Conditions for shear banding and material instability in finite elastoplastic deformation

Abstract

A necessary and sufficient condition for shear banding in two-dimensional space is derived for finite elastoplastic deformation of compressible materials. The criterion for the initiation of shear bands, a geometric instability, is that the governing field equations become hyperbolic. The results indicate that shear bands may occur before the material response reaches its peak load, irrespective of compressibility, and that the critical work-hardening rate, which represents the material factor governing shear banding, has the order of the ratio of yield stress to shear modulus. Moreover, the characteristics, or the orientations, of shear bands do not in general coincide with the direction of maximum shear stress, and so their directions may not be orthogonal. Also in the analysis, the critical stress ratio, which is a deformation factor controlling shear banding, is derived explicitly in terms of Poisson's ratio, the relative density of the aggregate, and the transverse stress ratio. The prediction of the orientations of shear bands explains well, at least qualitatively, experimental observations in the open literature. The criterion for material instability, unlike the onset of shear banding, is defined at a point when the stress-strain relation of the aggregate has no inverse. The criterion for material instability due to shear banding is derived. This provides a tool to distinguish shear band localization from shear fracture in general.