A copper crystal ( , ) contains two straight

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Dislocations and the onset of plastic flow

Problem

A copper crystal (

G = 48\,\mathrm{GPa}

b = 0.256\,\mathrm{nm}

) contains two straight, parallel edge dislocations lying along

z

, both gliding on the same slip plane

y=0

. Dislocation A sits at

x=0

with Burgers vector

\mathbf{b}_A = b\,\hat{\mathbf x}

; dislocation B sits at

x = d = 50\,\mathrm{nm}

with Burgers vector

\mathbf{b}_B = -b\,\hat{\mathbf x}

(same magnitude, opposite sign: an edge dislocation dipole). A uniform stress is applied to the crystal with

\sigma_{xy} = \tau = 15\,\mathrm{MPa}

and all other stress components zero. ((a)) Using the Peach-Koehler force

\mathbf f = (\boldsymbol\sigma\cdot\mathbf b)\times\boldsymbol\xi

(with

\boldsymbol\xi = \hat{\mathbf z}

), find the glide force per unit length on each dislocation, stating its direction along

x

. ((b)) Predict whether the pair glides together (towards annihilation) or apart, under this applied stress alone.

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