Generalised Least-squares Determination of Triaxial Stress States by X-ray Diffraction and the Associated Errors

Abstract

The determination of residual stresses via X-ray diffraction is briefly reviewed, with particular emphasis on the triaxial stress state. A new method is proposed for determining the general stress tensor, which considerably reduces the variances of the stresses due to counting statistics and gradients. The procedure involves a generalised least-squares solution of strains measured at various tilts of the X-ray beam to the sample, and a new set of tilts is recommended to minimise these errors.