Variation of the effective elastic constants in the sample coordinate system with tilt angle (ψ) for X-ray strain-stress analysis

Abstract

In X-ray strain-stress analysis of polycrystalline materials, the strains obtained by diffraction at each ψ-tilt originate from mutually exclusive sets of grains. Owing to the selectivity of the diffraction conditions, not all possible grain orientations occur in all sets with respect to the sample coordinates. Consequently, the elastic constants of the diffracting ensemble along a given direction on the surface of the sample must change with ψ-tilt. In this paper, the variation in Young’s modulus of individual grains along vector S, in the surface, and the average Young’s modulus along S1 for a given ψ-tilt in the sample coordinate system are investigated through numerical analysis. It is shown that there may be sets whose effective elastic constants may not equal that of the overall body even for fine-grained, random, quasi-isotropic single-phase materials. The differences in the effective elastic constants may be as much as 50% between sets diffracting with the same (hkl) reflection at different ψ-angles. © 1996, Taylor & Francis Group, LLC. All rights reserved.