A three-dimensional grain boundary formulation for microstructural modeling of polycrystalline materials

A three-dimensional grain boundary formulation is presented for the analysis of polycrystalline microstructures. The formulation is based on a boundary integral representation of the elastic problem for the single grains of the polycrystalline aggregate and it is expressed in terms of the intergranular fields, namely displacements and tractions, that play an important role in polycrystalline micromechanics. The artificial polycrystalline morphology is represented using the Hardcore Voronoi tessellation, which is simple to generate and able to embody the main statistical features of polycrystalline microstructures. The details of the microstructure generation and meshing, which involve only the discretization of the grains surface, and not their volume, thus resulting in a remarkable simplification of data preparation, are discussed. The single crystals are represented as anisotropic elastic regions. The integrity of the aggregate is restored by enforcing both continuity and equilibrium at the interface between contiguous grains. The developed technique has been applied to the numerical homogenization of cubic polycrystals and the obtained results agree well with available data, thus confirming the reliability of the method. Some numerical issues and directions of further investigations are highlighted and discussed.