Probabilistic analysis of PWR Reactor Pressure Vessel under Pressurized Thermal Shock

The beltline region is the most important part of the reactor pressure vessel, become embrittlement due to neutron irradiation at high temperature after long-term operation. Pressurized thermal shock is one of the potential threats to the integrity of beltline region also the reactor pressure vessel structural integrity. Hence, to maintain the integrity of RPV, this paper describes the benchmark study for deterministic and probabilistic fracture mechanics analyzing the beltline region under PTS by using FAVOR code developed by Oak Ridge National Laboratory. The Monte Carlo method was employed in FAVOR code to calculate the conditional probability of crack initiation. Three problems from Probabilistic Structural Integrity of a PWR Reactor Pressure Vessel (PROSIR) round-robin analysis were selected to analyze, the present results showed a good agreement with the Korean participants’ results on the conditional probability of crack initiation.

Fracture Toughness in Postulated Crack Area of PTS Evaluation in Highly-Neutron Irradiated RPV Steel

The Japanese Electric Association Code 4206-2016 requires that the semi-elliptical crack sized 10 mm in depth × 60 mm in length shall be postulated near the inner surface of a reactor pressure vessel (RPV) in pressurized thermal shock events. The fracture toughness distribution was investigated in the postulated crack area under the PTS events of unirradiated and highly-neutron irradiated RPV steels. Vickers hardness in heat-affected zone (HAZ) due to stainless overlay cladding and 10 mm from the cladding were higher than that of a quarter thickness position, where the surveillance specimens are machined, for both unirradiated (E1) and irradiated (up to 1 × 1020 n/cm2, WIM) materials. Fracture toughness of HAZ and 10 mm from the cladding was higher for the above highly-neutron irradiated material. The same result was obtained in the unirradiated material. Therefore, it was confirmed that fracture toughness obtained from surveillance specimens can provide conservative assessment of structural integrity of RPV.

Properties of Cladding With Respect to RPV Integrity

Inner surface of most of primary circuit components in PWR/BWR/WWER type reactors is covered by austenitic cladding that serves primarily as anticorrosion protection. This is also supported by the requirements for stress analysis of the vessel by most of the codes — austenitic cladding is not taken into account in the calculation of vessel wall thickness and on allowance of stress intensities for operating conditions. Its effect is taken, in some codes like for WWER components, in fatigue calculation and also for evaluation of vessel resistance against fast fracture during pressurized thermal shock (PTS) events.

Improved Bayesian Update Method on Flaw Distributions Reflecting Non-Destructive Inspection Result

We have developed a probabilistic fracture mechanics (PFM) analysis code named PASCAL4 for evaluating the failure frequency of reactor pressure vessels (RPVs) through consideration of neutron irradiation embrittlement and transients such as pressurized thermal shock events. It is well-known that flaw distributions, including flaw size and density, have an important role in the failure frequency calculations of a PFM analysis. NUREG-2163 report provides a methodology to obtain much more realistic flaw distributions based on a Bayesian updating approach by reflecting the non-destructive inspection (NDI) results, which is applicable for case when there are flaw indications through NDI. There may, however, be no flaw indications resulting after inspection of some RPVs. Therefore, we proposed likelihood functions applicable for both cases when flaws are detected and when there is no flaw indication as the NDI results. In the Bayesian updating method, the likelihood functions were applied to independently acquire the posterior distributions of flaw depth and density using the same NDI results. In this study, we further improve the likelihood functions to enable them to update flaw depth and density simultaneously. Based on this improved likelihood function, several application examples are presented where the flaw distributions are estimated by reflecting the NDI results through Bayesian update. In addition, PFM analyses are also performed considering those estimated flaw distributions. All the results indicate that the improved likelihood functions are useful for estimating flaw distributions.