Probabilistic Fracture Mechanics Analysis Research Articles

Probabilistic fracture mechanics analyses of a reactor pressure vessel using the irradiation embrittlement evaluation based on the Bayesian nonparametric method

In the structural integrity assessment of an embrittled reactor pressure vessel (RPV) based on probabilistic fracture mechanics (PFM), it is crucial to consider both of the mean value and the uncertainty of the embrittlement prediction. Typically, the embrittlement prediction uncertainty is given by a normal distribution, and its standard deviation is determined from the residuals of the measured and predicted values of all data used to develop the embrittlement prediction method. Therefore, the same uncertainty is assumed regardless of neutron fluence and the available data. To overcome this issue, the Japan Atomic Energy Agency recently developed the embrittlement prediction method based on machine learning and Bayesian statistics, i.e., the Bayesian nonparametric (BNP) method, and introduced it to the PFM analysis code. The BNP method can predict the probability distribution according to data scarcity and provide more reasonable uncertainty because it estimates significant uncertainties where the scatter of actual measured data is large and the number of data is small. In this study, PFM analysis for a Japanese model RPV in a pressurized water reactor is conducted using the PFM analysis of structural components in aging light water reactors, where the embrittlement probability distribution calculated using the BNP method is used. Furthermore, the effects of different embrittlement prediction methods and uncertainties on the failure frequency of RPVs are investigated in the PFM analyses, and the results are presented.

Stress Measurement of Stainless Steel Piping Welds by Complementary Use of High-Energy Synchrotron X-rays and Neutrons

Probabilistic fracture mechanics (PFM) is increasingly recognized as a viable approach for evaluating the structural integrity of nuclear components, such as piping, primarily affected by stress corrosion cracking (SCC). PFM analysis requires several input parameters, among which welding residual stress is critically important due to its significant influence on SCC initiation and propagation. Recently, a novel technique involving a double-exposure method (DEM) utilizing synchrotron X-rays was introduced as an effective means for measuring welding residual stress with high spatial resolution. In this paper, we applied DEM to assess the residual stress of a plate specimen, which was extracted from a welded pipe through electrical discharge machining. Consequently, detailed stress maps under a plane stress state were generated. Additionally, the residual stress distributions in the welded pipe under a triaxial stress state were evaluated using neutron diffraction. Based on these findings, we proposed a methodology to acquire detailed stress maps of welded pipes by combining high-energy synchrotron X-rays and neutron diffraction.

Probabilistic fracture mechanics analysis of heat transfer tube in floating nuclear power plant under multiple failure mechanisms

Probabilistic fracture mechanics analysis of heat transfer tube in floating nuclear power plant under multiple failure mechanisms

Verification of probabilistic fracture mechanics analysis code PASCAL for reactor pressure vessel

Verification of probabilistic fracture mechanics analysis code PASCAL for reactor pressure vessel

Failure probability evaluation for a weld of the heat pipe in the Mega-Power heat pipe cooled reactor

Heat pipe cooled reactor, featuring using heat pipes as passive cooling, has received renewed interest. A Monte-Carlo-based probabilistic fracture mechanics analysis code, including crack initiation and propagation model, is developed to estimate the probability of failure at a weld in the heat pipe due to stress corrosion cracking (SCC), fatigue, and high temperature creep. The application of this code is demonstrated on the heat pipe of the Mega-Power rector. The results show that SCC is more important in accelerating heat pipe failure than fatigue and high temperature creep. Failure probabilities under the condition of one or two adjacent failed heat pipes are abnormally close. Uncertainty analysis for input parameters proves initial crack size is more sensitive than temperature. This also provides a reference for heat pipe design and safety assessment of whole reactor.

Recent improvements of probabilistic fracture mechanics analysis code PASCAL for reactor pressure vessels

A probabilistic fracture mechanics (PFM) analysis code PASCAL was developed in Japan for probabilistic integrity assessment of reactor pressure vessels (RPVs) in pressurized water reactors (PWRs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) transients. To strengthen the practical applications of PFM methodology in Japan, PASCAL has been upgraded to a new version, PASCAL5, which enables PFM analyses of RPVs in both PWRs and boiling water reactors (BWRs) subjected to a broad range of transients, including PTS and normal operational transients. In this paper, the recent improvements in PASCAL5 are described such as the incorporated stress intensity factor solutions and corresponding calculation methods for external surface cracks and embedded cracks near the RPV outer surface. In addition, the analysis conditions and evaluation models recommended for PFM analyses of Japanese RPVs in BWRs are investigated. Finally, PFM analysis examples for core region of a Japanese BWR-type model RPV subjected to two transients (i.e., low-temperature over pressure and heat-up transients) are presented using PASCAL5.

