A statistical theory of dislocation dynamics with application to creep in LiF

Abstract

A statistical theory of dislocations has been proposed with specific application to creep in LiF and materials like it. The velocity of a dislocation is chosen to be a random variable. Based on various established mechanisms contributing to glide-controlled plastic flow, a semi-empirical continuity equation is set up for the velocity distribution function. The solution is obtained in terms of a power-series expansion of two small parameters, and the first four cumulants have been calculated within a certain approximation in which the third and fourth turn out negative, resulting in a distribution function having sharp edges on both sides. The average velocity of dislocations is shown to reduce linearly with the average density of dislocations, leading to an internal stress which is linear in the average density. The equation of motion of the dislocations exhibiting the drag, an equation for population dynamics of dislocations during creep, and a creep law proposed by Webster (1966) follow. The theory is applied to creep in LiF with excellent agreement. It also explains the shift in the stress-velocity relation in prestrained samples.