The ϕ-Integral Method for X-Ray Residual Stress Measurements

Abstract

AbstractResidual stress measurements were made on a ground rail steel (0.75 %C) using the newly developed ϕ-integral method and the conventional ψ-differential method. The strains <εϕψ> were measured as a function of the azimuth angle ϕ, the angle of rotation about an axis perpendicular to the specimen surface, from 0° to 360° in steps of 15°, at fixed tilt angles ψ, the angle between the normals to the specimen surface and the reflecting planes (hkl), set between 0° and 45° in steps of 9°.It was found that <εϕψ> plotted as a function of ϕ is not periodic with the period of 180° and consequently exhibits the so-called ψ-splitting when plotted as a function of sin2ψ at constant ϕ. The Fourier coefficients of the function <εϕψ> plotted versus ϕ were used to evaluate the strain tensor <εij> in the integral method. Assuming that isotropic elasticity theory is applicable, the stress tensor <σij> was calculated, and excellent agreement was found between the values determined with the ϕ integral and ψ-differential methods.