International Journal of Nuclear Energy

Volume 2015, Article ID 785041, 9 pages

http://dx.doi.org/10.1155/2015/785041

## Probabilistic Structural Integrity Analysis of Boiling Water Reactor Pressure Vessel under Low Temperature Overpressure Event

Institute of Nuclear Energy Research, Taoyuan 32546, Taiwan

Received 5 February 2015; Accepted 26 October 2015

Academic Editor: Arkady Serikov

Copyright © 2015 Hsoung-Wei Chou and Chin-Cheng Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The probabilistic structural integrity of a Taiwan domestic boiling water reactor pressure vessel has been evaluated by the probabilistic fracture mechanics analysis. First, the analysis model was built for the beltline region of the reactor pressure vessel considering the plant specific data. Meanwhile, the flaw models which comprehensively simulate all kinds of preexisting flaws along the vessel wall were employed here. The low temperature overpressure transient which has been concluded to be the severest accident for a boiling water reactor pressure vessel was considered as the loading condition. It is indicated that the fracture mostly happens near the fusion-line area of axial welds but with negligible failure risk. The calculated results indicate that the domestic reactor pressure vessel has sufficient structural integrity until doubling of the present end-of-license operation.

#### 1. Introduction

The reactor pressure vessels (RPVs) of nuclear power plant have to withstand the high pressure, high temperature, and neutron irradiation. During long-term operation, the fast neutron fluence causes the ferritic steel of RPV susceptible to brittle fracture, especially for the plate and weld materials in the beltline region corresponding to the reactor core. The embrittled vessel shell may fracture due to a preexisting fabrication flaw and leads to a through-wall crack. On the basis of operational safety of nuclear power plants in Taiwan, the regulatory body strictly requires the licensee to perform the in-service inspection (ISI) periodically and thoroughly on all shell welds according to the requirement of ASME Boiler and Pressure Vessel Code, Section XI. On the other hand, the surveillance capsules mounted in the reactor core used to assess the neutron fluence and radiation embrittlement of the RPV materials also need to be regularly drawn out, tested, and analyzed.

When evaluating the fracture behavior of RPV, the relevant parameters such as neutron irradiation, chemical composition of materials, and flaw characteristics are difficult to be accurately determined because of the uncertainties mainly from the inaccuracy of measurement or other undetermined factors. Therefore, evaluation based on deterministic method frequently makes conservative assumptions to envelop any potential uncertainties regarding multiple parameters and thus it inevitably produces an overconservative result. From the past two decades, the application of probabilistic fracture mechanics (PFM) has been widely applied to evaluate the structural integrity of RPV. The BWR Vessel and Internal Project (BWRVIP) and the United States Nuclear Regulatory Commission (USNRC) had utilized PFM to evaluate the fracture probabilities of boiling water reactor (BWR) pressure vessel shell welds and finally concluded that the in-service inspection (ISI) on the circumferential shell welds can be relieved conditionally [1, 2]. On the other hand, the USNRC’s new pressurized thermal shock (PTS) screening criteria for pressurized water reactor (PWR) pressure vessel were also determined by the PFM analysis results [3–5]. Using the Monte Carlo simulations, vessels can be sampled many times with random parameters affecting the fracture toughness of RPV materials based on the probability distribution functions. The probability of failure (POF) is determined from dividing the sum of total failure probability by the total number of iterations which have been performed.

In Taiwan, the PFM code, FAVOR (Fracture Analysis of Vessels-Oak Ridge) of Oak Ridge National Laboratory (ORNL), has been employed to perform the fracture probability analyses for domestic RPVs. A very conservative model based on the USNRC’s assumption used for regulation in 1998 [2] had been rebuilt to evaluate the structural integrity of the domestic BWR pressure vessels with their plant specific parameters [6, 7]. It was demonstrated that the domestic BWR pressure vessels can maintain adequate structural integrity even subjected to the specified worst accidental transient of low temperature overpressure (LTOP) event. However, the previous model was overconservative and so cannot reasonably represent the fracture mechanism of RPV. For example, the previous flaw model, the PVRUF-exponential best estimate distribution [2], assumed that all the preexisting flaws are surface breaking with a very conservative depth distribution. The flaw density of 108 flaws/vessel was assumed and all simulated surface breaking flaws were conservative with an aspect ratio of 10. As a matter of fact, it has been found that most preexisting fabrication flaws along the vessel wall are embedded with various aspect ratios. The flaw characteristics are mainly associated with the material types, welding process, bead size, and so on [8]. In the study, we aim at reanalyzing the fracture probability of a Taiwan domestic BWR pressure vessel by the more realistic model. First, a beltline region model which includes axial welds, circumferential welds, and plates of the domestic BWR pressure vessel was established for the advanced version of FAVOR code. Then, we utilized the VFLAW code developed by the Pacific Northwest National Laboratory (PNNL) in the United States [8] to generate the flaw files for FAVOR which describe the flaw characteristics of surface breaking flaws, weld embedded flaws, and plate embedded flaws. An improved radiation embrittlement correlation was also employed here. The transient of LTOP event was applied as the loading condition as the worst-case accident. Two levels of radiation embrittlement of the RPV were considered. The analysis result in the paper could be a reference for the BWR operations in Taiwan.

