It was recalled that the term, dislocation patterning, had been introduced over 20 years before, and a corresponding so-called gradient dislocation dynamics framework was proposed in order to describe such phenomena. In the Walgraef-Aifantis model then developed, it had been shown how coupled non-linear evolution equations of reaction-diffusion type for the forest (immobile) and gliding (mobile) dislocation densities could generate dislocation microstructures which corresponded to walls perpendicular to the slip direction in Cu crystals oriented for single slip under cyclic loading conditions. This model was adapted here to the multiple-slip case. A weakly non-linear analysis predicted that dislocation patterns should correspond to domains of walls perpendicular to each slip direction; separated by domain walls in the same orientations. This result was confirmed by numerical analysis and experimental observations. The present model generalized the original Walgraef-Aifantis model to the case of multiple slip and also explicitly considered gradient effects by allowing for non-uniform dislocation velocities and internal-stress effects.

On Dislocation Patterning - Multiple Slip Effects in the Rate Equation Approach. J.Pontes, D.Walgraef, E.C.Aifantis: International Journal of Plasticity, 2006, 22[8], 1486-505