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

摘要

Non-uniqueness in 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. This is sometimes approximated using ver low viscosity parameters in the regularized model, however at the cost of numerical difficulties. 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 H. Petryk and M. Kursa (Book of Abstracts of the 8th European Solid Mechanics Conference, Graz, G.A. Holzapfel and R.W. Ogden (eds.)). 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 Devincre et al. (Mat. Sci. Eng. A, 400-401 (2005), 182-185) show that cross hardening in face centered cubic crystals is far more important than self hardening. In such cases MDCP gives results distinctly different from its rate dependent counterpart. The proposed method is numerically implemented as user material subroutine into the finite element package ABAQUS within the small as well as large deformation framework, called MDCP and FinDMDCP respectively, such that the simulation of arbitrary load cases is possible.