Combined effects of radiation damage and hydrides on the ductility of Zircaloy-2

Interest remains high regarding the effects of zirconium hydride precipitates on the ductility of reactor Zircaloy components, particularly in irradiated material. Previous studies have reported that ductility reductions are much greater at room temperature compared to reactor component temperatures. It is often concluded that the effects of irradiation dominate the ductility reduction observed in test specimens, although there is no consensus as to whether hydriding effects are additive. Many of the tests reported in the literature are difficult to interpret due to variations in test specimen geometry and material history. In this paper, we present the results of an experimental program aimed at clearly describing the combined effects of irradiation and hydriding on ductility parameters under conditions of a realistic test specimen design and well characterized hydride content, distribution and orientation. Experiments were conducted at 295 and 605 K, respectively on Zircaloy-2 tubing segments containing 10–800 ppm hydrogen and neutron fluences between 0–9×10²⁵ n m⁻² (E>1 MeV). Tests utilized the well proven localized ductility specimen which applies plane strain tension in the hoop direction of the tubing segment. In all cases, hydrides were also oriented in the hoop or circumferential direction and were uniformly distributed across the tubing wall. Results indicate that at 605 K, the ductility of irradiated material was almost independent of hydride content, retaining above 4% uniform elongation and 25% reduction in an area for the highest fluences and hydrogen contents. Even at 295 K, measurable ductility was retained for irradiated material with up to 600 ppm hydrogen. In the paper, results of fractographic analyses and strain rate are also discussed. We conclude that at reactor component operating temperatures, radiation damage controls the ductility of Zircaloy-2 for conditions of these tests up to hydride levels of at least 800 ppm, and probably much higher. At room temperature the effect of hydride content and radiation damage appear to be additive.     

The various creep models for irradiation behavior of nuclear graphite

Graphite is a widely used material in nuclear reactors, especially in high temperature gascooled reactors (HTRs), in which it plays three main roles: moderator, reflector and structure material. Irradiation-induced creep has a significant impact on the behavior of nuclear graphite as graphite is used in high temperature and neutron irradiation environments. Thus the creep coefficient becomes a key factor in stress analysis and lifetime prediction of nuclear graphite. Numerous creep models have been established, including the visco-elastic model, UK model, and Kennedy model. A Fortran code based on user subroutines of MSC.MARC was developed in INET in order to perform three-dimensional finite element analysis of irradiation behavior of the graphite components for HTRs in 2008, and the creep model used is for the visco-elastic model only. Recently the code has been updated and can be applied to two other models—the UK model and the Kennedy model. In the present study, all three models were used for calculations in the temperature range of 280–450 °C and the results are contrasted. The associated constitutive law for the simulation of irradiated graphite covering properties, dimensional changes, and creep is also briefly reviewed in this paper. It is shown that the trends of stresses and life prediction of the three models are the same, but in most cases the Kennedy model gives the most conservative results while the UK model gives the least conservative results. Additionally, the influence of the creep strain ratio is limited, while the absence of primary creep strain leads to a great increase of failure probability.     

Fatigue crack growth under continuous radiation

This paper examines the possibility that a drastic reduction of the rate of propagation of a fatigue crack can occur if a sample undergoing failure is simultaneously irradiated with high energy particles. For an effect to exist it is necessary that the rate of irradiation damage and the frequency of the cyclic stress are such that appreciable irradiation hardening occurs within the plastic crack tip zone during each stress cycle. The analysis is based on a fatigue crack growth theory of one of the authors (JW) that considers the true stress intensity factor at a fatigue crack tip. Although in a post-irradiation fatigue experiment appreciable irradiation hardening will not necessarily produce a decrease in the fatigue crack growth rate, a decrease in the fatigue crack growth rate should always occur in material with a Paris law exponent larger than two if the irradiation takes place continuously during a fatigue test that is carried out at temperatures at which annealing processes are relatively slow.     

