Approximate Analytical Formulae to Evaluate the Uncertainty in X-Ray Stress Analysis

Abstract

The global uncertainty, in X-ray stress analysis, is due to many factors but one of the most important is the uncertainty on peak positions due to counting statistics and other random errors on peak positions. Although a lot of work has been done to estimate the latter, very little work has been devoted to its propagation through the least square regression. This work presents some analytical results in the general case of triaxial stress state (elliptic curve fit) and proposes approximate formulae to easily compute the uncertainty on normal and shear stress components from acquisition parameters such as the number N of y tilts and the maximum y value. It was found that the latter only influences significantly the uncertainty on the normal stress component and that the dependency of the uncertainty on N does not necessarily follow a 1/ N relation.