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Experimentally, it has been observed for single crystals of a number of metals that the critical resolved shear stress, $\backslash$tau $\_($crss $),$ is a function

of the dislocation density, $\backslash$rho $\_($D$),$ as

$\backslash$tau $\_($crss$)=\backslash$tau $\_(0)+$A$\backslash$sqrt$($P$\_($D$))$

where $\backslash$tau $\_(0)$ and A are constants. For some metal, the critical resolved shear stress is $4\mathrm{.}07$ MPa at a dislocation density of $2\mathrm{.}10\backslash$times $10^(5)$mm$^(-2).$

If it is known that the value of A for this metal is $3\mathrm{.}68\backslash$times $10^(-3)$MPa$-$mm$,$ compute the $\backslash$tau $\_($crss $)($in MPa $)$ at a dislocation density of $2\mathrm{.}17\backslash$times $10^(7)$

mm$^(-2).$

MPa

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