On the selection of active slip systems in rate independent crystal plasticity

Non-uniqueness of the set of active slip systems is a crucial issue in crystal plasticity. To avoid this problem one may perform viscoplastic regularization. This introduces a certain rate dependency, while many crystals are known to behave rate independently. One would require very low viscosity parameters in the regularized model to resemble the experimental behavior of rate independent crystals, which in turn entails numerical difficulties. Furthermore, no direct approach is known to model deformation banding using viscoplastically regularized models. Hence, to adequately treat rate independent crystal plasticity an alternative method is needed. The proposed method, Maximum Dissipation Crystal Plasticity (MDCP), achieves uniqueness by selecting the set of active slip systems according to its dissipation. In a finite element calculation, a system of coupled quadratic equations is solved at every integration point to define the material behaviour. This approach is formally equal to the method of incremental energy minimization recently proposed by Petryk et al. It can be shown that a viscoplastically regularized model is a limiting case of MDCP, giving similar results when cross hardening becomes negligible. Nevertheless, recent 3D dislocation dynamics calculations by Devrince et al. show that cross hardening in fcc crystals is far more important than self hardening. In such cases MDCP gives results distinctly different from its rate dependent counterpart. Fewer slip systems are selected by MDCP, resulting in more slip on the individual active systems. The proposed method is numerically implemented as an Abaqus user material subroutine within the large deformation framework, such that the simulation of arbitrary load cases is possible.