Nonequilibrium statistical mechanics of the evolution of dislocation structures

Abstract

We develop a form of nonequilibrium statistical mechanics designed to be applicable to the evolution of dislocation structure (or patterning) during metal deformation. The formalism can be applied both to time independent relaxed dislocation systems as well as to the time dependent relaxation itself. One specific application is to a simplified version of the "equilibrium" relaxed state, where we show that an effective temperature can be defined in terms of the noise in the system (back stress fluctuations). As the noise is decreased, varying degrees of order appear. In a second application to a simple two-dimensional (2D) dislocation computer model, we show how to obtain an effective time dependent free energy and temperature from the ensemble driving forces developed in earlier work. In this model, too, the underlying physics relates to a competition between the noise and energy. And, finally, we show that the behavior of the Boltzmann H function for the same 2D computer model can be tied to the rather complex physics of the evolving time dependent structure. © 2007 The American Physical Society.