KI–T estimations for embedded flaws in pipes – Part I: Axially oriented cracks

This study reports a numerical investigation on the linear-elastic KI and T-stress values over the front of elliptical cracks axially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs an interaction integral approach to compute the linear-elastic stress intensity factor (SIF) KI and T-stress values from very detailed crack-front meshes. The verification study confirms the accuracy of the adopted numerical procedure in computing the KI values based on existing results for external axial surface cracks in the wall of a cylindrical structure. The parametric investigation covers a wide range of geometric parameters including: the wall thickness to the inner radius ratio of the pipe (t/Ri), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the crack location measured by the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (eM/t). Subsequent efforts develop, from a nonlinear curve-fitting procedure, a new set of equations to estimate the T-stress and KI values at three critical front locations of the axial elliptical cracks: the crack-front point O nearest to the outer surface of the pipe, the crack-front point I nearest to the inner surface of the pipe and the crack-front point M on the centerline of the axial crack. These equations combine a second-order polynomial with a power-law expression to predict the pronounced variations in the T-stress and KI values with respect to the geometric parameters. The coefficients of the new KI and T-stress equations either take a constant value or incorporate the linear variation with respect to the pipe wall thickness over the inner radius ratio, t/Ri. The proposed equations demonstrate a close agreement with the finite element (FE) results, which indicate very strong dependence of the T-stress and KI values at point O and point I on the corresponding ligament lengths, eO and eI.