Probabilistic fracture mechanics of nuclear structural components: consideration of transition from embedded crack to surface crack

This paper describes a probabilistic fracture mechanics (PFM) analysis of aged nuclear reactor pressure vessel (RPV) material. New interpolation formulas of three-dimensional stress intensity factors are presented for both embedded elliptical surface cracks and semi-elliptical surface cracks. To investigate effects of transition from embedded crack to surface crack in PFM analyses, one of the PFM round-robin problems set by JSME-RC111 committee (i.e. aged RPV under normal and upset operating conditions) is solved, employing the interpolation formulas.     

Probabilistic fracture mechanics analyses of nuclear pressure vessels under PTS events

This paper describes some recent research activities on probabilistic fracture mechanics (PFM) for nuclear reactor pressure vessels (RPVs) performed by the RC111 research committee of the Japan Society of Mechanical Engineers (JSME) under a subcontract of the Japan Atomic Energy Research Institute (JAERI). To establish standard procedures for evaluating failure probabilities of nuclear RPVs, we have performed PFM analyses for aged RPV under pressurized thermal shock (PTS) events. The basic problems are chosen from some of US benchmark problems such as EPRI (Electric Power Research Institute) and US NRC (Nuclear Regulatory Commission) joint PTS benchmark problems and H.B. Robinson problems. Employed in this study are four PFM computer codes developed in Japan and in USA. Various sensitivity analyses are performed to quantitatively evaluate the influences of the input data, i.e. (a) initial crack shape, (b) the probabilistic distribution of initial crack depth, (c) cladding, (d) RT_NDT shift, (e) impurity content, (f) the through-wall distributions of material properties, (g) pre-service inspection (PSI) and (h) warm prestressing. It is clearly shown that in most cases, these data affect failure probabilities significantly. Therefore, we should use in the PFM analyses as reliable input data as possible. If any reliable data are not available, the data resulting in most conservative results could be chosen, referring the analysis results presented in this paper.     

Research activities on fracture mechanics for nuclear piping in Japan

This paper presents an overview of the piping studies, such as the studies on ductile fracture of piping and the development of fracture analysis methods, that have been or are being conducted in Japan.     

Recent Japanese activities for non-destructive examination and structural integrity of reactor components

Nuclear power generation has been spotlighted as a substitute for petroleum. Efforts are being exerted for the development of more reliable nuclear power plants. This paper describes the present status of such development activities in Japan, especially to enhance reliability of non-destructive flaw detection and to improve component integrity through the cooperative efforts of experts in materials, structural design, fracture mechanics, fabrication and non-destructive examination.     

Probabilistic assessment of thermal fatigue in nuclear components

A probabilistic framework is set up to assess the fatigue life of components of nuclear power plants. It intends to incorporate all kinds of uncertainties, such as those appearing in the specimen fatigue strength (number-of-cycles-to-failure of specimens), design margin factors (taking into account the size, surface finish and environmental effects), mechanical model (precisely, the uncertainty on the model input parameters) and the thermal loading. This paper presents the global methodology and details the statistical treatment of the fatigue specimen test data. A first analytical example shows that the reliability of a structure submitted to a periodic stress cycle S changes significantly with respect to the value of S, although the codified (deterministic) design criterion is equally fulfilled. A more comprehensive example involving a mechanical model of a pipe submitted to a deterministic inner temperature loading is finally analysed. The use of the first-order reliability method (FORM) allows to compute the probability of failure as a function of the foreseen lifetime and to rank the input random variables according to their importance in response sensitivity.     

Probabilistic fracture failure analysis of nuclear piping containing defects using R6 method

Failure analysis of in-service nuclear piping containing defects is an important subject in the nuclear power plants. Considering the uncertainties in various internal operating loadings and external forces, including earthquake and wind, flaw sizes, material fracture toughness and flow stress, this paper presents a probabilistic assessment methodology for in-service nuclear piping containing defects, which is especially designed for programming. A general sampling computation method of the stress intensity factor (SIF), in the form of the relationship between the SIF and the axial force, bending moment and torsion, is adopted in the probabilistic assessment methodology. This relationship has been successfully used in developing the software, Safety Assessment System of In-service Pressure Piping Containing Flaws (SAPP-2003), based on a well-known engineering safety assessment procedure R6. A numerical example is given to show the application of the SAPP-2003 software. The failure probabilities of each defect and the whole piping can be obtained by this software.     

Applications of probabilistic fracture mechanics to FBR components

A probabilistic fracture mechanics code which evaluates fracture probability of a plate model with an elliptical surface crack caused by creep-fatigue crack growth has been developed. The code named PCCF (Probabilistic Fracture Mechanics Code for Creep-Fatigue Crack Growth) uses simplified methods of C^* and J-integral for evaluation of creep-fatigue crack growth and a stratified sampling method for two input variables to improve the solution convergency. According to the test analyses focused on an applied stress level using PCCF code, leak probability is sensitive to a stress level and increases rapidly when an applied stress is close to a yield stress level.     

