A stochastic crystal plasticity framework for deformation of micro-scale polycrystalline materials

• Using numerical and experimental data, we identified the source of uncertainty in the mechanical properties.
• Dislocation scarcity, grain size distribution and crystal orientation cause stochastic response at small length scales.
• The effect of dislocation scarcity is more considerable compared to other sources.
• A length measure based on effective cell size is introduced for polycrystalline samples.
• This effective cell size controls the extent of uncertainty in the numerical and experimental results.

In this paper we investigate the stochastic behavior in the mechanical response of polycrystalline materials consisting of few grains to hundreds of grains at micron size scales. We study the transition from stochastic (at small scale) to deterministic (at large scale) deformation behavior in polycrystalline samples using both simulation and nanoindentation experiments. Specifically, we develop a stochastic crystal plasticity model combining a Monte Carlo method with a polycrystal continuum dislocation dynamics model in a self-consistent viscoplasticity framework. Using this framework, we numerically calculate the mechanical properties of the polycrystal and gather randomized sampling data of the flow stress. The numerical results are compared to nanoindentation experimental data from three samples with ultra-fine grain structures manufactured via the severe plastic deformation method. The controlling mechanisms of the observed stochastic yield behavior of polycrystals are then discussed using simulations and experimental results. Our results suggest that it is the combination of stochastic plasticity at small scales (where the strength may vary from grain to grain) coupled with the effects of microstructural features such as grain size distribution and crystallite orientations that govern the uncertainty in the mechanical response of the polycrystalline materials. The extent of the uncertainty is correlated to the “effective cell size” in the sampling procedure of the simulations and experiments. The simulations and experimental results demonstrate similar quantitative behavior in terms of coefficient of variation within the same effective cell size.