Probabilistic Fracture Mechanics Research Articles

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.

Mechanical Reliability Analysis of Control Rod Assembly for HTR-PM

The article analyzes the forces and weaknesses of the control rod assembly in the high temperature gas cooled reactor (HTGR) demonstration project-pebble bed modular HTGR plant (HTR-PM), using the the mechanical reliability theory and mechanical simulation, and identifies the weaknesses at the connection of the control rod assembly. In the reliability-life calculation method based on the probabilistic fracture mechanics, in combination with the influence of irradiation on the fatigue life model and in consideration of the stress, the authors establish the reliability-life model to calculate the reliability-life of HTR-PM control rod assembly at the irradiation attenuation coefficient of 0.7. The calculation results show that at the reliability level of 0.99, the life of HTR-PM control rod assembly is about 150,000 action cycles, and that the irradiation has a great influence on the life of the control rod assembly. In view of what mentioned above, this paper can provide reference for the equipment reliability management of the HTR-PM control rod assembly.

A Probabilistic Model for Forging Flaw Crack Nucleation Processes

Abstract A probabilistic model for quantifying the number of load cycles for nucleation of forging flaws into a crack has been developed. The model correlates low cycle fatigue (LCF) data, ultrasonic testing (UT) indication data, flaw morphology and type with the nucleation process. The nucleation model is based on a probabilistic LCF model applied to finite element analyses (FEA) of flaw geometries. The model includes statistical size and notch effects. In order to calibrate the model, we conducted experiments involving specimens that include forging flaws. The specimens were machined out from heavy duty steel rotor disks for the energy sector. The large disks, including ultrasonic indications on the millimeter scale, were cut into smaller segments in order to efficiently machine specimens including manufacturing related forging flaws. We conducted cyclic loading experiments at a variety of temperatures and high stresses in order to capture realistic engine operating conditions for flaws as they occur in service. This newly developed model can be incorporated into an existing probabilistic fracture mechanics framework and enables a reliable risk quantification allowing to support customer needs for more flexible operational profiles due to the emergence of renewable energy sources.

A fracture mechanics framework for optimising design and inspection of offshore wind turbine support structures against fatigue failure

Abstract. Offshore wind turbine (OWT) support structures need to be designed against fatigue failure under cyclic aerodynamic and wave loading. The fatigue failure can be accelerated in a corrosive sea environment. Traditionally, a stress–life approach called the S–N (stress–number of cycles) curve method has been used for the design of structures against fatigue failure. There are a number of limitations in the S–N approach related to welded structures which can be addressed by the fracture mechanics approach. In this paper the limitations of the S–N approach related to OWT support structure are addressed and a fatigue design framework based on fracture mechanics is developed. The application of the framework to a monopile OWT support structure is demonstrated and optimisation of in-service inspection of the structure is studied. It was found that both the design of the weld joint and non-destructive testing (NDT) techniques can be optimised to reduce in-service inspection frequency. Furthermore, probabilistic fracture mechanics as a form of risk-based design is outlined and its application to the monopile support structure is studied. The probabilistic model showed a better capability to account for NDT reliability over a range of possible crack sizes as well as to provide a risk associated with the chosen inspection time which can be used in inspection cost–benefit analysis. There are a number of areas for future research, including a better estimate of fatigue stress with a time-history analysis, the application of the framework to other types of support structures such as jackets and tripods, and integration of risk-based optimisation with a cost–benefit analysis.

Effect of environmental modelling and inspection strategy on the optimal design of floating wind turbines

In order to reduce design conservatism and consequently the cost of energy, appropriate and cost-optimal safety factors should be derived, in light of environmental load uncertainties and lifetime costs. In the present work, a linearized dynamic model has been used together with Monte Carlo simulations and a numerical design optimization procedure to evaluate the impact of the description of wind and wave loads on the fatigue reliability and optimal design of a 10 MW spar floating wind turbine. Trade-offs between design costs and inspection costs with different design fatigue factors (DFFs) have also been assessed. The analyses have been performed for a realistic wind park site, where an environmental model has been developed based on hindcast data. Considering stochastic turbulence intensity, wind-wave misalignment, wind directional distribution, and a two-peak wave spectrum reduced the long-term fatigue damage by approximately two-thirds along the fatigue-critical part of the support structure compared to the base model. Re-designing the tower and platform with the full environmental model resulted in 11% reduction in CAPEX. However, due to the applied design optimization procedure, consistent reliability levels were achieved along the tower length, which resulted in important system side effects for the total structural reliability. Trade-offs between CAPEX and OPEX were derived based on a probabilistic fracture mechanics model and reliability updating through inspections. The necessary inspection intervals to achieve the same accumulated reliability after 20 years of operation were identified with different DFFs, and cost-optimal safety factors were computed with different OPEX costs and interest rates.

