Applications of probabilistic fracture mechanics to light water reactor pressure vessels and piping

This paper reviews recent calculations of the statistical reliability of LWR reactor vessels and piping. The broad theoretical principles of these calculations are well established and it is therefore possible to compare the physical assumptions made in different calculations. Such a comparison shows that certain functions are not known at all well; for example, (i) the frequency of occurrence of cracks in weld-regions, (ii) the size distribution of cracks, (iii) the efficiency of methods of non-destructive examination and (iv) the transient loadings that the system experiences in service. On the other hand, relevant materials properties (toughness, crack growth characteristics) appear to be known adequately if not completely. Despite these quantitative uncertainties in the input, it seems possible to draw several broad conclusions from the results of these calculations. These concern (i) the low absolute rates of failure, (ii) the way these depend upon time in service, (iii) the effect upon them of in-service inspection and (iv) their sensitivity or otherwise to the physical assumptions which are made.     

Towards an elastic-plastic fracture mechanics predictive capability for reactor piping

Intergranular stress corrosion cracks have been discovered in the recirculation bypass piping and core spray lines of several boiling water reactor (BWR) plants. These cracks initiate in heat-affected zones of girth welds and grow circumferentially by combined stress corrosion and fatigue. Reactor piping is mainly type 304 stainless steel, a material which exhibits high ductility and toughness. A test program described in this paper demonstrates that catastrophic crack growth in these materials is preceded by considerable amounts of stable crack growth accompanied by large plastic deformation. Thus, conventional linear elastic fracture mechanics, which only applies to the initiation of crack growth in materials behaving in a predominantly linear elastic fashion, is inadequate for a failure analysis of reactor piping.This paper is based upon research initiated by a need to develop a realistic failure prediction and a way to delineate leak-before-break conditions for reactor piping. An effective engineering solution for the type of cracks that have been discovered in BWR plants was first developed. This was based upon a simple net section flow stress criterion. Subsequent work to develop an elastic-plastic fracture mechanics methodology has also been pursued. A survey of progress being made is described in this paper. This work is based on the use of finite element models together with experimental results to identify criteria appropriate for the onset of crack extension and for stable crack growth. A number of criteria have been evaluated. However, the optimum fracture criterion has not yet been determined, even for conditions which do not include all of the complications involved in reactor piping.     

Results of reliability test program on light water reactor piping

The Japan Atomic Energy Research Institute has conducted a piping reliability test program to demonstrate the safety and reliability of light water reactor primary piping. In this program, pipe fatigue test, leak-before-break (LBB) verification test and pipe rupture test were carried out to examine the integrity of piping, to verify the LBB and to demonstrate the effectiveness of protective measures against jet impingement and pipe whip loads under a pipe rupture event.In the pipe fatigue test, a procedure to predict the fatigue crack growth was developed, and the integrity of piping during the plant service life was evaluated. In the LBB verification test, the pipe fracture test and the leak rate test were performed to verify the LBB in the primary piping.In the pipe rupture test, the influence of jet impingement on the target disk and the deformation behavior of whipping pipe and restraint were investigated. Using the test results, the jet impingement behavior and the effectiveness of pipe whip restraint were demonstrated.     

Coupled phenomenological and fracture mechanics approach to assess the fracture behaviour of TWC piping component

The present study demonstrates the numerical prediction of experimental specimen J-R curve using Gurson-Tvergaard-Needleman phenomenologically based material model. The predicted specimen J-R curve is used to determine the geometric independent initiation fracture toughness (J_SZWc) value that compares well with experimental result. Using the experimentally determined and numerically predicted J_SZWc values and specimen J-R curves, the accuracy of predicting the fracture behaviour of the cracked component is judged. Thus the present study proposed a coupled phenomenological and fracture mechanics approach to predict the crack initiation and instability stages in cracked piping components using numerically predicted specimen J-R curve obtained from tensile specimens testing data.     

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.     

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.     

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.     

On the structural reliability of reactor safety containments

A method for reliability based design of reactor safety containments is suggested, and a brief review of classical reliability analysis is presented. Seismic and climatic load occurrences are modeled by uniform Poisson processes. Extreme value distributions are assumed to represent the seismic, climatic, external and internal pressure load intensities. Reliabilities are calculated for various design loads and load combinations.     

Degradation of fracture mechanics properties of reactor graphite due to burn-off

This paper evaluates the change in various mechanical and fracture mechanics properties of two kinds of graphite for high temperature gas-cooled reactors due to burn-off by air oxidation. Thermal shock resistance and thermal shock fracture toughness of the burn-off graphite are also quantitatively determined by using an arc discharge heating method. These results are expressed as a function of burn-off, B, by an empirical formula of the form; S = S₀exp(−nB), where S₀ and n denote respectively the initial value and the degradation exponent of the material. The empirical formulas for thermal shock are found to agree reasonably well with those calculated from the results of individually examining the effect of burn-off on the associated properties.     

