Question $4$

$($a$)$ Show that the tensile strength of a material can be expressed as $k{n}^n(exp{)}^{-n},$ given $=n$ at the tensile strength, and $k$ and $n$ are the strength coefficient and the strain hardening exponent, respectively.

$(10$ marks$)$

$($b$)$ In a tensile test on a metal specimen, true strain $=0\mathrm{.}08$ at true stress $=275M\frac{N}{m^2}.$ When the true strain $=0\mathrm{.}25,$ the true stress $=325M\frac{N}{m^2}.$ Determine the strength coefficient and the strain hardening exponent for this specimen. Hence, determine the tensile strength for this metal.

$(15$ marks$)$