A copper rod is cold-worked to a moderate dislocation density,

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch Real crystals: vacancies, dislocations and the strength of metals

Problem

\rho_{\rm disl} = 5\times10^{13}\ \mathrm{m^{-2}}

, well short of the heavily worked value of

10^{15}\ \mathrm{m^{-2}}

used in Section 13.6's worked example. ((a)) Estimate the resolved shear yield stress

\tau_{\rm c}

using

\tau_{\rm c} \approx \alpha_{\rm T}Gb_{\rm B}\sqrt{\rho_{\rm disl}}

, with

\alpha_{\rm T}=0.3

G=48\ \mathrm{GPa}

and

b_{\rm B}=2.556\ \mathrm{\mathring{A}}

for copper. ((b)) Convert this to an equivalent tensile yield stress for a polycrystal using the Taylor factor of about

3.06

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