Stochastic effects in plasticity in small volumes

Recent studies of micro- and nano-scale metallic structures have exposed considerable statistical distribution, in addition to significant size dependencies, in the yield strength. This intrinsic statistical variation is particularly evident in the micro-compression and microtension thin film tests. This work investigates the relationship between the initial dislocation density, the heterogeneous initial spatial dislocation distribution, and the resulting localized deformation with multiscale discrete dislocation dynamics simulations. This relationship is examined separately from commonly reported external factors affecting observed strength, such as variations in specimen geometry and base support. Towards this end, we performed multiscale dislocation dynamics simulations of geometries commonly employed in micro-scale testing techniques, including micro-pillar compression, microtensile thin film, and microbulge tests. The statistical variation of yield strengths from all three simulation geometries is in agreement with experimental data from the corresponding loading techniques. We show that the onset of plasticity is stochastic in small volumes containing a small density of dislocations: a contrast to classical deterministic plasticity theory. The yield stress in these small volumes is stochastic, not deterministic, because of statistical variation of the initial dislocation content. The numerical results exhibit a localized deformation process and demonstrate a strong dependence of the yield stress on the initial dislocation density, the initial dislocation spatial distribution, and the specimen geometry size. Leveraging nucleation theory, a stochastic model for the onset of plasticity in micro- and nano-scale structures is developed based on these results.