A new polynomial approximation method was proposed for the X-ray multiaxial stress analysis, in which the effect of stress gradient along the penetration depth of X-rays was taken into account. Three basic assumptions were made; (1) the stress gradient is linear in respect to the depth from the specimen surface, (2) the ponetration depth of X-rays is a function of Sin2ψ and (3) the strain measured by X-rays corresponds to the weighted average strain on the intensity of the diffracted X-rays. Consequently, the stress state within the thin layer near the surface was expressed by making use of three surface stresses and six stress gradients in the present method.
The average strains by X-rays were approximated by the third order polynomial equations of sin2ψ using a least square method at several φ angles on the coordinate system of specimen. Since the coefficients of these polynomials include these nine stress components mentioned above, it is possible to solve them as simultaneous equations. The calculating process of this method is simpler than that of the integral method.
An X-ray plane stress problem was analyzed as an application of the present method, and the residual stress distribution on a shot-peened steel plate was actually measured by use of Cr-Kα X-rays to verify the analysis. The result showed that the compressive residual stress near the surface determined by the present method was smaller than the weighted average stress by the Sin2ψ method because of the steep stress gradient. The present method is useful to obtain a reasonable value of stress for such a specimen with steep stress gradients near the surface.
