A review was presented of the problem of describing theoretically the evolution of a dislocation ensemble in a crystal during plastic deformation, and the development within it of dislocation self-organizational processes that could lead to slip localization and to a non-uniform distribution of dislocations in the crystal. The theoretical considerations were based upon a system of dislocational kinetic equations, of reaction-diffusion type, for the densities of mobile and immobile dislocations. One particular aspect of the derivation of these equations included the topological features of dislocations as linear, rather than point-like, formations. The processes which were involved included the multiplication, diffusion, annihilation and immobilization of dislocations. The mechanism of non-local diffusion of dislocations, due to their long-range interaction, was considered separately. The inclusion of these processes made it possible to formulate a model evolution equation, for the dislocation ensemble, that could serve as a basic equation for the quantitative analysis of particular effects that were associated with the cooperative aspects of plastic deformation. These included the formation of slip lines and bands in the initial stages of the plastic deformation of crystals.

G.A.Malygin: Fizika Tverdogo Tela, 1995, 37[1], 3-42 (Physics of the Solid State, 1995, 37[1], 1-19)