A mesoscale continuum theory of plasticity was presented here for multiple-slip systems of parallel edge dislocations. Firstly, the Bogolyubov-Born-Green-Yvon-Kirkwood integral equations were constructed which related differing orders of dislocation correlation functions via a grand canonical ensemble. Approximate pair correlation functions were obtained for single-slip systems having two types of dislocation and, subsequently, for general multiple-slip systems of both charges. The effect of the correlations was seen in the form of an entropic force, in addition to the external stress and the self-consistent internal stress.

Statistical Approach to Dislocation Dynamics - from Dislocation Correlations to a Multiple-Slip Continuum Theory of Plasticity. S.Limkumnerd, E.Van der Giessen: Physical Review B, 2008, 77[18], 184111