Elastic constants of polycrystals with generally anisotropic crystals

A homogenization model is developed that describes the effective elastic constants of polycrystalline materials with constituent crystallites of general anisotropy (triclinic symmetry). The model is solved through an iterative technique where successive iterations improve the estimates of the polycrystal's elastic constants. Convergence of the solution provides the self-consistent elastic constants, which are the polycrystal's elastic constants resulting from continuity between local and far-field stress and strains. Iterative solutions prior to convergence are the bounds on the elastic constants including the Voigt-Reuss and Hashin-Shtrikman bounds. The second part of the article establishes a formal link between the present model and single-crystal elastic anisotropy. An analysis from a dataset containing 2176 inorganic crystalline compounds, spanning all crystallographic symmetries, is provided. The role of elastic anisotropy and related properties such as crystalline structure and elastic stability are discussed as it relates to the model.