Verification Study of Probabilistic Fracture Mechanics Analysis Code for Reactor Pressure Vessel During Pressurized Thermal Shock

This investigation is to present a verification study of probabilistic fracture mechanics (PFM) analysis code for a reactor pressure vessel (RPV) during pressurized thermal shock (PTS). The probabilistic fracture mechanics code FAVOR, developed by Oak Ridge National Laboratory, is used to calculate the conditional probabilities of crack initiation and penetration for welds that are located in the RPV beltline region. The procedure includes deterministic analyses of the temperature and stress distributions through the vessel wall at the PTS, and probabilistic analyses on the vessel failure probability as a result of PTS transients. The RPV geometries, material properties, and properties related to embrittlement are those in taken from previous studies. Two previously suggested hypothetical transients, which may seriously affect RPV integrity, are also taken into account. To verify the results of PFM round robin analysis of RPV during PTS events, several models and Monte Carlo methods for determining PFM performance are used and they agree on the accuracy of the failure assessment is obtained. The present work can be regarded as various important factors about performing PFM that affect in evaluating the structural safety and operational stability of RPVs. The comparisons of the paper also support the finding that the FAVOR code is very practically useful in assessing failure probability.

Improvement of Probabilistic Fracture Mechanics Analysis Code PASCAL-SP Regarding Stress Corrosion Cracking in Nickel Based Alloy Weld Joint of Piping System in Boiling Water Reactor

Abstract In the past few decades, cracks because of stress corrosion cracking (SCC) have been detected in the dissimilar weld joints using nickel-based alloy in piping system of boiling water reactors (BWRs). Thus, the structural integrity assessment for such weld joints has become important. Nowadays, probabilistic fracture mechanics (PFM) analysis is recognized as a rational method for structural integrity assessment because it can consider inherent uncertainties of various influencing factors as probability distributions and quantitatively evaluate the failure probability of a cracked component. The Japan Atomic Energy Agency has developed a PFM analysis code PASCAL-SP for a weld joint of piping system in nuclear power plant. This study improves the analysis functions of PASCAL-SP for weld joint using nickel-based alloy in BWR susceptible to SCC. As an analysis example of the improved version of PASCAL-SP, the failure probability of a weld joint is quantitatively evaluated. Furthermore, sensitivity analyses are conducted concerning the effect of leak detection and in-service inspection. From the analysis results, it is concluded that the improved version of PASCAL-SP is useful for structural integrity assessment.

Verification of Probabilistic Fracture Mechanics Analysis Code for Reactor Pressure Vessel

Abstract Nowadays, it has been recognized that probabilistic fracture mechanics (PFM) is a promising methodology in structural integrity assessments of aged pressure boundary components of nuclear power plants, because it can rationally represent the influencing parameters in their inherent probabilistic distributions without over conservativeness. A PFM analysis code PFM analysis of structural components in aging light water reactor (PASCAL) has been developed by the Japan Atomic Energy Agency to evaluate the through-wall cracking frequencies of domestic reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) transients. In addition, efforts have been made to strengthen the applicability of PASCAL to structural integrity assessments of domestic RPVs against nonductile fracture. A series of activities has been performed to verify the applicability of PASCAL. As a part of the verification activities, a working group was established with seven organizations from industry, universities, and institutes voluntarily participating as members. Through one-year activities, the applicability of PASCAL for structural integrity assessments of domestic RPVs was confirmed with great confidence. This paper presents the details of the verification activities of the working group, including the verification plan, approaches, and results.

Effect of Coolant Water Temperature of Emergency Core Cooling System on Failure Probability of Reactor Pressure Vessel

Abstract Structural integrity assessment of reactor pressure vessel (RPV) is important for the safe operation of nuclear power plant. For an RPV in a pressurized water reactor (PWR), pressurized thermal shock (PTS) resulted from rapid coolant water injection due to a loss-of-coolant accident is an issue of particular concern. The coolant water temperature in the emergency core cooling system (ECCS) can influence the integrity of RPV subjected to PTS events; thus, this paper is focused on investigating the effect of coolant water temperature of ECCS on failure probability of an RPV. First, thermal-hydraulic (TH) analyses were conducted for a Japanese PWR model plant by using RELAP5, and different coolant water temperatures in ECCS were considered to investigate the effect of coolant water temperature on TH behaviors during a PTS event. Using the TH analysis results, probabilistic fracture mechanics (PFM) analyses were performed for the RPV of the Japanese model plant. Based on the PFM analysis results, the effect of coolant water temperature on failure probability of the RPV was quantified.

