This paper presents new elastic and elastic±plastic ®nite element solutions of the J-integral for a pipe containing o-center through-wall cracks under pure bending. The analysis is based on a three-dimensional nonlinear ®nite element method and small-strain theory. One hundred and ®ve analyses were performed using the ABAQUS commercial code for a wide variety of crack sizes, o-center crack angles, and material hardening exponents. The results from these analyses show that the J-integral values at the two crack fronts of an o-center crack are unequal due to the loss of symmetry with respect to the bending plane of the pipe. In addition, the J-integral is larger, and hence, critical at the crack front which is farther away from the bending axis of the pipe. This is because, at that crack front, the tensile stress is larger and the component of the applied bending moment about the crack centerline has a further crack-opening eect. Also at this crack front, the J values can be lower or slightly higher than those of a symmetrically centered crack, depending on the crack size and o-centered angle. For the crack front that is closer to the bending axis, the J values are always lower than those of a symmetrically centered crack. This implies that the load-carrying capacity of a pipe is usually larger for an o-center crack than that for a symmetrically centered crack. Finally, based on these ®nite element solutions, new analytical expressions of J-integral were developed for fracture analysis of pipes containing o-center cracks. 7

This paper presents a probabilistic methodology for fracture-mechanics analysis of off-center cracks in pipes subject to pure bending moment. It is based on: (1) a new analytical approximation of the J-integral; (2) statistical models of uncertainties in loads, material properties, and crack geometry; and (3) standard computational methods of structural reliability theory. The proposed analytical equations were applied to a probabilistic fracture-mechanics analysis of off-center cracks in pipes. The second-order reliability method was used to determine the probabilistic characteristics of the J-integral and failure probability based on the initiation of crack growth. Numerical examples are presented to illustrate the proposed methodology. The results show that the failure probability strongly depends on the offcenter crack angle and is generally lower than that of a pipe with a symmetrically centered crack. Hence, simplifying an off-center crack by a symmetrically centered crack can produce significant conservatism in predicting failure probabilities. In addition, uncertainty in the offcenter crack angle, if it exists, can increase the failure probability of pipes. ᭧