A microstructural approach to the incorporation of gradient terms into single-crystal plasticity theory was considered. A diffusion term which represented the cross-slip of dislocations was incorporated into the evolution equations for dislocation densities. Coupling between the micro-scale and the macro-scale was provided by the dislocation-based gradient plasticity model. The effect of the diffusion-like term, in the constitutive relationship, upon the formation of localized shear modes was studied. An analysis was presented for a plane-strain strip which was oriented for multiple slip in tension.

The Analysis of Shear Banding with a Dislocation Based Gradient Plasticity Model. L.J.Sluys, Y.Estrin: International Journal of Solids and Structures, 2000, 37[46-47], 7127-42