Atomistic Monte Carlo simulations were made of a Lennard-Jones crystal under uniaxial compression on single-crystal and polycrystalline samples in two dimensions. In single crystals, a size effect was observed in the initial yield: with smaller samples yielding at higher stress. A size effect was also found, in the plastic regime, which was accounted for by dislocation starvation. Two-dimensional polycrystalline samples were generated using a statistical physics model, and studied under uniaxial compression. The resulting microstructures showed higher stress within the grain boundary regions relative to that in the bulk, consistent with theoretical models and experimental results. The broad distribution of stresses within the polydomain sample was also examined and compared with recent experimental observations. While two-dimensional simulations could not predict the behaviour of real three-dimensional solids, they were valuable for exploring some of the fundamental mechanisms controlling mechanical response and served as a test-bed for theories of size effects in plasticity.

Atomistic Simulation Studies of Size Effects in Plasticity: Compression of Single- and Polydomain Crystals in Two Dimensions. N.S.Weingarten, R.L.B.Selinger: Modelling and Simulation in Materials Science and Engineering, 2011, 19[1], 015006