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.     

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.     

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.     

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.     

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.     

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.     

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.     

Constraint effects on fracture toughness of impact-loaded, precracked Charpy specimens

Impact-loaded, precracked Charpy specimens often play a crucial role in irradiation surveillance programs for nuclear power plants. However, the small specimen size B = W = 10 mm limits the maximum value of cleavage fracture toughness J_c that can be measured under elastic—plastic conditions without loss of crack tip constraint. In this investigation, plane strain impact analyses provide detailed resolution of crack tip fields for impact-loaded specimens. Crack tip stress fields are characterized in terms of J—Q trajectories and the toughness-scaling model which is applicable for a cleavage fracture mechanism. Results of the analyses suggest deformation limits at fracture in the form of b > MJ_c/σ₀, where M approaches 25–30 for a strongly rate-sensitive material at impact velocities of 3–6 m s⁻¹. Based on direct comparison of the static and dynamic J values computed using a domain integral formulation, a new proposal emerges for the transition time, the time after impact at which interial effects diminish sufficiently for simple evaluation of J using the plastic η factor approach.     

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.     

Fracture mechanics concepts for evaluation of irradiated reactor pressure vessel material behavior

Within the German research program Forschungsvorhaben Komponentensicherheit (FKS), irradiation experiments were performed with ferritic reactor pressure vessel (RPV) steels and welds. The materials cover a wide range of chemical composition and initial toughness to achieve different susceptibility to neutron irradiation. Different neutron flux was applied and the neutron exposure extended up to 8×10¹⁹ cm⁻². The change in material properties was determined by means of tensile, Charpy impact, drop-weight and fracture mechanics tests, including crack arrest. The results have provided more insight into the acting embrittlement mechanisms and shown that the fracture mechanics concept of the Code provides in general an upper bound for the material which can be applied in the safety analysis of the RPV.     

The influence of loading rate on fracture resistance of notched and precracked ISO-V-specimens

Higher loading rates are expected to have a disadvantageous influence on fracture parameters. This opinion derives probably from experience with ductile-cleavage transition whose temperature increases with increasing loading rate. As far as results on the influence of loading rate on crack resistance are published in the literature they show mostly increasing initiation values as well as increasing crack resistance with increasing loading rate.The paper deals with the influence of loading rate on fracture resistance of notched and precracked ISO-V-specimens measured on different materials. The crack resistance of notched specimens has been determined in analogy to that one of the precracked specimens. The influence of loading rate was separately investigated with regard to initiation as well as to tearing modulus.The results demonstrate that the ratio of dynamic to quasi-static values decreases with increasing toughness, the initiation values for dynamic loading may drop at high toughness below those for quasi-static loading, the slope of the crack resistance curve for dynamic loading is mostly larger than for quasi-static loading and the ISO-V-specimens fall well into line with the results of valid tests.     

Hydrogen assisted failure of precracked specimens of 316L stainless steel

The simultaneous action of cathodic hydrogen charging and slow mechanical loading on precracked samples of 316L stainless steel is examined in order to assess the flaw tolerance of this steel, which has been included in the group of possible structural materials for the first wall of the future fusion reactors. The steel is shown to retain a significant part of its flaw tolerance even in the most severe test conditions, but the loading rate is found to change the damage phenomenology of hydrogen from bifurcated crack extension to multi-cracking and enlargement of the blunted crack tip. This change is explained on the basis of a competition mechanism between hydrogen action and mechanical deformation.     

Elastic-plastic FEM-analysis of a nozzle corner crack and discussion of the results by some fracture mechanics concepts

This paper presents the results of an elastic-plastic threedimensional finite element analysis for a nozzle corner crack in a pressurized reactor test vessel. The calculations were performed by the finite element program ADINA incorporating von Mises' yield condition and isotropic hardening. The crack plane was taken parallel to the axis of the vessel and the crack front straight and perpendicular to the symmetry line of the nozzle corner in order to obtain the worst position for a nozzle corner crack. The calculations were performed up to that pressure level where general yield of the ligament in the nozzle corner section takes place. The results of the finite element analysis are compared with figures obtained from analytical procedures of elastic-plastic fracture mechanics.     

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 moiré methods in experimental fracture mechanics

This report deals with the basis of the Moiré method for strain analysis, crack edge rotation and crack opening measurement (COD determination) demonstrated here within the scope of the experimental fracture mechanics. The practical performance of new, simple methods, and how to generate a mismatch are described in detail. The advantages and disadvantages as well as the limits of the Moiré method are shown and compared with different methods used in experimental deformation measurement.     

