigma }_t=\frac{FL}{A_0{L}_0}$ and ${\epsilon }_t=\text{In}\frac{L}{L_0}$ .

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 radius 6.4 mm (before the test). The initial gauge length is L₀= 25 mm. 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 newtons (N) and the area is calculated in m², the unit of the stress is pascals (Pa).

F (N)	0	13,031	21,485	31,963	34,727	37,119	37,960	39,550
L (mm)	25.4	25.474	25.515	25.575	25.615	25.693	25.752	25.978

F (N)	40,758	40,986	41076	41,255	41,481	41,564
L (mm)	26.419	26.502	26.600	26.728	27.130	27.441