Rate equation approach to dislocation dynamics and plastic deformation

Strain localization and dislocation microstructure formation are typical features of plastic deformation in metals and alloys. Plastic deformation occurs by the glide of dislocations, and, although dislocation distributions are rather uniform at its onset, they usually become unstable when deformation proceeds and undergo successive transitions towards various types of microstructures such as cells, deformation bands, persistent slip bands, labyrinth structures, etc. This phenomenon is experimentally well documented, but, despite a huge number of theoretical investigations, its modeling is still in its infancy. In the spirit of multiscale modeling, an intermediate step between micro- and macroscopic descriptions, consists in the derivation of mesoscopic rate equations describing the dynamical evolution of dislocation densities. It will be shown on some classical examples why this approach is interesting for the description of mechanical systems undergoing plastic instabilities, and how it may be used to determine the key physical processes for dislocation patterning. It will also be shown that the localization of plastic deformation is a natural consequence of collective behaviors induced by reaction and transport in dislocation populations.