Two cylindrical bars are loaded in separate experiments.
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 Strain and stress in a deformed solid
Problem
Two cylindrical bars are loaded in separate experiments.
((a)) A polished brass bar is pulled in uniaxial tension σ0 along its axis. Treat the bar as a uniform continuum. Using the principal stresses and Mohr's circle for uniaxial tension, find the angle between the bar's axis and the normal of the planes on which the shear stress is greatest. Find the normal stress and the shear stress on such a plane, and say which of the two picks it out from all the others. Take as an idealisation that the broad slip bands seen on the surface, which cross many grains, follow these planes; the fine slip traces inside a single grain follow that crystal's own planes and are not predicted here.
((b)) A bar of brittle grey cast iron is clamped and twisted about its axis (pure torsion) until it fractures, the shear stress on the cross-section reaching τ0. Predict the orientation, relative to the axis, of (i) the planes of greatest shear and (ii) the plane of greatest tension, and explain why a brittle bar, which tears across the plane of greatest tension, breaks along a helix rather than straight across the axis.