As a further extension to the structural strain method first introduced by Dong et al [1], this paper presents an enhanced structural strain method which incorporates material nonlinearity and for two typical weld structures, i.e. weldment with plate sections (e.g. gusset weld or cruciform weld etc.) and weldment with beam sections. (e.g. pipe structures). A modified Ramberg-Osgood is introduced to capture nonlinear stress strain behavior of the material. A set of numerical algorithms is used to deal with complex stress state induced by structural effect such as beam section and plane strain condition. The proposed structural strain method is then applied to analysis of fatigue data of weldment made from different materials including steel, aluminum and titanium. It is shown that the enhanced structural strain method provides a unified way to correlate fatigue life of weldment in both high cycle and low cycle fatigue regime. The method is also used to study ratcheting problem raised up by Bree. A modified Bree diagram is given by considering material nonlinearity.

The fatigue assessment of safety relevant components is of importance for ageing management with regard to safety and reliability of nuclear power plants. Reactor internals are subjected to thermo-mechanical fatigue induced by operational temperature transients and to flow induced vibrations. The resulting complex loading collectives induce low cycle (LCF), high cycle (HCF) and even very high cycle (VHCF) fatigue and their interaction. The existing methodological gaps within the current fatigue assessment approach are to be closed. Design code fatigue analyses use defined loads and frequencies of occurrence (specified or measured). High cycle and very high cycle fatigue loadings are not explicitly considered except for endurance limit studies of reactor internals. Furthermore, design fatigue curves in the applicable international design codes were extended by extrapolation from originally 10 6 up to 10 11 load cycles. However, the existing data base for load cycles equal to or above 10 7 is still highly insufficient. The cyclic deformation behavior of the material in question (austenitic stainless steel 1.4550) is different depending on the fatigue regime respectively the applied load or deformation amplitude. While the LCF behavior is already well investigated and the basic behavior in the HCF regime is fairly well known the VHCF cyclic deformation behavior has not been characterized in sufficient detail so far. As a consequence, the real damage accumulation of variable amplitude combinations consisting of LCF- and HCF/VHCF loads is still widely unknown. A new cooperative R&D project of MPA Stuttgart, TU Kaiserslautern and Framatome GmbH addresses the existing gaps of knowledge presented above and has recently been launched. The scheduled first phase of the project will entail the following key items: • Substantiation of the threshold strain amplitude ε a ≥ 0.1% for the consideration of Environmentally Assisted Fatigue (EAF) conditions in the HCF regime; • Basic characterization of the HCF and VHCF fatigue behavior at relevant operational temperatures in air at 10 6 − 10 10 load cycles; • Fatigue behavior at variable amplitude loading (combination of LCF / HCF and LCF / VHCF); • Fatigue behavior of welds in the region of high numbers of load cycles (HCF regime > 10 5 load cycles and VHCF > 10 7 ); • Validation of the existing design and assessment procedures (base material and welded material); • Development of a fatigue assessment methodology for reactor internals under consideration of the transient endurance limit and damage accumulation effects. A later second phase of the project will concentrate on the following items: • Examination of the fatigue behavior of welded specimens and representative components; • Consolidation of the design process from laboratory specimen to real structures and components; • Examination of the operational loading characteristics of reactor internals with respect to dominant loadings; • Probabilistic consideration of the influence of fatigue assessment on the plant risk (core damage). The project structure will be discussed in detail in the paper.

In the fatigue analysis in Section III design by analysis, the evaluation is performed in terms of alternating stress, but the evaluation curves are alternating strain – life curves that were converted to alternating pseudo-stress by formally multiplying elastic-plastic (total) strains by a modulus of elasticity that is representative of the elastic regime. The corresponding evaluation method would be an elastic-plastic analysis where the calculated strain amplitude is multiplied by the modulus of elasticity that is provided with the Code fatigue curve to obtain the alternating pseudo-stress. When the alternating stress is calculated by elastic analysis but is found to be in excess of the elastic regime, corrections need to be applied that account for the difference between stress from an elastic analysis and the pseudo-stress that would be obtained from an elastic-plastic analysis. Performing such a correction is the objective of simplified elastic-plastic fatigue analysis. An alternative to the simplified elastic-plastic fatigue analysis in Appendix XIII, XIII-3450, is given by Code Case N-779. A new proposal has been developed recently, with the objective to be less conservative in most cases than the very conservative method in Appendix XIII, XIII-3450, and more straightforward to apply than Code Case N-779. The new proposal has been validated with elastic-plastic analysis results. The present paper details a comparison to Code Case N-779 over a large range of parameters. The causes for discrepancies and implications are discussed in detail.

