Study of Consistency between Two-Dimensional, sin<sup>2</sup><i>ψ</i>, cos<i>α</i> and Fourier Transformation Methods for X-Ray Residual Stress Measurement by Debye Ring Simulation

Abstract

We investigated the consistency of four methods by analyzing the distorted Debye rings with various stress states. Firstly, the distorted Debye rings were generated under various uni-, bi-and tri-axial stress states by using the fundamental stress-strain relationship in two dimensional X-ray stress analysis theory. Secondly, we performed reverse analysis of stress states in the frameworks of sin2ψ and cosα methods from the simulated Debye rings. Moreover, the profiles of simulated Debye rings were Fourier transformed and the stress states were calculated in accordance with the obtained 1st and 2nd order Fourier coefficients. As a result, it was confirmed that all these methods provide the same stress values. That is to say, all these methods are consistent. Therefore, we can guarantee the validity of choosing any appropriate method considering the geometrical restrictions of experiment.