Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics

The problem of the collective behavior of straight parallel edge dislocations is investigated. Starting from the equation of motion of individual dislocations a continuum description is derived. It is shown that the influence of the short range dislocation-dislocation interactions on the dislocation dynamics can be well described by a local back stress which scales like the square root of dislocation density plus a non-local diffusion-like term. The value of the corresponding diffusion coefficient is determined numerically, and implications for size effects in plasticity are discussed. (C) 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.