VARIATION OF THE EFFECTIVE ELASTIC-CONSTANTS IN THE SAMPLE COORDINATESYSTEM WITH TILT ANGLE (PSI) FOR X-RAY STRAIN-STRESS ANALYSIS

In X-ray strain-stress analysis of polycrystalline materials, the stra ins obtained by diffraction at each psi-tilt originate from mutually e xclusive sets of grains. Owing to the selectivity of the diffraction c onditions, 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 psi-tilt. In this paper, the variation in Young's modulus of individual grains along vector S-1 in the surface, and the average Young's modulus along S-1 for a given psi-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 effecti ve elastic constants may be as much as 50% between sets diffracting wi th the same (hkl) reflection at different psi-angles.