ANALYSIS OF SHEAR INSTABILITY IN THERMAL VISCOPLASTIC SOLIDS

Abstract

This paper presents a state-of-the-art brief review as regards the analysis of shear band formation in thermal viscoplastic solids through the thermo-mechanical mechanism. Governing equations are derived for the one-dimensional simple shearing deformation of a material slab that has a finite width h in the x2 direction whereas it extends indefinitely in the x1 and x2 directions, where x1,x2, x3 represent a system of rectangular Cartesian coordinates. The material behavior is characterized by the dependence of the plastic strain rate on the flow stress, temperature and plastic strain. We divide the deformation history into the pre-initiation regime and the post-initiation regime in view of the instability phenomenon considered. Analysis of the pre-initiation regime include the qualitative effects of strain rate sensitivity, thermal softening, strain hardening, inertia and wave length of initial imperfections on the onset of localization. Analysis of the post-initiation regime is concerned - on the other hand - with the attainment of a final band thickness where steady state thermal deformation conditions prevail. We present exact implicit local solutions for the behavior of the plastic strain rate. These solutions are then used in order to derive a localization damage parameter for viscoplastic solids.