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.     

Application of statically indeterminate fracture mechanics, SIFM, to a circumferentially cracked cylinder problem

The method of statically indeterminate fracture mechanics called SIFM is an application of elastic–plastic fracture mechanics to statically indeterminate problems. Application of SIFM has been developed for axially cracked cylinder problems. Its application was modified to a circumferentially cracked cylinder. The component might be loaded by combined transient thermal and mechanical loading. This was applied to simulate pressurized thermal shock, PTS, experiment, NKS-3, carried out by MPA. The predicted result from SIFM shows good agreement with the NKS-3 experimental one.     

The application of the boundary-integral equation method to the solution of engineering stress analysis and fracture mechanics problems

This paper reviews the development and application of an influence function method for calculating stress intensity factors and residual fatigue life for two- and three-dimensional structures with complex stress fields and geometries. Through elastic superposition the method properly accounts for redistribution of stress as the crack grows through the structure. The analytical methods utilized and the computer programs necessary for computation and application of load independent influence functions are presented. A new exact solution is obtained for the buried elliptical crack, under an arbitrary Mode I stress field, for stress intensity factors at four positions around the crack front. The IF method is then applied to two fracture mechanics problems with complex stress fields and geometries. These problems are of current interest to the electric power generating industry and include (1) the fatigue analysis of a crack in a pipe weld under nomial and residual stresses and (2) fatigue analysis of a reactor pressure vessel nozzle corner crack under a complex bivariate stress field.     

Probabilistic fracture mechanics analysis of nuclear structural components: a review of recent Japanese activities

This paper describes a review of recent Japanese activities on probabilistic fracture mechanics (PFM) analyses. Japan Atomic Energy Research Institute (JAERI) has sponsored research committees on PFM organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for more than 10 years. The purpose of the continuous activity is to establish standard procedures for evaluating failure probabilities of Japanese nuclear structural components such as PV&P and steam generator tube, combining the state-of-the-art knowledge on structural integrity of nuclear structural components and modern computer technology such as parallel processing. This paper shows two topics of the newest results of JWES committee, PFM analysis of aged reactor pressure vessel considering embedded cracks and PFM analysis of piping considering seismic loading, and one topic by JAERI itself, development of PTS analysis code for transient loading (PASCAL).     

An elastic–plastic fracture mechanics based methodology to characterize cracking behavior and its application to environmental assisted processes

Cracking processes suffered by new structural and piping steels when used in petroleum or other energy installations have demonstrated the need for a cracking resistance characterization methodology. This methodology, valid for both elastic and elastoplastic regimes, should be able to define crack propagation kinetics as a function of their controlling local parameters. This work summarizes an experimental and analytical methodology that has been shown to be suitable for characterizing cracking processes using compact tensile specimens, especially subcritical environmentally assisted ones, such as those induced by hydrogen in microalloyed steels. The applied and validated methodology has been shown to offer quantitative results of cracking behavior and to correlate these with the existing fracture micromechanisms.     

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.     

Application of fracture mechanics concepts to the failure of wide plates

An analysis is presented to predict the failure behaviour of wide plates with different crack lengths in a temperature range where brittle, elastic-plastic and fully ductile behaviour is observed. Comparing the characteristic material properties derived from small scale specimens with the corresponding loading conditions in terms of J_appl using two- and three-dimensional finite element analyses, the failure loads can be calculated as a function of temperature. Based on these analyses it is possible to predict the different failure behaviour of the wide plates characterized by the transition temperatures T_gy and T_i.     

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.     

Some recent developments of the endochronic theory with applications

In this paper we presented a comprehensive review of recent developments of the endochronic theory of plasticity. The endochronic theory was first proposed by Valanis in 1971 with the aim of circumventing some of the difficulties associated with classical theories of plasticity, such as the concept of a yield surface and its motion in the stress space, criteria for unloading, hardening rules, etc. The theory is developed by using irreversible thermodynamics of internal variables. In the early version of the theory the intrinsic time was defined as a measure of length in strain space. This version is now called the simple endochronic theory. The derived constitutive equations have been applied with success to a number of problems of practical interest, e.g. cyclic response, cross hardening, cross ratcheting, etc. However, it has been shown by the first author that the simple theory leads to an unloading response which is not elastic at its onset. As a consequence infinitesimal hysteresis loops in the first quadrant of the stress-strain space are open, in disagreement with observed behavior in metals. Recently Valanis introduced a new intrinsic time scale which is a measure of length in the plastic strain space. As a result, a new model of endochronic theory has been developed which leads to closure of hysteresis loops in the small as well as the large. It is also shown that the new model predicts the existence of a yield surface. Hardening rules proposed in the classical theory of plasticity appear as special results.It is also shown that the constitutive equations derived from the new model are very powerful in their quantitative prediction of steady cyclic response under constant strain amplitude conditions. In the case of cyclic creep the theory predicts the dependence of cumulative axial creep on the plastic shear strain amplitude but that it overestimates the dependence of the latter on the number of cycles. At the present time we think that this difficulty cannot be overcome on the basis of an isotropic theory. This suggests a future area of investigation and application of the endochronic theory.     

