Frank-Read sources within a continuum simulation

A continuum level simulation of dislocation dynamics has been developed and used to study the evolution of Frank-Read sources. The model is based on isotropic elasticity theory and includes the self-stress of the dislocations, as well as the dislocation-dislocation interactions. The critical stress of a Frank-Read source is calculated as a function of the source length. The simulations are used to study the strain produced by a Frank-Read source as a function of time. It is noted that the total area swept out by the source as a function of time t scales as t 3 . This scaling appears to hold for a linear dependence of the dislocation velocity on stress, as well as for a stress cubed dependence. It is noted that under some conditions, a subcritically stressed Frank-Read source may produce strain for a significant length of time before complete exhaustion of its motion.