Dislocation Dynamics in 2 + epsilon Dimensions: Slip Planes, Thin Films, and Grain Boundaries

Dislocations are line defects and the primary carriers of plastic deformation incrystalline materials. In this article, we give an introduction to the dislocationtheory and review the recent advances in modeling and simulation of disloca-tion dynamics in two or nearly two dimensions, including the Peierls-Nabarromodel and its generalizations for the structure and dynamics of dislocations in asingle slip plane, dislocation dynamics in thin films, and dislocation models forgrain boundaries. We call these problems 2+ε dimensional problems because thephysical extent of one of the 3 dimensions is much smaller than the other two.This reduction of dimension plays an important role both on the nature of thestructures formed and/or on how the evolution of these structures is simulated.This reduction of dimension also leads to the formation of special dislocation mi-crostructures, whose energetics and dynamics play important roles in the plasticdeformation behavior and to several other related physical properties. Dislocationdynamics simulation provides an excellent tool for such investigations