Abstract

Under moderate applied stresses, dislocations move through the periodic Peierls potential via the thermal nucleation of kink pairs. The nucleation rate, and hence the dislocation velocity, is an extremely nonlinear function of the applied stress and temperature. Previous theoretical calculations of the rate either involve computer simulations at the atomic scale (which are too computationally demanding for modelling plasticity) or produce approximate formulae (valid only for small or large applied forces). In this talk I will derive a simple, general, and exact formula for the rate, directly from the stochastic equation of motion for the dislocation, using methods drawn from quantum field theory. This formula fits experimental and numerical data very well, and also applies to the many other physical systems modelled by elastic strings interacting with periodic potentials.