A dislocation based gradient plasticity model

A crystal plasticity model including gradient terms was suggested for a double slip geometry. The dislocation densities for the two slip systems were considered as internal variables of the model. Diffusion-like second derivative terms were attributed to dislocation cross-slip. A relation between the 'diffusion coefficient' and the micromechanical quantities, such as the dislocation cross-slip probability and the cross-slip distance was established. To demonstrate that a model of this type can be successfully used in conjunction with finite element analysis, a simplified case of a shear layer, with two slip systems sharing a common slip plane, was studied.