Probability-based assessment and maintenance of welded joints damaged by fatigue

This paper presents a probabilistic reliability assessment procedure for steel components damaged by fatigue. The study combines the structural reliability theory with a maintenance strategy. The fatigue assessment model is based on a modelisation of the fatigue phenomenon issued from the principles of fracture mechanics theory. The safety margin includes the crack growth propagation and allows to treat fatigue damage in a general manner. Damaging cycles and non damaging cycles are distinguished. The sensitivity study of the different parameters shows that some variables can be taken as deterministic. Applications are made on a welded joint ‘stiffener/bottom-plate' of a typical steel bridge. The model is then used for taking into account inspection results. Non destructive inspection (NDI) techniques are also used for updating failure probabilities. The results show their ability to be inserted in a maintenance strategy for optimizing the next inspection time. This has led to define cost functions related to the total maintenance cost; this cost is then minimized for determining the optimal next inspection time. An example of welded joint cracked by fatigue highlights the different concepts. The approach presented in the paper is not only restrained to fatigue problems, but can be applied to a wide variety of degrading phenomena.     

Sodium effects on mechanical performance and consideration in high temperature structural design for advanced reactors

Sodium environmental effects are key limiting factors in the high temperature structural design of advanced sodium-cooled reactors. A guideline is needed to incorporate environmental effects in the ASME design rules to improve the performance reliability over long operating times. This paper summarizes the influence of sodium exposure on mechanical performance of selected austenitic stainless and ferritic/martensitic steels. Focus is on Type 316SS and mod.9Cr-1Mo. The sodium effects were evaluated by comparing the mechanical properties data in air and sodium. Carburization and decarburization were found to be the key factors that determine the tensile and creep properties of the steels. A beneficial effect of sodium exposure on fatigue life was observed under fully reversed cyclic loading in both austenitic stainless steels and ferritic/martensitic steels. However, when hold time was applied during cyclic loading, the fatigue life was significantly reduced. Based on the mechanical performance of the steels in sodium, consideration of sodium effects in high temperature structural design of advanced fast reactors is discussed.     

Development of thermal fatigue testing apparatus with BWR water environment and thermal fatigue strength of austenitic stainless steels

A thermal fatigue testing apparatus was developed in order to clarify the fatigue behavior in BWR environment. Pressurized high and low temperature pure water were alternately supplied into an autoclave with a small cylindrical specimen. Then a fatigue specimen was subjected to homogeneous thermal stress through the wall thickness. Fatigue crack initiation behavior was observed with the replication method and compared with the mechanical fatigue strength performed in air and high temperature water. The thermal fatigue strength of type 304 and 316 nuclear grade (316NG) stainless steels agreed closely with the mechanical fatigue strength, when transforming the nominal stress amplitude to the fictitious stress amplitude by using the mean value of strain amplitudes for room temperature and 288°C.     

考虑应力松弛和辐照影响的堆内构件压紧弹簧疲劳可靠性评估方法

针对反应堆堆内构件压紧弹簧疲劳失效模式,在考虑应力松弛和辐照影响的条件下基于仿真方法开展可靠性评估。首先结合疲劳模型和平均应力松弛Landgraf模型,考虑辐照对疲劳参数的影响,构建了压紧弹簧疲劳寿命模型。在压紧弹簧疲劳寿命模型基础上,根据广义应力-强度干涉模型定义压紧弹簧可靠度并开展灵敏度分析。以非能动压水堆AP1000压紧弹簧为例进行案例分析,在95%置信度水平下,分别计算了可靠度为95%和50%时对应的疲劳寿命。结果表明,若不考虑应力松弛,压紧弹簧总疲劳寿命下降88.3%;从经济性角度考虑寿命预测结果较为保守。通过灵敏度分析发现对可靠度影响较大的设计变量是弹性模量和疲劳强度系数,在一定可靠度下可以通过调整设计变量对压紧弹簧的疲劳可靠性评估进行优化。      

Low-cycle fatigue of welded joints: coupled initiation propagation model

This paper deals with the low-cycle fatigue (LCF) design of welded structures, the aim being the critical analysis of the rule used in the RCC-MR [Design and construction rules for mechanical components of FBR nuclear islands, AFCEN, 1993], for the design and construction of fast breeder reactors. The study takes into account the evolution of the material behavior laws and damage accumulation during the fatigue loading. The adopted model consists of analyzing separately the behavior and the damage evolutions. It allows us to determine the damage ratio corresponding to initiation and propagation of a significant crack in order to determine the life duration. This model suggests the existence of a threshold level of loading, above which micro-cracks initiate. The initiation fatigue life can then be neglected below the threshold level. This work shows also that the RCC-MR rules are valid below this threshold load level.     

