Statistics of the thermally activated glide of a dislocation through a random array of point obstacles

This paper treats the statistics of thermally activated glide of a dislocation, modelled as a string of constant tension, through an array of randomly distributed identical immobile point obstacles. The parameters governing thermally activated glide are defined, and equations are developed giving the expected value and variance of the time to activate through an obstacle array or sequence of arrays in terms of the properties of the obstacle configurations encountered. The proper statistical definition of the velocity of glide is dicussed. It is shown that the velocity of glide, as determined from the strain rate, is simply proportional to the inverse of the expected time to transit the array (or sequence of arrays). Simplifying approximations are identified for use at low temperature or high stress. We finally discuss how these statistical relations and approximations may best be used in numerical simulation of thermally activated glide.