A theory of dislocation cell formation based on stochastic dislocation dynamics

A stochastic effective medium theory is developed that accounts for the geometrically necessary fluctuations of the local stress and strain rate resulting from dynamic dislocation interactions. The concept is applied to the formation of dislocation cells in multiple slip. Starting from a Langevin-type evolution equation for the total dislocation density rho, a corresponding Fokker-Planck equation for the probability distribution p(s)(rho) is derived. Cell formation is related to a noise-induced non-equilibrium phase transition associated with a qualitative change of p(s)(rho). The cell size is found to be in inverse proportion to the Bow stress (principle of similitude). Critical conditions for, and the role of cross slip in, cell formation are discussed.