Reassessment of evaluation methods for the analysis of near-surface residual stress fields using energy-dispersive diffraction

In this paper two evaluation methods for X-ray stress analysis by means of energy-dispersive diffraction are reassessed. Both are based on the sin²ψ measuring technique. Advantage is taken of the fact that the d_ψ^hkl–sin²ψ data obtained for the individual diffraction lines E^hkl not only contain information about the depth and orientation dependence of the residual stresses, but also reflect the single-crystal elastic anisotropy of the material. With simulated examples, it is demonstrated that even steep residual stress gradients could be determined from sin²ψ measurements that are performed up to maximum tilt angles of about 45°, since the d_ψ^hkl–sin²ψ distributions remain almost linear within this ψ range. This leads to a significant reduction of the measuring effort and also makes more complex component geometries accessible for X-ray stress analysis. Applying the modified multi-wavelength plot method for data analysis, it turns out that a plot of the stress data obtained for each reflection hkl by linear regression versus the maximum information depth τ_ψ=0^hkl results in a discrete depth distribution which coincides with the actual Laplace space stress depth profile σ(τ). The sensitivity of the residual stress depth profiles σ(τ_ψ=0^hkl) to the diffraction elastic constants ½S₂^hkl used in the sin²ψ analysis can be exploited to refine the grain-interaction model itself. With respect to the universal plot method the stress factors F_ij which reflect the material's anisotropy on both the microscopic scale (single-crystal elastic anisotropy) and the macroscopic scale (anisotropy of the residual stress state) are used as driving forces to refine the strain-free lattice parameter a₀ during the evaluation procedure.