A review of irradiation effects on LWR core internal materials - IASCC susceptibility and crack growth rates of austenitic stainless steels

Austenitic stainless steels (SSs) are used extensively as structural alloys in the internal components of light water reactor (LWR) pressure vessels because of their relatively high strength, ductility, and fracture toughness. However, exposure to neutron irradiation for extended periods changes the microstructure (radiation hardening) and microchemistry (radiation-induced segregation) of these steels, and degrades their fracture properties. Irradiation-assisted stress corrosion cracking (IASCC) is another degradation process that affects LWR internal components exposed to neutron radiation. The existing data on irradiated austenitic SSs were reviewed to evaluate the effects of key parameters such as material composition, irradiation dose, and water chemistry on IASCC susceptibility and crack growth rates of these materials in LWR environments. The significance of microstructural and microchemistry changes in the material on IASCC susceptibility is also discussed. The results are used to determine (a) the threshold fluence for IASCC and (b) the disposition curves for cyclic and IASCC growth rates for irradiated SSs in LWR environments.     

Deformation and fracture properties in neutron irradiated pure Mo and Mo alloys

The effect of neutron irradiation on the mechanical properties of select molybdenum materials, unalloyed low carbon arc-cast (LCAC) Mo, Mo-0.5% Ti-0.1% Zr (TZM) alloy, and oxide dispersion-strengthened (ODS) Mo alloy, was characterized by analyzing the temperature dependence of mechanical properties. This study assembles the tensile test data obtained through multiple irradiation and post-irradiation experiments, in which tensile specimens were irradiated up to 13.1 dpa at 80-1000 °C and tested at −194 to 1000 °C. Irradiation at 80-609 °C increased yield stress significantly, up to 170%, while the increase of yield stress after irradiation at 784-936 °C was not significant. The plastic instability stress was strongly dependent on test temperature but was nearly independent of irradiation dose and temperature. The true fracture stress showed weak dependences on test temperature, irradiation dose and temperature when ductile failure occurred. Among the test materials the stress-relieved ODS material in the longitudinal direction (ODS-LSR) displayed the highest resistance to irradiation embrittlement due to its relatively high fracture stress. The critical temperature for shear failure (CTSF) was defined and evaluated for the test materials and the CTSF values were compared with the ductile-to-brittle transition temperatures (DBTT) based on ductility data.     

On the analogy between thermally and irradiation induced creep

Employing an analogy between thermally induced and irradiation induced creep, physical arguments are used first to deduce a one-dimensional constitutive relation for metals under stress in a high temperature and high neutron flux field. This constitutive relation contains modified superposition integrals in which the temperature and flux dependence of the material parameters is included via the use of two reduced time scales; linear elastic, thermal expansion and swelling terms are also included. A systematic development based on thermodynamics, with the stress, temperature increment and defect density increment as independent variables in the Gibbs free energy, is then employed to obtain general three-dimensional memory integrals for strain; the entropy and coupled energy equation are also obtained. Modified superposition integrals similar to those previously obtained by physical argument are then obtained by substituting special functions into the results of the thermodynamic analysis, and the special case of an isotropic stress power law is examined in detail.     

Fracture mechanics issues for irradiated blanket structures

This paper reviews some of the factors that will affect fracture behavior of fusion reactor structures and summarizes some component life predictions based on linear elastic fracture mechanics analysis. The review includes discussion of the environments to which the components will be subjected, the response of materials to these environments, the time dependent nature of the structural response, and the fracture related failure mechanisms.Radiation environments and complex loading conditions in a fusion reactor cause a variety of material phenomena. These phenomena include irradiation swelling and creep, strength changes due to matrix hardening, helium embrittlement, and surface effects such as sputtering and blistering.The interaction of thermal creep, irradiation creep, and swelling results in complex time, temperature, and neutron fluence dependent stress histories in first wall and blanket structures. These effects reduce compressive thermal stresses during the burn portion of a reactor operating cycle and result in residual tensile stress during the non-burn portion of the cycle. The cyclic nature of these stresses, particularly in a tokamak reactor, and the presence of undetected flaws provide a basis for the application of fracture mechanics. Linear elastic fracture mechanics analysis techniques have been applied to predict component life for several conceptual tokamak fusion reactor designs. These analyses show that the structural life may be limited by growth of initial flaws to a coolant leakage. Results indicate that for neutron wall loadings below 2 to 3 Mw/m², life is likely to be controlled by stresses during the burn period and, at higher wall loadings, by residual stresses during the non-burn period.Fracture toughness properties tend to be reduced by irradiation. Therefore, brittle fracture will be a potentially critical failure mode. Fatigue crack growth and fracture characteristics of the design will affect the operating mode of a reactor and influence the performance of different types of reactors. Tests are currently planned to develop material crack growth and fracture toughness data [1] for candidate alloys because these properties have been shown to be important.     