Stress analysis incorporating fracture mechanics and materials aspects for components under complex loading

The title deals with a complex subject. Stress analysis with consideration of fracture mechanics and material properties is subject to research and development worldwide. A final answer is not possible. This is only an attempt to discuss the problem.In the following, three examples are discussed. Due to the size of the problems, extensive use of references (with more detailed information) is made. The examples are: a pressure vessel nozzle, a disc with crack, and a thick walled vessel.     

Computational methods assuring nuclear power plant structural integrity and safety: an overview of the recent activities at VTT

Numerical, simplified engineering and standardised methods are applied in the safety analyses of primary circuit components and reactor pressure vessels. The integrity assessment procedures require input relating both to the steady state and transient loading actual material properties data and precise knowledge of the size and geometry of defects. Current procedures hold extensive information regarding these aspects. It is important to verify the accuracy of the different assessment methods especially in the case of complex structures and loading. The focus of this paper is on the recent results and development of computational fracture assessment methods at VTT Manufacturing Technology. The methods include effective engineering type tools for rapid structural integrity assessments and more sophisticated finite-element based methods. An integrated PC-based program system MASI for engineering fracture analysis is described. A summary of the verification of the methods in computational benchmark analyses and against the results of large scale experiments is presented.     

3D nonlinear finite element/fracture mechanics analysis of pressurized nuclear reactor container ring

Nuclear reactor containers, without inner liners, must withstand internal pressurization with minimal leak to the outside through the cracks. This paper reports on a 3D finite element (FE) simulation of a prestressed nuclear reactor container ring subjected to internal pressure. Discrete cracks are used, and the effect of crack surface pressurization on crack openings is investigated.It is shown that the discrete crack model can provide a suitable alternative to the smeared crack one, and that for the selected ring, the effect of additional crack pressurization is minimal.     

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.     

Validation of simplified fracture mechanics methods by testing of real components

The evaluation of integrity of structural components is often based on the proof of leak-before-break (LBB). Leak-before-break behaviour in piping constitutes a fail-safe condition. Which means that, during multiplied loading conditions, a defect results at first in a leakage. The crack length which leads to the leakage is smaller than the critical through-wall crack length. Simplified fracture mechanics concepts are used for the demonstration of LBB. For this the conservative, safe calculation of the critical through-wall crack length for ductile failure is necessary. To validate simplified calculation methods for circumferential cracks (flow stress concept (FSC); plastic limit load (PLL)) and for axial cracks (Battelle approach (BMI); Ruiz approach (RUIZ)) all available experiments on real structural components, especially on pipes, were analysed and evaluated by the mentioned simplified methods (approximately 460 experiments). The methods were adapted by application of correction factors, mainly on the flow stress, to result in conservative (safe) and realistic (as near as possible to the experiments) predictions. Depending on method (FSC, PLL, BMI, RUIZ), crack orientation (circumferential and axial cracks) and type of material (ferritic and austenitic material) different definitions of flow stresses were established.     

Probabilistic assessment of the fracture mechanics behaviour of an HTR-module primary circuit pressure boundary

In this paper the fracture mechanical behaviour of the primary circuit pressure boundary of a planned HTR-module reactor for electricity and steam generation under normal operation is assessed probabilistically. First and second order reliability methods (FORM-SORM) are used to calculate failure probabilities. They also allow a simplified analysis of the leak-before-break (LBB) behaviour. No LBB was probabilistically identified for the reactor pressure vessel. However, failure of the pressure vessel unit in normal operation probably originates from the connecting pressure vessel or the steam generator pressure vessel. They show LBB in probabilistic terms.     

Failure probability assessment of wall-thinned nuclear pipes using probabilistic fracture mechanics

The integrity of nuclear piping system has to be maintained during operation. In order to maintain the integrity, reliable assessment procedures including fracture mechanics analysis, etc., are required. Up to now, this has been performed using conventional deterministic approaches even though there are many uncertainties to hinder a rational evaluation. In this respect, probabilistic approaches are considered as an appropriate method for piping system evaluation. The objectives of this paper are to estimate the failure probabilities of wall-thinned pipes in nuclear secondary systems and to propose limited operating conditions under different types of loadings. To do this, a probabilistic assessment program using reliability index and simulation techniques was developed and applied to evaluate failure probabilities of wall-thinned pipes subjected to internal pressure, bending moment and combined loading of them. The sensitivity analysis results as well as prototypal integrity assessment results showed a promising applicability of the probabilistic assessment program, necessity of practical evaluation reflecting combined loading condition and operation considering limited condition.     

