Heterogeneous elastic behavior of HCP titanium polycrystalline aggregates simulated by cellular automaton and finite element

The present work uses cellular automata (CA) for the micromechanical simulations of polycrystalline structures and provides interesting insights on the stress–strain localization in elastically anisotropic materials. CA model were applied to a hexagonal close packed (HCP) titanium polycrystalline microstructure where each grain is represented as a cell. Automata were formed of 900 cells associated with randomly distributed orientations. An elastic loading was applied to the automata and the macroscopic deformation is localized using an adapted Eshelby approach in which each cell is considered as a heterogeneous spherical inclusion within its neighboring environment. The results are compared with a fully explicit Finite Element (FE) model of polycrystalline aggregates of 343 grains. CA model gave very similar results to those of FE model despite its simplifying hypotheses. Local stress–strain distributions obtained by both numerical methods are investigated and discussed, particularly regarding the effect of neighbors on the behavior of central grains.