Question $3$: Answer the Following Problems

a$)$ Experimentally, it has been observed for single crystal of a number of metals that the

critical resolved shear stress is a function of the dislocation density according to the

relation:

${}_{crss}={}_o+A\sqrt[\phantom{2}]{{}_D}$

For aluminium, the critical resolved shear stress of undeformed crystal is $0\mathrm{.}72$ MPa while a

dislocation density of ${10}^4$ per $m{m}^2$ is measured. Compute the critical resolved shear stress

for aluminium, if the material dislocation density is increased to ${10}^8$ due to deformation up

to the yield point. Use ${}_o(Al)=0\mathrm{.}075$MPa.