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Description of the behavior of a dislocation ensemble with allowance for dislocation multiplication

A new approach to the description of processes of plastic deformation is developed. Within this approach, the evolution of a dislocation ensemble is determined by both dislocation multiplication and dislocation transformations with both the processes occurring against the background of elastic stresses produced by the dislocation ensemble itself. Apart from the equations of detailed balance that determine time changes in the densities of mobile (glissile) and immobile (sessile) dislocations, an equation that describes the operation of dislocation sources is suggested and a new parameter that characterizes the time of adjustment of the dislocation density to external stress is introduced. Deformation curves are analyzed at various values of the system parameters and the main features of plastic deformation for some materials are described. The nonmonotonic behavior of deformation curves that is observed in some cases upon transition from elastic to plastic deformation is suggested.