Analyses of a restrained growth graphite irradiation creep experiment

Graphite is used as a moderator, reflector and structural component in pebble bed and prism High Temperature Reactors (HTRs). It is fortunate to reactor designers that irradiated graphite shows remarkably high creep behaviour under the influence of fast neutron irradiation at temperatures far below those required for significant creep strains to be generated in unirradiated graphite. This creep behaviour is important in the design of nuclear graphite reactor cores because the self-induced shrinkage stresses generated in typical core components during irradiation can be relieved. However, there are no reliable data on high fluence irradiation creep and the mechanistic understanding of the irradiation creep is insufficiently developed to reliably extrapolate to the high fluences expected of graphite in future HTR designs. The understanding of irradiation creep is further complicated because it has been experimentally observed that irradiation creep strain in graphite modifies other properties in particular the coefficient of thermal expansion. In addition modified changes in Young's modulus in crept specimens have been reported and it has also been postulated that irradiation creep may also modify dimensional change. The assessment of irradiation creep in graphite components is based on empirical laws derived from data obtained from small samples irradiated in a materials test reactor. However, due to the complicated irradiation rigs required and the amount of dimensional and property measurements needed to be taken, constant stress irradiation creep experiments are difficult and very expensive to carry out successfully. However, restrained creep experiments are simple to implement, less expensive and can be easily included as part of other, more conventional irradiation graphite experimental programmes. However, in the past, the disadvantage of these experiments has been that the results have been difficult to interpret using the then available analytical methods. In this paper the restrained creep experiment is revisited and analysed numerically and the possible benefit of using a restrained creep experiment in future graphite irradiation experiments is investigated. It is shown that a numerical simulation of the restrained creep experiment behaviour would be an essential tool to ensure that the stress within the specimen remains within defined limits so that specimen failure can be avoided.     

Subject index

In 1965 eight surveillance subassemblies were placed in row 12 of the EBR-II sodium-cooled fast breeder reactor with an irradiation temperature near the sodium-inlet temperature of 371°C. At the same time, two other surveillance subassemblies were placed in the primary storage basket, which receives minimal neutron exposure but is immersed in primary sodium and experiences a temperature of 371°C. Each of the subassemblies contained 18 preloaded springs made of Inconel X750. Springs from four of the in-core subassemblies and one subassembly from the storage basket have been evaluated to determine irradiation-enhanced deformation rates to neutron exposures of 4.2 dpa.It was found that the creep coefficient derived from the stress relaxation measurements on Inconel X750 springs was 1.0 × 10^?12 (Pa-dpa)^?1 for springs irradiated up to 4.2 dpa (3751 d) at an in-reactor temperature of 371°C. The relaxation behavior was adequately described by a creep law that was linear in neutron fluence and applied stress. Springs encapsulated in helium showed identical in-reactor relaxation rates to springs exposed to the flowing primary sodium. The creep coefficient derived from the present work on Inconel X750 springs was shown to be the same as the creep coefficients determined from various austenitic stainless steel alloys.     

Mechanical modeling of creep, swelling and damage under irradiation for polycrystalline metals

A constitutive equation of creep, swelling and damage under irradiation for polycrystalline metals applicable to structural analyses in multiaxial state of stress is developed. After reviewing microscopic mechanisms of irradiation creep and swelling, the relevant theories proposed so far from the view point of metallurgical physics and their applicability are discussed first. Then a constitutive model is developed by assuming that creep under irradiation can be decomposed into irradiation-affected thermal creep and irradiation-induced creep. By taking account of the Stress-Induced Preferential Absorption (SIPA) mechanism, the irradiation-induced creep is represented by an isotropic tensor function of order one and zero with respect to stress, which is, at the same time, the function of neutron flux and neutron fluence. The volumetric part of the irradiation-induced creep is identified with swelling. The irradiation-affected thermal creep is described by modifying Kachanov-Rabotnov theory for stress-controlled creep and creep damage by incorporating the effect of irradiation. Finally irradiation creep and swelling of 20% cold-worked type 316 stainless steel at elevated temperature are predicted by the proposed constitutive equations, and the numerical results are compared with the corresponding experimental results.     