In this paper, simulations using various cyclic hardening models are performed to determine the effect of the hardening model that is used in a finite element analysis. Bi-linear, Armstrong-Frederick kinematic hardening model and Chaboche (third order non-linear) combined hardening model are used in finite element (FE) analysis to simulate material behavior under cyclic loading condition. Hardening parameters included in bilinear and non-linear hardening models are determined from monotonic stress-strain curve obtained from monotonic tensile test and parameters in Chaboche hardening model are determined from hysteresis loop obtained from cyclic tensile test. Simulation of notched C(T) test under cyclic loading is performed using three hardening models. Plastic strain, stress and plastic strain energy at notch tip of specimen are extracted from FE analysis results. Using energy based fatigue analysis, cycle to failure, the cycle at which crack initiation occurs at notch tip, are predicted and compared with experimental results. Through the comparisons, the effect of hardening model on the simulation result under cyclic load is confirmed.

Welds are one of the commonly used joint types and are employed extensively in subsea oil and gas production equipment. Commonly used weld joints in subsea components are fillet, butt, full-penetration, plug, and girth. Fatigue is one of the critical failure modes for welded joints. Welded joints are complex to analyze for fatigue loading due to the microstructure change during the welding process. The welding process also induces residual stress in the heat affected zone (HAZ) surrounding the weld. This, in turn, can adversely affects the fatigue life of the joint. The S-N fatigue approach is commonly used for weld fatigue analysis due to the simplicity of this method. Industry standards such as DNV, IIW, BS-7608, and ASME BPVC Sec VIII Div. -2 or -3 are typical references for this type of analysis. For subsea specific applications, DNV-RP-C203 and BS-7608 are generally used because these two standards provide S-N curves for welds in “air” as well as in “seawater with cathodic protection”. These two codes also provide S-N curves for various weld geometries ranging from simple fillet welds to complex tubular joints. Some of the weld fatigue analysis techniques used in the subsea industry are the: nominal stress approach, structural hot spot stress approach, effective notch stress approach (ENS), structural stress method (ASME VIII-2, -3) and the Fracture mechanics based fatigue crack propagation (FCG) approach. This paper presents the fatigue analysis of fillet welds in bore inserts using the ENS method. In the ENS method, a 1mm radius notch is modelled at the weld root or toe, see Figure 1, which yields a finite weld root stress. The stress analysis is carried out using FEA and the stresses on the notch along with the appropriate fatigue curve are used to estimate the weld root fatigue life.

The European Pressure Vessel Standard EN 13445 provides in its part 3 (Design) a simplified method (Clause 17) and a detailed method for fatigue assessment (Clause 18) of unwelded and welded components. Clause 18 “Detailed Assessment of Fatigue Life” is under principal revision within the framework of the European working group “CEN/TC 54/WG 53 – Design methods” in order to reach a significant increase in user-friendliness and a clear guideline for the application. This paper is focused on the new recommendations for the thermal fatigue evaluation given in the new informative annex NA “Instructions for structural stress oriented finite element analyses using brick and shell elements”. In this annex NA different application methods for the determination of structural stresses are explained in connection with the requirements for finite element models and analyses. This paper will give a short overview of the proposed approaches of structural stress determination in the new draft annex NA of the revised EN 13445-3 with special recommendations for thermal fatigue evaluation application. This constitutes an extension of the usual and established application of the structural stress approach for welds subjected to mechanical loading conditions. It will present the current state of the approaches based on the results of fatigue analyses according to EN 13445-3 Clause 18 for two different application examples. For validation purposes, these different approaches are compared with the results of Clause 17 of the EN 13445 and other pressure vessel design codes.

