Macroscopic measure of the rate of deformation produced by micro-shear banding

Abstract

Physical model of shear strain rate produced by active micro-shear bands in metals is formulated and mathematical idealization of micro-shear bands system by means of the theory of singular surface of order one is proposed. Extension of the known averaging procedure over the representative volume element traversed by a strong discontinuity surface is presented. As a result, the macroscopic measure of velocity gradient produced in the course of elastic-plastic deformation with micro-shear banding is derived. The corresponding macroscopic measures of the rate of deformation and material spin, necessary to formulate constitutive description, are also determined.