2002 Volume 51 Issue 6Appendix Pages 74-81
When the sin2ψ method is applied to the residual stress measurement of a curved surface, a large-sized X-ray irradiation area causes some errors in the residual stress measured. However, it is difficult to set a sufficiently small irradiation area to a curved surface with a small radius of curvature when the diffraction intensity is weak or the sizes of grains are large. In this study, the focus is put on a spherical surface, and the relation between the residual stress measured and the size of the X-ray irradiation area is investigated experimentally and analytically. Tangential residual stresses of steel-balls used in ball-bearings were measured for various sizes of the X-ray irradiation areas. Numerical analyses simulating the X-ray stress measurement were performed under various conditions: materials, characteristic X-rays and values of the stress. It is found that the geometric effect appears in the gradient of the 2θ-sin2ψ, diagram chiefly and that the non-linearity in the 2θ-sin2ψ relation owing to the geometric effect is not so remarkable. As a result, we have shown a threshold of the geometric effect as a reference standard by a ratio of the irradiation size to the diameter of the sphere, and have proposed a practical formula estimating the actual circumferential stress on the spherical surface from the tangential stress measured and the geometric factors: the diameter of the sphere, the size of the X-ray irradiation area, and the thickness of the masking plate.
