Results of probabilistic fracture mechanics analyses for pressurized thermal shock transients in the reactor pressure vessel of BIBLIS-B

Probabilistic fracture mechanics investigations of the contribution of pressurized thermal shock transients to reactor pressure vessel failure probability of the reference plant for the German reactor safety study phase B, BIBLIS-B, are presented. The applied methods and the calculation model are discussed. The most important result of parametric analyses is that the postulated flaw distribution in the vessel has a dominant influence on the calculated conditional failure probability. With regard to the transient behavior the results show, that the temperature drop induced by the thermal shock has great influence on the conditional failure probability, whereas the decay rate of the temperature change has minor influence.     

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.     

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.     

Elastic-plastic fracture mechanics analysis of a pressure vessel with an axial outer surface flaw

The stress and strain state in pressure vessel containing an axial semi-elliptical surface flaw is analyzed by elastic-plastic finite element (FE) calculations. The variation of J along the crack front is presented. Stresses and strains in the vicinity of the surface flaw are compared with those of a compact specimen of the same material at a similar J level. The FE results are taken to examine the ductile crack growth obtained in a vessel test and to discuss the validity of J-controlled crack growth. It is shown that the local constraint of the component affects the crack resistance significantly and that, therefore, J_R-curves have to account for the varying triaxiality of the stress state. This improved two parameter approach yields a much better prediction of the stable crack growth and, especially, is able to describe the canoe shape of the surface crack.     

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 analysis of a pressure vessel with a semi-elliptical surface crack using elastic-plastic FEM-calculations

Results of an elastic-plastic three dimensional finite element analysis for a semi-elliptical surface crack inside a pressure vessel is presented. The calculations were performed by the finite element program ADINA, incorporating von Mises yield condition and isotropic hardening. The calculations were performed up to that pressure level where general yield of the ligament takes place. The results of the finite element analysis are compared with figures obtained from analytical procedures of elastic as well as of elastic-plastic fracture mechanics.     

Irradiation effects on fracture toughness of four nuclear reactor pressure vessel submerged-arc welds

This study applies statistical analyses to fracture toughness results for four irradiated “current practice” submerged-arc welds and an A533 grade B class 1 plate. Charpy V-notch, tensile, and 25 mm thick compact specimens were irradiated at 288°C to neutron fluences of 0.7 to 2.0 × 10²³ neutrons/m² (>1 MeV). The plate material contained 0.14% Cu and 0.67% Ni. The four submerged-arc welds contained 0.04 to 0.12% Cu and 0.10 to 0.63% Ni. The plate material showed a Charpy V-notch impact transition temperature increase of 68°C, and a Charpy V-notch upper-shelf energy drop of 16%. The four submerged-arc welds showed smaller changes than the plate material did. The fracture toughness results from the 25 mm thick compact specimens showed approximately the same temperature shift as the Charpy V-notch results. The results imply that submerged-arc welds with both low-copper and low-nickel contents can exhibit essentially zero radiation embrittlement and that nickel can contribute to radiation embrittlement even when the copper content is low.     

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.     

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.     

A direct fracture toughness model for irradiated reactor vessel weld material based on reference temperature

The master curve method has opened a new means to acquire a directly measured material-specific fracture toughness curve based on testing a small number of replicate specimens. This process enables, for the first time, the construction of a material-specific fracture toughness curve for an irradiated material directly from fracture tests. Currently, only an inferred fracture model is available through a combination of the ASME Boiler and Pressure Vessel Code and a regulatory guide from the U.S. Nuclear Regulatory Commission. This approach uses the fracture toughness curve of a generic, unirradiated reactor vessel steel that is shifted by a reference temperature (RT_NDT) based on Charpy impact test data. The master curve method yields a key material parameter called reference temperature, T₀, which indicates the location of the transition range fracture toughness curve on the temperature axis. When a small number of pre-cracked Charpy specimens were tested at several different fluence levels, the material specific reference temperatures can be shown as a function of fluence. One such model for the WF-70 weld material is presented in this paper. The irradiated specimen data and analyses from Oak Ridge National Laboratory (ORNL) and the B&W Owners Group (B&WOG) are utilized for this model. This model is based on fracture toughness data, independent of Charpy impact energy levels, percent shear, and most importantly, material properties of unirradiated condition.     

A probabilistic method for leak-before-break analysis of CANDU reactor pressure tubes

In modern CANDU nuclear generating stations, pressure tubes of cold-worked Zr-2.5Nb material are used in the reactor core to contain the fuel bundles and the heavy water (D₂O) coolant. The pressure tubes operate at an internal pressure of 10 MPa and temperatures ranging from 250°C at the inlet to 310°C at the outlet. Over the expected 30 year lifetime of these tubes, they would be subjected to a total fluence of 3×10²⁶ n m⁻². In addition, these tubes gradually pick up deuterium as a result of a slow corrosion process. When the hydrogen plus deuterium concentration in the tubes exceeds the hydrogen/deuterium solvus, the tubes are susceptible to a crack initiation and propagation process called delayed hydride cracking (DHC). If undetected, such a cracking mechanism could lead to unstable rupture of the pressure tube. The service life of the pressure tubes is determined, in part, by changes in the probability for the rupture of a tube. This probability is made up of the probability for crack initiation by DHC multiplied by the sum of the probabilities of break-before-leak and leak-before-break (LBB). A probabilistic model, BLOOM, is described which makes it possible to estimate the cumulative probabilities of break-before-leak and LBB. The probability of break-before-leak depends on the crack length at first leak detection and the critical crack length. The probability of a LBB depends on the shut-down scenario used. The probabilistic approach is described in relation to an example of a possible shut-down scenario. Key physical input parameters into this analysis are pressure tube mechanical properties, such as the crack length at first coolant leakage, the DHC velocity and the critical crack length. Since none of these parameters are known precisely, either because they depend on material properties, which vary within and between pressure tubes, and/or because of measurement errors, they are given in terms of their means and standard deviations at the different temperatures and pressures defined by the shut-down scenario.     

