KI–T estimation for embedded flaws in pipes – Part II: Circumferentially oriented cracks

This paper, in parallel to the investigation on axially embedded cracks reported in the companion paper, presents a numerical study on the linear-elastic KI and T-stress values over the front of elliptical cracks circumferentially 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 the interaction-integral approach to compute the linear-elastic stress-intensity factor (SIF) KI and T-stress values for embedded cracks with practical sizes at different locations in the wall of the pipe. The parametric study covers a wide range of geometric parameters for embedded cracks in the pipe, including: the wall thickness to the inner radius ratio (t/Ri), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and 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). The parametric investigation identifies a significant effect of the remaining ligament length on both the T-stress and KI values at the crack-front location (denoted by point O) nearest to the outer surface of the pipe and at the crack-front location (denoted by point I) nearest to the inner surface of the pipe. The numerical investigation establishes the database to derive approximate functions from a nonlinear curve-fitting procedure to predict the T-stress and KI values at three critical front locations of the circumferentially embedded crack in a pipe: points O, I and M. The proposed T-stress and KI functions utilize a combined second-order polynomial and a power-law expression, which presents a close agreement with the T-stress and KI values computed from the very detailed finite element models. The comparison between the circumferentially embedded crack and the axially embedded crack indicates that both the T-stress and KI values at crack-front points O and I in a circumferential crack equal approximately 50% the T-stress and KI values at the corresponding front locations in an axial crack with the same crack depth ratio, the same crack aspect ratio and the same pipe wall thickness to the inner radius ratio.