Plasticity without phenomenology: a first step

Sabyasachi Chatterjee, Giacomo Po, Xiaohan Zhang, Amit Acharya, Nasr Ghoniem

A novel, concurrent multiscale approach to meso/macroscale plasticity is demonstrated. It utilizes a carefully designed coupling of a partial differential equation (pde) based theory of dislocation mediated crystal plasticity with time-averaged inputs from microscopic Dislocation Dynamics (DD), adapting a state-of-the-art mathematical coarse-graining scheme. The stress- strain response of mesoscopic samples at realistic, slow, loading rates up to appreciable values of strain is obtained, with significant speed-up in compute time compared to conventional DD. Effects of crystal orientation, loading rate, and the ratio of the initial mobile to sessile dislocation density on the macroscopic response, for both load and displacement controlled simulations are demonstrated. These results are obtained without using any phenomenological constitutive assumption, except for thermal activation which is not a part of microscopic DD. The results also demonstrate the effect of the internal stresses on the collective behavior of dislocations, manifesting, in a set of examples, as a Stage I to Stage II hardening transition.