Finite element simulation of large-strain single-crystal viscoplasticity: An investigation of various hardening relations

Hardening relations describe the increase in resistance to deformation during plastic flow. Three hardening relations are compared here in the context of conventional large-strain single-crystal viscoplasticity. The first is an isotropic hardening relation. The second is a hardening relation that is expressed as an ordinary differential equation in the slip resistance. The third is a new relation, originally developed in the context of gradient crystal plasticity, in which the slip resistance is expressed explicitly in terms of the accumulated slip on each slip system. The numerical solution of the governing equations is found using the finite element method coupled with a predictor-corrector type algorithm. The features of the hardening relations are elucidated using a series of numerical benchmark problems. The parameters for the hardening relations are calibrated using a model problem. Various crystal structures are investigated, including single- and double slip, and face-centred cubic crystals. The hardening relations are compared and their relative features discussed.