It was recalled that, because of the statistical nature of obstacle configurations, the stress required to force a dislocation to glide through a random environment of obstacles depended upon the dislocation length and upon the glide distance. In order to study this finite-size effect, a line tension model was used together; with an evolution algorithm inspired by larger-scale dislocation dynamics simulations. It was shown that, in finite arrays, the estimated critical resolved shear stress was larger than its infinite-array limit. The lower the resistance and the density of the obstacles, the greater was the over-estimation. The controlling parameters, estimated from Friedel’s law, were the average number of obstacles along the dislocation line and the average number of obstacle configurations met by the dislocation in its glide. This effect was analyzed using a model which was based upon an analogy with branching processes.

Finite-Size Effects in Dislocation Glide through Random Arrays of Obstacles - Line Tension Simulations. T.Nogaret, D.Rodney: Physical Review B, 2006, 74[13], 134110 (6pp)