Statistical mechanics treatment of the evolution of dislocation distributions in single crystals
Abstract
A statistical mechanics framework for the evolution of the distribution of dislocations in a single crystal is established. Dislocations on various slip systems are represented by a set of phasespace distributions each of which depends on an angular phase space coordinate that represents the line sense of dislocations. The invariance of the integral of the dislocation density tensor over the crystal volume is proved. From the invariance of this integral, a set of Liouvilletype kinetic equations for the phasespace distributions is developed. The classically known continuity equation for the dislocation density tensor is established as a macroscopic transport equation, showing that the geometric and crystallographic notions of dislocations are unified. A detailed account for the shortrange reactions and cross slip of dislocations is presented. In addition to the nonlinear coupling arising from the longrange interaction between dislocations, the kinetic equations are quadratically coupled via the shortrange reactions and linearly coupled via cross slip. The framework developed here can be used to derive macroscopic transportreaction models, which is shown for a special case of singleslip configuration. The boundary value problem of dislocation dynamics is summarized, and the prospects of development of physical plasticity models for single crystals are discussed.
 Publication:

Physical Review B
 Pub Date:
 May 2000
 DOI:
 10.1103/PhysRevB.61.11956
 Bibcode:
 2000PhRvB..6111956E
 Keywords:

 62.20.Fe;
 Deformation and plasticity