Probabilistic Fracture Mechanics Approach Research Articles

Probabilistic fracture mechanics approach to investigate the difference in Charpy requirements for pressure vessels

Probabilistic fracture mechanics approach to investigate the difference in Charpy requirements for pressure vessels

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.

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.

Bi-Linear Fatigue and Fracture Approach for Safety Analysis of an Offshore Structure

The design of welded structures for the fatigue limit state is normally carried out by means of either linear or bilinear S-N curves, which have been found adequate to predict crack initiation only. To properly assess the effects of the design, fabrication, inspection, and repair strategy for structure degradation due to crack growth, fracture mechanics (FM) models need to be applied. In this paper, alternative S-N and FM formulations of fatigue are investigated. The probabilistic fracture mechanics approach predicts the fatigue life of welded steel structures in the presence of cracks under random spectrum loading. It is based on a recently proposed bi-linear relationship to model fatigue crack growth. Uncertainty modeling, especially on fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bilinear crack growth relationship. Results pertaining to the fatigue reliability and fatigue crack size evolution are presented using the Monte Carlo simulation technique and the emphasis is placed on a comparison between the linear and bilinear crack growth models. Variations in the system configuration, service life, and coefficients of crack growth laws have been studied on the parametric basis

Economic Life Evaluation of Wagon Side Frame Based on Durability Analysis

Based on the probabilistic fracture mechanics approach, durability test on the fine details of wagon side frame is simulated, the structural damage degree is evaluated from the four aspects of the survival probability, the stress amplitude, the crack formation time and economic repair limit size according to general EIFS distribution, and its economic life is predicted by combining with the stress spectrum measured in practice. The result shows that the EIFS follows the Weibull distribution and passes the K-S test, the structural damage degree can be quantitatively measured on the basis of the probabilistic model of crack exceedance, the economic life predicted tends to increase with the increase of crack exceedance probability, the rationality and validity of the analysis method is proved.

Probabilistic fracture mechanics with uncertainty in crack size and orientation using the scaled boundary finite element method

The geometry of cracks in a structure are often difficult to determine accurately, leading to uncertainties in structural analysis. This paper presents a probabilistic fracture mechanics (PFM) approach to evaluate the reliability of cracked structures considering the uncertainty in crack geometry. The shape sensitivity analysis of the stress intensity factor (SIF) is performed efficiently using the scaled boundary finite element method (SBFEM). No remeshing is required as the size and orientation of a crack vary. Reliability is estimated using various probabilistic techniques. Numerical examples demonstrate the accuracy and simplicity of the present method.

Probabilistic Prediction of Crack Depth Distributions Observed in Structures Subjected to Thermal Fatigue

The application of risk-based technologies not only to in-service inspections but also to the design of components and systems, encompassing a plant life-cycle, is the way to be pursued for the improvement of design of new reactors such as fast breeder reactors. When doing so, it is necessary to develop an analytical method that is capable of estimating failure probabilities without a failure database that can only be established on the long-time accumulation of operational experiences. The prediction method should estimate failure probabilities based on actual mechanisms that cause failure. For this purpose, this study developed a structural reliability evaluation method using probabilistic prediction of crack depth distributions for thermal fatigue, which is one of representative failure modes to be prevented in components of nuclear plants. This method is an extension of probabilistic fracture mechanics approach but is capable of modeling crack initiation, crack propagation, and crack depth density distribution at a given cycle. To verify the methodology, crack depth distribution observed in thermal fatigue test specimens was evaluated, and it was shown that the method could reproduce the observed crack depth distributions fairly well. This is considered to explore the possibility that probabilistic fracture mechanics approach can be verified by experiments, which was deemed impossible so far. Further improvement such as explicit implementation of interaction mechanisms between adjacent cracks will allow this methodology to be applied to the procedure of optimization of in-service inspection planning, as well as to the optimization of safety factors in component design of nuclear plants.

Advanced methodology for assessing distribution characteristics of Paris equation coefficients to improve fatigue life prediction

This paper offers a methodology for coping with information loss following consolidation of data on fatigue crack propagation rates derived from different experiments. It is customary, both in the literature and in standardization, to consolidate results of several experiments conducted under similar conditions, using identical materials. This reduces the ability to implement a probabilistic fracture mechanics approach in order to reliably calculate the distribution of the number of cycles needed to reach a critical value (CV; onset of instability or failure). Such reliable calculation requires, among other things, an estimation of the distribution characteristics of the crack progression curves coefficients represented by models such as Paris or NASGRO, and an estimation of joint distributions of equation coefficients representing such models. Consolidated data reduce the ability to estimate these required distribution characteristics. This work suggests an analytical approach that uses consolidated data, but enables the information to be treated as if it were possible to attribute the data to the various experimental specimens from which they were obtained. Consequently, information required for the evaluation of the distribution of the number of cycles needed to reach a CV can be obtained. The proposed approach is generic and can be applied in additional scientific fields that can benefit from separation of data obtained from different experiments.

