A comparison between Japanese and French A16 defect assessment procedures for fatigue crack growth

This paper presents the results of a benchmark on fatigue crack growth evaluation for plates subjected to cyclic bending loads. The simplified fatigue crack growth evaluation methods of JNC in Japan and A16 procedures proposed by CEA in France are presented. The methods, based on the reference stress approach, are compared with each other. They are found to differ in estimating crack closure, in the expression used for the reference stress solution and in the formulations used to take plasticity into account. The methods are then employed to predict the fatigue crack growth behavior observed experimentally. At R=0.1, the methods provide predictions of crack growth in good agreement with the experimental data. At R=−1.0, significant differences are observed between the predictions. The discrepancies are mainly due to the crack closure effect used to calculate the effective SIF range.     

A comparison between Japanese and French A16 defect assessment procedures for creep-fatigue crack growth

This paper presents the results of a benchmark on creep-fatigue crack growth evaluation for a plate subjected to cyclic bending loads with a 1 h dwell. The simplified creep-fatigue crack growth evaluation methods of JNC in Japan and A16 procedures proposed by CEA in France are presented. The methods, based on the reference stress approach, are compared each other. They are found to differ in the expression used for the reference stress solution used to estimate the creep strain. It is also pointed out that in contrast to the A16 procedures, the JNC method takes heterogeneous creep strain distribution into account for small scale yielding condition. The predictions obtained by the methods are also compared to the experimental data. It is found that the methods exhibit conservatisms which are significantly reduced when integrating the creep curve continuously without initialisation during the experiment [Proceeding of SMiRT 14(G13/2), Creep-Fatigue Crack Growth on CT25 Specimens in 316L(N) stainless steel at 650 °C].     

CEA and JNC approaches for creep–fatigue evaluation of weldments and inter-comparison through benchmark analyses

Creep–fatigue is an important failure mode in elevated temperature components especially for weldments. To establish rational design-by-analysis methods for weldments, the CEA and JNC have developed creep–fatigue evaluation methods. Both organizations have compared data and ideas through two kinds of benchmark analyses. The CEA benchmark is fatigue and creep–fatigue evaluation of welded plates under reverse bending at 550 °C. The JNC benchmark is creep–fatigue evaluation of a welded vessel under cyclic thermal transients. The main differences in the methods are the strain concentration factors for base metal fatigue strength reduction factors of weldments. To evaluate inferior performance of weldments to base metal, the CEA pays attention to material strength reduction in the weld metal, while the JNC examines strain redistribution between the base and weld metals. Both the CEA and JNC calculations gave good results for welded plates. Both methods obtained conservative results for a welded vessel because evaluation methods for base metal are conservative.     

Crack growth determination on laboratory components

The present work outlines the reasoning behind the selection of laboratory component tests for the validation of design and remanent life models governing crack growth behaviour. For the case of creep crack growth a ferritic and an austenitic alloy have been studied and a reference stress based solution used to successfully relate the stress rupture behaviour of internally and externally, axially and circumferentially notched, tubular components to base line creep data. Using the same reference stress based approach, it has been demonstrated that the notched component creep crack growth rates exhibit the same C^* dependence as conventional compact tension specimens. For 316L stainless steel components subjected to thermal fatigue conditions simulative of the fusion reactor first wall, a modified version of the superposition method of Buchalet and Bamford has been applied to estimate the stress intensity range as a function of crack length during the test. By this approach the crack growth rate dependency on stress intensity range for a variety of notch geometries is seen to be broadly in line with the conventional specimen mechanical fatigue data. Recent studies of crack growth under combined creep and thermal fatigue conditions are described and some early results are reported.     

Crack growth under cyclic thermal shock loading

Experimental and theoretical results of fatique crack growth under cyclic thermal shock loading are presented. The experiments were done by cooling hot steel plates by a water jet. Linear elastic fracture mechanics is applied to predict fatigue crack growth theoretically. For this stress intensity factors of semi-elliptical surface cracks were calculated by use of the weight function method. Measured fatigue crack growth is compared with predictions from the theory.     

Development of the evaluation method for crack propagation due to thermal striping

The evaluation code “THERST” was developed to estimate the fatigue crack propagation behavior under thermal stresses due to high-frequency temperature fluctuations, called “thermal striping”. This paper presents fundamental formulations of the evaluation method and verifications of the evaluation method by FEM analyses. Experimental data were obtained in high cycle thermal fatigue tests and the effect of a multiple crack which is characteristic for a crack under thermal stress is discussed in addition to the results of the FEM analyses. A modification of the evaluation method was performed to take multiple crack effects into account.     

