Questions $2.$ A copper sample, $1-cm$ long and $2-$mm in diameter, is tested in tension at a

strain rate of ${10}^{-4}{s}^{-1}.$ Its true stress$/$true strain behaviour is governed by the following

equation

$=A*{}^N{}^{}{?}^m$

where $A=400$MPa$*s$;$N=0\mathrm{.}5$;$m=0.$

$($a$)$ If the sample is tested and unloaded without necking or failure and its new length is $1\mathrm{.}2$ cm $,$ what plastic engineering strain was imparted to the sample?

$($b$)$ What plastic true strain was imparted to the sample?

$($c$)$ What true stress must have been applied to the sample to achieve this deformation?

$(10$ marks$)$