Sin2ψ-based residual stress gradient analysis by energy-dispersive synchrotron diffraction constrained by small gauge volumes. I. Theoretical concept

The influence of the gauge volume size and shape on the analysis of steep near-surface residual stress gradients by means of energy-dispersive synchrotron diffraction is studied theoretically. Cases are considered where the irradiated sample volume is confined by narrow-slit systems, in both the primary and the diffracted beam, to dimensions comparable to the 'natural' 1/e information depth tau(1/e) of the X-rays. It is shown that the ratio between tau(1/e), defined by the material's absorption, and the immersion depth h(GV) of the gauge volume into the sample is the crucial parameter that shapes the d(psi)(hkl) or epsilon(hkl)(psi) versus sin(2)psi distributions obtained in the Psi mode of X-ray stress analysis. Since the actual information depth < z >(GV) to which the measured X-ray signal has to be assigned is a superposition of geometrical and exponential weighting functions, ambiguities in the conventional plot of the Laplace stresses versus < z >(GV) may occur for measurements performed using narrow-slit configurations. To avoid conflicts in data analysis in these cases, a modified formalism is proposed for the evaluation of the real space residual stress profiles sigma(parallel to)(z), which is based on a two-dimensional least-squares fit procedure.