Sleeve and socket welds are often used in small bore nuclear power plant pipework where access is too limited to allow a conventional butt-weld. These welds are also used in process plants and pipelines as a permanent repair to reinforce areas such as cracks and corrosion that might threaten the structural integrity of the component. The fillet weld associated with this type of joint is particularly susceptible to lack of fusion defects which can be problematic to detect using conventional volumetric inspection techniques. The stress concentration associated with this type of defect will impact the fatigue life and pressure retaining ability of the joint. This paper provides examples of Copper/Nickel (CuNi) sleeve weld defects and presents an approach for determining the fatigue life of socket welds due to pressure cycling within a Pressurised Water Reactor (PWR) environment. This approach is based on modelling lack of fusion features using a database of sleeve and socket weld Non-Destructive Testing (NDT) records and calculating the stress range in the remaining ligament using textbook calculations. Sensitivity studies presented herein show the impact of lack of fusion and pipe size/thickness on fatigue life.

Environmental fatigue evaluation is a key technology to extend Nuclear Power Plant design life. Since USNRC issued the RG 1.207 in 2007, many studies on fatigue evaluation in Light water Reactor coolant environments have been carried out by referencing documents such as NUREG/CR-6909, EPRI-TR-1025823, ASME BPVC Sec. III NB-3600/3200 Code, ASME Code Case, and so on. These documents presented environmental fatigue evaluation methods about each single-metal such as carbon steels, low-alloy steels, nickel-chromium-iron (Ni-Cr-Fe) alloys, and austenitic stainless steels. However, the environmental fatigue evaluation method for interface of dissimilar metal welding is mostly insufficient. Dissimilar metal welding has been widely used in nuclear industry. If environmental fatigue analysis method for dissimilar metal welding is developed, it will facilitate the design of piping for more safety. Therefore, the development of environmental fatigue evaluation for the interface of dissimilar metal welding should be studied. This paper presents environmental fatigue evaluation for the interface of dissimilar metal welded piping. The environmental fatigue evaluation for a dissimilar metal welded piping model was performed based on above documents.

In a particular nuclear application, separation between structural components is maintained by a helical spring such that the separating load bears across the diameter of the spring coils. Relative motion between the structural components due to changing load and temperature is accommodated by rolling of the spring. This rolling motion while under radial load results in cyclic loading of the spring material. Fatigue analysis of the cyclic loading must take into consideration the material degradation due to the unique operating environment, so testing of ex-service material is required. Standard fatigue test specimens are not possible due to the small dimensions of the spring component, so cyclic stress is applied to the material via a reciprocating rolling motion between two platens. Stress analysis of this arrangement provides the stress range and mean stress necessary for fatigue analysis. A three dimensional finite element dynamic simulation of the test process is applied to a nominal test specimen to determine detailed history of the stress distribution. Numerical challenges are addressed to ensure representative loading conditions are properly applied, and that steady-state response is achieved. Bounding stress ranges are determined, and the implications of the results in fatigue analysis are discussed. It is concluded that response at the ends of the specimens is important in properly evaluating test data.

The RCC-M code [1] is a well recognized international code and provides rules for the design and the construction of mechanical equipment for pressurized water reactors. It is used today for the nuclear industry exclusively, in countries such as France, South Africa and China and it is the basis for the design of the UK EPR to be built in Hinkley Point. The RCC-M code’s fatigue rules emanate from the ASME Boiler and Pressure Vessel Code and are hence very similar, albeit they have evolved in their own way over time to include some R&D results and other evolutions. These rules are published by AFCEN which involves a wide range of international organizations from the nuclear industry such as Apave, Areva, Bureau Veritas, CEA, DCNS, EDF, EDF Energy, ONET-MHI, Rolls-Royce and Westinghouse. The EN-13445-3 [2] is a European standard which is mostly in use today in the conventional industry. Its fatigue rules are a compilation of rules from various national European codes, such as the German AD-Merkblatt, the British Standards, the Eurocodes for civil works and the French CODAP. The rules for fatigue are compiled in Chapters 17 and 18 of EN-13445-3 and have been the result of the work of contributors from major European organizations from the nuclear, oil and gas, chemical and mechanical industries: these include, among others, Areva, the Linde Group, CETIM, TÜV, and the TWI (The Welding Institute). Since the beginning of 2015, AFCEN has created a technical Working Group (WG) on the topic of fatigue with the objective of identifying the Safety Factors and Uncertainties in Fatigue analyses (SFUF) and of potentially proposing improvements in the existing fatigue rules of the code. Nevertheless, the explicit quantification of safety factors and uncertainties in fatigue is an extremely difficult task to perform for fatigue analyses without a comparison to the operating experience or in relation to another code or standard. Historically, the approach of the code in fatigue has indeed been to add conservatism at each step of the analyses which has resulted in a difficult quantification of the overall safety margin in the analyses. To fulfill its mission, the working group has deemed necessary to lead a benchmark with the EN-13445-3 standard given its wide use through other industries. Two cases were identified: either the comparison with EN-13445-3 is possible and in this case, the identification of safety factors and uncertainties is performed in relation to this standard; either the comparison is not possible, in which case the overall conservatism of the RCC-M code is evaluated in relation with operating experience, test results, literature, etc... This paper aims at describing the overall work of the group and focuses more specifically on the results obtained through the benchmark with the EN-13445-3 standard.

