SHEAR BAND SUSCEPTIBILITY - WORK-HARDENING MATERIALS

A phenomenological model of a rigid, work hardening, plastic material, with rate hardening and thermal softening, is analysed to determine susceptibility to the formation of adiabatic shear bands. The approach used is to examine perturbation equations that are linearized about a homogeneous solution of the full nonlinear problem. It is found that, in general, solutions to these linearized equations exhibit a strong initial boundary layer in time, and that the traditional approach, that is, analysis of frozen eigenvalues, cannot be relied upon to determine stability against initial perturbations. A variety of special techniques are used to approximate solutions for the fully time-dependent behavior. These techniques include asymptotic expansions of exact representations, WKB analysis of the equations that govern the Fourier components, and numerical analysis by spectral methods of both the linearized and nonlinear equations. Although solutions to the linearized equations are valid only for finite time when perturbations are growing, it is still possible to obtain a basic scaling law for comparing susceptibility of different materials.