Evaluation of strongly non-linear surface-stress fields $\sigma$xx(z) and $\sigma$yy(z) from diffraction experiments

For single-phase polycrystalline materials the relation is discussed between the elastic strain ϵ(ψ, φ) obtained from X-ray diffraction experiments and the polynomial expansion of the stress components σφ(σ) and σφ+90(z) with respect to the distance z from the external surface of the specimen. A universal plot is proposed for ϵ(ψ, τ0, (hkl)) = ½ (ϵ(φ) + ϵ(ψ + 90)) curves measured for different penetration depths τ0 of the radiation and for different reflecting lattice planes. This expression also allows absolute scaling of the ϵ values. The formalism is applied for discussing ϵ(ψ, φ, τ0, (hkl)) curves obtained with synchrotron radiation from a cold-rolled nickel plate. They indicate strongly non-linear variations of stress in a surface layer about two μm thic