A thin-walled aluminium alloy tube ( , Burgers vector

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 thin-walled aluminium alloy tube (

G = 26\,\mathrm{GPa}

, Burgers vector

b = 0.286\,\mathrm{nm}

, tensile yield stress

\sigma_Y = 200\,\mathrm{MPa}

) carries simultaneously an axial tension that produces

\sigma_{xx} = 120\,\mathrm{MPa}

and a torque that produces a surface shear

\sigma_{xy} = 60\,\mathrm{MPa}

(

x

along the tube axis,

y

circumferential,

\sigma_{yy}=0

). ((a)) Using Mohr's circle for this plane stress state, find the shear stress resolved on a plane whose normal lies at

45^\circ

to the tube axis, and hence the shear strain there from the isotropic Hooke's law of the tube's aluminium. ((b)) A dislocation with Burgers vector

b=0.286\,\mathrm{nm}

lies in that plane, aligned with the resolved shear direction. Find the Peach-Koehler force per unit length on it. ((c)) Using the same stress state, decide by both the Tresca and the von Mises criteria whether the tube has yielded, quoting the equivalent stress each criterion gives.

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