Finite-size effects in dislocation glide through random arrays of obstacles: Line tension simulations

Abstract

The stress required to force a dislocation to glide through a random environment of obstacles depends on both the dislocation length and the glide distance because of the statistical nature of the obstacle configurations. In order to study this finite size effect, we employ a line tension model in conjunction with an evolution algorithm inspired from larger scale dislocation dynamics simulations. We show that with finite arrays, the estimated critical resolved shear stress is larger than its infinite array limit. Moreover, the lower the resistance and the density of the obstacles, the larger the overestimation. The controlling parameters, estimated from Friedel's law, are the average number of obstacles along the dislocation line and the average number of obstacle configurations met by the dislocation in its glide. We analyze this effect through a model based on an analogy with branching processes.