Size effects and dislocation patterning in two-dimensional bending

We perform atomistic Monte Carlo simulations of bending a Lennard-Jones single crystal in two dimensions. Dislocations nucleate only at the free surface as there are no sources in the interior of the sample. When dislocations reach sufficient density, they spontaneously coalesce to nucleate grain boundaries, and the resulting microstructure depends strongly on the initial crystal orientation of the sample. In initial yield, we find a reverse size effect, in which larger samples show a higher scaled bending moment than smaller samples for a given strain and strain rate. This effect is associated with source-limited plasticity and high strain rate relative to dislocation mobility, and the size effect in initial yield disappears when we scale the data to account for strain rate effects. Once dislocations coalesce to form grain boundaries, the size effect reverses and we find that smaller crystals support a higher scaled bending moment than larger crystals. This finding is in qualitative agreement with experimental results. Finally, we observe an instability at the compressed crystal surface that suggests a novel mechanism for the formation of a hillock structure. The hillock is formed when a high angle grain boundary, after absorbing additional dislocations, becomes unstable and folds to form a new crystal grain that protrudes from the free surface.