A self-consistent method for X-ray diffraction analysis of multiaxial residual-stress fields in the near-surface region of polycrystalline materials.I. Theoretical concept

In recent work, the scattering-vector method was shown to be well suited fo r the detection of residual stress fields, which vary significantly within the penetration depth tau of the X-rays. It allows the separate evaluation of individual components sigma(ij)(tau) of the stress tensor directly from a series of measured epsilon(phi psi)(hkl, tau) depth profiles, which are o btained after stepwise rotation of the sample around the scattering vector g(phi psi) for fixed angle sets (phi, psi). In this paper, a solution of im proved stability for deriving the Laplace stress profiles sigma(ij)(tau) is presented. It is based on the extreme sensitivity of the individual epsilo n(phi psi)(hkl, tau) profiles with respect to the strain-free lattice spaci ng d(0)(hkl), which can be used as a criterion for a simultaneous determina tion of d(0)(hkl) itself as well as of optimized sigma(ij)(tau) profiles.