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality (MIFQ) is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Prediction of ship brittle fracture casualty rates by a probabilistic method

It has been proposed that grade A should be replaced with a tougher steel for ship construction. This recommendation is not supported by casualty statistics. Brittle fractures have decreased from once every 10 ship years at the time of the Liberty ships, to once every 100 ship years in the 1950s, and now stand at around once every 10,000 ship years. The authors have developed a probabilistic fracture mechanics approach indexed to the Charpy 27 Joule temperature, T 27J. This is used here to analyse the Liberty ship failures. Comparison with a databank of T 27J values for grade A steel spanning 1920 to 1995 suggests that the Liberty ship steel was unusually brittle. The probability analysis shows good agreement between predicted and observed fracture casualty rates for the Liberty ships and helps explain why brittle fractures are now uncommon in grade A steel ships.

TIMCOAT: An Integrated Fuel Performance Model for Coated Particle Fuel

An integrated fuel performance model for coated particle fuel has been developed to comprehensively study the behavior of TRISO-coated fuel. Modeling of both pebble-bed and prismatic configurations is possible. In the case of the pebble-bed concept, refueling of pebbles is simulated to account for the nonuniform environment in the reactor core and history-dependent particle behavior. Monte Carlo sampling of particles is employed in fuel failure prediction to capture the statistical features of dimensions; material properties; and, in the case of the pebble-bed concept, the statistical nature of the refueling process. An advanced fuel failure model has been developed based on a probabilistic fracture mechanics approach. The mechanical analysis includes effects of anisotropic irradiation-induced dimensional changes and isotropic irradiation-induced creep, and the fluence-dependent Poisson ratio in irradiation creep. The stress analysis is benchmarked against the calculations of Japanese High Temperature Test Reactor (HTTR) first-loading fuel and finite element result on one case performed by the Idaho National Engineering and Environmental Laboratory. The failure model predictions are compared with NPR1, NPR2, and NPR1A capsule irradiation data. The model results compare very favorably with postirradiation examination results both in terms of failure probability, number of failed particles, and Kr85m R/B evolution during irradiation.

Fatigue and fracture simulation of welded bridge details through a bi-linear crack growth law

This paper deals with the application of a probabilistic fracture mechanics approach to predict the fatigue life of welded steel details in the presence of cracks under bridge spectrum loading. It is based on a recently proposed bi-linear relationship to model fatigue crack growth and incorporates a failure criterion to describe the interaction between fracture and plastic collapse. The formulation leading to the expected number of cycles to failure is first outlined, followed by a simple example on a butt-welded detail. Uncertainty modelling, especially on fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bi-linear crack growth relationship. Results pertaining to fatigue reliability and fatigue crack size evolution are presented using simulation with Latin Hypercube Sampling, and emphasis is placed on a comparison between linear and bi-linear crack growth models. The latter is found to lead to higher fatigue life estimates and significantly different crack size distributions, both of which have implications on inspection schemes for steel bridge components.

Main Features of Designing With Brittle Materials

Brittle material behavior and mode of failure are contrasted with those characteristics of ductile materials. The stochastic nature of brittle fracture, which results from the random occurrence of fracture-initiating microstructural imperfections, necessitates a probabilistic fracture mechanics approach to design with brittle materials. It is also clearly shown which main properties of brittle materials have to be optimized to improve the reliability of mechanically loaded components made of brittle materials. Important features of designing with brittle materials are elucidated and illustrated by an exemplary design calculation of a ceramic disc spring. It is shown how even environmentally induced subcritical crack growth, characteristic of ceramic materials, can be adequately accounted for in the assessment of reliability.

Probabilistic design of mechanical components

During the design stage, realistic life time predictions for components help to reduce test cycles and allow for an optimization with respect to both production and repair costs. However, frequently used calculation procedures rely on the introduction of empirically or semi-empirically derived safety factors and often lead to a very conservative design. In this paper, a probabilistic fracture mechanics approach is proposed, that allows for accurate predictions of the life time distribution. In order to reduce the computational effort, the computational procedure is divided into a deterministic and a stochastic part. While for the deterministic part, the complexity of the model can be rather high, the stochastic part requires simplifying assumptions and efficient simulation schemes. These assumptions and their consequences are in the focus of this paper. The quality of the proposed approach is assessed by comparison of results obtained for industrial applications with experiments.

A reliability assessment of reactor pressure vessels

A theoretical investigation is presented on the reliability assessment of nuclear reactor pressure vessels. In the analysis, a Poisson-type random walk model is assumed to represent the randomly occurred transients, which have randomly distributed stresses. These transient stresses cause a predominant initial crack size to grow and, therefore, degrade the reliability of a pressure vessel. Following the probabilistic fracture mechanics approach, the variability of the material properties is considered. A numerical calculation is carried out based on available empirical data. It is found that for a typical BWR pressure vessel, the failure probability lies in the order of 10 −6 and the failure rate is approximately in the order of 10 −8 per vessel year. The result is in agreement with other published results.