The development of dislocation structures in cubic metal crystals which were cyclically deformed in single slip was treated as being a self-organization process. The proposed model comprised crystal plasticity equations, the equation of motion of glide dislocations and the balance equation for stored dislocations (dipolar loops). The model incorporated hardening by loops, sweeping of the loops by glide dislocations, drift of the loops in stress gradients, mutual loop interaction and their generation and annihilation. By using analytical methods, it was shown that - in the early stages of deformation - a vein or extended wall structure was formed. In the saturated state, when all of the newly-formed dislocations were annihilated, the strain became localized. The dislocation structure could be rearranged in the lamellae of concentrated slip (persistent slip boundaries). The transformation of veins into walls was a typical rearrangement in persistent slip boundaries.

Self-Organization Model of Localization of Cyclic Strain into PSBs and Formation of Dislocation Wall Structure. J.Kratochvíl: Materials Science and Engineering A, 2001, 309-310, 331–5