A stochastic effective medium theory was developed which accounted for the geometrically necessary fluctuations of the local stress and strain rate which resulted from dynamic dislocation interactions. The theory was applied to the formation of dislocation cells in multiple slip. Beginning with a Langevin-type evolution equation for the total dislocation density, a corresponding Fokker-Planck equation was derived for the probability distribution. Cell formation was related to a noise-induced non-equilibrium phase transition that was associated with a qualitative change in the probability distribution. The cell size was found to be inversely proportional to the flow stress.

P.Hähner: Acta Materialia, 1996, 44[6], 2345-52