Probabilistic Fracture Mechanics for Mature Service Frame Rotors

AbstractLarge gas turbine design and service business are challenged with increased demands toward flexible operations, increasing number of start-stop cycles, and intermediate cycles. Probabilistic fracture mechanics simulation design tools have matured and became robust and reliable. We present a probabilistic reevaluation of Siemens E-class turbine disks by the combination of probabilistic two-dimensional axisymmetric part analysis of the disk and a novel probabilistic approach for the three-dimensional blade attachment. The first addresses the risk of inherent forging flaws, the latter combines the risk of surface crack initiation, growth, and failure. Both models consider the heterogeneous nature of material properties, flaw geometries, and detectability. These novel concepts developed at Siemens allow for an optimization of resource usage and safety, as well as the development of new service and inspection concepts for a variety of service frames and classes.

Comparison of sensitivity measures in probabilistic fracture mechanics

Probabilistic fracture mechanics (PFM) simulates the behavior of cracked structures and propagates uncertainties from input parameters to a failure probability or its uncertain estimate. In nuclear technology, this approach supports the assessment of the rupture probability of highly reliable pipes, which is an important parameter for the safety analysis of a nuclear power plant. For the appropriate probabilistic modelling of a structure with consideration of uncertainties, but also for the analysis of PFM application cases, the question arises, which input parameter of a probabilistic model has a higher impact on the estimate of computed failure probability, and which has a minor impact. This question is associated with the sensitivity measures or importance factors of the input parameters and their ranking concerning their influence.In this paper, six different approaches for the quantification of the sensitivity of parameters PFM evaluations are investigated: the amplification ratio, the direction cosine, the degree of separation, the analysis of the most probable failure point, the separation of uncertainty method, and the simple sample-based sensitivity study. Each method is described, visualized, applied to a common test case, and compared. The application case and the comparison are part of the Coordinated Research Project (CRP), “Methodology for Assessing Pipe Failure Rates in Advanced Water-Cooled Reactors (AWCRs)” by the International Atomic Energy Agency (IAEA), which is dedicated to the development of failure rates of piping in AWCRs. The participants used different PFM computer codes to analyze the test case and individual sensitivity methods to rank the input parameters, which motivated the comprehensive survey.The predicted parameter ranking of the approaches is consistent between the methods and between different PFM codes, but the approaches differ in the scope and the required effort. A conclusion is drawn and recommendations for the six different approaches are given.

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.

A Systematic Review of Structural Reliability Methods for Deformation and Fatigue Analysis of Offshore Jacket Structures

This paper presents the state of the art in Structural Reliability Analysis (SRA) methods with a view of identifying key applications of each method and its proposed variations, qualifying characteristics, advantages, and limitations. Due to the increasing complexity and scale of modern offshore jacket structures, it becomes increasingly necessary to propose an accurate and efficient approach for the assessment of uncertainties in their material properties, geometric dimensions, and operating environments. SRA, as a form of uncertainty analysis, has been demonstrated to be a useful tool in the design of structures because it can directly quantify how uncertainty about input parameters can affect structural performance. Herein, attention was focused specifically on the probabilistic fracture mechanics approach because this accounts accurately for fatigue reliability mostly encountered as being dominant in the design of such structures. The well-established analytical/approximate methods such as the First- and Second-Order Reliability Methods (FORM/SORM) are widely used as they offer a good balance between accuracy and efficiency for realistic problems. They are, however, inaccurate in cases of highly non-linear systems. As a result, they have been modified using methods such as conjugate search direction approach, saddle point approximation, subset simulation, evidence theory, etc. in order to improve accuracy. Initially, direct simulations methods such as the Monte Carlo Simulation Method (MCS) with its various variance reduction techniques such as the Importance Sampling (IS), Latin Hypercube Sampling (LHS), etc. are ideal for structures having non-linear limit states but perform poorly for problems that calculate very low probabilities of failure. Overall, each method has its own merits and limitation, with FORM/SORM being the most commonly used, but recently, simulation methods have increasingly been used due to continuous advances in computation powers. Other relevant methods include the Response Surface Methods (RSM) and the Surrogate Models/Meta-models (SM/MM), which are advanced approximation methods and are ideal for structures with implicit limit state functions and high-reliability indices. Combinations of advanced approximation methods and reliability analysis methods are also found in literature as they can be suitable for complex, highly non-linear problems.