The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

Overview of recent developments in pellet injection for ITER

Pellet injection is the primary fueling technique planned for core fueling of ITER burning plasmas. Also, the injection of relatively small pellets to purposely trigger rapid small edge localized modes (ELMs) has been proposed as a possible solution to the heat flux damage from larger natural ELMs likely to be an issue on the ITER divertor surfaces. The ITER pellet injection system is designed to inject pellets into the plasma through both inner and outer wall guide tubes. The inner wall guide tubes will provide high throughput pellet fueling while the outer wall guide tubes will be used primarily to trigger ELMs at a high frequency (>15 Hz). The pellet fueling rate of each injector is to be up to 120 Pa m³/s, which will require the formation of solid D–T at a volumetric rate of ～1500 mm³/s. Two injectors are to be provided for ITER at the startup with a provision for up to six injectors during the D–T phase. The required throughput of each injector is greater than that of any injector built to date, and a novel twin-screw continuous extrusion system is being developed to meet the challenging design parameters. Status of the development activities is presented, highlighting recent progress.     

The application of constraint based fracture mechanics to engineering structures

Elastic-plastic crack tip fields can be characterised by two parameters, J and T/Q which describes crack tip constraint. This forms the foundation of a constraint based fracture mechanics in which toughness is expressed as a function of constraint in the form of a J–(T/Q) locus. The enhanced toughness associated with shallow cracks and defects can be used in a systematic manner by constraint matching, and implemented through a simple modification to a failure assessment diagram. This methodology enables the conservatism associated with the use of deeply cracked fracture toughness measurements to be relaxed. In this work these methods have been applied to a tubular welded joint.     

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.     

Application and evaluation of fracture mechanics failure concepts to precracked vessels

The elastic-plastic fracture mechanics concepts R-curve method, Two Criteria Approach, COD concept and Battelle formula were applied on three tested vessels made of low and high tough and fine grained structural steel and X 8 Ni 9 with an axial notch on the outer surface. Apart from the R-curve method for the vessel made of low tough material, failure loads were conservatively calculated. The COD concept could not be applied to these vessels and failure geometries using the well known design curve. A modification of the COD concept by means of FE-calculations was made so that a correlation between the displacement at the crack tip and at the vessel surface could be determined. With this procedure, the calculated load at fracture was only 8% below the experimental result.     

Stress corrosion fracture of zircaloy cladding in fuel rods subjected to power increases: A model for crack propagation and the failure threshold stress

A crack may form and propagate by a stress corrosion mechanism, in the zircaloy cladding of a water cooled fuel rod, if it is subjected to a sufficiently severe power increase (ramp), the likely responsible chemical species being iodine produced by fissioning of the fuel. By formulating and analysing a model, and relating the theoretical predictions to observations on the size of plastic zones associated with a propagating crack, valuable information is obtained concerning the micro-mechanics of stress corrosion fracture in zircaloy; this information is then used as input for a theoretical analysis of crack formation. A model describing the crack formation process is developed and it is shown that the threshold stress can be low in relation to the yield stress of Irradiated zircaloy, a prediction that accords with some recent experimental observations. Implications of the results with respect to both fuel failure predictions and possible cladding improvements by means of texture changes are discussed.     

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.     

The use of fracture mechanics and non-destructive testing to reduce the risk of catastrophic failure

Structural integrity assessments involve the use of fracture mechanics together with appropriate design, quality assurance and inspection techniques. Recent application to nuclear pressure vessels has led to improvements in the fracture toughness data base, in methods for measuring fracture toughness and in the use of elastic/plastic and J?R curve concepts. Fatigue crack growth studies in water of realistic flow rate and oxygen content have shown that the effect of a PWR water environment is not as severe as previously reported and has related this to show strain rate cracking. The role of the pressure test has beenn examined, throwing emphasis on the importance of effective non-destructive inspection to detect and characterise flaws. Recent developments to improve and to validate very high levels of effectiveness of NDT are summarised.     

Application of fracture mechanics in the design and operation of PWRs in France

Fracture mechanics techniques are used to evaluate the risks associated with material aging, the occurrence of fabrication defects or stress corrosion cracks, and to determine the margins with respect to fast fracture resulting from the design and manufacturing practices. Important programs are underway to improve the accuracy and domain of validity of the fracture mechanics methods.     

Recent developments in the field of thermally induced waves and vibrations

The paper presents a review of the work done during the last few years on the dynamic interaction between thermal fields and solid bodies. In most of the problems, elastic behaviour is assumed, but memory effects, both in the mechanical and thermal response (i.e. viscoelasticity and second sound), are also discussed. This reflects the intense interest which has been shown recently in this field, owing to the great practical importance of dynamic effects in modern aeronautics and astronautics, nuclear reactors, high-energy particle accelerators, and its potential importance in cryogenic applications. First, a brief summary of the general theory of continuum thermomechanics is given. Second, problems of thermoelasticity, i.e. problems of thermoelastic coupling and surface and radiation heating, are reviewed. Memory effects in the mechanical or thermal response, i.e. thermoviscoelasticity and second sound, are discussed. Recent generalizations of the Clausius-Duhem inequality are then reviewed, and references are made to thermoplastic and magneto-thermoelastic waves. Finally, general methods of solution are discussed. An extensive bibliography is included.