X-Ray Elastic Constants of Polycrystalline Materials with Arbitrary Crystal Structure

Abstract

The X-ray diffraction technique for stress measurement can nondestructively determine residual stress in a localized surface layer of polycrystalline materials. In this method, the stress is determined from measured lattice strains using the X-ray elastic constants. Since the lattice strains of a particular lattice plane in the crystal grains are measured selectively, the X-ray elastic constants are different from the macroscopic constants of isotropic materials. The equations are derived for calculating the X-ray elastic constants for polycrystalline materials having arbitrary crystal structures from single crystal data. The Reus and Kroner models are used for the premise on the deformation of polycrystal. Measured X-ray elastic constants of steel, α-silicon carbide and α-alumina, which have cubic, hexagonal and trigonal structures respectively, were compared with the theoretical values. The values calculated using the Kroner model agreed most closely with the measured values.