Analysis of three-dimensional hexagonal and cubic polycrystals using the boundary element method

This work presents the analysis of three-dimensional polycrystals in the microscale with different lattice structures, hexagonal closed package (HCP) and face centered cubic (FCC). In these materials, the grained medium is considered as a continuum elastic body. An artificial polycrystalline structure is modeled using the Voronoi tessellation to generate random morphological microstructures. To reproduce the stochastic effects, arbitrary crystalline orientations are distributed over the structure. The boundary element method (BEM) is used to obtain the static displacement and traction fields, with a fundamental solution for 3D general anisotropic materials based on double Fourier's series. The macroscopic effective elastic properties are evaluated using the average homogenization technique and compared to the reference values through convergence statistical analysis. Explicit schemes are presented in order to improve the computational load and decrease the time required by the main BEM application implemented on distributed memory architectures. Numerical examples are presented showing the convergence of the results and comparisons of anisotropy level between these FCC and HCP materials using a recently proposed anisotropy factor.