Stochastic Dislocation Dynamics. An Effective Medium Approach to Dislocation Patterning

Dislocation dynamical theories of spatio-temporal pattern formation during plastic flow meet with the problem of accounting for long-range dislocation interactions. This can be addressed by means of a "stochastic dislocation dynamics" (SDD). Its basic idea consists in considering the geometrically necessary fluctuations of the local effective stress and of the shear strain rate that are due to the dislocation interactions during glide. The auto- and cross-correlation functions of the effective stress and of the strain rate can be related to the strain-rate sensitivity and the mechanical power dissipation. On a mesoscopic scale, a crystal undergoing plastic deformation may thus be considered an effective fluctuating medium by formulating stochastic differential equations (Langevin-type) for the evolution of the dislocation densities. Dislocation patterning can be associated with noise-induced phase transitions far from equilibrium. The paper presents applications of SDD to dislocation cell formation during multislip and to single slip fatigue patterning. This gives qualitatively new ideas of the plastics of dislocation patterning which cannot be obtained from deterministic considerations.JRC.(IAM)-Institute For Advanced Material