Atomistic Monte Carlo simulations were made of the bending a Lennard-Jones single crystal in 2 dimensions. Dislocations nucleated only at the free surface, as there were no sources within the interior of the sample. When the dislocations attained a sufficient density, they spontaneously coalesced to nucleate grain boundaries, and the resultant microstructure depended strongly upon the initial crystal orientation of the sample. In the initial yielding, a reverse size effect was found, in which larger samples exhibited a higher scaled bending moment than did smaller samples for a given strain and strain rate. This effect was associated with source-limited plasticity and high strain rate relative to dislocation mobility, and the size-effect in initial yield disappeared when the data were scaled so as to account for strain-rate effects. Once the dislocations coalesced to form grain boundaries, the size-effect reversed and it was found that smaller crystals supported a higher scaled bending moment than did larger crystals. This finding was in qualitative agreement with experimental results. Finally, an instability was observed at the compressed crystal surface that suggested a novel mechanism for the formation of a hillock structure. The hillock was formed when a high-angle grain boundary, after absorbing additional dislocations, became unstable and folded so as to form a new crystal grain that protruded from the free surface.

Size Effects and Dislocation Patterning in Two-Dimensional Bending. N.S.Weingarten, R.L.B.Selinger: Journal of the Mechanics and Physics of Solids, 2007, 55[6], 1182-95