The structural integrity assessment of a nuclear Reactor Pressure Vessel (RPV) during accidental conditions, such as loss-of-coolant accident (LOCA), is a major safety concern. Besides Conventional deterministic calculations to justify the RPV integrity, Electricite´ de France (EDF) carries out probabilistic analyses. Since in the USA the probabilistic fracture mechanics analyses are accepted by the Nuclear Regulatory Commission (NRC), a benchmark has been realized between EDF and Oak Ridge Structural Assessments, Inc. (ORSA) to compare the models and the computational methodologies used in respective deterministic and probabilistic fracture mechanics analyses. Six cases involving two distinct transients imposed on RPVs containing specific flaw configurations (two axial subclad, two circumferential surface-breaking, and two axial surface-braking flaw configurations) were defined for a French vessel. In two separate phases, deterministic and probabilistic, fracture mechanics analyses were performed for these six cases.
In Electricite´ de France (EDF), it’s used to taking as a conservative constant value for the temperature of Refueling Water Storage Tank (RWST) in the deterministic and probabilistic analyses for Reactor Pressure Vessel (RPV) life management. The water contained in this storage tank supplies Security Injection during accidental conditions, such as loss-of-coolant accident (LOCA), so the temperature of this water is a very important input parameter for fracture mechanics analyses. In the continuation of [1], the aim of our study is to evaluate the variability of this temperature. Since 1999, EDF has been collecting the RWST temperature for several sites and several nuclear plant units. Using statistical analyses, this study aims at first to identify the most important RPV exploitation life events that influence this temperature and, at secondly, to obtain statistical density distributions in order to describe its variability in the most realistic way possible.
The structural integrity assessment of a nuclear Reactor Pressure Vessel (RPV) during accidental conditions such as loss-of-coolant accident (LOCA) is a major safety concern. Besides conventional deterministic calculations to justify as a nuclear operator the RPV integrity, Electricite´ de France (EDF) carries out probabilistic analyses. Probabilistic analyses become most interesting when some key variables, albeit conventionally taken at conservative values, can be modelled more accurately through statistical variability. In the context of low failure probabilities, this requires however a specific coupling effort between a specific probabilistic analysis method (e.g. Form-Sorm method) and the thermo-mechanical model to be reasonable in computing time. In this paper, the variability of a key variable — the mid-transient cooling temperature, tied to a climate-dependent tank — has been modelled, in some flaw configurations (axial sub-clad) for a French vessel. In a first step, a simplified analytical approach was carried out to assess its sensitivity upon the thermo-mechanical phenomena; hence, a direct coupling had to be implemented to allow a probabilistic calculation on the finite-element mechanical model, taking also into account a failure event properly defined through minimisation of the instantaneous failure margin during the transient. Comparison with the previous (indirectly-coupled) studies and the simplified analytical approach is drawn, demonstrating the interest of this new modelling effort to understand and order the sensitivity of the probability of crack initiation to the key variables. While being noticeable in the cases studied, sensitivity to the safety injection temperature variability proves to be less than the choice of the toughness model. Finally, regularity of the thermo-mechanical model is evidenced by the coupling exercise, suggesting that a modified response-surface based method could replace direct coupling for further investigation.
Assessing the structural integrity of a nuclear Reactor Pressure Vessel (RPV) subjected to pressurized-thermal-shock (PTS) transients is extremely important to safety. In addition to conventional deterministic calculations to confirm RPV integrity, Electricite´ de France (EDF) carries out probabilistic analyses. Probabilistic analyses are interesting because some key variables, albeit conventionally taken at conservative values, can be modeled more accurately through statistical variability. One variable which significantly affects RPV structural integrity assessment is cleavage fracture initiation toughness. The reference fracture toughness method currently in use at EDF is the RCCM and ASME Code lower-bound KIC based on the indexing parameter RTNDT. However, in order to quantify the toughness scatter for probabilistic analyses, the master curve method is being analyzed at present. Furthermore, the master curve method is a direct means of evaluating fracture toughness based on KJC data. In the framework of the master curve investigation undertaken by EDF, this article deals with the following two statistical items: building a master curve from an extract of a fracture toughness dataset (from the European project “Unified Reference Fracture Toughness Design curves for RPV Steels”) and controlling statistical uncertainty for both mono-temperature and multi-temperature tests. Concerning the first point, master curve temperature dependence is empirical in nature. To determine the “original” master curve, Wallin postulated that a unified description of fracture toughness temperature dependence for ferritic steels is possible, and used a large number of data corresponding to nuclear-grade pressure vessel steels and welds. Our working hypothesis is that some ferritic steels may behave in slightly different ways. Therefore we focused exclusively on the basic french reactor vessel metal of types A508 Class 3 and A 533 grade B Class 1, taking the sampling level and direction into account as well as the test specimen type. As for the second point, the emphasis is placed on the uncertainties in applying the master curve approach. For a toughness dataset based on different specimens of a single product, application of the master curve methodology requires the statistical estimation of one parameter: the reference temperature T0. Because of the limited number of specimens, estimation of this temperature is uncertain. The ASTM standard provides a rough evaluation of this statistical uncertainty through an approximate confidence interval. In this paper, a thorough study is carried out to build more meaningful confidence intervals (for both mono-temperature and multi-temperature tests). These results ensure better control over uncertainty, and allow rigorous analysis of the impact of its influencing factors: the number of specimens and the temperatures at which they have been tested.
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