This document is aimed at comparing the fatigue analysis methods based on the RCC-M code and on the harmonized standard EN 13445-3 with a view to quantifying the associated deviations and uncertainties, at each step of the calculation, by taking into account every aspect of each code such as calculation thickness of the FE model, physical properties, combination method and fatigue curve. This comparison study consists in analyzing the 4 Test Cases (TC) described below: • TC1: Study of the cylindrical-edge transition cone with its upper shell/shell type full-penetration butt weld. • TC2: Study of the feedwater nozzle (FWN) with its full-penetration weld on the nozzle support ring. • TC3: Study of the misalignment effect of neutral axes at shell/shell type full-penetration butt weld level. • TC4: Study of the out-of-roundness effect at shell/shell type full-penetration butt weld level. The welds considered in this study are full-penetration butt welds whose RCC-M quality is Level 1, whose welding procedure has been qualified, which are dressed, made flush with base metal by grinding and which have been fully (100%) inspected by NDE.

Fatigue is identified as a significant degradation mode that affects nuclear power plants world-wide. The various international codes and standards (ASME, RCC-M, JSME, etc...) offer rules to predict its damaging effect on the locations of the various components of an NPP. These rules, which ensure conservatism and safe operation, have grown in complexity over the years because they have integrated R&D results showing aggravating effects (such as PWR environment degradation) that were not explicitly included in the original analyses (such as Environmental Assisted Fatigue [1] [2]) but also because an economically viable design of components has required optimization and refinement of mechanical assessment methods. EDF has been developing since 1989 its own in-house FEA code baptised code_aster that is included in the Salome-Meca mechanical package. Salome-Meca is open-access and can be used freely by international users. It is continuously improved with a release at a rate of one new software version per year and it integrates the most recent results obtained by the EDF R&D, in fields as broad as fracture mechanics, XFEM and fatigue. The fatigue post-processing in code_aster offers a span of criteria (Dang Van, Stress Intensity, etc...) to pick and choose from and even offers the possibility to make up owns one fatigue criteria. It also offers the possibility to post-process fatigue according to the RCC-M rules: this is implemented in code_aster through the so-called POST_RCCM operator. Recent developments have enabled EDF to update the POST_RCCM operator in order to bridge the gap with modern fatigue industrial codes. The update effort has included in particular the development of a new option to evaluate fatigue for nozzles according to the RCC-M Annex ZE-200 as well as the clarification of the methodologies used for combining time points and transients. In addition, POST_RCCM includes the possibility to perform calculations with integration of environmental effects, with significant freedom to design one’s own corrections. The option is even left open to integrate a correction per the methodology proposed in [2]. The overall work scope and progress as of early 2016 was reported in [3] and is now in its validation phase. The validation of a fatigue computer code is not an easy task as the full validation using hand calculations would be a highly tedious effort, given the technicality and the multiple choices to make along the various steps of the fatigue analysis. As a result, an accepted way of validating the results obtained with a given code is to perform a benchmark analysis against another industrial fatigue code. This strategy was adopted for the validation of the new POST_RCCM functionalities and this paper presents the work performed and the results obtained.