Design relationships and failure theories in probabilistic form

The engineering profession has become increasingly concerned with the adequacy of design calculations. This concern indicates a need for critical evaluation of designs based on arbitrary multipliers, such as safety factors or worst-case treatment. Design has customarily been based on applied loading, geometry, and handbook property values to give a deterministic solution. This paper presents (1) the Soderberg, Goodman, Gerber, and elliptical design relationships; and (2) the maximum shear and distortion energy failure theories in probabilistic form. Inherent in these equations are the facts that (a) design variables are generally characterized by spectra of values, rather than unique values; and (b) a small, but finite, probability of failure must be recognized in any design. By coupling the mean static and mean alternating stresses (and their standard deviations) with the strengths available in a material (and their standard deviations) in one of the four design relationships using an appropriate theory of failure, the reliability of a given design can be calculated. Conversely, for a given reliability, the appropriate size can be determined. Illustrations are provided. The influence of range (different standard deviations) of variables on reliability is demonstrated. A comparison is made between safety factor and reliability.     

Statistical models for estimating fatigue strain-life behavior of pressure boundary materials in light water reactor environments

The existing fatigue strain versus life (S-N) data for materials used in nuclear power plant components have been compiled and categorized according to material, loading and environmental conditions. Statistical models have been developed for estimating the effects of the various service conditions on the fatigue life of these materials. The results have been used to estimate the probability of initiating a fatigue crack. Data in the literature were reviewed to evaluate the effects of the size, geometry and surface finish of a component on its fatigue life. Fatigue S-N curves for components have been determined by adjusting the probability distribution curves of smooth test specimens for the effect of mean stress and then applying design margins to account for the uncertainties that arise because of component size, geometry and surface finish. The significance of the effect of the environment on the current code design curve and on the proposed interim design curves published in NUREG/CR-5999 is discussed. Estimations of the probability of fatigue cracking in sample components from boiling water reactors and pressurized water reactors are presented.     

Reliability of reactor components and systems subject to fatigue and creep

The operation of nuclear reactors at elevated temperatures involving pressure- and temperature-cycling as well as corrosion and irradiation is associated with the gradual deterioration of the mechanical resistance of their critical components. The rate of deterioration depends not only on the intensity of the loading conditions and the level of the operating variables, but is sensitive to their sequence and interaction. The lack independence that is reflected by the development, under operating conditions, of creep and inelastic cyclic strain, as well by the deterioration of the strength properties accompanying such deformation (creep rupture, fatigue), introduces additional potential failure modes or conditions, consideration of which, in the reliability analysis, shifts the emphasis of this analysis from the catastrophic limiting states of failure under remote extremal conditions, of recurrence periods that are large multiples of the design (service) life of the structural element or system, to states of significant structural failure that seriously affect the operability of the reactor but are repairable, as well as to conditions of relatively minor structural failure of reactor elements during operation that are critical because they might lead to escape of contaminating fission products. After basic consideration of the formulation of structural reliability analysis and risk assessment for major structural failures in nuclear reactor plant systems, a review of the problems of design for creep and fatigue — with interaction between creep and fatigue effects — under reactor operational conditions is given.     

A knowledge based system for creep–fatigue assessment

A knowledge based system was developed in the BRITE-EURAM C-FAT project to store the material property information necessary to perform complex creep–fatigue assessments and to thereby improve the effectiveness of data retrieval for such purposes. The C-FAT KBS incorporates a multi-level database which is structured to contain not only ‘reduced’ deformation and fracture test data, but also to enable ready access to the derived parameter constants for the constitutive and model equations used in a range of assessment procedures. The data management scheme is reviewed. The C-FAT KBS also has a dynamic worked example module which allows the sensitivity of predicted lifetimes to material property input data to be evaluated by a number of procedures. Complex cycle creep–fatigue endurance predictions are particularly sensitive to the creep property data used in assessment, and this is demonstrated with reference to the results of a number of large single edge notched bend specimen feature tests performed on a 1CrMoV turbine casting steel at 550°C.     

An overview of the Boltzmann transport equation solution for neutrons,photons and electrons in Cartesian geometry

Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the P_N approximation, the S_N method (discrete ordinates method) and their variants. In the discrete ordinates (S_N) formulations of the transport equation, it is assumed that the linearised Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this paper, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we describe the recent advances in the class of deterministic methods applied to one and two dimensional transport problems for photons and electrons in Cartesian Geometry. First, we describe the Laplace transform technique applied to S_N two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker–Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a mono-energetic electron beam in a rectangular domain. The main idea relies on applying the P_N approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker–Planck equation and then applying the Laplace Transform in the spatial x variable. Numerical results are given to illustrate the accuracy of deterministic methods presented.     

