A discrete dislocation simulation was developed in order to investigate thin-film plasticity at the mesoscopic scale. Dislocation interactions and dislocation self-stresses were calculated within isotropic linear elasticity theory. The simulation was used to model the formation of dislocation pile-ups in a single columnar grain. The boundaries were assumed to be impenetrable obstacles. By analogy with the Hall-Petch model, global plastic deformation was assumed to occur when the stress which was exerted on the boundary, by the pile-up, exceeded a critical value. The production of dislocations by a Frank-Read source, and dislocation evolution in the glide plane, were simulated. In the case of sources which were small compared to the grain size, and for small numbers of dislocations, the flow stress could be well described by an analytical model if a suitable Hall-Petch constant was used. If the source-size scaled with the grain size, the flow stress depended upon the inverse grain size instead of on the square root of the reciprocal of the grain size.

Dislocation Sources in Discrete Dislocation Simulations of Thin-Film Plasticity and the Hall-Petch Relation. B.von Blanckenhagen, P.Gumbsch, E.Arzt: Modelling and Simulation in Materials Science and Engineering, 2001, 9[3], 157-69