A comparison of X-ray stress measurement methods \\based on the fundamental equation

TL;DR

This paper unifies various X-ray diffraction stress measurement methods through fundamental equations and diffraction vector representation, comparing three common methods based on their diffraction vector choices and error estimation.

Contribution

It demonstrates that different XRD stress measurement methods can be unified and compared using a common framework based on fundamental equations and least-squares analysis.

Findings

The fundamental equations of different XRD methods are identical in diffraction vector representation.

Differences between methods lie in the choice of diffraction vectors and stress calculation approaches.

The paper compares three methods using measurement error estimation.

Abstract

Stress measurement methods using X-ray diffraction (XRD methods) are based on so-called fundamental equations. The fundamental equation is described in the coordinate system that best suites the measurement situation, and, thus, making a comparison between different XRD methods is not straightforward. However, by using the diffraction vector representation, the fundamental equations of different methods become identical. Furthermore, the differences between the various XRD methods are in the choice of diffraction vectors and the way of calculating the stress from the measured data. The stress calculation methods can also be unified using the general least-squares method, which is a common least-squares method of multivariate analysis. Thus, the only difference between these methods turns out to be in the choice of the set of diffraction vectors. In light of these ideas, we compare three commonly used XRD methods: the sin^2 psi method, the XRD^2 method, and the cos alpha method using the estimation of the measurement errors.