Title: A Rigorous Analysis of Diffraction Stress Formalism
Description: Diffraction strain/stress analysis has been widely used in the determination of residual and applied stresses in the surface layers and bulk volumes of materials for a long time. The technique has been used for almost 100 years. However, there are still issues that have not been yet addressed.In this dissertation, we address these issues. The basic theory of diffraction strain/stress analysis is extensively reviewed and the weaknesses of the analysis are explained carefully. The current definitions that have been used for describing residual stresses are unified under this expanded analysis. In addition, the homogeneous continuum analysis is extended to the polycrystalline materials under various loading types. To search for answers to the questions asked in this dissertation, finite element modeling. was used. This approach provides both local and global stress and strain information at all locations of a virtual specimen. The results show that St. Venant regions such as edges, voids, or geometric constraints cause local inhomogeneous strain/stress distribution which can cause deviations from linear deformation theory.

Even if the far-field load region is sampled by X-rays, the representative volume element should be determined by preliminary experiments because almost all single-phase polycrystalline materials (with the exception of tungsten) are composite materials within which variations of elastic moduli are observed along with sample directions. In the multiphase polycrystalline materials, this problem becomes more serious due to the differential deformation of each phase with respect to each other. Therefore, an experimenter needs to be careful during the experiment, in acquiring representative data; this requires significant preparation and material characterization. With the findings of the dissertation, a set of rules are written for users and experimenters to apply during or before the experiments to collect accurate and representative data.