Simulation of stress corrosion cracking behavior in a tube-shaped specimen of nickel-based alloy 600

Stress corrosion cracking (SCC) simulation code has been developed for the evaluation of SCC behavior in specimens in the shape of field components. The code utilizes numerical calculation of stress/strain states at a crack tip using finite element methods and a formula describing the crack tip reaction kinetics containing unknown environmental parameters. The applicability of this simulation code was investigated by applying the code to the evaluation of SCC behavior in a mock-up of a bottom mounted instrumentation tube for a pressurized water reactor subjected to complex stress/strain states. The results indicate that crack growth rate in a component suffering from certain environments can be estimated using the developed SCC simulation code with pre-determined unknown parameters, using the experimental crack growth rate data measured on other specimens in the same environment.     

A study on the evolution of crack networks under thermal fatigue loading

The crack network is a typical cracking morphology caused by thermal fatigue loading. It was pointed out that the crack network appeared under relatively small temperature fluctuations and did not grow deeply. In this study, the mechanism of evolution of crack network and its influence on crack growth was examined by numerical calculation. First, the stress field near two interacting cracks was investigated. It was shown that there are stress-concentration and stress-shielding zones around interacting cracks, and that cracks can form a network under the bi-axial stress condition. Secondly, a Monte Carlo simulation was developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. The local stress field formed by pre-existing cracks was evaluated by the body force method and its role in the initiation and growth of cracks was considered. The simulation could simulate the evolution of the crack network and change in number of cracks observed in the experiments. It was revealed that reduction in the stress intensity factor due to stress feature in the depth direction under high cycle thermal fatigue loading plays an important role in the evolution of the crack network and that mechanical interaction between cracks in the network affects initiation rather than growth of cracks. The crack network appears only when the crack growth in the depth direction is interrupted. It was concluded that the emergence of the crack network is preferable for the structural integrity of cracked components.     

2D simulation of the initiation and propagation of crack array under thermal fatigue

Various components of nuclear reactors are submitted to various thermo-mechanical loadings. Thermal fatigue cracking has been clearly detected in reactor heat removal system (RHRS) of pressurized water reactors (PWRs). The present study focuses on AISI 304 L stainless steel used in PWRs. The thermal fatigue behavior of this steel has been investigated using a specific thermal fatigue facility called “SPLASH”. This test equipment allows the reproduction of multiple crack networks similar to those detected during component inspections. The present study deals with the modeling of crack networks initiation and propagation. It is structured in two parts: (i) experimental details and main characteristics of the cracks networks, and (ii) numerical simulation of multiple cracks initiation and growth problem, using an elastic–plastic thermal–mechanical computation and a generalized Paris’ law. The model presented in this study gives predictions in a good agreement with observations, as far as the evolution of the mean and deepest cracks during cycling is concerned.     

The frequency effect on the fatigue crack growth rate of 304 stainless steel

Under cyclic loading condition, the fatigue crack growth (FCG) rate governed by stress intensity factor and stress ratio is well known; Walker’s equation, Forman’s equation and Elber’s equation are typical formulae to describe the fatigue crack growth rate. However, the loading frequency effect on the fatigue crack growth rate has yet to be explored. Recently, studies have focused on the loading frequency effect on some visco-elastic materials, and have provided a clearer understanding of the frequency effect on the fatigue crack growth rate. In a physical sense, knowledge about the loading frequency effect on the fatigue crack growth rate for 304 stainless steel is still lacking. James conducted a lot of experiments, and through data analysis, he concluded an evaluation equation which is based upon the experimental illustration. In this study, the physical properties of the material are used to illustrate the modification of fatigue crack growth rate, and a new formula which is based upon the modified Forman’s equation, is provided.     

Fatigue crack propagation testing using subsized rotating bending specimens

In many industrial applications, mechanical properties characterization is needed yet sufficient amount of material for standardsized specimens is not available. Miniaturized specimen testing technique has to be employed. Currently there are a lot of effort in developing subsized specimen technique for impact, fracture toughness and tensile properties. Work on fatigue properties testing is limited and largely confined to stress/strain life tests. In the current work, evaluation of fatigue crack propagation behaviour using surface crack growth in a rotating bending rod has been attempted. Nine different rod geometries have been tested. The resulting fatigue crack propagation data is more sensitive to rod diameter than to rod length. Difference in crack growth behaviour can largely be understood when crack closure is taken into account. All in all, the crack propagation data obtained from these small sized rods agree well with those obtained from standard testing employing compact tension specimens. A more precise picture about the crack growth behaviour can be obtained if crack closure is considered. If crack closure is not monitored, rods with longer length and smaller diameter are more likely to give the conservative upper bound fatigue crack propagation behaviour.     

