A grain boundary model for gradient-extended geometrically nonlinear crystal plasticity: Theory and numerics

摘要

A grain boundary model is presented based on the dislocation density tensor within a geometrically nonlinear crystal plasticity framework. The formulations are derived using the linear momentum balance equation and surface related considerations which lead to a grain boundary yield criterion with isotropic and kinematic hardening. To decrease the implementation effort, a three-level solution algorithm is presented which allows to extend an already existing local single crystal material subroutine to account for gradient contributions. As an additional feature, the analytical linearization of the weak form regarding geometrically nonlinear crystal plasticity is presented. The effects of grain boundary strength and internal length scale on the material behavior as well as the role of grain boundaries as obstacles to dislocation transmission are discussed in several examples. Further, the results show interesting grain boundary hardening effects in cyclic loading.