Depth-resolved X-ray residual stress analysis on samples with cylindrically shaped surface topography

Angle- and energy-dispersive diffraction are applied to investigate the influence of the X-ray beam diameter on the results of residual stress analysis on a sample with an inhomogeneous surface topography. For sin²ψ measurements on parts of the surface featuring a cylindrical topography, modifications of the fundamental equation of X-ray stress analysis are proposed to correct the experimentally determined residual stresses for the rotational effect caused by the different orientation of the local principal stress coordinate system within the irradiated part of the sample. It is shown that the hoop and longitudinal stress components require different treatments in this respect. For the hoop stress component a correction factor is proposed which considers the variation in the illuminated surface area during the ψ tilt of the sample. Correction of the longitudinal stress component requires knowledge of the hoop stress component, which affects the slope of the sin²ψ regression line and thus partially acts as a normal stress component. For cases in which ψ tilting is not possible for geometric reasons, the applicability of the transverse contraction method is discussed. Experimental verification is carried out on a ferritic steel sample into which grooves of the same diameter were milled to different depths, resulting in different central angles.