$5\mathrm{.}19$ A typical cross$-$head speed in a tensile testing machine is $0\mathrm{.}2in\frac{.}{m}in.$

$($a$)$ What is the nominal engineering strain rate imposed by this cross$-$head speed on a typical

engineering tensile specimen with a $2$ inch gage length? $(2$ pts$)$

$($b$)$ Estimate the dislocation velocity that would be obtained at this strain rate in an iron specimen

with a dislocation density of ${10}^{10}c\frac{m}{c}{m}^3.$ Assume that the Burgers vector of iron is $0\mathrm{.}248$ nm $.(5$

pts$)$

$($c$)$ If in a very slow tensile test a strain$-$rate of ${10}^{-7}{s}^{-1}$ is used, what dislocation velocity would be

expected in the above iron specimen? $(5$ pts$)$