Kinematics of finite elastoplastic deformation

Abstract

A model in which plastic deformation occurs as a result of crystallographic slip is used to derive a formula for decomposing a deformation gradient into parts attributable to elastic and plastic deformation processes. The dislocation kinematics are those in long use, for example by Rice (1971, J. Mech. Phys. Solids 19, 433) and by Hill and Havner (1982, J. Mech. Phys. Solids 30, 5). The analysis presented here differs from that given by these authors in that it concerns total deformation (and its elastic and plastic parts) rather than incremental deformation. The decomposition obtained is inherent in the physics of the deformation process, arising naturally when the spatial discreteness of the active slip planes is taken into account. Expressions for the decomposition components are obtained by means of volumetric averaging of contributions of elastic deformation and slip to the total deformation. The decomposition captures the effects of isoclinic orientation central to Mandel's (1973, Int. J. Solids Struct. 9, 725) theory, but without introduction of the intermediate configuration that arises when the deformation is assumed to be expressible as though the plastic and elastic deformations occurred sequentially. Because no intermediate configuration arises, the established objectivity principle applies without modification and the concept of elastic embedding that is essential to proper selection of temporal rates is implemented quite naturally. Although the new decomposition is motivated by dislocation-mechanical considerations, the result is a continuum-mechanical expression that can be used in other contexts in which the sites of inelastic deformation are spatially separated in the material.