Residual stress measurement using X-ray diffraction



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Texas A&M University


This paper briefly describes the theory and methods of x-ray residual stress measurements. Residual stresses can be defined as the stresses which remain in a material in the absence of any external forces. There are many stress determination methods. Some of those methods are destructive and some are nondestructive. X-ray residual stress measurement is considered as a nondestructive method. X-ray diffraction together with the other diffraction techniques of residual stress measurement uses the distance between crystallographic planes as a strain gage. The deformations cause changes in the spacing of the lattice planes from their stress free value to a new value that corresponds to the magnitude of the residual stress. Because of Poisson?s ratio effect, if a tensile stress is applied, the lattice spacing will increase for planes perpendicular to the stress direction, and decrease for planes parallel to the stress direction. This new spacing will be the same in any similarly oriented planes, with respect to the applied stress. Therefore the method can only be applied to crystalline, polycrystalline and semi-crystalline materials. The diffraction angle, 2θ, is measured experimentally and then the lattice spacing is calculated from the diffraction angle, and the known x-ray wavelength using Bragg's Law. Once the d-spacing values are known, they can be plotted versus 2 sin ψ, ( ψ is the tilt angle). In this paper, stress measurement of the samples that exhibit a linear behavior as in the case of a homogenous isotropic sample in a biaxial stress state is included. The plot of d vs. 2 sin ψ is a straight line which slope is proportional to stress. On the other hand, the second set of samples showed oscillatory d vs. 2 sin ψ behavior. The oscillatory behavior indicates the presence of inhomogeneous stress distribution. In this case the xray elastic constants must be used instead of E and ν values. These constants can be obtained from the literature for a given material and reflection combination. It is also possible to obtain these values experimentally. Calculation of the residual stresses for these samples is beyond the scope of this paper and will not be discussed here.