On the diffractive determination of single-crystal elastic constants using polycrystalline samples

The diffractive determination of single-crystal elastic constants using polycrystalline samples represents the inverse problem to the (`direct') experiment of conventional diffractive residual-stress analysis. Both problems are rather sensitive to the quality of the experimental data and to the applied micro-mechanical models. This especially holds for the case of samples for which texture cannot be neglected. The current methods in the field are briefly described and specific difficulties are discussed. The key relations for the BPGeo micro-mechanical model (in which a texture-weighted geometric mean is applied in the stress analysis) are given for the general case. The necessity for careful analysis of the reliability of the results of planned experiments using theoretically modelled `experimental' data obtained with the applied micro-mechanical models is demonstrated for a set of line-shift data from a uniaxial tensile experiment on steel. The possibility of resolving the so-called d₀ problem using the original line-position data for a structure refinement is demonstrated.