Statistical Analysis of X-Ray Stress Measurement by Centroid Method

Abstract

The X-ray technique allows a nondestructive and rapid measurement of residual stresses in metallic materials. The centroid method has an advantage over other X-ray methods in that it can determine the angular position of a diffraction line, from which the stress is calculated, even with an asymmetrical line profile.
An equation for the standard deviation of the angular position of a diffraction line, σ_p, caused by statistical fluctuation was derived, which is a fundamental source of scatter in X-ray stress measurements. This equation shows that an increase of X-ray counts by a factor of k results in a decrease of σ_p by a factor of 1/√k. It also shows that σ_p increases rapidly as the angular range used in calculating the centroid increases. It is therefore important to calculate the centroid using the narrow angular range between the two ends of the diffraction line where it starts to deviate from the straight background line.
By using quenched structural steels JIS S35C and S45C, the residual stresses and their standard deviations were calculated by the centroid, parabola, Gaussian curve, and half-width methods, and the results were compared. The centroid of a diffraction line was affected greatly by the background line used. The standard deviation of the stress measured by the centroid method was found to be the largest among the four methods.