PSI - Issue 60

P.A. Jadhav et al. / Procedia Structural Integrity 60 (2024) 631–654 P.A. Jadhav et. al./ Structural Integrity Procedia 00 (2019) 000 – 000

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CSA Standard (2016) also permits the use of a probabilistic evaluation for assessing the safety of the flawed PT for part-through flaw as well as LBB applications. The probabilistic methods applied to safety assessment of PTs is reported extensively in literature. Walker (1990) has given a probabilistic assessment of PT with a through-wall crack. This crack grows in size due to DHC and is likely to become critical after some time duration. Author has presented the cumulative distribution function of the time duration between the start of leakage and the break of PT. Puls et. al. (1998) have extended the probability model given by Walker (1990) to include the events like Beetle alarm, Dew Point Alarm which are part of the leak detection system, in their probability model. The probability of rupture of the PT under the presence of a leaking axial flaw is reported, considering the activation or absence of these alarms. Kwak et. al. (2002) have reported probabilistic fracture mechanics studies on PTs, considering the diameter and thickness variation which occurs due to creep. The failure probabilities are evaluated for semi-elliptical part through wall flaws. They have modeled the uncertainty in crack size, fracture toughness, DHC velocity and the hydrogen concentration in the tube for the assessment. In their results they have given the effect of dimension change and the cool-down procedure on the probability of leakage and break. In the paper by Oh et. al. (2012), a probabilistic flaw assessment method to evaluate the probability of initiation on DHC ahead of a volumetric flaw and the probability of rupture of this flaw as a function of reactor operating years, is described. The uncertainty in flaw dimensions, hydrogen uptake rate, and PT dimensional changes were taken into account in the model. The results showed that the probability estimation is significantly influenced by the distribution of flaw size, but the uncertainty in hydrogen uptake rate and dimensional changes over the lifetime of the reactor did not have a significantly impact. In another paper, Oh and Chang (2014), have proposed a methodology to perform probabilistic assessment of PT. They have proposed an integrated assessment of failure arising due to a flaw which involves DHC initiation, growth and through the wall penetration. Subsequently, the probability of rupture is estimated which can be equated to probability of not meeting the LBB requirement. The results are extended to the possibility of presence of multiple flaws in the PT in the reactor core. Pandey and Sahoo (2010) have given a semi-probabilistic method for LBB evaluations of PTs. They have generated partial safety factors for the design variables for a range of probability of failure. Radu and Roth (2012) in their paper present methodology for assessing the likelihood of PT failure in CANDU reactors during cool-down cycles, using the principles of probabilistic fracture mechanics. They have used the limit state given in the CSA standard (2005) as well as that given by the R6 method (2009). The CSA standard permits the use of probabilistic methods as flaw acceptance criteria. For the flaws detected during the inspection of limited PTs, it is to be demonstrated that the frequency of PT rupture in the entire core is less than an allowable value. Cho et. al. (2017) have described with example the current application of this philosophy as used in the Canadian nuclear industry. This process includes evaluating the potential of flaws to initiate cracking, the potential of cracks to grow until they reach through-wall penetration, and the potential for PT rupture as a result of unstable crack growth, all prior to a safe shutdown of the reactor. Laxman and Carroll (2016) and Wasiluk et. al. (2019) have discussed the probabilistic assessment criteria for safety assessment of PT and the technical basis for the same from the regulatory perspective. In the work reported here, the probability of initiation of a DHC ahead of a volumetric flaw is evaluated and its subsequent growth is modeled to estimate the probability of Break-Before-Leak (BBL). The uncertainty in the flaw size and the material properties of the PT are modeled in terms of a probability distribution function. Monte Carlo based simulation method is used to predict the probability. The variance reduction is achieved by employing radial and stratified sampling. The results are presented for parametric variation in mean values of crack sizes, values of hydrogen uptake rate and residual stress value. The statistics of the through-wall-crack (TWC) formed by a growing DHC crack is also reported. The statistics of the time taken by TWC to become critical is also evaluated. This study is useful to establish the LBB behavior of the PT. Nomenclature

flaw depth 2 flaw width 2 flaw length

upper-bound estimate of deuterium pickup during operation