Application of Flaw Updating Process on Probabilistic Integrity Analysis for a Reactor Pressure Vessel Subjected to Pressurized Thermal Shocks

The structural integrity of a reactor pressure vessel (RPV) is a crucial issue for an operating nuclear power plant, especially in the beltline region, which suffers the highest neutron irradiation. Owing to its capability of considering parameters based on statistical distributions and provision of objective risk-informed results, the probabilistic fracture mechanics (PFM) method is widely used in evaluating the structural integrity of RPVs. However, the flaw characteristics used for PFM analysis are mainly derived from particular vessel inspection information such as from the Pressure Vessel Research User Facility and Shoreham vessels, which may not be able to truly represent the vessel-specific condition of an analyzed RPV. In this work, the Bayesian inference, which combines prior flaw data with new inspection results as well as uncertainties, is used to develop posterior vessel-specific flaw distributions. Then, the updated flaw model is used for PFM analysis to investigate the effects on the fracture probability assessment of RPVs subjected to pressurized thermal shocks (PTSs). Considering the updated flaws based on the inspection data, the PFM analysis result could be more realistic to predict the fracture risks of RPVs during operation.

Evaluation of crack opening displacement of through-wall circumferential-cracked pipe using direct weight function method

This paper presents a direct weight function-based method to evaluate the crack opening displacement (COD) which is a key parameter in leak-before-break (LBB) assessment and in probabilistic fracture mechanics (PFM) assessment of nuclear piping systems. The focus of this study is a circumferential-cracked pipe with non-linearly through-wall distributed stress loaded on the crack face. Parametric finite element analyses (FEA) were performed to calculate COD associated with different crack face pressure (CFP) loadings. The analyses matrix covers a wide range of pipe size and crack lengths. The crack mouth COD values at three locations: at outside surface, inner surface and mid-thickness were considered. The numerical results were then used to determine the coefficients that construct the direct weight functions. The proposed solution can be used to predict the COD resulted from given weld residual stress (WRS) field with the general prediction error being less than 8%. The research outcome can provide more computational efficiency in both deterministic LBB assessment as well as PFM analyses of pressurized pipes.

Guideline on Probabilistic Fracture Mechanics Analysis for Japanese Reactor Pressure Vessels

Abstract In Japan, to prevent nil-ductile fracture of reactor pressure vessels (RPVs) due to neutron irradiation embrittlement, deterministic fracture mechanics evaluation in accordance with the codes provided by the Japan Electric Association is performed for assessing the structural integrity of RPVs under pressurized thermal shock (PTS) events considering neutron irradiation embrittlement. In recent years, a structural integrity assessment methodology based on probabilistic fracture mechanics (PFM) has been introduced into the regulations in the United States and a few European countries. PFM is a rational methodology for evaluating the failure frequency of important pressure boundary components by considering the probabilistic distributions of various influence factors related to aged degradation due to the long-term operation. In Japan Atomic Energy Agency (JAEA), a PFM analysis code called PASCAL has been developed to evaluate the failure frequency of RPVs considering neutron irradiation embrittlement and PTS events. In addition, we have developed a guideline for structural integrity assessment of RPVs based on PFM to improve the applicability of PFM in Japan and enable persons who have knowledge on fracture mechanics to perform PFM analyses and evaluate through-wall cracking frequency (TWCF) of RPVs easily. The guideline consists of a main body, explanation, and several supplements. The technical basis for PFM analysis is provided, and the latest knowledge is included in the guideline. In this paper, an overview of the guideline and some typical analysis results obtained based on the guideline and the Japanese database related to PTS evaluation are presented.

Round robin analysis of vessel failure probabilities for PTS events in Korea

Round robin analyses for vessel failure probabilities due to PTS events are proposed for plant-specific analyses of all types of reactors developed in Korea. Four organizations, that are responsible for regulation, operation, research and design of the nuclear power plant in Korea, participated in the round robin analysis. The vessel failure probabilities from the probabilistic fracture mechanics analyses are calculated to assure the structural integrity of the reactor pressure vessel during transients that are expected to initiate PTS events. The failure probabilities due to various parameters are compared with each other. All results are obtained based on several assumptions about material properties, flaw distribution data, and transient data such as pressure, temperature, and heat transfer coefficient. The realistic input data can be used to obtain more realistic failure probabilities. The various results presented in this study will be helpful not only for benchmark calculations, result comparisons, and verification of PFM codes developed but also as a contribution to knowledge management for the future generation.

