Measurement of Stress Gradient by X-Rays

Abstract

The measurement of stress by means of X-rays has an advantage over any other methods in being more fit to measure the stress of local areas. However, we are often disappointed even by this method in such cases as where the stress has a high gradient in localized regions, such for instance as the stress field near the root of sharp notches. In the present paper a practical method of finding the stress gradient existing in a localized area by applying X-ray diffraction is discussed. It is also found that the Poisson's ratio ν can be determined by this analysis.It is well known that the breadth of X-ray diffraction line is influenced by the micro-strain included in the material. If the microstrain is replaced by a stress field in a localized area having stress gradient, the profile of diffraction lines emanating from such an area would be likewise broadened and the breadth of the diffraction line would be affected by the stress gradient. On the basis of this consideration, it was intended to analyse the relation between the breadth of diffraction line and the stress gradient, assuming the similarity of the profile of diffraction line to the Gaussian curve.The results of the analysis can be written as follows;G=CM√β22-β12where G is the stress gradient, C the constant which is decided by the geometry of slit system, M the constant given by the equationM=Ecotθ/√π{(1+ν)sin2ψ-ν}, where E, ν; elastic constantsθ; Bragg's angleψ; angle between the surface normal of specimen and the diffraction plane normal, and β2 and β1 are the integral breadths of diffraction lines of the specimen with and without stress gradient, respectively. In fine, the stress gradient can be determined by measuring the integral breadths before and after applying stress gradient.The analysis is examined experimentally by measuring the integral breadth of diffraction line obtained from the side surface of a thin plate specimen subjected to bending stress. The results of the experiments show an agreement with the results of the analysis with the maximum scatter of about ±7kg/mm2/mm in stress gradient.