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

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Abstract
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 σij(τ) of the stress tensor directly from a series of measured ∊φψ(hkl, τ) depth profiles, which are obtained after stepwise rotation of the sample around the scattering vectorgφψfor fixed angle sets (φ, ψ). In this paper, a solution of improved stability for deriving the Laplace stress profiles σij(τ) is presented. It is based on the extreme sensitivity of the individual ∊φψ(hkl, τ) profiles with respect to the strain-free lattice spacingd0(hkl), which can be used as a criterion for a simultaneous determination ofd0(hkl) itself as well as of optimized σij(τ) profiles.

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