Application of fracture mechanics methods in safety analysis of piping components in subcreep and creep behavior

A survey and review program for the application of fracture mechanics methods in elevated temperature design analysis and safety evaluation was initiated in December 1976. The first report [1] surveyed and assembled the material for a critical review of the theories of fracture and the application of fracture mechanics methods to life prediction and safety analysis of piping components. The second report [2] provided the basic concepts and a review of the problem areas associated with the development of analytical and experimental programs for a systematic evaluation and comparison of the currently available fracture mechanics theories. The basis for such an evaluation was described in terms of a series of benchmark problems which accurately specify conditions of geometry, loading and environment characteristic of large diameter piping systems in nuclear service.The objective of this third report is to establish a data base and detail the additional analytical techniques needed to confirm the validity of existing analytical methods and improve the state of the art in current problematic areas effecting the interpretation and extension of safety evaluation methods. The need for such a program in the elevated temperature field has been demonstrated by a number of independent surveys on various safety aspects of LMFBR related structural analysis methods and matetials problems. The results of this program, however, will be applicable not only to reactor plants operating at elevated temperatures, but will also lead to improvements of light water reactor evaluation methods for operating and accident conditions.The current state of elevated temperature reactor design technology is embodied in the standards and codes which provide guidance and minimum requirements for systematic design and evaluation procedures. These, however, do not necessarily provide specific absolute values which, if satisfied in the course of design, will guarantee thirty to forty years of uninterrupted life. There are numerous assumptions and approximations embodied in these standards concerning materials behavior, damage mechanisms, and failure modes at elevated temperature. There are also numerous areas of uncertainty and conflicting opinion in the interpretation of the existing test data and in the analysis and evaluation methods. Furthermore, the standards and codes leave some areas to the judgement of the designer, some of which require explicit justifications, but no standards or rules are provided.The overall safety therefore lies, at the present time, in the combination of rigorous enforcement of current standards, judicious application of experience with high temperature equipment even if not in nuclear service, and the surveillance of actual operating conditions. In the past, one criterion proposed for elevated temperature design has been that the time for crack initiation should exceed the design life. However, due to the complexities of the piping structures and the nature of the stress history during service, the evaluation of initiation times is difficult and often leads to uneconomical designs. In addition defects may exist in the component before it enters service. Hence, the knowledge of the growth rates of cracks and the residual strength of the components containing cracks is important in a realistic design evaluation. For more brittle materials and lower temperature applications where plasticity is restricted, linear elastic fracture mechanics methods have been developed. For more ductile materials where the plastic zones near the cracks are larger, linear fracture mechanics methods are not directly applicable, but in these nonelastic cases the opening displacement and J integral methods of assessment have been proposed. In the complex situation encountered in nuclear power plant design, the analysis must also account for cyclic thermal strains, time dependent creep, and the effect of harmful environments which are not explicitly treated in the above-mentioned methods. In this report an in-depth review is presented in sufficient detail to illustrate the degree of agreement between the theoretical and empirical methods available in the literature and indicate the scope of the additional analyses and experimental work needed for the development of reliable safety evaluation methodology.For pure cylindrical bending, cracks perpendicular to the load start to grow when reaches a critical value which is generally larger than the corresponding critical uniaxial tension value. There appears to be a thickness effect in the bending case which is probably due to interference from the compressive sides of the crack.For a circular plate with lateral pressure and small lateral displacements, results agree with the bending data when using the nominal bending stress . For larger displacements when bulging occurs, the results agree with the tensile data when the nominal tensile stress is used.For curves surfaces, such as a cylinder under internal pressure, the data agree with the expression developed by Folias both for axial cracks under hoop stress σ and for circumferential cracks under axial stress σ Generally, the expressions were accurate up to , showing a tendency to be lower than the experimental data at higher values of the parameter. The parameter is a promising one.To study the influence of cracks at different angles to the applied load, analysis and data are available including the stress component parallel to the crack in the stress field around a crack tip. This, together with the concept of a critical circumferential stress at a critical distance (α = 0.1) ahead of the crack provides improved correlation with fracture predictions for both the angle of fracture and the critical stress intensity factor for the angled cracks in flat plates.For a hollow cylinder under torsion with angled cracks, the best correlation was given by the same analysis although the results were not as conclusive as for the flat plate. From elastic theory useful curves for the variation of K₁, K₂, and K₃ around the border of an elliptically shaped crack are available.In a plane stress fracture the addition of a biaxial stress produces an increase in the apparent fracture toughness compared with the uniaxial case. However, there is as yet no evidence to show that there would be the same increase in a plane strain situation. Hence, in the absence of biaxial information the uniaxial fracture data may be the most conservative for flat plates. However, for shells there will also be a curvature effect.In an analogous manner, fatigue crack propagation rates appear to be less rapid under biaxial stresses than under uniaxial stress. However, this shift is not great and generallly will be masked by other effects such as environment and temperature service situations.The analysis of cracks in weldments with residual stress effects are also available. In the case of a crack in a weld the estimated residual stress distribution agreed reasonably well with some experimental data for elastic conditions. Results indicate that there can be a tensile stress intensity factor even when the original residual stress distribution has changed to compressive. A point to remember is that residual stresses near welds can be beyond yield.An analysis based on Lagrangean mechanics is useful for indicating the different effects of liquids and gases as pressurizing media in hollow pipes. The results show that whereas gases maintain their pressure as a crack begins to propagate, the pressure in the liquid can quickly decrease so that subsequent catastrophic failure is less likely even in large diameter piping.     

