Influences of the dynamic strain aging on the J–R fracture characteristics of the ferritic steels for reactor coolant piping system

The leak-before-break (LBB) design of the piping system for nuclear power plants has been based on the premise that the leakage due to the through-wall crack can be detected by using leak detection systems before a catastrophic break. The piping materials are required to have excellent J–R fracture characteristics. However, where ferritic steels for reactor coolant piping systems operate at the temperatures where dynamic strain aging (DSA) could occur, the fracture resistance could be reduced with the influence of DSA under dynamic loading. Therefore, in order to apply the LBB design concept to the piping system under seismic loading, both static and dynamic J–R characteristics must be evaluated.Materials used in this study are SA516 Gr.70 for the elbow pipe and SA508 Cl.1a for the main pipe and their welding joints. The crack extension during the dynamic and the static J–R tests was measured by the direct current potential drop (DCPD) and the compliance method, respectively. This paper describes the influences of the dynamic strain aging on the J–R fracture characteristics with the loading rate of the pipe materials and their welding joints.     

A review of the ASME low upper shelf toughness evaluation procedures for nuclear reactor pressure vessels

The ASME Section X1 Working Group on Flaw Evaluation has proposed criteria for the evaluation of reactor pressure vessel beltline materials which have an upper shelf energy less than 50 ft-lbs (69 J). These criteria have been assessed and applied to Linde 80 weld materials in recent investigations; this assessment and evaluation are described in the paper.

A key element in the evaluation procedure is the J_R curve for the relevant material. Recent experimental studies have demonstrated that the J_R curve is size dependent for some materials, in the sense that the J_R curve slope decreases with increasing specimen thickness. This paper assesses this experimental work and discusses it in the context of the integrity of nuclear reactor pressure vessels.     

Statistical re-evaluation of the ASME KIC and KIR fracture toughness reference curves

Historically the ASME reference curves have been treated as representing absolute deterministic lower bound curves of fracture toughness. In reality, this is not the case. They represent only deterministic lower bound curves to a specific set of data, which represent a certain probability range. A recently developed statistical lower bound estimation method called the ‘Master curve’, has been proposed as a candidate for a new lower bound reference curve concept. From a regulatory point of view, the master curve is somewhat problematic in that it does not claim to be an absolute deterministic lower bound, but corresponds to a specific theoretical failure probability that can be chosen freely based on application. In order to be able to substitute the old ASME reference curves with lower bound curves based on the master curve concept, the inherent statistical nature (and confidence level) of the ASME reference curves must be revealed. In order to estimate the true inherent level of safety, represented by the reference curves, the original database was re-evaluated with statistical methods and compared to an analysis based on the master curve concept. The analysis reveals that the 5% lower bound master curve has the same inherent degree of safety as originally intended for the K_IC-reference curve. Similarly, the 1% lower bound master curve corresponds to the K_IR-reference curve.     

A faster procedure for the calculation of the J(ξ, β) function

One of the biggest difficulties in obtaining an analytical expression for the J(ξ, β) function is its explicit dependence on the Doppler broadening function ψ(x,ξ). The objective of this paper is to present a method for the fast and accurate calculation for the J(ξ, β) function based on the recent advances in the calculation of the Doppler broadening function and on a systematic analysis of its integrand. The methodology proposed uses an analytical formulation for the calculation of ψ(x, ξ) and a representation in series for error functions with complex argument. The results were satisfactory from the accuracy and processing time standpoint and are an option to other calculation methods found in the literature.     

JR curves of the low alloy steel 20 MnMoNi 5 5 with two different sulphur contents in oxygen-containing high temperature water at 240°C

