Failure probability of nuclear vessels

Given the absence of statistics for occurred events, the only way to estimate the failure probability of nuclear vessels is by an analytical way on the basis of the probabilistic distribution of the involved parameters and of the available fracture mechanics models. The relevant parameters include toughness of the material, the number of cracks initially present in the component, the probability that they are detected during the pre-operational and in-service tests, the fatigue crack growth rate, etc. 

The result of these probabilistic evaluations is useful to verify the safety level of the vessel, to highlight areas on which research effort is still needed, to estimate the safety improvement due to further provisions as an increase of the in-service inspections, changes in design, material and operating conditions, etc. 

The following describes the method and the results of the most accurate work on this subject the Marshall Report (UKAEA, 1982). 

The probability of a catastrophic rupture is determined by the probability associated to presence of cracks in the original component detection of them during the pre-operational and in-service inspections growth of cracks in service toughness of the material measured by the critical stress intensity factor (see Appendix 7 on Fracture Mechanics) stresses from normal operation transients and accidents. 

Concerning the original presence of cracks, it has to be said that their generation mechanisms are not all well understood. Generally they occur in welds. Concerning their shape, obviously the field of the various possibilities is infinite and therefore, for quantitative evaluations, it is necessary to apply simple conservative assumptions. Usually it is assumed that the cracks are semi-elliptical and superficial, with a depth a. The length 2c of the crack is assumed as a fixed multiplier of its depth (typically ajlc = 1/6). 

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