A two-stage approach to evaluating the probability of leak appearing in the flange joint as a result of a failure of the securing studs is described. First the probability of only one stud failing is calculated. This probability depends on, specifically, the integrity of all other studs. The probabilities of different combinations of the relative arrangements of whole and failed studs are calculated at the second stage. The method is illustrated for the calculation of the probability of a leak in the region of the collector cover for a PGV-1000 steam generator. Normative data on the strength and mechanical characteristics of the structural materials and loads corresponding to the nominal operating regimes are used in the calculations.A salient feature of the calculation of the strength reliability of flange joints of pipe lines and pressured vessels in reactor systems is that their strength, in contrast to the strength of weld joints, is due to many securing components. For this reason, a flange joint must be regarded as a system of interacting carrying elements (studs) each of which can be in one of two states -intact or broken. When some of the studs break, the seal becomes degraded and a leak, whose size depends on the number and relative arrangement of the broken studs, can appear. If the failure of a stud is regarded as a random event, then the calculation of the probability of a leak reduces to calculating the probability of the appearance of different relative arrangements of the intact and broken studs. The probability of stud failure as a result of the appearance and growth of cracks depends on the amplitudes, duration, and cyclicality of the force loads as well as the temperature, corrosion-chemical, and radiation conditions of operation. The force loads on the studs depend on, specifically, the relative arrangement of intact and broken studs.The probability of failure of a flange joint is calculated in two stages. First, the probability of failure of one stud for different arrangements of the broken studs is calculated taking account of the stresses obtained from a calculation of the stress-strain state of a stud. The number of arrangements considered at the first stage can be reduced substantially by assuming that the stresses in the stud under consideration depend on the number of only neighboring broken studs.The probability of the formation of different combination of the relative arrangements of intact and broken studs is calculated at the second stage taking account of the probability of failure of one stud p(i, j), where i and j are the number of broken neighboring studs on both sides. Assuming all studs to be intact initially, the probability P(k) of the formation of an arc consisting of k broken studs in a flange joint with N studs is calculated using the probability P(k − 1) and failure probability p(i, j), and it can be written in the form of recurrence equations for finding P(k) for any k ≤ N: P(k) = F[p k′ (i, j), P(k -k′); k′ = 1, ..., k; i + j = 0, ..., k -1], k = 1, ..., N,(1) where P(0...