The effect of radiation induced gas on the stress rupture properties of an aluminium-lithium alloy

The changes in stress-rupture properties of an aluminium-lithium alloy induced by the presence of inert gas bubbles after neutron irradiation have been investigated in the temperature range of 175 °C to 300 °C. A bubble distribution with a mean diameter of 47 Å at an average spacing of 1400 Å produces a decrease in the minimum creep rate of two orders of magnitude below that for the bubble-free material under the same test conditions. For very fine bubble distributions and distributions which contain a narrow size range of large bubbles, a breakaway to a very high stress-sensitivity at low stresses occurs. This is absent in alloys which contain stronger bubble obstacle arrays which include a wide range of bubble sizes. All inert gas concentrations reduce creep ductility of aluminium-lithium alloy but the severity of embrittlement increases markedly with gas concentration and testing temperature.     

Combined effects of neutron irradiation and hydrogen absorption on mechanical properties of pure iron

To obtain a fundamental knowledge of the combined effect of neutron-irradiation and hydrogen, mechanical properties and the fracture mode were studied for pure neutron irradiated iron, followed by hydrogen charging. The effect of interaction between neutron irradiation and hydrogen absorption for a pure iron could be clarified. Under the hydrogen charged condition, the ductility is higher in the neutron irradiated specimen than in the unirradiated. The cause could be sought in hydrogen trap sites of the iron and the fracture mode. As a result of interaction between many irradiation defects and hydrogen atoms, the fracture mode of a hydrogen charged specimen after irradiation, is a mixed mode of quasi-cleavage crack and dimple pattern. That of a hydrogen charged unirradiated specimen is predominantly intergranular cracking.     

V型凹口对液态熔盐堆用核石墨构件应力分析的影响

本文利用了一个根据球床模块堆(Pebble Bed Modular Reactor,PBMR)用核石墨材料辐照性能数据编写的用户自定义材料模型(User defined Material model,UMAT),按照美国橡树岭国家实验室(Oak Ridge National Laboratory,ORNL)的液态燃料熔盐试验堆(Molten Salt Reactor Experiment,MSRE)用核石墨构件尺寸,为钍基熔盐堆(Thorium-based Molten Salt Reactor,TMSR)设计了一款方型核石墨构件。利用新编UMAT对该核石墨构件进行了初步的应力分析。分析结果表明,在没有预制裂纹的情况下辐照梯度越大核石墨构件中心区域最大主应力值越大,构件的断裂位置可能出现在构件中心位置处;对于有V型凹口预制裂纹的情况,应力集中部位均出现在预制裂纹尖端附近,这将可能导致裂纹尖端附近出现裂纹扩展,从而引起构件断裂失效。     

Fast neutron induced creep in pyrocarbon under constant stress

Pyrocarbon is used as a coating material in the fuel of high-temperature nuclear reactors, and a thorough understanding of its irradiation behaviour includes a knowledge of its ability to creep under fast neutron irradiation. An experiment is described which demonstrates fast neutron-induced creep of a pyrolytic carbon under constant applied stress. This differs from previous work which has obtained creep ductility data from restrained shrinkage tests. The specimens were centre-loaded discs freely supported at the rim, thus subjected to a constant biaxial bend stress. On each specimen, elastic and plastic strains were produced and measured using the same geometry and loading arrangement, to allow the creep strain to be expressed simply in terms of initial elastic strain units. Results were obtained on specimens of initial density 1.95 g/cm and 1.64 g/cm³ up to a fast neutron dose of 4 × 10²⁰ n/cm² (DNE) at a temperature of 1000°C. The low-density specimens showed both the greater shrinkage and the greater creep strain, and average creep rates were 0.5 and 1.0 elastic units per 10²⁰ n/cm² (DNE) for the high and low-density specimens respectively. These constant-stress creep results are shown to be consistent with other data on pyrocarbon. They differ from graphite creep data in that the two pyrocarbons give creep strains per unit initial elastic strain which depend on their initial densities.     

