Problem $4$

$($a$)$ The critical resolved shear stress for iron is $27$ MPa $.$ Determine the maximum possible yield strength for a single crystal of Fe pulled in tension.

$($b$)$ Two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross$-$sectional areas $($while maintaining their circular cross sections$).$ For one specimen, the initial and deformed radii are $16$ mm and $11$ mm $,$ respectively. The second specimen, with an initial radius of $12$ mm $,$ must have the same deformed hardness as the first specimen; compute the second specimen's radius after deformation.