Self-organization model of localization of cyclic strain into PSBs and formation of dislocation wall structure

Development of dislocation structures in cubic metal crystals cyclically deformed in single slip is treated as a self-organization process. The proposed model consists of the crystal plasticity equations, the equation of motion of glide dislocations, and the balance equation for stored dislocations (dipolar loops). The model incorporates hardening by the loops, sweeping of the loops by glide dislocations, drift of the loops in the stress gradients, the mutual loop interaction, their generation and annihilation. By using analytical methods it is briefly shown that in the early stage of deformation the vein or extended wall structure is formed. In the saturation state when all newly formed dislocations are annihilated strain becomes localized. In the lamellae of concentrated slip (PSBs) the dislocation structure may be but need not to be rearranged. The criterion for rearrangement is specified. The transformation of veins to walls is a typical rearrangement in PSBs.