On modelling the elasto-viscoplastic response of metals using polycrystal plasticity

Abstract

A constitutive framework for the elasto-viscoplastic response of metals that utilizes polycrystal plasticity is presented together with a corresponding numerical integration procedure. The single crystal equations are written in an intermediate configuration obtained by elastically unloading the deformed crystal without rotation from the current configuration to a stress-free state. The elastic strains are assumed always to be small. The accompanying numerical integration is implicit and proceeds by decoupling the volumetric and the deviatoric crystal responses. The extended Taylor hypothesis is used to relate the response of individual crystals to that of the polycrystal. Various homogeneous deformations have been simulated using the constitutive model and the integration scheme to compute the stress response and texture development. Aggregates of either face centered cubic (FCC) or hexagonal close-packed (HCP) crystals are subjected to both monotonic and non-monotonic loading histories. Numerical results demonstrate the performance of the model as well as show the stability and accuracy of the integration procedure. The present constitutive model and corresponding numerical procedures can be used to predict elastic effects (e.g. residual stresses) during the large deformation of polycrystalline materials while accounting for texture development and the associated anisotropy.