$5\mathrm{.}23(10$ pts $)$ The slope, $m,$ of the curve drawn through the data points in Fig. $5\mathrm{.}35$ is approximately

equal to $2\mathrm{.}55{10}^{-4}kgm{m}^{-2}.cm.$ Compute the increase in the dislocation density that would

correspond to an increase in flow stress from $588$ to $784$ MPa $($use the titanium data of Jones and

Conrad$).$

FIG. $5\mathrm{.}35$ The variation of the flow$-$stress $$ with the square root of the

dislocation density ${}^{\frac{1}{2}}$ for titanium specimens deformed at room tem$-$

perature, and at a strain rate of ${10}^{-4}se{c}^{-1}($After Jones, R$.$ L$.,$ and

Conrad, H$.,$ TMS$-$ALME, $245779[1969].)$