On dislocation patterning: Multiple slip effects in the rate equation approach

Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion, along with accompanying production/annihilation processes, lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result to the development of various types of dislocation microstructures (dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc.), depending on the externally applied loading and the intrinsic lattice constraints. The term “dislocation patterning” was introduced over 20 years ago by the third author and a corresponding “gradient dislocation dynamics” framework was suggested to describe such phenomena. In the W–A model proposed at that time by the last two authors, it was shown how coupled nonlinear evolution equations of the reaction-diffusion type for the forest (immobile) and gliding (mobile) dislocation densities can generate dislocation microstructures which correspond to walls perpendicular to the slip direction for Cu-crystals oriented for single slip under cyclic loading conditions. This model is adapted to the multiple slip case here. Weakly nonlinear analysis predicts that dislocation patterns should correspond to domains of walls perpendicular to each slip direction and separated by domain walls in the same orientations. This result is confirmed by numerical analysis and experimental observations. The present model generalizes the original W–A model to the case of multiple slip and considers also explicitly gradient effects by allowing for non-uniform dislocation velocities and internal stress effects.