Determination of Residual Stress by X-Ray Diffraction with the Cos-Alpha Method and Its Application

Abstract

Today, residual stress determination by X-ray diffraction is a well-known method. While all X-ray stress determinations rely on Braggs law to measure the difference in lattice spacing of differently orientated lattice planes, the traditional sin2psi-2θ method uses different incident angles, and the cos-alpha method uses the complete Debye-Scherrer ring diffracted from the sample surface to acquire signals from differently orientated lattice planes. To calculate the residual stress from a Debye-Scherrer ring, the shift and distortion of the ring compared to a ring of an unstressed sample are plotted over cos-alpha. The slope of that plot indicates the stress on the sample surface. While the principal stress directions mostly shift the ring or change its diameter, the shear stresses distort the ring. Using one measurement direction, a plane stress can be calculated. To calculate stresses with the out-of-plane shear stress components, the opposite direction (φ0 = 0°; 180°) is needed additionally. To determine the complete stress, tensor measurements from four directions (φ0 = 0°; 90°; 180°; 270°) are necessary. Because of the relatively small dimensions of the equipment and the low radiation exposure caused by the device, the method is highly suitable for measuring not only in the lab but also onsite and within production areas. Since the samples do not need to be moved during the measurement, the sample size and weight are not limited. Examples include bearing rings for cranes or mining tools that can be measured onsite.