The Use of Person VII Distribution Functions in X-Ray Diffraction Residual Stress Measurement

The fitting of a parabola by least squares regression to the upper portion of diffraction peaks is commonly used for determining lattice spacing in residual stress measurement. When Kα techniques are employed, the presence of the Kα doublet is shown to lead to significant potential error and non- linearities in lattice spacing as a function of Sin 2 ψ caused by variation in the degree of blending of the doublet. An algorithm is described for fitting Pearson VII distribution functions to determine the position of the Kα component, eliminating errors caused by defocusing of diffraction peaks of intermediate breadth. The method is applied to determine the subsurface residual stress distribution in ground TI-6 AI- 4 V, comparing directly the use of parabolic and Pearson VII peak profiles, and is shown to provide precision better than ± 1%% in elastic constant determination.