A solid aluminium block ( ) sits on the sea floor about down

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 solid aluminium block (σY=270 MPa\sigma_Y = 270\,\mathrm{MPa}) sits on the sea floor about 10 km10\,\mathrm{km} down, where the water pressure is p=100 MPap = 100\,\mathrm{MPa}. A fixture clamped to it adds a shear stress τ\tau on one pair of faces, so that far from any edge the stress is σxx=σyy=σzz=−p\sigma_{xx}=\sigma_{yy}=\sigma_{zz}=-p and σxy=τ\sigma_{xy}=\tau, with every other component zero. ((a)) Find the three principal stresses in terms of pp and τ\tau. ((b)) Find the shear τ\tau at which the block first yields by Tresca's criterion and by the von Mises criterion. ((c)) Say how both answers would change if the same block were twisted in the same way on the deck of the ship, at p=0p=0.

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