An overview of the Boltzmann transport equation solution for neutrons, photons and electrons in Cartesian geometry

Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the P_N approximation, the S_N method (discrete ordinates method) and their variants. In the discrete ordinates (S_N) formulations of the transport equation, it is assumed that the linearised Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this paper, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we describe the recent advances in the class of deterministic methods applied to one and two dimensional transport problems for photons and electrons in Cartesian Geometry. First, we describe the Laplace transform technique applied to S_N two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a mono-energetic electron beam in a rectangular domain. The main idea relies on applying the P_N approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker-Planck equation and then applying the Laplace Transform in the spatial x variable. Numerical results are given to illustrate the accuracy of deterministic methods presented.     

Incorporating reliability analysis into the design of passive cooling systems with an application to a gas-cooled reactor

A time-dependent reliability evaluation of a two-loop passive decay heat removal (DHR) system was performed as part of the iterative design process for a helium-cooled fast reactor. The system was modeled using RELAP5-3D. The uncertainties in input parameters were assessed and were propagated through the model using Latin hypercube sampling. An important finding was the discovery that the smaller pressure loss through the DHR heat exchanger than through the core would make the flow to bypass the core through one DHR loop, if two loops operated in parallel. This finding is a warning against modeling only one lumped DHR loop and assuming that n of them will remove n times the decay power. Sensitivity analyses revealed that there are values of some input parameters for which failures are very unlikely. The calculated conditional (i.e., given the LOCA) failure probability was deemed to be too high leading to the identification of several design changes to improve system reliability. This study is an example of the kinds of insights that can be obtained by including a reliability assessment in the design process. It is different from the usual use of PSA in design, which compares different system configurations, because it focuses on the thermal–hydraulic performance of a safety function.     

Probabilistic fracture mechanics

This paper develops the methodology for probabilistic fracture mechanics analysis (PFM) of structural components with crack-like imperfections. Details are given for the development and application of both a simple nomographic method and a basic numerical tool for PFM applications. The tool is a computer program that uses Monte-Carlo simulation to predict the probability distribution of a structural performance parameter from known distributions of input parameters used to model the problem. The structural performance parameter might be the strength margin (strength minus stress), the life ratio (actual fatigue life divided by design fatigue life), or any other relevant model of the failure modes. Two illustrative applications based on linear elastic fracture mechanics are included to demonstrate the utility of PFM to problems of interest to the electric power generation industry.The first example selects the mean yield strength of an alloy in order to minimize the probability of failure for a hypothetical component with two failure modes, yielding and brittle fracture. The example shows that no single value of mean yield stress or of yield-related safety factor, such as specified as part of conventional engineering practice, suffices to minimize failure for all combinations of working stress and flaw size distribution. PFM analysis is required to compute the optimum value of mean yield stress for a given working stress and material quality (flaw size distribution). A second example is presented for which the residual life of a turbine rotor is assumed to be related to three parameters. The parameters are applied stress, material crack growth rate, and initial flaw size. Known variations of the input parameters are translated into variations in residual life. The residual life distribution is required to formulate improved fatigue design criteria. The effects on the turbine life distribution of mutual interdependence of the input random variables and of finite crack initiation life are examined. The second example points out the need for and current unavailability of required input data. It is recommended that data collection efforts be increased to quantify the variational characteristics of the required input parameters, as well as mean, typical, or worst-case values.     

Design and performance analysis of structural components for a Korean He Cooled Ceramic Reflector TBM in ITER

Korea has developed a Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) testing in ITER, which was considered one of the fusion DEMO-relevant blankets in Korea. The design and performance analysis of the TBM body have been carried out considering the uniqueness of the KO TBM and design requirements by the IO and KO design concept: (1) KO TBM has 4 sub-modules considering a post irradiation test (PIE) and its delivery. (2) A first wall (FW) design was changed into a 15 × 11 rectangular shape and its performance was confirmed by thermal-hydraulic and thermo-mechanical analyses using commercial ANSYS code. The results showed that the revised design model satisfied 1.5S_m and 3S_m of the allowable stress (S_m) in the RCC-MR code at the maximum stress region of the components for mechanical and thermo-mechanical analyses, respectively. (3) Considering the tritium breeding and cooling, a breeding zone (BZ) design was investigated. Three Li and Be layers, and one graphite layer, were proposed by the iteration, and the appropriate temperature distribution was obtained. The design for other components such as a side wall (SW) and back manifold (BM) is on-going considering 9 MPa of channel pressure and its functions of flow distribution as a manifold.     

