Applications of a Probabilistic Fracture Mechanics Model to the Influence of In-Service Inspection on Structural Reliability

A probabilistic fracture mechanics model of structural reliability is described that considers failure to occur as the result of subcritical and catastrophic growth of pre-existing cracks that escape detection. The model considers cracks to be two-dimensional and is capable of treating many of the input parameters as random variables and can consider arbitrary inspection schedules. The two-dimensional model is greatly simplified when one-dimensional cracks are considered, and an analytical treatment of the influence of in-service inspection for the one-dimensional case reveals that the ratio of failure rates with and without inspection is independent of the crack size distribution. Numerical results for two-dimensional cracks in a weld joint in a large reactor pipe show that the ratio of failure rates is not highly dependent on the initial crack distribution, even for this more general case. Thus, it appears that an assessment of the relative benefit of in-service inspection does not require accurate knowledge of the initial crack distribution. Additionally, the results show that leaks in large pipes are not very probable, but are much more likely to occur than a sudden double-ended pipe break.