Pattern decomposition for residual stress analysis: a generalization taking into consideration elastic anisotropy and extension to higher-symmetry Laue classes

Abstract

The residual stress state of ion-conducting layers (yttria stabilized zirconia) and protective hard coatings (α-aluminium oxide, titanium carbonitride) was investigated using X-ray diffraction techniques. Its evaluation within the tetragonal, trigonal and cubic phases present was performed by a whole powder pattern decomposition procedure according to Pawley. Going beyond previous work, the applied refinements directly include the influence of elastic anisotropy on the residual stress results. Starting from the single-crystal elastic coefficients, the X-ray elastic constants according to the Voigt and Reuss models were calculated. Finally, the Neerfeld–Hill model as a generalization was implemented to introduce thehkl-specific X-ray elastic constants for calculating the residual stress magnitude within the least-squares minimization routine. It was possible to resolve the residual stress state in stacked layers of different chemical and phase composition and to reproduce the results obtained by the classical χ- and ω-inclination sin2Ψ techniques.