The dynamic version of the continuum theory of dislocations in the form presented by Kosevich was accepted as a starting point for the development of a model of dislocation pattern formation. However, instead of the classical concept of the dislocation densitytensor, more refined measures were used for the description of the dislocation population: (i) a density of stored dislocations in the form of dislocation loops and (ii) densities of glide dislocations considered separately for different initial dislocation orientations. The linear stability analysis of a simplified version of the proposed model showed that the density of stored dislocations formed patterns akin in geometry to those observed in the early stage of the formation of dislocation structure in cyclically deformed cubic metal crystals oriented for single slip.

Pattern Formation in the Framework of the Continuum Theory of Dislocations. J.Kratochvíl, R.Sedláček: Physical Review B, 2003, 67[9], 094105 (10pp)