About Error Calculation in X-Ray Stress Measurement

Abstract

It is shown that the knowledge of standard deviations (Δσij) of the components of a stress tensor (σij) is not sufficient to calculate also standard deviations of quantities derived from the stress tensor, as principal stresses (σI, σII, σIII), von Mises stress, Tresca stress, and the components of the deviatoric stress tensor σ'ij. For such a calculation one needs all information about the measurement and the method for the calculation of σij. This information is: the accuracy of each measured lattice plane distance and the x-ray elastic factors Fij(φ,ψ,hkl) of each measured point. Equations are given for the calculation of the standard deviations of all the mentioned quantities. For special cases of measurement strategy the wanted calculations become easier. This is also given.