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 for the detection of residual stress fields, which vary significantly within the penetration depth τ of the X-rays. It allows the separate evaluation of individual components σ_ij(τ) of the stress tensor directly from a series of measured [epsilon]_φψ(hkl, τ) depth profiles, which are obtained after stepwise rotation of the sample around the scattering vector g_φψ for fixed angle sets (φ, ψ). In this paper, a solution of improved stability for deriving the Laplace stress profiles σ_ij(τ) is presented. It is based on the extreme sensitivity of the individual [epsilon]_φψ(hkl, τ) profiles with respect to the strain-free lattice spacing d₀(hkl), which can be used as a criterion for a simultaneous determination of d₀(hkl) itself as well as of optimized σ_ij(τ) profiles.