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 i sotropic 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. Th e 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 sou rce as a function of time t scales as t(3). This scaling appears to hold fo r 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 subcr itically stressed Frank-Read source may produce strain for a significant le ngth of time before complete exhaustion of its motion.