Pattern formation in the framework of the continuum theory of dislocations

The dynamic version of the continuum theory of dislocations in the form presented by Kosevich is accepted as a starting point for the development of a model of dislocation pattern formation. However, instead of the classical concept of the dislocation density tensor, more refined measures are 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 shows that the density of stored dislocations forms 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.

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