The European Pressure Vessel Standard EN 13445 provides in its part 3 (Design) a simplified method (Clause 17) and a detailed method for fatigue assessment (Clause 18). Clause 18 “Detailed Assessment of Fatigue Life” is under revision within the framework of the European working group CEN/TC 54/WG 53 - Design methods to reach a significant increase in user-friendliness and a clear guideline for the application. This paper is focused on the new informative annex NA “Instructions for structural stress oriented finite elements analyses using brick and shell elements”. As an essential amendment for the practical user the determination of structural stress ranges for fatigue assessment of welds is further specified in this new annex. Different application methods for the determination of structural stresses are explained in connection with the requirements for finite element models and analyses. This paper will give an overview of the proposed approaches of structural stress determination in annex NA of the revised EN 13445-3. It will present the results of fatigue analyses according to EN 13445-3 Clause 18 from a round robin test with participants of the German working group for different application examples. The estimated structural stress ranges for the proposed approaches of structural stress determination will be compared. This comparison leads to general remarks and open points for the different approaches. Furthermore it is concludes that further comparisons, e.g. with results of other pressure vessel design codes are desirable.

Traditional design fatigue analyses of pressure vessels and piping equipment have typically used linear-elastic stress analyses, where the stresses caused by various loads, such as thermal, pressure, bending moments, etc. are combined using the principle of linear superposition. Based on high stress locations, geometric and material discontinuities, and other engineering judgements, stress classification lines (SCLs) were defined for where fatigue usage factors would be calculated. It was then necessary to apply simplified elastic-plastic penalty factors, based on the through-wall linearized stresses, to the peak stress amplitudes, in order to account for the nonlinear behavior of materials. Nonlinear finite element analysis that directly calculates strains were not typically used, because of computing and material modeling limitations. However, such analyses, even for complex three-dimensional structures, have become much more practical today with advancements in computing speed and storage capacity. ASME Section III Subarticle NB-3200 includes a provision for performing nonlinear (or “plastic”) analysis (NB-3228.4(c)), but little to no guidance is provided for how to perform the analysis itself. In addition, the procedure for computing the strain range, as currently written in the Code, has been identified as being limited to a uniaxial stress condition and is fundamentally inconsistent with the traditional elastic methodology. This paper provides a proposal for an improved approach for computing fatigue usage and strain rates using nonlinear plastic analysis. Additional guidance for performing these analyses is provided, as they are expected to be used more frequently into the future.

The French nuclear industry has to face nowadays a series of challenges it did not have to face a decade ago. The most significant one is to ensure a reliable and safe operation of Nuclear Power Plants (NPP) in a context of both an ageing reactor fleet and new builds. The new constructions need rules that integrate a strong operation feedback while the older NPPs need rules that will guarantee the life extension beyond 40 years of operation. In this context, a new edition of the French RCC-M Code is planned for 2016. This new edition integrates the modifications made to the Code as a result of Requests for Modification (RM), which can be submitted by anyone and which help to continuously improve the quality and robustness of the Code. Concerning fatigue analyses, the RCC-M Code steering committee has acknowledged end of 2014 the reception of two RM to modify the fatigue design curve for austenitic stainless steels and Nickel base alloys, as well as to integrate environmental effects in the fatigue evaluation for austenitic stainless steel components. The contents of these two RM were based on the proposals presented in Reference [1]. AFCEN required a technical review of these two RM and this task was performed by a working group composed by French and international experts. This process concluded to the approval of these two RM to be integrated to the 2016 edition of the RCC-M Code. This paper offers a presentation of these two new Rules in Probation Phase (RPP), this format being quite similar to Code Cases proposed by ASME Code.

This paper examines conservatisms associated with two aspects of piping fatigue life as applied in NB 3600 fatigue calculations. First, piping component allowable cyclic life is defined by stress-life (S-N) curves based on constant displacement push-pull test results of small diameter (≤ 0.375 inch (≤ 9.5 mm)) smooth test specimens in air at room temperature. These life estimates are subsequently applied to all Class 1 piping components regardless of their actual size or thickness. Secondly, all component cyclic stresses are treated as uniform through-thickness membrane stresses when most transients induce stresses that vary across the thickness of the pipe. The application of fatigue usage correction factors that account for: 1) increased cyclic life associated with the growth of engineering size fatigue cracks in thicker components and 2) the presence of actual through-thickness stress gradients is considered. An example case study indicates that, depending on the nature of the applied cyclic loading and pipe section thickness, considerable reductions in design fatigue usage can be obtained.

