Problem $2(25$ points$)$:

The following stress strain curves from an axial tensile test of a pure $($elemental$)$ metal sample that underwent two different heat treatment conditions. The black line represents a highly annealed sample. The red line represents a material that was rapidly quenched and not annealed after production.

A$)$ Determine the approximate elastic modulus and yield strength of each material.

B$)$ Assume the difference in properties is due to a grain size difference only. Which material has a larger grain size?

C$)$ Given a Burger's vector of $0\mathrm{.}12$ nm $,$ a Hall$-$Petch constant of $0\mathrm{.}2$MPa$**$sqrt$()$m$,$ and that the shear modulus can be assumed to be $1//2$ of the axial modulus, calculate the approximate grain size of the smaller grain size materials