Prediction of pressure vessel failure: A critical review of the probabilistic approach

Abstract

Considered is a pressure vessel in the presence of crack-like defects. The probability of fast fracture, at any time, is formulated in terms of a characteristic defect size exceeding a critical value. The probability is conditional, given the random event of the annual occurrence of particular loading conditions. Much of the literature is reviewed, and erroneous formulations in previous work are noticed. The concept of probability of annual failure employed in the present account has to be distinguished from the concepts of reliability and failure rate used in reliability theory. Two sets of data are extracted from experimental evidence reported in the literature. One concerns the size distribution and total number of defects. The other pertains to the critical values of defect size for several loading conditions, together with the probability of the annual occurrence of these conditions. The effect of ultrasonic inspection on defect occurence is taken into account. As an illustrative example, an analytic, closed-form solution for the failure probability is presented for a typical, modern, pressurized water reactor vessel under end-of-life conditions. The different contributions to failure probability of various normal and off-normal loading conditions are clearly displayed, and the importance of a judicious choice of both modern low-residual-element pressure vessel steels and an improved ultrasonic inspection technique is demonstrated.