PROBLEM $7(10$ pts$)$

An approximate stress$-$strain curve for brass is shown in Figure $2.$

Figure $2$: Approximate stress$-$strain relationship for brass.

The elastic modulus is $40$GPa, the yield stress is $150$MPa, the ultimate stress is $525$MPa, and the

ultimate strain is $0\mathrm{.}38(m\frac{m}{m}m).$ Perform the following tasks for this material.

a$.$ Compute the tangent modulus between the yield stress and the ultimate stress.

b$.$ What strain is realized if the material is stressed from $0$ to $387$MPa $?$

c$.$ If the stress then decreases from $387$MPa to $0$MPa, what is the permanent strain?