Dynamic qualification of complex structural components of nuclear power plants

The safety requirements and the lack of accessibility for any future repair, impose the design requirement that the integrity of reactor components of nuclear power plants be assured for the lifetime of the plant. To meet this design requirement it is essential to qualify the component, i.e. prove its capability to perform the design function for the design life. In performing its design function, the component is subjected to both static and dynamic loads. The qualification for static loads is rather simple and reliable, but qualification for dynamic loads is complex and often uncertain. This is because analytical tools are often inadequate for a realistic dynamic qualification and exact structurally simulated experimental models are almost always difficult to build. In such a situation, methods using tests on simple experimental set-ups supplemented by conservative analytical back-ups must be evolved. This paper highlights the intricacies involved in the conservative dynamic qualification of the complex components by considering the example of the moderator sparger tube. This component is a perforated tube submerged in water and excited by flow. For such a case, a completely analytical or a totally experimental qualification is not possible. This paper describes a procedure by which the required dynamic characteristics such as added mass, damping and fluid forces are generated from simple experiments and the component is qualified by analysis using these data.     

Numerical simulation of post yield fracture mechanics experiments as a basis for the transferability to components

As a necessary step in the chain of transferability from small specimens to actual structures the numerical evaluations of two crack-growth resistance experiments on the basis of the J-integral and utilising sidegrooved compact specimens of different sizes, tested at room temperature and at 285°C are discussed. The necessary experimental and numerical techniques are presented:

• -The partial unloading technique as applied in the IWM is applicable with high accuracy and reproducability in the relevant temperature range up to operating temperature.

• -The J-evaluation combined with a node shifting and releasing technique as implemented in the IWM-version of ADINA proved to be a powerful and economic tool even for parameter studies.

The results of the experiments and of the numerical evaluations are presented as force-displacement diagrams and as J-integral vs. crack extension curves. The good qualitative and quantitative agreement supports the experimental evaluation of J from the force-displacement diagram and validitates the numerical procedures to be applied and extended to real structues.

Contributions of structural mechanics to safety and reliability of German nuclear power stations

Traditionally structural mechanics considerations have played a competent role in the design of German nuclear power stations and their fuel. Structural mechanics development and validation programs have set standards of “gooddesign practise” and established the proof of safety against catastrophic failure.     

Fundamental principles for a nuclear design and structural analysis code for HTR components operating at temperatures above 800°C

With reference to the special characteristics of an HTR plant for the supply of nuclear process heat, the investigation of the fundamental principles to form the basis for a high temperature nuclear structural design code has been described. As examples, preliminary design values are proposed for the creep rupture and fatigue-behaviour. The linear damage accumulation rule is for practical reasons proposed for the determination of service life, and the difficulties in using this rule are discussed. Finally, using the data obtained in structural analysis, the main areas of investigation which will lead to improvements in the utilization of the materials are discussed. Based on the current information, the working group “Design Code” believes that a service life of 70 000 h for the heat-exchanging components operating at above 800°C can be.     

Intensely irradiated steel components: Plastic and fracture properties, and a new concept of structural design criteria for assuring the structural integrity

In order to develop a systematic and reasonable concept assuring the structural integrity of components under intense neutron irradiation, two basic tensile properties, true stress-true strain (TS-TS) curves and fracture strain, were investigated on an austenitic stainless steel and martensitic steel. Application of Swift equation is confirmed to a large plastic strain range of TS-TS curves. Fracture strain ?_f data were well correlated as ?_f + ?₀ = const. where ?₀ is the pre-strain representing the irradiation hardening.Based on those formulations and available experimental information, several critical issues to be dealt with in developing the concept were identified possible reduction in ductility, significant change in mechanical properties, remarkable cyclic softening and other unique cyclic properties observed during a high-cycle fatigue testing, and the redundancy of the plastic collapse concept to bending. Existing structural codes are all based on the assumption that there will be no significant changes in mechanical properties during operation, and of high ductility. Therefore, a new concept for assuring structural integrity is required for application not only to components with high ductility but also components with reduced ductility. First, potential failure modes were identified, and a new and systematic concept was proposed for preventing these modes of failure, introducing a new concept of categorizing the loadings by stability of deformation process to fracture (as type F and M loadings). Based on the basic concept, a detailed concept of how to protect against ductile fracture was given, and loading type-dependent limiting parameters were set.Finally, application of the detailed concept was presented, especially on determination of loading type (in numerical approach, the formulation of TS-TS curves and fracture strain derived above are needed), and on how to determine the limiting parameters as allowable limits. Experiments were done to identify the loading type of a tensile loading acting on a structure with a discontinuity. Tensile loadings acting on an intensely neutron-irradiated flat plate with a hole in the center cause plastic tensile instability and necking at the minimum ligament section but do not initiate any surface crack at the initiation of necking.