Fatigue studies on carbon steel piping materials and components: Indian PHWRs

This paper describes the results of fatigue studies on carbon steel piping materials and components of Indian Pressurized Heavy Water Reactors (PHWRs). The piping components include pipes and elbows, of outer diameter 219 mm, 324 mm and 406 mm, made of carbon steel (SA333 Gr.6 grade) material. Tests on actual pipes and elbows with part through notch were carried out to study the behaviour of crack growth under cyclic loading for different pipe sizes, notch aspect ratios, stress ratios, etc. During the tests, numbers of cycles for crack initiation from blunt notch were recorded with an accuracy of 0.1 mm. In conjunction with component tests, the experimental studies were also conducted on standard specimens to understand the effect of different variables such as size (thickness), type of specimen and components (elbow and pipe), welding, stress ratio, notch orientation on fatigue crack growth rate. The fatigue crack growth curve (da/dN versus ΔK) obtained from three-point bend specimen and pipe was compared with that given in ASME Section XI. The comparison shows that da/dN versus ΔK curves obtained from the specimen and pipe tests are nearly same. The analytical predictions for crack initiation and crack growth for the tested components were compared with experimental results. Such comparisons validate the modeling procedure for crack initiation and growth.     

Comparison of fracture toughness measurements from ferritic steel compact and surface-flawed specimens

Comparisons are made between predicted values of stress for initiation of crack growth in surface-flawed specimens and experimentally determined values. The comparisons are made for test temperatures corresponding to the lower shelf and the lower transition region which have elastic and elastic-plastic conditions, respectively. Predictions of stress levels for initiation of crack growth are based on Appendix A, Section XI of the ASME Boiler and Pressure Vessel Code and on an approach developed by Newman-Raju. The experimental results are based on acoustic emission techniques used to detect loads corresponding to crack initiation; their use in the comparison involved both the measured elastic-plastic stress value and an “equivalent” elastic stress.Evaluation of the analytical approaches showed that neither method was consistently more conservative over the full range of input dimensions. For tests conducted at lower-shelf temperatures (where very little plastic deformation occurs), the predicted stresses were lower than experimental values. At higher temperatures (where increasing amounts of plastic deformation occurs), some nonconservative predictions were made.A correlation is noted between the predicted-to-experimental stress ratio and a parameter used to quantify the severity of the surface flaw. This correlation may provide a basis for an empirical method for predicting the stress required to initiate crack growth.     

Fatigue crack growth under residual stress field in low-carbon steel

The influence of residual stress on fatigue crack growth was experimentally and analytically investigated for surface crack. Fatigue tests were performed on straight pipe components of low-carbon steel having a circumferential inner surface crack in laboratory air environment. Some of the test pipes had been subjected to special heat treatments so as to have compressive or tensile residual stresses along the inner surface.The results show that the compressive residual stress remarkably suppresses the surface crack growth while the tensile residual stress doesn't accelerate the crack growth very much.The crack growth analyses were conducted by the application of power relationship between ΔK and . The stress intensity factors due to the non-linear stress field were calculated by the weight function method. The analyses resulted in a confirmation of the behavior of the crack growth observed in the experiments.     

