A Simple Model on Dislocation Dynamics

Abstract

SUMMARYThe complete solution of the problem of the dynamical interaction of two parallel edge dislocations is obtained by a suitable transformation. Then we consider the influence of the stress field of a fixed dislocation dipole and external periodic forcing and study the generation of stable fixed points of the associated Poincaré map and the corresponding basins of attraction. INTRODUCTIONOver the past decade several numerical investigations have been performed to study the dynamical properties of dislocation systems [1][2][3][4][5][6][7][8]. One of the most interesting questions stimulating these works is to understand the origin of dislocation patterning. Due to the longrange dislocation-dislocation interaction, however, the direct numerical integration of the equation of motion of a system large enough to produce patterning is extremely computation time consuming. It has been recently proposed by Bakó and Groma [9] that the nearest neighbor dislocation interaction could be well approximated by an appropriate stochastic process. For systems containing several hundreds of dislocations it is proved numerically that the stochastic approach results in the same dynamical behavior as the "exact" integration.The motivation of the present work is to figure out what is the minimal dislocation number, which can be well described by the above-mentioned stochastic approximation. In order to