This paper points out some relevant aspects of the simplified elasto-plastic fatigue analysis as addressed in the ASME Code Section III Subsection NB and its application to two structural components that are subjected to a slow or to a fast thermal transient. The structural components considered are a thick-walled pipe and a nozzle-to-vessel junction. For the case of the thick-walled pipe, a closed form analytical solution proposed by Albrecht for pipes subjected transient temperature loading was implemented and its results were compared to coupled thermal and mechanical finite element analyses using a commercial finite element software. The application of the analytical solution allows for an optimization of the time consumed to obtain the stresses that occur across the thickness of the pipe as a function of time, i.e. the membrane plus bending plus peak stress range, S p . The analytical solution equally allows for the linearization of the stress components actuating along the pipe thickness for all time steps considered within the thermal stress solution. This yields the membrane plus bending stress range, S n , and allows for a design code conforming plasticity correction by means of K e factors. In the considered case of the nozzle-to-vessel junction, a finite element solution was used. It was one aim of the study to point out, that under fast transients loading situations the relevant stresses S p and S n do not necessarily coincide with each other. In the ASME Code the alternating stress S a is a function of the factor K e and of the range of S p , with K e being a function of the range of S n and of the material properties. Consequently, a non-conservative fatigue analysis may result in the case of performing cycle counting only based on the time history of the critical S p values and simply assigning the corresponding S n and K e values. This paper exemplifies one of those cases and proposes a method to overcome this problem.

Different pressure vessel and piping design codes and standards have adopted different fatigue analysis methods. In order to make some contribution to current efforts to harmonize international design codes and standards, a review of fatigue analysis methods for a number of selected nuclear and non-nuclear design codes and standards has been carried out. The selected design codes and standards are ASME Boiler and Pressure Vessel Code Section III Subsection NB and Section VIII Division 2, EN 12952, EN 13445, EN 13480, PD 5500, RCC-M, RCC-MRx, JSME, PNAEG and R5. This paper presents the initial review results. The results of the study could be used as part of the on-going work of the Codes and Standards Task Force of the World Nuclear Association (WNA) Cooperation in Reactor Design Evaluation and Licensing (CORDEL) Working Group.

Neuber’s rule is commonly applied in fatigue analysis to estimate the plasticity of purely elastic FEA results. In certain cases, this is more efficient than running elastic-plastic models. However, the applicability of Neuber’s rule is not well understood for complex models and may not always be appropriate. In this paper, the applicability of Neuber’s rule is investigated. The background of Neuber’s rule is discussed, theoretical limitations are derived, and algorithmic outlines of the procedures are presented. Neuber’s plasticity correction procedure is applied to both the Ramberg-Osgood elastic-plastic constitutive relation and the advanced Chaboche isotropic/kinematic nonlinear hardening relation. Throughout the manuscript, the aspects of each model are discussed from an educational perspective, highlighting each step of the implementation in sufficient detail for independent reproduction and verification. This level of detail is often absent from similar publications and, it is hoped, may lead to the wider dissemination of Neuber’s rule for plasticity correction. The final component of the paper presents a multiaxial correction of the Chaboche hardening model. To the best of the authors’ knowledge, this is the first published application of Neuber’s rule to the multiaxial plasticity correction of the Chaboche combined isotropic/kinematic hardening model. Examples are used to illustrate the behavior of the method and to present some of the commonly overlooked components when assessing the applicability of Neuber’s method.

Product durability and reliability validation requires fatigue testing of limited samples and the corresponding statistical and probabilistic analyses of the test data. The uncertainties introduced into the tests with limited sample size and the assumptions made about the underlying probabilistic distribution function will significantly impact the analysis results and the result interpretation. In this paper, a large amount of fatigue life data collected from several programs are analyzed. The values of the parameters estimated from the two-parameter and three-parameter probabilistic distribution functions, Weibull in particular, are compared. Finally, the observations are summarized and some recommendations are provided.