Influence evaluation of sampling methods of the nondestructive examination on failure probability of piping based on probabilistic fracture mechanics analysis

Influence evaluation of sampling methods of the nondestructive examination on failure probability of piping based on probabilistic fracture mechanics analysis

Recent verification activities on probabilistic fracture mechanics analysis code PASCAL4 for reactor pressure vessel

Recent verification activities on probabilistic fracture mechanics analysis code PASCAL4 for reactor pressure vessel

Improvements on Evaluation Functions of a Probabilistic Fracture Mechanics Analysis Code for Reactor Pressure Vessels

Abstract In Japan, a probabilistic fracture mechanics (PFM) analysis code PASCAL was developed for structural integrity assessment of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) events. By reflecting the latest knowledge and findings, the evaluation functions are continuously improved and have been incorporated into PASCAL4 which is the most recent version of the PASCAL code. In this paper, the improvements made in PASCAL4 are explained in detail, such as the evaluation model of warm prestressing (WPS) effect, evaluation function of confidence levels for PFM analysis results by considering the epistemic and aleatory uncertainties in probabilistic variables, the recent stress intensity factor (KI) solutions, and improved methods for KI calculations when considering complicated stress distributions. Moreover, using PASCAL4, PFM analysis examples considering these improvements are presented.

Reliability Analysis of a Pre-Cracked Structure in Accidental Operation Conditions

Evaluating the integrity of a structure consists in proving its ability to realize its mechanical functions for all modes of loading, normal or accidental, and throughout its lifetime. In the context of nuclear safety, the most important structures consider the presence of a degradation grouping several aspects, such as cracks. In this context, the fracture mechanics provide the tools needed to analyze cracked components. Its purpose is to establish break criteria for judging loading margins in normal or accidental operating conditions. The seismic load is one of the dominant loads for the failure assessment of the pipes. Its probabilistic dispersion, however, was not taken into account in the past probabilistic fracture mechanics analysis. The objective of this paper is to simulate and analyze the effect of abnormal stress on the reliability of tow pipe sizes. As result the seismic stress has more effect on the break probability, but not for the leak probability. In the case without a seismic load, the break probability is mainly dominated by an initial crack size. The earthquake has much effect on the break probability for the large diameter pipe, not for the small diameter pipe. In the large diameter pipe, the break probability increases gradually with the time. The leak probability of both pipe sizes is not affected by the seismic curve.

Probabilistic fracture mechanics analysis of three-dimensional cracked structures considering random field fracture property

This paper presents a probabilistic fracture mechanics approach to evaluate the reliability of three-dimensional (3D) cracked structures considering spatially varying random fracture property. The applied loads and initial crack length are modeled as random variables, and the fracture toughness is modeled as a spatially-varying random field. Based on the weakest link model, a system reliability model for 3D cracked structures is constructed through discretizing the crack front into a finite number of elements. The dimensional reduction integration approach is then modified to calculate the reliabilities of elements in the crack front as well as the correlations among them simultaneously, such that the system reliability model can be efficiently solved. Numerical examples are presented to illustrate the validity of the proposed method, and the thickness and size effects on the results are discussed. The results show that the predicted probabilities of fracture based on the proposed method are very consistent with the Monte Carlo simulation results, and in the meanwhile, it has a satisfactory computational efficiency. In addition, it is found that the fracture probability increases with the increasing of the thickness and size due to the existing of more possible effective failure elements or the larger stress intensity factors.

A new probabilistic evaluation model for weld residual stress

Weld residual stress (WRS) is one of the most important factors in the structural integrity assessment of piping welds, and it is considered a driving force for crack growth. It is characterized by large uncertainty. For more rational assessment, it is important to consider the uncertainty of WRS for evaluating crack growth behavior in probabilistic fracture mechanics (PFM) analysis. In existing PFM analysis codes, WRS uncertainty is set by statistically processing the multiple WRS data obtained from finite element analyses. This process depends on the individual performing PFM analysis, which may lead to uncertainties derived from the PFM analyst. In this study, we developed a new WRS evaluation model based on Fourier transformation, and the model was incorporated into the PFM analysis code PASCAL-SP, which has been developed by Japan Atomic Energy Agency. Through improvements to the code, WRS uncertainty can be considered automatically and appropriately by inputting multiple WRS data directly as input for PFM analysis.