J_R curves of the low alloy steel 20 MnMoNi 5 5 with two different sulphur contents (0.003 and 0.011 wt.%) were determined at 240°C in oxygen-containing high temperature water as well as in air. The tests were performed by the single-specimen unloading compliance technique at load line displacement rates from 1 × 10⁻⁴ down to 1 × 10⁻⁶ mm s⁻¹ on 20% side-grooved 2T CT specimens in an autoclave testing facility at an oxygen content of 8 ppm and a pressure of 7 MPa under quasi-stagnant flow conditions.In the case of testing in high temperature water, remarkably lower J_R curves than in air at the same load line displacement rate (1 × 10⁻⁴ mm s⁻¹) were obtained. A decrease in the load line displacement rate as well as an increase in the sulphur content of the steel caused a reduction of the J_R curves. At the fastest load line displacement rate a stretch zone could be detected fractographically on the specimens tested in air and in high temperature water and consequently J_i could be determined. When testing in high temperature water, the J_i value of the higher sulphur material type decreases from 45 N mm⁻¹ in air to 3 N mm⁻¹, much more than that of the optimized material type from 51 N mm⁻¹ in air to 20 N mm⁻¹ at 1 × 10⁻⁴ mm s⁻¹.     

Implementation and assessment of the renormalization group (RNG), quadratic and cubic non-linear eddy viscosity k– models in GOTHIC

In GOTHIC, the standard k– model is used to model turbulence. However, for practical reasons, one usually employs relatively large meshes near physical boundaries (walls). In an attempt to enhance the turbulence modelling in the code for simulation of mixing driven by highly buoyant discharges, in the framework of this simplified approach appropriate for containment analysis codes, we have implemented three additional models which are modifications/extensions of the standard k– model: the renormalization group k– model, and the non-linear (quadratic and cubic) eddy viscosity k– models. These models which for the time being, are only implemented in the ‘gas’ phase, were tested with different simple test-problems and their predictions were compared to the corresponding ones of the standard k– model. Furthermore, a simple study was performed to assess the sensitivity of the predictions to the mesh size.     

The spherical harmonics method for the multigroup transport equation in x−y geometry

A spherical harmonics equation in the form of a second-order differential equation is derived for the 2-D x−y geometry, including higher-order scattering within a group. Using this equation, a multigroup transport code for the spherical harmonics method of a general order of approximation is developed. Some numerical examples, including typical problems for the ray effect, are presented and compared with those obtained by the discrete-ordinates method. It is shown that the present method gives more accurate results than the discrete-ordinates method, although this spherical harmonics code requires more computer memory than the discrete-ordinates code.     

Evaluations of the Irwin βIc adjustment for small specimen fracture toughness data

Thickness size effects and large amounts of data scatter often occur in the cleavage fracture toughness testing of steel. It is shown that the Irwin β_Ic equation provides an effective adjustment for thickness size effects as well as reduces data scatter. Examples of applying the Irwin β_Ic adjustment to both static and dynamic toughness data are given. The significance of cleavage microcracking in the initiation of fast fracture is discussed and it is reasoned that this phenomenon is closely related to the sensitivity of the cleavage fracture toughness to triaxiality and strain rate.     

Use of load path dependent material fracture toughness values (WPS) in the safety analysis of RPV stade

The effect of warm prestressing (WPS) has been investigated for the specific material and loading conditions of the central circumferential weld of the reactor pressure vessel of KKS under emergency core cooling. Warm prestressing results in a significant rise of effective fracture toughness. The magnitude of the WPS-effect as a function of warm prestressing, path of unloading, amount of cooling (e.g. change of yield stress) can be predicted on the basis of a theoretical model of Chell et al.. Crack initiation can be excluded for emergency core cooling (ECC)-loading and for material conditions beyond end of life for the central circumferential weld of the pressure vessel of KKS.     

Effects of thermal aging on the low cycle fatigue behavior of austenitic–ferritic duplex cast stainless steel

Thermal aging is observed in a primary reactor cooling system (RCS) made of cast stainless steel. The observation occurs when the RCS is exposed for a long period of time to a reactor operating temperature between 290 and 330°C. An investigation of the effect of thermal aging on the low cycle fatigue characteristics of CF8M is required. The purpose of the present investigation is to find the effect of thermal aging of CF8M on a low cycle fatigue life. The specimen of CF8M is prepared by an artificially accelerated aging technique maintained for 300 and 1800 h at 430°C, respectively. The low cycle fatigue tests for the virgin and two aged specimens are performed at room temperature for the strain amplitudes (_ta) of 0.3, 0.5, 0.8, 1.0, 1.2 and 1.5%. In the experiment, it is found that the fatigue life is rapidly reduces with an increase of aging time. The experimental fatigue life estimation formula, between the virgin and two aged specimens are obtained.     

