Estimation of the critical resolved shear stress for dislocation glide through a random mixture of distinct obstacles

Abstract

Using techniques drawn from the statistical theory of branching processes, we approximate the critical resolved shear stress for the athermal planar glide of a dislocation, idealized as a flexible line of constant tension, through a random mixture of immobile point obstacles of distinct types. The approach simultaneously permits an estimate of the geometric properties of the particular obstacle configuration which determines the critical resolved shear stress. The estimates are shown to be in good agreement with empirical results obtained through direct computer simulation of glide through a random mixture of ’’strong’’ and ’’weak’’ points. A simple extension permits an estimate of the velocity of thermally activated glide through an array of mixed obstacle types at low temperature.