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

Abstract

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 τψ=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(τψ=0 hkl ) to the diffraction elastic constants ½S 2 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 a 0 during the evaluation procedure.