Probabilistic analysis of off-center cracks in cylindrical structures

This paper presents a probabilistic methodology for fracture-mechanics anal ysis of off-center cracks in pipes subject to pure bending moment. It is ba sed on: (1) a new analytical approximation of the J-integral; (2) statistic al models of uncertainties in loads, material properties, and crack geometr y; 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 reliabi lity 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. T he results show that the failure probability strongly depends on the off-ce nter crack angle and is generally lower than that of a pipe with a symmetri cally centered crack. Hence, simplifying an off-center crack by a symmetric ally centered crack can produce significant conservatism in predicting fail ure probabilities. In addition, uncertainty in the off-center crack angle, if it exists, can increase the failure probability of pipes. (C) 2000 Elsev ier Science Ltd. All rights reserved.