Continuum-level simulations of dislocation dynamics were developed and were used to study the evolution of Frank-Read sources. The model was based upon isotropic elastic theory, and included the self-stress on dislocations as well as dislocation-dislocation interactions. The critical stress of a Frank-Read source was calculated as a function of the source length. The simulations were used to study the strain which was produced by a Frank-Read source as a function of time. It was noted that the total area which was swept out by the source was proportional to the cube of time. This scaling appeared to hold for a linear dependence of the dislocation velocity upon stress, as well as for a stress-cubed dependence. It was noted that, under some conditions, a sub-critically stressed Frank-Read source could produce strain for a significant period of time before complete exhaustion of its motion occurred.

Frank-Read Sources within a Continuum Simulation. A.K.Faradjian, L.H.Friedman, D.C.Chrzan: Modelling and Simulation in Materials Science and Engineering, 1999, 7[4], 479-94