X-ray Stress Measurement by the Gaussian Curve Method

Abstract

Stress measurement by X-ray diffraction is considered to be the most appropriate method for nondestructively determining the residual stress distribution, because it can measure the stress in a small area on the surface of polycrystalline materials. To measure this stress precisely, it is important to choose a diffraction line located in as high an angular position as possible, because the sensitivity of the strain measurement is proportional to tan θ, where θ is the Bragg angle. Simplified equations for calculating the peak position and the stress by the Gaussian curve method are given, together with the equations for calculating the standard deviation, which represents the magnitude of the variation in these values caused by random counting statistics. Since the Gaussian curve method does not need background correction, it is especially useful for determining the peak position of those diffraction lines whose background line cannot be determined. One of the useful applications of the Gaussian curve method is the precise stress measurement of α-alumina with cobalt Kα radiation, using the Kα1 diffraction peak from the (410) plane which has the highest angular position of 168.4°.