A computational fatigue analysis of cyclic thermal shock in notched specimens

Thermal shock induced fatigue plays a role in the assessment of the lifetime of different components in the primary cooling circuit of a nuclear plant. In spite of the implementation of substantial and costly safety factors, a few, unexpected cases of fatigue failure have occurred. Here we report on a laboratory experiment which mimics the thermal loading observed in such components. A finite element thermal stress analysis using a calibrated, elasto-plastic, combined kinematic-isotropic cyclic hardening material model is presented. The distribution of transient stresses and strains in the specimens subjected to cyclic thermal shock, are used to predict the number of cycles to crack initiation with a fatigue curve that has been calibrated experimentally with data from equivalent specimens under pure mechanical fatigue. Our results indicate that cyclic thermal shock induced ratcheting occurs locally near the tip of the notch in the specimens, and the potential impact on the number of cycles to crack initiation is explored.     

Creep—fatigue test of a thick-walled vessel under thermal transient loadings

To improve the damage evaluation methods in the design code for Fast Breeder Reactors (FBRs), a series of creep—fatigue tests of structural models under thermal transient loadings are going on at Oarai Engineering Center of the Power Reactor and Nuclear Fuel Development Corporation (PNC). Test models are designed to incorporate representative structures of components and pipings used in FBRs and are subjected to severer cyclic thermal transients than those experienced in FBRs. The test is planned to be continued until failure occurs. This paper describes the creep—fatigue test results and their damage evaluation for the first test model.A 40 mm thick vessel model made of SUS304 austenitic stainless steel was subjected to cyclic thermal transients, in which sodium at 600°C and 250°C flowed repeatedly. The period of each transient was 2 h. Cracks were observed at seven test portions in the model after 1002 cycles of the thermal transients.Elastic and inelastic analyses were performed to evaluate creep—fatigue damage and crack propagation. The safety margins included in the creep—fatigue design methods based on elastic analysis as well as those based on inelastic analysis are discussed. Finally fracture mechanics analyses were performed to explain the observed crack growth.     

Defect assessment procedures at high temperature

Within Nuclear Electric PLC, a comprehensive assessment procedure for the high-temperature response of structures is being produced. The procedure is referred to as R5 and is written as a series of step-by-step instructions in a number of volumes. This paper considers in detail those parts of R5 which address the behaviour of defects. The defect assessment procedures may be applied to defects found in service, postulated defects, or defects formed during operation as a result of creep-fatigue loading. In the last case, a method is described for deducing from endurance data the number of cycles to initiate a crack of a specified size. Under steady loading, the creep crack tip parameter C* is used to assess crack growth. Under cyclic loading, the creep crack growth during dwell periods is still governed by C* but crack growth due to cyclic excursions must also be included. This cyclic crack growth is described by an effective stress intensity factor range. A feature of the R5 defect assessment procedures is that they are based on simplified methods and approximate reference stress methods are described which enable C* in a component to be evaluated. It is shown by comparison with theoretical calculations and experimental data that reliable estimates of C* and the associated crack growth are obtained provided realistic creep strain rate data are used in the reference stress approximation.     

The J integral evaluation of a nozzle corner crack under thermal transient loading condition

This paper presents the results of the evaluation of the three dimensional J integral of a nozzle corner crack which is initiated by fatigue under thermal transient loading conditions of a BWR type reactor vessel. Analyses are carried out by using the finite element method in the following two cases. One case consideres the effect of the stainless steel cladding deposited over the inside surface of the reactor vessel, and the other neglects it. In both cases, the extended J integral concept, called integral, is used to obtain the path independent J value in the thermal stress fields.By changing the shapes and the dimensions of the crack, some elastic analyses are carried out in the two dimensional space. The effects of the cladding are studied qualitatively, and the integrals are compared with the critical J value, and discussed.Three dimensional values along the three dimensional crack front are evaluated for the embedded crack. The results are compared with those for two dimensional analysis.The nozzle corner crack is treated under thermal transient condition and distributions of values, and their change with time is obtained. The shapes and dimensions are changed by the assumption that the crack growth occurs at the point where the vector has its maximum, and the three dimensional shape of the propagating crack is estimated.