Statistical Analyses for Probabilistic Assessments of the Reactor Pressure Vessel Structural Integrity: Building a Master Curve on an Extract of the “Euro” Fracture Toughness Dataset, Controlling Statistical Uncertainty for Both Mono-Temperature and Multi-Temperature Tests

Abstract

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.