Dislocation sources in discrete dislocation simulations of thin-film plasticity and the Hall-Petch relation

A discrete dislocation simulation has been developed to investigate thin-film plasticity on a mesoscopic scale. Dislocation interactions and dislocation self-stresses are calculated within the isotropic linear elasticity theory. The simulation is used to investigate the formation of dislocation pile-ups in a single columnar grain, where the boundaries are introduced as impenetrable obstacles. In analogy to the Hall-Petch model global plastic deformation is assumed to occur when the stress on the grain boundary exerted by the pile-up exceeds a certain critical value. The production of dislocations by a Frank-Read source and the dislocation evolution in the glide plane are simulated. For sources which are small compared to the grain size and for small numbers of dislocations the flow stress is well described by an analytical model of Friedman and Chrzan (1998 Phil. Mag. A 77 1185) if an appropriate Hall-Petch constant is used. If the source size scales with grain size, the flow stress depends on the inverse grain size instead of the square root of the inverse grain size below a critical size.