Strain-gradient elasto-plastic self-consistent crystal plasticity: Applications to predicting the evolution of geometrically necessary dislocations and size sensitive mechanical response

Abstract

A novel strain gradient (SG) formulation of the mean-field elasto-plastic self-consistent (EPSC) crystal plasticity model is developed. The SG-EPSC formulation stems from the intragranular orientation spreads calculated from the second moments of the stress fields that give rise to the fluctuations in the lattice rotation rates in the grains of a polycrystalline aggregate. A procedure for creating spatial arrangements of the orientation spreads in grains is developed to obtain a functional form of the rotation tensor fields to facilitate the calculations of spatial derivatives. The right stretch tensors for orientations belonging to the intragranular spreads are obtained to form the polar decomposition of the elastic deformation gradients. The spatial derivatives involving the “curl” operation are then used to obtain the Nye dislocation tensor from the elastic deformation gradients. The Nye tensor is used to calculate geometrically necessary dislocations (GNDs) within the overall finite deformation formulation. A hardening law based on statistically stored dislocation density and an advanced composite grain model for handling twinning available in EPSC are enhanced to include the effects of GNDs. Finally, a GND-based backstress law is implemented to influence the activation of slip systems. The potential and utility of the developed model to efficiently simulate the evolution of GNDs, microstructure, and mechanical fields in polycrystalline metals are demonstrated via a few simulation cases including compression tests of α-Ti and a set of strain-path change deformation conditions of AA6016-T4.