#### 2. Evaluation Methodology

The advanced FAVOR code was employed to analyze the fracture probability of the domestic BWR pressure vessel. Related to the previous version of FAVOR code, the principal modifications of the advanced version are as follows [9, 10]: (1) having the capability to model the flaw populations such as internal or external surface breaking flaws, thus permitting it to analyze either cool-down or heat-up transient effects on RPVs and (2) modifying the stress intensity factor influence coefficients (SIFICs), which consider various flaw orientations, geometries, categories, and aspect ratios to calculate the mode I stress intensity factor for each simulated flaw, to be applicable to ratio of RPVs from 10 to 20 for either PWR or BWR geometry. In this work, FAVOR’s two processors, FAVLoad and FAVPFM, were used. For the preprocessor FAVLoad, we have to prepare the input file which contains the material properties, RPV geometry, and thermal-hydraulic data of transients. FAVLoad reads the input file and then generates the output file that contains the temperature, stress, and stress intensity factor histories of flaw tips regarding various location, length, and aspect ratio along the wall thickness. Then, FAVPFM calculates the instantaneous conditional probability of initiation (cpi) of each simulated flaw tip at each time step, , during the transient according to the Weibull probability function, given by [9]:wherewhere is the reference temperature of nil-ductility transition of metal materials. , , and are coefficients of Weibull probability function. In FAVPFM, the conditional probability of initiation (CPI) of each simulated flaw during the transient is defined as the maximum value of . The warm-prestress (WPS) effect is also taken into account. WPS is a phenomenon of improvement of apparent fracture toughness of ferritic steels in lower shelf region by preloading them at upper shelf region [11]. Therefore, under some cooling type transients most crack initiation may be excluded when the WPS is considered [12, 13], even if is larger than . If a flaw is in a state of WPS, it is not eligible for initiation (or reinitiation after the flaw has ever been arrested) until the following conditions are met [9]:

(1) of the flaw tip is greater than in (1) for the temperature at the flaw tip ().(2)A raising field, that is, the time-rate-of-change of is positive ().(3)In a rising field, must exceed the previously established maximum value experienced by the flaw tip during the transient up to the current point in time under consideration (applied-).After a crack initiation, FAVOR assumes that the flaw becomes surface breaking with infinite aspect ratio and then enters the Initiation-Growth-Arrest (IGA) submodel to evaluate the crack propagation and ductile-tearing behavior. The arrest fracture toughness, , in FAVOR was developed by the statistical model based on the ORNL database as a lognormal distribution given by [9]:

The IGA submodel in FAVPFM is complicated and will not be described here. The conditional probability of failure (CPF) is defined as CPI multiplied by the ratio that the initiated flaw propagates to 90% vessel wall thickness.

For the flaw distribution in the analysis, we utilized the PNNL’s VFLAW code to generate the surface breaking flaw file, S.dat, weld embedded flaw file, W.dat, and plate embedded flaw file, P.dat, for FAVOR [8]. These files describe the flaw characteristics such as location, size, and aspect ratio. The corresponding parameters based on the RPV fabrication input for VFLAW are listed in Table 1, and the mean flaw number distributions of the RPV beltline region against the percentage of the vessel wall thickness simulated by 1000 Monte Carlo simulations of VFLAW are shown in Figure 1. FAVOR classifies all simulated flaws into three categories: Flaw Category 1: the surface breaking flaws; Flaw Category 2: the embedded flaws which exist in the base material between the clad/base interface and ; and Flaw Category 3: the embedded flaws in the base material between and . FAVOR assumes inner Category 1 flaws are circumferentially oriented based on the vessel fabrication, which has austenitic stainless-steel cladding applied to the inner surface of the vessel. Weld embedded flaws in axial welds are oriented axially and in circumferential welds are oriented circumferentially. As for the plate embedded flaws, they are 50% for axially oriented and 50% for circumferentially oriented, respectively [9, 14]. In addition, the Flaw Population Option 3 of the FAVOR which allocates the flaw tips throughout the entire wall thickness from inner to outer surface was used. In the option, the external surface breaking flaws will be equally divided between axial and circumferential orientations.