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

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 suits the measurement situation, and so 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 reside 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 the light of these ideas, three commonly used XRD methods are compared: the sin²ψ method, the XRD² method and the cosα method, using the estimation of the measurement errors. The XRD² method with 33 frames (data acquisitions) shows the best accuracy. On the other hand, the accuracy of the cosα method with three frames is comparable to that of the XRD² method.