Measurements of the (n, np+d) activation cross sections with 13.4–14.9 MeV neutrons using a fusion neutronics source/JAERI

The activation cross sections for 20 (n, np+d) reactions were measured in the energy range between 13.4 and 14.9 MeV by the activation method. The mass-separated isotopes of ⁸⁷Sr, ^95,100Mo, ¹⁰⁴Ru, ¹⁰⁶Pd, ^113,116Cd, ^118,119,120Sn, ^123,128,130Te, ^184,186W, and ^189,190Os were irradiated. The 16 cross sections, excepting those for ¹¹⁸Sn, ¹²⁸Te and ^184,186W, were obtained for the first time. The d–T neutron source of the fusion neutronics source (FNS) at the Japan Atomic Energy Research Institute (JAERI) was used for irradiation. All cross section values were determined relative to that of the ²⁷Al (n, ) ²⁴Na reaction (ENDF/B-VI). To measure weakly induced activities, an efficiency calibration technique with a well-type HPGe detector was applied. The present results were compared with the comprehensive evaluated data in the JENDL-3.3, the JENDL-Activation File, the ENDF/B-VI and the FENDL/A-2.0. Most of the data in the JENDL-3.3 and the JENDL-Activation File were in good agreement with the present result. However, relative to our values, 13 of the 20 evaluated data in FENDL/A-2.0 were overestimated more than 2 times or underestimated by less than one tenth.     

A method of caustics for the direct experimental measurement of the T-integral in nonlinear and dynamic fracture mechanics problems

This paper presents a methodology for the direct experimental measurement of the T^*-integral. The method of caustics (the shadow pattern method) has proven to be a powerful optical method with which to measure stress intensity factors in static and dynamic fracture mechanics problems. An attempt has been made to extend the method of caustics to problems in nonlinear and dynamic fracture mechanics. The formation process of the caustic pattern for an elastoplastic crack tip in a compact-tension specimen was simulated by a finite-element analysis. The stimulated and actual caustic patterns agreed with each other very well. The relations between the T^*-integral and the size of the caustic pattern were obtained for various optical set-ups.The experimental measurement of the caustic pattern in the dynamic tear test specimen of a nuclear pressure vessel steel was also carried out. High-speed photographs of the caustic patterns were taken using a laser caustic method, which can be quickly synchronized to the initiation of impact loading by a hammer that was dropped on the specimen. The time variation of the T^*-integral during impact loading was evaluated by using the relation between the T^*-integral and the size of the caustic pattern that was obtained by the numerical simulation. The hybrid numerical-experimental method developed here, in conjunction with laser caustic high-speed photography, has made it possible to measure the T^*-integral for an elastoplastic material under impact loading conditions.     

Simulation of the defect pair VPb–VO in PbMoO4 crystals

A simulation study has been performed to investigate the defects in PbMoO₄, based on the interatomic potentials empirically fitted to the known crystal properties. The formation energies of the isolated point defects , , the cluster defects , and have been calculated. It is theoretically demonstrated that most of and in the as-grown PbMoO₄ crystal exist in the form of the vacancy pair , which would play important roles in the formation and transformation process of photo-chromic effect in PbMoO₄ crystal.     

Investigation of liquid film behavior at the onset of flooding during adiabatic counter-current air–water two-phase flow in an inclined pipe

The liquid film characteristics at the onset of flooding in an inclined pipe (16 mm i.d. and 2.2 m in length) have been investigated experimentally. A constant electric current method and visual observation were utilized to elucidate the flow mechanisms at the onset of flooding. Two mechanisms are clarified to control the flooding in lower flooding and upper flooding, respectively. The lower flooding occurred at lower liquid flow rate and high pipe inclination angle. In this mechanism, the liquid film does not block the pipe cross-section. On the other hand, the upper flooding occurred at higher liquid flow rate and low pipe inclination angle. In this case, blocking of the pipe cross-section by large wave and entrainment plays an important role. The experimental data indicated that there was no reversal motion of liquid film at the onset of flooding during the operation of both lower flooding and upper flooding. The effects of pipe inclination angle on the onset of flooding are also discussed.     

