It was recalled that the current challenge in dislocation dynamics was to describe the collective behavior of the dislocations which formed during plastic deformation. The methods which were used fell into the categories of continuum model or computer simulation, and an important aim was to establish a link between the 2 approaches, for a simplified dislocation configuration. As the simplest possible dislocation system, an assembly of parallel edge dislocations was considered here. It was shown that, by neglecting short-range correlation effects, a self-consistent field description could be derived from the equations of motion of individual dislocations. The advantage of the applied derivation method was that it took account of the precise form of the dislocation-dislocation interaction; thus establishing a link between microscopic-scale and mesoscopic-scale descriptions without making ad hoc assumptions. A stability analysis of the trivial solution to the 2 governing equations of dislocation evolution revealed that the elastic dislocation-dislocation interaction was not enough to produce patterning but, due to the existence of marginally stabile perturbations, the introduction of dislocation multiplication, regardless of its strength, led to self-organization. Dislocation-density evolution was investigated numerically under various conditions. The development of well-defined, more or less periodic, structures was observed whose characteristic length-scales depended strongly upon the deformation mode.

Investigation of Dislocation Pattern Formation in a Two-Dimensional Self-Consistent Field Approximation. I.Groma, P.Balogh: Acta Materialia, 1999, 47[13], 3647-54