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.

Probabilistic inspection planning of offshore welds subject to the transition from protected to corrosive environment

In this paper, a novel method is proposed to optimize inspection plans for fatigue accounting for the situations where corrosion-free or protected environments are changed to a corrosive environment, denoted as the Transitional Environmental Protection (TEP) process. Probabilistic fracture mechanics and S-N curve approaches are calibrated to simulate crack propagations and planning of inspections and repairs of offshore welds. The method presented is relatively simple and conservative: The transition between protected and corrosive environments is addressed by shifting the S-N curve parameters during the damage calculations, performing crack size recalibration and modifying the crack growth material parameters. These concepts are incorporated in an algorithm, which is applicable to new designs or existing structures where no data from previous inspections is available. An example illustrates the potential of the algorithm.

Probabilistic study on the macro-crack initiation of the rib-to-deck welded joint on orthotropic steel deck

The inherent randomness of the fatigue issues on the orthotropic steel deck (OSD) requires a probabilistic investigation. With respect to the unfavorable crack on the rib-to-deck welded joint of OSD, the macro-crack initiation, namely the process of the crack growth until it is detected, is studied using the probabilistic fracture mechanics (PFM). The PFM model is established based on the two-stage crack growth model and validated by test results. It is applied in the Monte-Carlo simulation (MCS) to reproduce the crack growth under the realistic traffic load obtained by the WIM data on an OSD for one year, suggesting that a lognormal function can be used in fitting the distribution of the life till the crack grows to half of the deck plate thickness. Based on the MCS results, further analysis is carried out on the macro-crack initiation by considering the probability of detection (PoD) of two different ways of non-destructive evaluation (NDE) method. Due to the lack of ability in detecting tiny cracks, it is stated that the endeavors in finding cracks in the early years could be inefficient, especially for the first 10 years. Fortunately, it is highly possible to detect the crack when it grows to a larger size by applying multiple times of inspections. With consideration of the repairs works for detected cracks, the probability that the crack grows to the critical size, e.g. half of the deck plate thickness, can be calculated. Accordingly, the inspections for the fatigue-prone sites can be optimized in a probabilistic way for the maintenance and management of the bridge.

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.

Demonstration of Structural Integrity of Boiling Water Reactor Pressure Vessels Under Ultimate Response Guideline Operation

In recent years, the compound beyond-design-basis accident (BDBA), which combines earthquake, tsunami, or some other severe events to impact a nuclear power plant (NPP), has received more attention. After the Fukushima nuclear disaster, the licensee of NPPs in Taiwan established the ultimate response guideline (URG) that instructs operators to perform reactor depressurization, low-pressure water injection, and containment venting to prevent core meltdown and hydrogen explosion once long-term loss-of-power and water-supply events occur. In this paper, we employed the probabilistic fracture mechanics (PFM) method to evaluate the structural integrity of boiling water reactor (BWR) pressure vessels under URG operation. At first, models of the beltline shell welds for BWR vessels associated with the Pressure Vessel Research Users Facility-Exponential flaw distribution were built for the PFM Fracture Analysis of Vessels–Oak Ridge (FAVOR) code. Then, the thermal-hydraulic data of URG transients for Taiwan domestic BWRs were imposed as the loading conditions. The analysis results demonstrate that performing URG operation will not cause significant fracture probability even at extreme embrittlement conditions. If long-term station blackout occurs due to a compound BDBA, the URG procedures can prevent core damage and hydrogen explosion, while maintaining the structural integrity of the reactor pressure vessels.

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.

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

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

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.