An interdiffusional model for prediction of the interaction layer growth in the system uranium–molybdenum/aluminum

The codes PLACA and DPLACA, elaborated in this working group, simulate the behavior of a plate-type fuel containing in its core a foil of monolithic or dispersed fissile material, respectively, under normal operation conditions of a research reactor. Dispersion fuels usually consist of ceramic particles of a uranium compound in a high thermal conductivity matrix. The use of particles of a U–Mo alloy in a matrix of Al requires especially devoted subroutines able to simulate the growth of the interaction layer that develops between the particles and the matrix. A model is presented in this work that gives account of these particular phenomena. It is based on the assumption that diffusion of U and Al through the layer is the rate-determining step. Two moving interfaces separate the growing reaction layer from the original phases. The kinetics of these boundaries are solved as Stefan problems. In order to test the model and the associated code, some previous, simpler problems corresponding to similar systems for which analytical solutions or experimental data are known were simulated. Experiments performed with planar U–Mo/Al diffusion couples are reported in the literature, which purpose is to obtain information on the system parameters. These experiments were simulated with PLACA. Results of experiments performed with U–Mo particles disperse in Al either without or with irradiation, published in the open literature were simulated with DPLACA. A satisfactory prediction of the whole reaction layer thickness and of the individual fractions corresponding to alloy and matrix consumption was obtained.     

Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress–strain curves owing to dislocation theory

In the present study, strengthening of steels due to Cu precipitates in the nanometer scale is investigated. These precipitates lead to a significant increase of the matrix yield stress due to impeded dislocation movement. This effect can be treated quantitatively on the mesomechanical level of dislocation theory. The impact on the macroscopic failure behaviour of ferritic steel is investigated in the framework of damage theory. The presented strategy can be also applied to related materials science problems.     

Influence of the void fraction profile on the distribution parameter C0 for a bubbly gas–liquid flow in a horizontal round pipe

This paper presents the results of a numerical experiment on the influence of the void fraction profile on the distribution parameter C₀ in a horizontal bubbly two-phase flow. It was shown that for non-symmetric void fraction profiles, which occur normally in horizontal flows, the distribution parameter may be less than 1. In this case, the ratio of the volumetric flow quality β to the average void fraction α can also be less than 1.     

The calculation of neutron yields in mixtures and compounds from the thick target (α,n) yields in the separate constituents

A simple relation is derived between the thick target yield of neutrons produced following (α,n) reactions in compounds or homogeneous mixtures and the yields in the separate constituents.It is necessary to assume that the Bragg law of additivity of stopping powers holds for the compound and to make the approximation that the stopping powers of all materials vary with energy in the same way, apart from constant factors.The range of validity of the second hypothesis is examined in some detail. It is shown to be far superior to the approximation of a stopping power independent of energy.     

Computer simulation of sputtering at the low index (1 0 0), (1 1 0) and (1 1 1) surfaces of Ni3Al in a STEM

The present study is relevant to the preferential Al sputtering and/or enhancement of the Ni/Al ratio in Ni₃Al observed by the scanning transmission electron microscopy fitted with a field emission gun (FEG STEM). Atomic recoil events at the low index (1 0 0), (1 1 0) and (1 1 1) surfaces of Ni₃Al through elastic collisions between electrons and atoms are simulated using molecular dynamics (MD) methods. The threshold energy for sputtering, E_sp, and adatom creation, E_ad, are determined as a function of recoil direction. Based on the MD determined E_sp, the sputtering cross-sections for Ni and Al atoms in these surfaces are calculated with the previous proposed model. It is found that the sputtering cross-section for Al atoms is about 7-8 times higher than that for Ni, indicating the preferential sputtering of Al in Ni₃Al, in good agreement with experiments. It is also found that the sputtering cross-sections for Ni atoms are almost the same in these three surfaces, suggesting that they are independent of surface orientation. Thus, the sputtering process is almost independent of the surface orientation in Ni₃Al, as it is controlled by the sputtering of Ni atoms with a lower sputtering rate.