A probabilistic approach to update lower bound threshold stress intensity factor (KIH) for delayed hydride cracking

Zirconium alloys are susceptible to a stable cracking process called delayed hydride cracking (DHC), which can compromise the integrity of pressurized components in the nuclear reactor. Therefore, the fitness for service assessment of pressure retaining components requires demonstrating that there is sufficient margin against the rupture. The CSA-Standard N285.8 specifies a lower-bound value of the threshold stress intensity factor (K_IH) that would provide adequate protection against fracture that can potentially originate from existing cracks. Since fracture toughness is a variable material property, a probabilistic approach is necessary to establish the lower bound of K_IH. The paper presents a probabilistic definition of the lower bound K_IH, and its Bayesian interpretation to address both aleatory and epistemic uncertainties. The paper proposes a new method to update the lower bound K_IH as new surveillance data become available from the testing of components removed from operating reactors. A concept of a control chart is introduced to support the disposition of new surveillance data. The main advantage of the proposed approach is that it provides a practical, risk-informed basis for fracture toughness assessment of pressurized components.     

New stress intensity factor solutions for an elliptical crack in a plate

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work was conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes), which is also of practical importance, has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension.This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and free surface proximity (a/d ratio, where d is the distance from the center of the ellipse to the closest free surface). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18,000 to 26,000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension).These solutions have been introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.     

Review of the thermodynamic basis for models of delayed hydride cracking rate in zirconium alloys

A review is given of the thermodynamic basis of a model developed by Dutton and Puls for the rate of subcritical crack propagation by delayed hydride cracking in zirconium alloys. This review was prompted, in part, by the publications of a series of recent papers by Kim and co-workers in which it is claimed that the thermodynamic basis of the Dutton and Puls model and its subsequent refinements is incorrect, prompting them to propose a new model. This review demonstrates the validity of the original model and shows the origin of the error made by Kim in claiming that the Dutton and Puls model was incorrectly formulated. It also explains the reasons why Kim’s new delayed hydride cracking model is incorrect. This review was further prompted by the author’s realization that the series of papers documenting the development of the various versions of the original Dutton and Puls model contain typographical errors, differences in sign convention, differences in input data, minor errors and/or changes in formal representation as well as occasional misleading, confusing or incorrect statements of the physical significance of the thermodynamic basis of the model. All of these shortcomings could have resulted in misunderstandings regarding the correct formulation of the model and the physical significance of the results. Therefore another important purpose of this review is to provide an updated treatment of the original version that puts all subsequent versions of the DHC model on a consistent thermodynamic basis.     

Crack growth pattern and threshold stress intensity factor, KIH, of Zr–2.5Nb alloy with the notch direction

The objective of this study is to obtain a better understanding of the threshold stress intensity factor for an initiation of delayed hydride cracking (DHC) in a Zr–2.5Nb pressure tube. By changing the crack propagation from the longitudinal direction to the circumferential direction, the threshold stress intensity factor, K_IH, and the crack growth pattern were investigated in the Zr–2.5Nb pressure tube with a strong circumferential texture. The threshold stress intensity factor, K_IH, was discussed phenomenologically based on the crack growth pattern and analytically as a function of the tilting angle of hydride habit planes to the cracking plane. A supplementary experiment was conducted to demonstrate a linear decrease of K_IH with an increase in the basal pole component in the cracking plane. Thus, it is concluded that the DHC is controlled by the nucleation and growth of the hydride precipitates on the habit plane.     

Threshold conditions for iodine-induced stress corrosion cracking of unirradiated zircaloy-4 tubing under internal pressurization

The results are presented of stress corrosion cracking (SCC tests in which nuclear power reactor grade zircaloy-4 tubing specimens were internally pressurized with a mixture of helium and iodine at ($\text{633 ± 5}$) K. Both as-received and artificially preflawed specimens were tested at an initial iodine availability of ~60 g/m² zircaloy surface. It is shown that the failure times in these tests correlate more reliably with hoop stress than with nominal stress intensity or failure strain, and that a threshold hoop stress of ~295 MPa exists for SCC failure within test times up to 605 ks. The origin of this threshold stress is discussed and it is concluded that the observed behavior is consistent with either a critical stress or a critical strain rate being required for the formation of iodine-induced stress corrosion cracks in unirradiated zircaloy tubing.     

Simulation of stress corrosion cracking behavior in a tube-shaped specimen of nickel-based alloy 600

Stress corrosion cracking (SCC) simulation code has been developed for the evaluation of SCC behavior in specimens in the shape of field components. The code utilizes numerical calculation of stress/strain states at a crack tip using finite element methods and a formula describing the crack tip reaction kinetics containing unknown environmental parameters. The applicability of this simulation code was investigated by applying the code to the evaluation of SCC behavior in a mock-up of a bottom mounted instrumentation tube for a pressurized water reactor subjected to complex stress/strain states. The results indicate that crack growth rate in a component suffering from certain environments can be estimated using the developed SCC simulation code with pre-determined unknown parameters, using the experimental crack growth rate data measured on other specimens in the same environment.     

The effect of Nb additive on Te-induced stress corrosion cracking in Ni alloy: a first-principles calculation

Nb can improve the resistance of Ni-based Hastelloy N alloy to Te-induced intergranular embrittlement. First-principles calculations are performed to research this mechanism by simulating the Ni（111） surface and the ∑ 5（012） grain boundary. The calculated adsorption energy suggests that Te atoms prefer diffusing along the grain boundary to forming the surface-reaction layer with Nb on surface of the Ni alloy. First-principles ten- sile tests show that the Nb segregation can enhance the cohesion of grain boundary. The strong Nb-Ni bonding can prevent the Te migration into the inside of the alloy. According to the Rice-Wang model, the strengthen- ing/embrittling energies of Nb and Te are calculated, along with their mechanical and chemical components. The chemical bonds and electronic structures are analyzed to uncover the physical origin of the different effects of Te and Nb. Our work sheds lights on the effect of Nb additive on the Te-induced intergranular embrittlement in Hastelloy N alloy on the atomic and electronic level.     

