Numerical estimation of effective mechanical properties in polycrystalline materials from a microscale analysis using the Boundary Element Method

In this paper, the effective mechanical properties of polycrystalline materials are determined from a microscale analysis using the Boundary Element Method. The macroscopic behavior of polycrystalline materials, such as ceramics and metals, is directly related to their microstructure. Therefore, it is of interest to determine the apparent mechanical properties of the material, based on its heterogeneous behavior at the microscale. These materials have a microstructure composed of several grains, with different orientations and, consequently, different mechanical properties. For this reason, a multiregion formulation of the Boundary Element Method is used in the analysis of polycrystalline microstructures, in which each grain is treated as a domain with orthotropic behavior and random crystallographic orientation. The formulation is based on the displacement boundary integral equation, with the use of anisotropic fundamental solution, so that the entire problem is written in terms of the displacements and tractions measured at the grain boundaries. The integrity of the polycrystalline aggregate is ensured by imposing interface conditions that guarantee the equilibrium of tractions and prevent relative displacements between the faces of two adjacent grains. The artificial morphology of the polycrystalline aggregate is generated using Voronoi tesselations. The described formulation is applied to the analysis of polycrystalline aggregates in order to determine their effective mechanical properties.