Considerations of Irradiation-Induced Transient Creep in Fuel Particle Modeling*

An analytical assessment is made of the potential effects of irradiation-induced transient creep on the behavior of the TRISO-coated fuel particles of the New Production Modular High Temperature Gas-Cooled Reactor (NP-MHTGR). An analytical solution is presented for the three-layer particles, which includes transient creep in addition to steady-state creep behavior. The solution allows for evaluating the effects that transient creep has on individual particle stresses and for determining failure probabilities for particle batches using the Monte Carlo approach. Because experimental data needed to determine parameters for a transient component in a creep model for the pyrocarbons is not available, a range of possible parameter values were considered in the assessments. It was shown that transient creep measurably affects particle stresses early in the irradiation life of the particle. At that time, the hoop stress in the primary load bearing layer of the particle is in compression and the article is not vulnerable to pressure vessel failure. Later in irradiation, the effects of transient creep were typically shown to be less significant. Thus, transient creep had less than an order of magnitude effect on batch failure probabilities for prototypical NP-MHTGR fuel particles and was much less significant than steady-state creep. Whether the presence of transient creep increased or decreased the particle failure probability was dependent on the specific values used for the transient creep material properties.     

Crack propagation characteristics in neutron irradiated type 316 stainless steel microspecimens

In order to better relate the macroscopic mechanical behavior of irradiated alloys to their associated microstructural condition, unirradiated and neutron irradiated microspecimens were tensile tested at 25–600°C in a quantitative load elongation stage while under continuous observation in a high voltage electron microscope (HVEM). The microtensile specimens, 40 μ m thick, of type 316 stainless steel were irradiated at ambient temperature to a fluence of 1 × 10²² n/m² with 14 MeV neutrons in the Lawrence Livermore Rotating Target Neutron Source II (RTNS) facility.Crack angles, directions and length plotted against total specimen elongation were used to describe the manner in which a crack progressed through each specimen. Rapid crack propagation is accompanied by rapidly changing crack angles and direction and conversely slow propagation corresponds to slowly changing variables. A graph of cumulative crack length plotted against total elongation exhibits a slope which increases as specimen ductility decreases. This graph reflects changes due to the effect of neutron irradiation.     

A regression model for zircaloy cladding in-reactor creepdown: Database, development, and assessment

This paper presents a cladding deformation model developed to analyze cladding creepdown during steady state operation in a pressurized water reactor (PWR) and a boiling water reactor (BWR). This model accounts for variation in the zircaloy cladding heat treatments - cold worked and stress relieved material typically used in a PWR and fully recrystallized material typically used in a BWR. This model calculates cladding creepdown as a function of hoop stress, fast neutron flux, exposure time, and temperature. This paper also presents a comparison between cladding creep calculations by the creepdown model and corresponding test results from the KWU/CE program, ORNL HOBBIE experiments, and EPRI/Westinghouse Engineering cooperative project. The comparisons show that the creepdown model calculates cladding creep strains reasonably well.     

Creep ductility of cold-worked Zr-2.5 wt% Nb and Zircaloy-2 tubes in-reactor

Deformation of internally pressurized 15 mm diameter tubes of cold-worked Zr-2.5 wt% Nb and Zircaloy-2 has been measured in axial and hoop directions for irradiations up to 24 000 h at 571 K. Specimens have deformed up to 18.1% in the hoop direction, with hoop stresses up to 495 MPa, without rupture. Since the stress sensitivity of creep rate is high (>5) under the test conditions, and is low (≈1) under operating conditions for pressure tubes, creep ductility of pressure tubes should be very high.     

The development of a stress analysis code for nuclear graphite components in gas-cooled reactors

Most of the UK nuclear power reactors are gas-cooled and graphite moderated. As well as acting as a moderator the graphite also acts as a structural component providing channels for the coolant gas and control rods. For this reason the structural integrity assessments of nuclear graphite components is an essential element of reactor design. In order to perform graphite component stress analysis, the definition of the constitutive equation relating stress and strain for irradiated graphite is required. Apart from the usual elastic and thermal strains, irradiated graphite components are subject to additional strains due to fast neutron irradiation and radiolytic oxidation. In this paper a material model for nuclear graphite is presented along with an example of a stress analysis of a nuclear graphite moderator brick subject to both fast neutron irradiation and radiolytic oxidation.