DISLOCATION DYNAMICS IN 2 + ε DIMENSIONS: SLIP PLANES, THIN FILMS, AND GRAIN BOUNDARIES

Dislocations are line defects and the primary carriers of plastic deformation in crystalline materials. In this article, we give an introduction to the dislocation theory and review the recent advances in modeling and simulation of dislocation dynamics in two or nearly two dimensions, including the Peierls-Nabarro model and its generalizations for the structure and dynamics of dislocations in a single slip plane, dislocation dynamics in thin films, and dislocation models for grain boundaries. We call these problems 2+ε dimensional problems because the physical 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 the structures formed and/or on how the evolution of these structures is simulated. This reduction of dimension also leads to the formation of special dislocation microstructures, whose energetics and dynamics play important roles in the plastic deformation behavior and to several other related physical properties. Dislocation dynamics simulation provides an excellent tool for such investigations.