Impact of grain shape on the micromechanics-based extraction of single-crystalline elastic constants from polycrystalline samples with crystallographic texture

Abstract

A micromechanics-based method (“inverse self-consistent approximation”) that can extract all the independent elastic constants of single crystals from those of polycrystals with crystallographic texture was newly developed. In the developed method, all the elastic constants in an anisotropic polycrystal were measured by resonant ultrasound spectroscopy, and the crystallographic orientations and shapes of the grains were analyzed. Then, the elastic constants of a single crystal, which reproduce those of the polycrystal, were determined on the basis of Eshelby's inclusion theory and the effective-medium approximation, taking into account the elastic interaction between the grains, which reflects their shapes and orientations. The developed method determined the elastic constants of pure Cu and pure Mg single crystals from those of polycrystals quite precisely. The differences between the elastic constants obtained using our method and the values measured using single crystals were only ∼ 1%. In contrast, the application of an inverse Voigt–Reuss–Hill approximation, which cannot consider the effect of the grain shape on the elastic interaction, resulted in a relatively poor evaluation for pure single-crystalline Cu which exhibits strong elastic anisotropy. This indicates that the grain shape clearly affects the elastic interaction between the grains exhibiting high elastic anisotropy and influences the extracted single-crystalline elastic constants. In terms of the actual application of the inverse self-consistent approximation, the single-crystalline elastic constants of AZ31 Mg alloy, whose single crystals cannot be prepared easily, were clarified.