Computational and experimental investigation into the effect of the free surface, X-ray elastic constant model and orientation distribution function used in X-ray stress analysis

X-ray stress analysis requires accurate X-ray elastic constants (XECs). One of the challenges for XEC calculation is that the modelling approach, preferred orientation and, to a lesser extent, the free surface affect the result. In this work, we investigate these factors. The surface effect is calculated under the assumption that within a surface layer the Poisson action along the normal direction caused by in-plane stresses must not be impeded by grain–matrix interaction in the normal direction due to the free surface. The model is evaluated for the pure surface effect for zero penetration and for a layer thickness equal to the grain size; the latter is calculated as the attenuation-weighted depth average of the surface grain layer and the bulk. Further comparisons are made with other XEC models and with measured XECs for different lattice planes ( hkl ), different X-ray wavelengths and varying penetration depths. The effect of preferred orientation is studied through variations of the grain orientation distribution function (ODF). It was found that the pure-surface-effect model performed best. ODF variations can significantly affect the XECs of individual ( hkl ), while the effect on the ( hkl ) average appears small.