Round robin analysis of pressurized thermal shock for reactor pressure vessel

A comparative assessment study is performed here for deterministic fracture mechanics analysis of a pressurized thermal shock (PTS). A round robin problem is proposed using the data available in Korea and all organizations interested in the PTS analysis are invited. The problems consisting of two transients and 10 cracks are solved and their results are compared to generate a reference solution that could serve as benchmarks for future qualification of analytical method. Nine participants from seven organizations responded to the problem and their results are compiled in this paper.     

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.     

Experience of the integrity assessment of the highly embrittled reactor pressure vessel for the life extension

The reactor pressure vessel (RPV) is the key component of pressurized water reactor. It has to comply with various rules and regulatory guides to ensure sufficient safety and operating margins during the plant lifetime. Thus, it is crucial to assure the integrity of RPV for an effective plant lifetime management program. In this paper, the status and the experiences of various integrity issues of the highly embrittled RPV are introduced. A circumferential weld in the beltline region of the Kori Unit 1 RPV was projected to be unable to satisfy the minimum upper-shelf energy requirement and the reference temperature-pressurized thermal shock requirement before the end of 40-year design lifetime. The detailed integrity assessments had been performed to resolve both issues and the results summarized. In addition several actions have been taken as aging management programs to assure the integrity of Kori Unit 1 RPV during the extended operation. Details of the activities such as, redefining initial reference temperature-nil ductility transition temperature, installing ex-vessel dosimetry, and withdrawal and testing of additional surveillance capsule are explained. Finally, the applicability of these and other activities including thermal annealing to mitigate the effects of the irradiation embrittlement are evaluated.     

An engineering fracture mechanics analysis of the Pilgrim I nozzle-to-pressure vessel weld discontinuities

The influence function method for calculation of stress intensity factor K_I(a) is applied to the case of a semicircular surface crack, of radius a, used to model a discontinuity revealed by in-service inspection of a nozzle-to-shell weld in the Pilgrim I pressure vessel. Results of the analysis are discussed in detail.     

The coolability limits of a reactor pressure vessel lower head

Configurations II and III of the ULPU experimental facility are described, and results from a comprehensive set of experiments are provided. The facility affords full-scale simulations of the boiling crisis phenomenon on the hemispherical lower head of a reactor pressure vessel submerged in water, and heated internally. Whereas Configuration I experiments (published previously) established the lower limits of coolability under low submergence, pool-boiling conditions, with Configuration II we investigate coolability under conditions more appropriate to practical interest in severe accident management; that is, heat flux shapes (as functions of angular position) representative of a core melt contained by the lower head, full submergence of the reactor pressure vessel, and natural circulation. Additionally, with Configuration III, we examine the effect of a channel-like geometry created by the reactor vessel thermal insulation. Critical heat fluxes as a function of the angular position on the lower head are reported and related to the observed two-phase flow regimes.     

Deformation analysis of a 900 MW reactor pressure vessel head by means of holographic interferometry

During pressure build-up in a 900 MW reactor pressure vessel, the head of the vessel was holographed. It will be shown how a maximum of information can be extracted from the hologram using computer generated interferograms. Based on a trial and error method the deformation assumption for the head is altered until a best correlation is reached between computer generation and experiment.     

Monitoring the embrittlement of reactor pressure vessel steels by using the Seebeck coefficient

The degree of embrittlement of the reactor pressure vessel (RPV) limits the lifetime of nuclear power plants. Therefore, neutron irradiation-induced embrittlement of RPV steels demands accurate monitoring. Current federal legislation requires a surveillance program in which specimens are placed inside the RPV for several years before their fracture toughness is determined by destructive Charpy impact testing. Measuring the changes in the thermoelectric properties of the material due to irradiation, is an alternative and non-destructive method for the diagnostics of material embrittlement. In this paper, the measurement of the Seebeck coefficient () of several Charpy specimens, made from two different grades of 22 NiMoCr 37 low-alloy steels, irradiated by neutrons with energies greater than 1 MeV, and fluencies ranging from 0 up to 4.5 × 10¹⁹ neutrons per cm², are presented. Within this range, it was observed that increased by ≈500 nV/°C and a linear dependency was noted between and the temperature shift ΔT_41 J of the Charpy energy vs. temperature curve, which is a measure for the embrittlement. We conclude that the change of the Seebeck coefficient has the potential for non-destructive monitoring of the neutron embrittlement of RPV steels if very precise measurements of the Seebeck coefficient are possible.     

Three-dimensional transient sealing analysis of the bolted flange connections of reactor pressure vessel

The failure of sealing system of the bolt flange connections is the primary failure mode of the nuclear reactor pressure vessel (RPV). For the safety and integrity of RPV, it is important to predict the sealing behaviour of the bolt flange connections under various loading conditions. Based on the finite element (FE) method for coupled thermal elastoplastic contact problems, a three-dimensional (3D) transient sealing analysis program of nuclear reactor pressure vessels is developed with the consideration of the non-linearity from both surface and material, transient heat transfer and multiple coupled effects. A contact correction approach is proposed to simulate the loading of the bolt connection under the condition of pre-stressing. An automatic pre-processing program is developed for FE modelling of RPVs. Using these programs, a 1:4 scaled model of a 300 MW RPV is analyzed under the loading conditions including pre-stressing, pressurization, heating and cooling. The computational results obtained are in a good agreement with the data of experimental tests. These programs are also successfully used in analyzing the full-scale model of the RPV in a nuclear power plant.