Neighborhood and surface effects on polycrystal stress field extreme values: An analysis in linear elastic range by means of cellular automaton

Within polycrystals, significant stress concentrations can arise due to their heterogeneous nature. These stress intensities strongly influence the onset of nonlinear behaviors, such as plasticity and fatigue damage. One often overlooked source of heterogeneity is the crystal anisotropy and its resulting neighborhood effect. Previous research introduced a data-driven analytical model based on a cellular automaton (CA) to account for the neighborhood effect on a grain’s stress level within an infinite aggregate under elastic conditions. It was demonstrated that, in some rare specific cases, grains could experience stress levels twice as high as the applied load. The current work extends the CA model by incorporating the effects of a free surface. Randomly oriented polycrystals under uniaxial loading were studied using a regular aggregate structure (Kelvin structure), where all grains are considered spherical and of identical size. Compared to full-field simulations, the extended CA model demonstrated an excellent capability to capture heterogeneities, even in cases where high stress concentrations are generated by the neighborhood. By leveraging the model’s speed, a distribution function for grain stress levels was optimized to accurately capture the probability of extreme values. This allows for the estimation of the most likely highest stress within randomly oriented aggregates composed of billions of grains, along with its most probable localization relative to a free surface and the specific crystallographic configurations leading to it.