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 ɛ 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 ɛ ϕψ ( hkl , τ) profiles with respect to the strain‐free lattice spacing d 0 ( hkl ), which can be used as a criterion for a simultaneous determination of d 0 ( hkl ) itself as well as of optimized σ ij (τ) profiles.