Effect of thermal softening on Swift and Hill instability limits in forming

Abstract

Swift's theory of diffuse necking and Hill's theory of localized necking in sheets subjected to in-plane biaxial stresses have been generalized to take into account thermal effects. Using a characteristic material constant M which combines the density, specific heat, and rate of thermal softening of the material, it is shown that adiabatic conditions correspond to the M-value approaching zero. At the other extreme, isothermal conditions correspond to an M-value approaching infinity. Practically, a material such as titanium, with a low M-value (M ≤ 2), will be particularly prone to thermally assisted shear instability, whereas materials such as copper, with high M-values, will be resistant to thermally assisted shear instability except at high rates of strain. As the M-value decreases, it is shown that the Swift and Hill instability loci (plotted in terms of principal strains) shrink towards the origin. Thermally assisted shear mechanisms will affect other limit situations for which the Swift or Hill theories do not apply.