The dynamics of free, straight dislocation pairs. I. Screw dislocations

Analytic expressions are derived for the motion of a pair of interacting, straight, parallel (or antiparallel) screw dislocations in an applied stress field. Analysis of the equations of motion of the dislocations shows that, under most circumstances, the velocity of a dislocation is proportional to the driving force (i.e., the motion is overdamped), and, in this limit, the results are exact. However, when the two dislocations are very close together, inertial terms begin to play a role, and the resultant "finite-mass" corrections are treated perturbatively. For the case of antiparallel screw dislocations, a capture cross section exists and is given by the product of the shear modulus and the Burgers vector over the applied stress. Based on these results, a simple statistical analysis of the motion of a large number of screw dislocations is presented.