On the role of strain gradients and long-range internal stresses in the composite model of crystal plasticity

Abstract

The aim of this study was to extend the simple two-component composite model of plasticity of single-phase materials containing a heterogeneous dislocation distribution by including the effect of finite strain gradients in the transition from the regions of high local dislocation density and flow stress to neighbouring regions of low dislocation density and flow stress. For this purpose, a simple one-dimensional model of a dislocation wall structure was considered. In this model, a periodically varying local density of statistically stored dislocations, associated with alternating positive and negative gradients of the local flow stress, was assumed. Special attention was focused on the role of the geometrically necessary dislocation distribution and the deformation-induced long-range internal stresses. It was shown that the geometrically necessary dislocations ensure compatibility of deformation by giving rise to long-range internal stresses which, superimposed on the external stress, cause a redistribution of the stress on a local scale, thus permitting the simultaneous deformation of soft and hard regions. Moreover, it could be shown that the local density of the geometrically necessary dislocations can be described alternatively in terms of either the local strain gradient or the local flow stress gradient and that it is related unambiguously to the local distribution of the statistically stored dislocations. The macroscopic flow stress, formulated as the spatial average of the local flow stress, has been found not to depend explicitly on the density of geometrically necessary dislocations, unless the geometrically necessary dislocations of one glide system are intersected by glide dislocations of another glide system. This result implies that, in Taylor-type descriptions of the macroscopic flow stress, the simple superposition of the (mean) density of geometrically necessary dislocations on the (mean) density of statistically stored dislocations is not well founded.