A cold-worked copper rod has a dislocation density

PHYSICS · Subjective · 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} = 8\times10^{14}\ \mathrm{m^{-2}}

. After annealing it at

700\,{}^\circ\mathrm{C}

for ten minutes, its dislocation density falls to

3\times10^{11}\ \mathrm{m^{-2}}

. A technician argues that, since annealing removes crystal defects, the rod must now be stronger than before. 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, compute the shear yield stress before and after annealing, say whether the technician is right, and explain why in terms of what a dislocation obstacle is.

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