Some exactly solvable models for the statistical evolution of internal variables during plastic deformation

A class of exactly solvable statistical models for the evolution of interna l (microstructural) variables in the course of plastic deformation is discu ssed. The common feature of these models is that the microstructural evolut ion is described in terms of stochastic differential equations (Langevin eq uations) which by a non-linear transformation can be mapped onto a Wiener o r Ornstein-Uhlenbeck process. Examples include the textural evolution of pl anar polycrystals, the evolution of dislocation density distribution in uni directional plastic deformation, and the combined dynamics of mobile disloc ations and dislocation obstacles leading to slip-channel formation. (C) 200 0 Elsevier Science Ltd. All rights reserved.