Probabilistic analysis of off-center cracks in cylindrical structures

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 off-center 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 off-center crack angle, if it exists, can increase the failure probability of pipes. (C) 2000 Elsevier Science Ltd. All rights reserved.