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 σe and strain εe are defined by

σe = F/A0 and εe = L €“ Lo/L0, where L0 and A0 are the initial gauge length and the initial cross-sectional area of the specimen, respectively. The true stress σt and strain εt are defined by σt = F/A0 L/L0 and εt = ln L/L0.
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 31963 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 41255 41,481 41,564 L (mm) 26.419 26.502 26.600 26.728 27.130 27.441