A statistical analysis of a stress constant and elastic constants in X-ray stress measurements by the fixed time method.

Abstract

In X-ray stress measurement, to obtain accurate results, it is necessary to determine experimentally the X-ray stress constant. However, values measured by X-ray diffraction have variability arising from inherent X-ray counting statistics. Therefore, it is important to investigate the reproducibility of the measured values by using the standard deviation representing the size of the variability caused by counting statistics. The equations are derived analytically for calculating the standard deviations of the stress, X-ray stress constant, and elastic constants. These equations give the standard deviations from a single measurement. The variances in these values are expressed in terms of a linear combination of the variances in peak positions of the diffraction line. The standard deviations of these values decrease in a manner inversely proportional to the X-ray counts. The X-ray stress constant and the elastic constants, along with their standard deviations, were deter-mined by the Gaussian curve method using a quenched and tempered steel.