Comparison of stress intensity factor solutions for cylinders with axial and circumferential cracks

Numerous stress intensity factor solutions have been proposed so far depending on the objects of evaluation including the variations of structures, cracks, and applied loads. In applying the flaw evaluation methodology to components of nuclear power plants, the use of reliable stress intensity factor solutions is essential. In this study, cracked cylinders were focused on as one of the typical configurations in actual plants. Existing stress intensity factor solutions for cracked cylinders were reviewed, and the accuracy of these solutions was investigated thorough the comparison with each other. Specific solutions were then recommended for cylindrical structures. Approximate expressions were newly derived for axially through-wall cracked cylinder subjected to linear stress distribution and for circumferentially through-wall cracked cylinder subjected to bending to realize simple evaluation of stress intensity factor. Considering that the cylindrical structures are often replaced with flat plates in the evaluation of actual components, the propriety of the replacement was also studied.     

Fatigue and fracture emanating from notch; the use of the notch stress intensity factor

The analysis of the stress distribution at notch tip shows a pseudo-stress singularity characterised by the notch stress intensity factor (NSIF) K_ρ. The critical value of this parameter K_ρ^ccan be used to determine the fracture toughness of very brittle materials from notched specimens. The range of the notch stress intensity factor ΔK_ρ plays an important role in initiation of fatigue emanating from notches and in the notch fatigue sensitivity index.     

Investigation of the growth rate of cracks in shells made of the alloy Zr-1%Nb under conditions of iodine corrosion cracking under stress

Conclusions A method has been developed to determine the growth rate of a crack under conditions of iodine corrosion cracking of Zr-1%Nb claddings under stress. The dependence of the growth rate a crack on the stress-intensity factor in Zr-1%Nb claddings was determined and the threshold stress-intensity factor, equal to 4.8 MPa·m^1/2, was determined. Main Science Center of the Russian Federation — A. A. Bochvar All-Russia Scientific-Research Institute of Standardization in Machine Engineering. Translated from Atomnaya énergiya, Vol. 80, No. 2, pp. 87–91, February, 1996.     

Stress intensity factor evaluation of a circumferential crack in a finite length thin-walled cylinder for arbitrarily distributed stress on crack surface by weight function method

A weight function to evaluate the stress intensity factor (SIF) of a circumferential crack, subjected to arbitrarily distributed stress on the crack surfaces, in a finite length thin-walled cylinder was derived based on the closed form SIF equation previously developed by the authors. It is easy to evaluate the effects of structural parameters and stress distribution on the SIF with this weight function. Numerical examples confirmed the validity of the weight function. These examples showed that the effect of cylinder length on the SIF is quite large.     

Stress intensity factors for complete circumferential surface cracks at the outer wall of a pipe loaded by stress gradients

Stress intensity factors were calculated for complete circumferential surface cracks at the outer wall of a pipe by means of the weight functions method. The pipe with an inner radius to wall thickness ratio of 10 is loaded by axial tensile stress varying through the wall. The results are compared to stress intensity factors of circumferential cracks at the inner wall of a pipe.     

Calculation of the stress concentration factor for semi-elliptical cracks between a nipple and the reactor vessel

Moscow Engineering Physics Institute. Gidropress Special Design Office. Translated from Atomnaya Énergiya, Vol. 73, No. 2, pp. 87-91, August, 1992.     

Specifications and qualification of uranium/aluminum alloy plate target for the production of fission molybdenum-99

In all probability, the same criteria applied to evaluate the safety of the reactor fuel shall be used to evaluate the safety of the targets used for the production of fission molybdenum-99. Thus, neutronic and thermal hydraulics considerations will dictate the maximum power of the targets, their uranium content, and the uniformity requirements for their loading. Radiography technique is capable of characterizing both meat location and density. Specifically, target plates that meet fuel density specifications can be irradiated with little risk of power peaking and hot spots. An adequate characterization and qualification of target plate cladding is also critical, because cladding breaches will contaminate the reactor coolant. Bend testing is a dependable way of testing bond strength while Ultrasonic Testing (UT) examinations qualify both bonding homogeneity and minimum thickness of that cladding. The bonding quality is inspected by means of a blister test. Lastly, optical microscopy is applied for clad thickness, which further supports the veracity of the UT characterization method. Natural U/Al alloy plate targets have been safely irradiated in the core of Pakistan Research Reactor-1.     

A study of the stress intensity factors for single or multiple cracks in thick-walled cylinders

The variation of stress intensity factors of a single semi-elliptical crack and multiple semi-elliptical cracks which are radial symmetric or unsymmetric array in an internal pressurized thick-walled cylinder is studied by use of the “frozen-stress” photo-elastic method. The method of determining mixed-mode stress intensity factors K_I and K_II is given. By means of experimental results and the relative results of other authors, the approximate expression for evaluating stress intensity factors of straight border, semi-circular, semi-elliptical internal surface cracks in thick-walled cylinders are presented.     

Microstructure of the Kh18N10T steel irradiated in a BOR-60 reactor

Khar'kov Physical-Technological Institute (KhFTI). V. I. Lenin Scientific-Research Institute of Nuclear Reactors (NIIAR). Translated from Atomnaya Énergiya, Vol. 70, No. 3, pp. 159–163, March, 1991.