Characteristics relevant to ductile failure of bimetallic welds and evaluation of transferability of fracture properties

Life management and structural integrity assessment of bimetallic welds in its state-of-the-art form relies on practical methods derived on the basis of years of experience in operation and simplistic strength of materials analyses. The complex conditions and properties of the weldment, as resulting from the elaborate interaction of different microstructures with gradients in material properties, have limited the ability of currently existing methods to construct the assessment on the basis of actual failure mechanisms of bimetallic welds. Current work addresses the assessment procedure by combining experimental and numerical fracture mechanics comprising a micro-mechanical evaluation of the relevant damage mechanisms. The studied dissimilar ferrite (SA508)–austenite (AISI 304) circumferencial weld is one with a Ni-enriched buttering layer.The experimental work comprises tensile and fracture mechanical characterization of the different microstructural zones of the bimetallic weld. Tensile properties are determined with microstructure specific flat bar specimens as well as round bar specimens enabling better inference of true stress–strain curves. Fracture resistance curves are established by applying small-specimen testing techniques. Different crack configurations are modeled by finite element analysis (FEA) to assess the relationships between fracture types, toughness and local near crack tip constraint parameters. Transferability and characterization question are considered by determining J–Q-trajectories and employing small-scale yielding corrections (SSYCs). On the basis of the experimental and numerical results and a fractographical investigation, the micromechanics of fracture are interpreted. Differences in strain hardening capacities of microstructural zones are found to most severely affect the toughness transitions of the weld and the associated failure modes. Two prime failure types are noted, one for cracks located at outer heat affected zone (HAZ) resulting in an unstable crack deflection towards the fusion line (FL) and another type associated with cracks positioned near the fusion line, wherein a low-toughness ductile fracture process results. Small fracture mechanics specimen is found applicable for fracture resistance determination of bimetallic weldments.     

Effect of prior crack growth on cleavage fracture of low toughness precracked Charpy specimens

Cleavage fracture of reactor pressure vessel steels in the upper ductile to brittle transition region generally occurs with prior significant ductile crack growth. For low upper shelf materials and using PreCracked Charpy v-notch (PCCv) specimens that can be obtained from conventional surveillance programs, the effect of prior crack growth could be particularly important. In practice, the shape of the Master Curve and the failure distribution could be affected by ductile crack growth. To quantify the effect in practical applications, the effect of prior ductile on cleavage is evaluated on PCCv specimen.The methodology use finite element calculations to grow a ductile crack and infer the brittle failure probability using the local approach to fracture. It is found that for very low upper shelf toughness materials, ductile crack growth enhances the failure probability, induces a steeper failure distribution and affects the shape of the Master Curve. However, for low toughness materials, the enhanced failure probability due to crack growth is compensated by loss of constraint.     

Prediction of lower bound fracture toughness for lifetime evaluation of reactor pressure vessels

The potential damage of embrittlement in service is a very important problem of MnMoNi steels used for the nuclear reactor pressure vessel. A decrease of critical flaw size may occur when embrittlement proceeds. The remaining lifetime of the reactors should be assessed taking into account the embrittlement of the steel paying special attention to the degradation of dynamic fracture toughness. The present study introduces the basic concept of the remaining lifetime assessment. Examined was a small specimen fracture toughness test for measuring the dynamic fracture toughness of nuclear reactor pressure vessel (RPV) steels. The result was applied in the measurement of the dynamic fracture toughness of 12 heats of RPV steels. The test results were analyzed to find more practical applications and a method is presented to predict the lower bound dynamic fracture toughness using the Charpy impact test and tensile test results.     

Critical parameter study of PWR primary coolant pipe leak failure using probabilistic fracture mechanics

This paper discusses the critical parameters which influence the failure probabilities of a PWR primary coolant loop. Probabilistic fracture mechanics (PFM) is applied for the parametric study, using the Monte Carlo program PRAISE to predict the failure probabilities of a PWR primary coolant loop from various distributions of input parameters. Parameters such as nondetection probability of preservice and inservice inspection, vibratory stress, residual stresses, and their correlations are extensively studied. Critical crack depth which causes immediate failure are calculated in the presence of various vibratory stresses with and without residual stresses. Crack growth schemes are determined with various initial defect depth and depth-length ratio as a function of plant operation time. The results show quantitatively how PWR primary coolant loop reliability can be greatly improved by increasing the sensitivity and decreasing the uncertainty of preservice nondestructive inspection.