Advanced flaw production method for in-service inspection qualification mock-ups

One of the key issues in in-service inspection qualification is the representativeness of the defects used in qualification specimens. The best representativeness is achieved with realistic defects. However, present specimen production techniques have some significant weaknesses, such as unrealistic defects or additional alterations induced in the surrounding material. Specimens manufactured, for example, by weld implantation or with weld solidification defects always result in one or more extra weld interfaces. These interfaces can be detected by NDT. To overcome problems with the current specimens, a new defect manufacturing technique was developed. The new technique produces natural, representative defects without introducing additional weld metal or other unwanted alterations to the specimen.The new method enables artificial production of single, separate fatigue cracks by thermal loading. The method is based on a natural thermal fatigue damage mechanism and enables production of real cracks directly into the samples. Cracks are produced without welding or machining and without any preliminary surface treatment or artificial initiator such as a notch or a precrack. Single crack or a network of cracks can be induced into the base material, welded areas, HAZ, weld claddings, threaded areas, T-joints, etc. The location, orientation and size of produced cracks can be accurately controlled. Produced cracks can be used to simulate different types of service-induced cracks such as thermal fatigue, mechanical fatigue and stress corrosion cracks. It is shown that artificially produced thermal fatigue cracks correspond well with the real, service-induced cracks and overcome the problems of traditional qualification specimen manufacturing techniques.     

Cryogenic mechanical testing of ITER prototype axial breaks

Within the superconducting magnet program for ITER, cryogenic components need to be tested to verify their design. Especially for the helium supply of the magnet system, feeders are needed integrating at the same time high voltage insulation to separate the inner magnet system electrically from the outer cryostat shell. Beside of high voltage and helium flow properties, these axial breaks will be exposed to a limited mechanical loading during operation of the magnet system. Therefore, mechanical tests needs to be performed at room temperature as well as at cryogenic temperature of 77 K.A possible breaker design was provided by Babcock Noell. To verify this design mechanically quasi-static and fatigue tests under bending, torsion and axial loading were done. Results on the performance of the prototypes are presented approving a superior mechanical quality.     

Determination of the usage factor of components after cyclic loading by means of high-resolution microstructural examination

Materials subjected to cyclic loading experience a change in the microstructure which may affect the service life. Quantification of the microstructural changes and allocation of the microstructural condition to the corresponding point on the fatigue curve for the component material allows the usage factor to be derived. Taking the low-alloy, fine-grained structural steel 20MnMoNi55 (quenched and tempered structure) as an example, the relationship between microstructure and number of load cycles can be represented in the form of a reference curve. High-resolution examination allows the usage factor to be determined up to η = N/N_f = 0.5 under the given cyclic loading. Only a small specimen volume is required for examination using a transmission electron microscope. It can be taken from the component without affecting the required minimum wall thickness. The location of the specimen must, however, be stipulated, e.g. the location of highest loading according to calculations. When removing the specimen, care must be taken to ensure that the micro-structure is not affected. If these requirements are observed, high-resolution microstructural examination provides a method for checking the usage factor of a component.     

Short fatigue crack propagation and effect of notch plastic field

In engineering application, almost all structures and components contain notches or holes. They often experience severe fatigue loading, and have been recognized as a potential site for small fatigue crack initiation and propagation. In this paper, the effects of notch plastic field on small fatigue crack initiation and propagation from notch member, under cyclic tensile loading control, are investigated. Experiment shows that small crack initiates from notch specimen at far higher rate than that of smooth specimen; small crack propagation is still faster than that of smooth specimen within notch plastic field, though this difference is progressively lessening; beyond notch plastic zone, small crack growth rate is approaching long crack growth rate. Analysis via finite element and analytical method reveals that notch plasticity has key influence on small crack initiation, crack tip generated plasticity has critical impact on small crack propagation within notch plastic field, while plasticity induced crack closure has dominant effect on crack propagation out of notch plastic field. A comparison between experimental and analytical results is made to identify the mechanisms of small fatigue crack initiation and propagation within notch plastic field.     

不锈钢管道焊缝金属240℃循环变形行为的试验研究

基于增量步和成组法低周疲劳试验,研究了1Cr18Ni9Ti不锈钢管道焊缝金属在240℃下的循环变形行为。结果表明,材料为循环软化材料,具有轻微Non-masing行为特征。相同总应变范围的循环应力、应变（CSS）行为存在很大分散性,意味着任何外载,即使恒幅载荷也将导入一个随机应变载荷史,现有确定性方法可能导致偏于危险的设计分析,有必要引入概率方法表征材料的循环变形行为。基于验证的应力幅统计分布－正态分布,建议了概率Ramberg-Osgood CSS曲线的描述方法。文中试验结果分析验证了方法的有效性。