Computation of the anisotropic cubic elastic Green's tensor function and the elastic energy coefficients of point defects in crystals

Abstract

In situ synchrotron X-ray and neutron diffraction experiments provide a powerful approach to measure lattice strains in bulk polycrystalline materials. They are being increasingly used for quantitative characterization of microscale deformation within and between grains and phases. Here we use a self-consistent micromechanics model to obtain a general analytic solution of the grain-level lattice strains and diffraction elastic constants for a broad class of elastically isotropic polycrystals with cubic crystal symmetry. This analytic solution reveals a direct linear relationship between the reciprocal of the elastic diffraction constant and the orientation index parameter along the direction of any diffraction vector, including tensile loading and transverse directions. The straightforward numerical implementation of this solution provides diffraction elastic constants for 26 representative cubic polycrystals. Analytic solutions of this kind can serve to benchmark in situ diffraction measurements of lattice strains and also facilitate high-throughput studies of microscale stresses and diffraction elastic constants in polycrystalline materials.