Computational modeling of gradient hardening in polycrystals

A gradient hardening crystal plasticity model for polycrystals is introduced in Ekh et al. (2007). It is formulated in a thermodynamically consistent fashion and is capable of modeling a grain-size-dependent stress-strain response. In this contribution we extend that model to also include cross-hardening. A free energy is stated which includes contributions from the gradient of hardening along each slip direction. This leads to hardening stresses depending on the second derivative of the plastic slip. The governing equations for a nonlinear coupled system of equations is solved numerically with the help of a dual-mixed finite element method. The numerical results show that the macroscopic strength increases with decreasing grain size as a result of gradient hardening: Moreover, cross-hardening further enhances the strengthening gradient effect