Adiabatic shear banding and the micromechanics of plastic flow in metals

Abstract

This article studies the conditions that dislocation generation and motion must fulfil to promote the development of adiabatic shear bands in crystalline metals. First, we derive a stability criterion for the formation of shear bands, by linearising the conservation equations of thermo-plasticity. We then apply this criterion on the micromechanics-based Orowan equation for plastic flow, introducing a number of increasingly sophisticated constitutive assumptions on the model. It is found that there are two crucial promoters of shear band formation: the unfettered generation of dislocations that may be found in stage I plasticity; and the softening of the elastic constants with increasing temperature. In turn, we show that limiting the speed of dislocations tends to inhibit the formation of dislocations, even when the temperature dependence of the dislocation’s drag is accounted for. This leads to the existence of an upper temperature limit above which shear band formation appears unlikely.