Strain Gradient Crystal Plasticity: Thermomechanical Formulations and Applications

Abstract

Since the pioneering work of [3] (see [4] for a review), strain gradient plasticity has aroused increasing interest in the mechanics of materials community, leading to a large panel of non local plasticity models. However, comparisons between these models remain seldom [19], and he full thermomechanical framework is usually not provided. The attention is focused here on models incorporating modified or additional balance equations and therefore additional boundary conditions in order to solve practical boundary value problems. The reader is referred to [1] for models sticking to classical structure of the boundary value problem. The aim of the present work is to bring together and to some extent reconcile three main trends of strain gradient plasticity models applied to metal single crystals : the gradient of internal variable, second grade and Cosserat approaches. In particular, the thermodynamical setting for all three models will be described in a unified way, in order to make actual differences between theories really visible. For simplicity and clarity, the analysis is restricted to single slip and rate–independent constitutive equations. Extensions to the general viscoplastic multislip case are straightforward, based on multicriterion elastoviscoplasticity. Each model presentation follows the three following main steps :