A review was presented of the problem of theoretically describing the evolution of dislocation distributions in a crystal undergoing plastic deformation, and the development of a self-organization that could lead to slip localization and to a non-uniform arrangement of the dislocations. The present work was based upon a system of dislocation kinetic equations, of reaction-diffusion type, for the densities of mobile and immobile dislocations. The derivation of the equations was considered with regard to the topological features of dislocations as linear, rather than point-like, formations. Experimental data and theoretical estimates were used to evaluate the microscopic processes that governed the evolution and self-organization of dislocation ensembles in real crystals. These processes included the multiplication, diffusion, annihilation, and immobilization of dislocations. The non-local diffusion of dislocations, due to their long-range interaction, was considered separately. The incorporation of these processes made it possible to formulate a model evolution equation, for the dislocation ensemble, that could serve as a basic tool in the quantitative analysis of particular effects that were associated with the cooperative nature of plastic deformation, such as the formation of slip lines and bands in the initial stages of such deformation.

Dislocation Self-Organization and Slip Localization in Crystals Undergoing Plastic Deformation. G.A.Malygin: Fizika Tverdogo Tela, 1995, 37[1], 3-42 (Physics of the Solid State, 1995, 37[1], 1-19)