Weight function and stress intensity factor for a semi-elliptical surface saddle crack in a tubular welded joint

Owing to the complex geometry and non-uniform stress distribution, it is extremely difficult to obtain an accurate value for the analytical stress intensity factor (SIF) solution for a surface crack in a tubular welded joint. It is usually predicted using three-dimensional T-butt SIF solutions in conjunction with appropriate load-shedding models. The problem with this approach is that the effect of the tube curvature is ignored. Thus it may not represent the accurate stress intensity at the tip of the crack and stress redistribution resulting from the reduction of member stiffness with crack growth. Assuming that the relative influence of the weld toe for the deepest point SIF of a semi-elliptical surface crack in a thin pipe is the same as that for an edge crack of the same depth in a flat plate under the same stress distribution and using the weight function for longitudinal cracks in thin pipes as the reference solution, a new weight function in a closed form has been derived for the deepest point of a semi-elliptical surface crack at the saddle position in a tubular welded T-joint in this study. Based on this weight function and the uncracked T-butt through-wall stress distribution database, a new set of SIF parametric equations has been derived for membrane and bending loading respectively. This set of equations has incorporated the crack aspect ratio influence and the effects of the weld toe including the weld toe angle, weld attachment length, and weld radius. With the hot-spot stress, degree-of-bending values and appropriate load-shedding models, they can be used to predict the deepest point SIFs for semi-elliptical surface saddle cracks in tubular welded T-joints. The curvature effect of tubes to the SIFs is identified by comparing the predictions with three-dimensional T-butt finite element data and the results from three-dimensional T-butt weight-function-based SIF solutions. A comparison of the predictions with tubular joint fatigue test results, especially early crack growth data, has shown that this new SIF solution can work very well with the non-linear moment release model. Together with the extended Du-Hancock aspect ratio development model, they provide a fast SIF calculation procedure for the deepest points of surface saddle cracks during fatigue crack growth in tubular welded joints.