A cube$-$shaped object with dimensions of $0\mathrm{.}05$ m for each side is

loaded uniformly with an applied force of $60,000$ Newtons that

compresses it in the y$-$direction. The material has a Young's

Modulus of $40$ GPa $.$

Please answer the following

A$.$ What is the expected elastic strain in the $y-$direction at the applied force of

$60,000N$ assuming no yielding? $(1$ pt$)($Make sure your answer shows the

value as a compressive strain.$)$

B$.$ The reported elastic strain in the $x-$and $z-$directions is $0\mathrm{.}00017.$ What is

Poisson's ratio for this material? $(2$ pts$)$

C$.$ Estimate the elastic energy in Joules for the cube at the applied force of

$80,000N.(1$ pt$)$

D$.$ Find the sum of the strains in the $x,y,$ and $z$ directions using the Poisson's

Ratio you found in B$.$ This is also the expected percent volume change $($or

volume strain$)$ under elastic loading. $(1$ pt$),$

E: What would the volume change be if the strain ratio was $0\mathrm{.}5,$ which we

often see for plastic deformation of metals? $(1$ pt$)$

The plot below shows the grain size dependence of yield strength for Mo

at various temperatures.

A$.$ According to the Hall$-$Petch relationship shown what would you expect to

be the grain size, $d,$ in meters when the yield stress is $100$ MPa for a test

temperature of $350$ K $?(2$ pts $)$