LAUSR

Abstract This paper presents the development of a Cellular Automaton (CA) capable of describing polycrystalline structures heterogeneous behavior in the elastic domain. Based on Eshelby’s inclusion problem, this model is the first step to a better consideration of heterogeneities in polycrystals by including the neighborhood effect in grain’s behavior. Neighborhood effects have been defined, quantified, and approximated from observations made in the first of this two-part paper, using finite element method (FEM). Considering these approximations, and based on FEM simulations results, an analytical model of the neighborhood effect was proposed in the present paper on which the CA model was built. As a first step in the model development, a regular aggregate structure (Kelvin structure) is used where grains are considered spherical and having identical size. The stress field predictions obtained with the FEM for a polycrystalline aggregate submitted to an elastic loading were compared with the CA predictions, grain by grain, for two different crystal structures (Fe and Ti). Considering the FEM as a reference tool, CA model predictions show an excellent propensity at predicting the local stress fields in polycrystals by capturing the neighborhood effect induced by grain orientations for a low computation time cost. The CA model has also shown its facility to evaluate quickly a grain influence on another grain stress level, and therefore, the orientations generating high stress concentrations in a grain can be easily identified. Using this capacity, the neighborhood effect has been shown to be able to at least double a grain stress level without the material showing any particular texture.