Probabilistic fracture mechanics approach to pressure vessel reliability evaluation

The paper introduces basic mathematical tools to describe material fracture as a probabilistic event. Materials fracture toughness, size and distribution of preexisting flaws and the stochastic nature of applied loads are the main sources of uncertainties underlying the probabilistic pattern of fracture events. Random variables with specific distribution laws are the natural concept for quantifying sources of uncertainty. Within this framework, a probabilistic failure risk analysis is presented and a general fracture model, based on exponential distribution of crack sizes, is developed. The proposed model results in a Rayleigh distribution as the limit distribution of stress intensity factor. A rationale for a quick failure risk (failure probability) is presented along with a discussion about the link between traditional safety factor methods and probabilistic approaches. Furthermore, the influence of uncertainties involving nondestructive inspection, i.e. the influence of probability of detection (POD), is considered within the framework of the proposed rationale. Various key sensitivity analyses related to the influence of the assumed statistical distribution of fracture toughness are outlined. Also reported is a procedure for a conservative estimate of safety based on a general-purpose nomogram, witch would enable a quick failure proability assessment under static loading conditions. Finally, a failure risk analysis related to spherical pressure vessels, befor and after the repair of cracks, is presented. This example emphasizes the potential of probabilistic fracture mechanics to better manage significant decisions tha afect industrial safety.