A single crystal of magnesium ( , Burgers vector ) is measured to begin plastic flow…

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

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

Problem

A single crystal of magnesium (

G = 17\,\mathrm{GPa}

, Burgers vector

b = 0.32\,\mathrm{nm}

) is measured to begin plastic flow at a resolved shear stress

\tau_Y = 0.70\,\mathrm{MPa}

. ((a)) Treating this yield stress as the operating stress of a Frank-Read source, estimate the pinning length

L

of the source responsible. ((b)) A separate measurement finds a dislocation density of

\rho_d = 2\times10^{10}\,\mathrm{m^{-2}}

in the same crystal, giving a typical line spacing

\rho_d^{-1/2}

. Compare this spacing with the estimated

L

and say whether the two are of the same order.

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