Integration of nondestructive examination reliability and fracture mechanics

A multi-year program on the Integration of Nondestructive Examination and Fracture Mechanics (NDE/FM) has been funded by the U.S. Nuclear Regulatory Commission at the Pacific Northwest Laboratory. Many activities are being pursued under this program. This paper highlights some of the activities: input to the NRC Pipe Crack Task Group, an evaluation of manual ultrasonic testing of centrifugally cast stainless steel, interaction matrix, advanced UT technique evaluation, qualification document, evaluation of crack characterization techniques, international NDE reliability work, siamese imaging technique for imaging planar-type radial defects in reactor piping, fracture mechanics analysis for PTS-type flaws and piping reliability, and a position paper on piping ISI.     

Integration of nondestructive examination reliability and fracture mechanics

A multi-year program at the Pacific Northwest Laboratory is in progress to determine the reliability of ultrasonic ISI that is performed on light-water reactor primary systems, using probabilistic fracture mechanics (FM) analysis to determine the impact of NDE unreliability on system safety, and to evaluate advanced ultrasonic techniques. This paper is a review of the last year's highlights. Emphasis is placed upon the results of a pipe inspection round robin, advanced technique evaluation, joint study with Westinghouse, qualification document, underclad crack detection sizing studies, and a FM analysis using the PRAISE code for studying inspection parameters.     

Application of warm prestressing effects to fracture mechanics analyses of nuclear reactor vessels during severe thermal shock

Recent experiments on pressure vessel steels have shown that the fracture toughness can be significantly increased at low temperatures if the material is prestressed at a higher temperature. A conservative method is formulated to use this warm prestressing effect in the fracture mechanics analysis of nuclear pressure vessels under thermal shock. This method uses the basic premise that a crack will not initiate when the stress intensity factor is dropping with time (or constant), whether or not the temperature is dropping. A considerable amount of supportive experimental information is presented and a thorough justification of the method is given. One example is presented to illustrate the beneficial aspects of warm prestressing during a thermal shock. The results show that, when warm prestressing is used, the minimum initiation crack depth can be greater, in some cases, by a factor of ten than that calculated by standard methods.     

Applicability of AE monitoring technique to evaluate structural integrity of fast breeder reactor piping component

The availability of acoustic emission technique for detecting and monitoring defects of piping components in fast breeder reactors has been studied in the FAET Committee of the Japan Welding Engineering Society sponsored by,the Power Reactor & Nuclear Fuel Development Corporation. The researches which extended over four years have covered a wide range of experiments and evaluations in order to ensure the usefulness of the acoustic emission technique as a monitoring tool of plant operation.     

Application of statistical linear elastic fracture mechanics to pressure vessel reliability analysis

An evaluation of the failure probability for a pressure vessel is made on the basis of linear elastic fracture mechanics (LEFM). Failure is identified by actual crack length equal to critical crack length. The probability of failure is the joint probability that there exists a crack (i.e. K_I) greater than a given crack (i.e. K) and that the critical crack (i.e. K_IC) is smaller than that same crack, where K_I and K_IC are considered for same time and location. K_IC as well as K_I are treated as statistical variables with probability density functions (p.d.f.), which are functions of material, location and time. The variability of K_IC (that is the p.d.f. of K_IC) is a result primarily of the statistical nature of the material properties and to a lesser degree of the increasing neutron-done experienced by certain parts of the pressure vessel. The variability of K_I (that is the p.d.f. of K_I) is a result of the following parameters:

1. (1) initial distribution of cracks (that is the crack distribution at the start-up of the reactor) regarded as a statistical variable, because of the uncertainty in the non-destructive testing of the pressure vessel prior to start-up.

2. (2) stresses, regarded as a statistical variable because of the uncertainty in the stress analysis and the geometry of the vessel.

3. (3) crack growth by fatigue, which is a result of the normal (with probability equal to 1.0) and abnormal (with a p.d.f.) operational transients. The statistical nature of the crack growth is due to the statistical variation of the abnormal operational transients.

4. (4) material properties (that is K_IC, yield strength and the factors governing the fatigue crack growth) regarded as statistical variables.

The p.d.f.s of the abovementioned parameters are evaluated on the basis of the available literature. The integrated calculations of failure probability are performed by a computer program utilizing the Monte Carlo technique with importance sampling, which gives a greater freedom in selection of p.d.f.s. Calculations of failure probability for existing reactors are presented.     

A fracture mechanics interpretation model for acoustic emission signals caused by thermal fatigue shocking on a reactor pressure vessel nozzle

The analysis of acoustic emission measurements during cyclic thermal-shock tests on a pressure vessel nozzle (HDR) with cracks indicated a time-dependent emission of signals that partially contradicts the usual fracture mechanics approach (according to Paris).If one assumes a time-dependent corrosion crack growth (normally of secondary importance) as the dominating factor of influence, a qualitatively good agreement between acoustic emission and fracture mechanics is achieved.     

Matrix displacement methods in fracture mechanics analysis of reactor vessels

The technology of fracture mechanics is developing rapidly in response to increased requirements for integrity of engineering structures. It enables structural engineers to evaluate brittle failure resistance of structures within appropriate regimes of temperature, materials and geometry. The evaluation includes the combined effects of material toughness, flaw characteristics, environment and service loadings. Calculations of stress intensity factors associated with the flaws, geometry and applied loading form the basis of fracture analysis and control procedures for reactor vessels.     

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.