Uncertainties of creep model in stress analysis and life prediction of graphite component

The irradiation-induced creep is a key factor in stress analysis and life prediction of nuclear graphite in high temperature gas-cooled reactors (HTRs). Numerous creep models have been established and good agreements have been observed with uni-axial creep experiments. However, the effect of creep strain ratio has not been fully addressed, and the primary creep strain is considered in some cases less important in comparison with the secondary one. These uncertainties in creep model might result in large discrepancies in the evaluation of stresses and service lives of graphite components. In this paper, the variation of creep strain ratio and the impact of the primary creep strain are studied numerically and the corresponding discrepancies in stresses and life prediction of graphite components in HTRs are discussed. Two implicit formulations of the incremental finite element solution for the parameter variations of creep models are presented and integrated into a finite element code developed by INET. The numerical results show that both increase of the creep strain ratio and absence of the primary creep strain will lead to an increase of stress levels and decrease of service life dramatically, suggesting that uncertainties of creep models have to be taken into account in the design of graphite components in HTRs.     

Development of Thermal/Irradiation Stress Analytical Code “VIENUS” for HTTR Graphite Block

A new thermal/irradiation stress analysis code “VIENUS” has been developed for the graphite block in the High-Temperature Engineering Test Reactor (HTTR). The VIENUS is a two- dimensional finite element visco-elastic analysis code to take account of graphite behavior under irradiation in detail. In the analysis, the effects of both fast neutron fluence and temperature on material properties are considered.

The code has been evaluated by the irradiation test results of the Peach Bottom fuel elements to confirm the thermal/irradiation stresses in the graphite block. It is clarified that the calculated results are able to estimate a tendency of the test results, and that both the irradiation- induced creep and dimensional change are the most important parameters in the thermal/irradiation stress analysis. From the present study, it is suggested that the VIENUS code is a useful tool to evaluate the thermal/irradiation stresses in the HTTR graphite blocks.     

Irradiation swelling, creep and thermal-stress analysis of LWR fuel elements, computer code isune-2

The irradiation swelling, creep, and thermal-stress analysis of light-water reactor (LWR) oxide (UO₂) fuel elements is analysed. The analysis is based on the basic physical and mathematical assumptions and the experimental data of the fuel and cladding (or canning) materials. In the analysis, the nuclear, physical, metallurgical, and thermo-mechanical properties of the fuel and cladding materials under irradiation environment are examined carefully. The objectives of the paper are mainly (1) to formulate and carry out the irradiation swelling, irradiation creep, and thermal-stress analysis of fuel elements for LWR power reactors, and (2) to develop a computer code which will facilitate the computations for fuel element design, safety analysis, and economic optimization of the power reactors. In a general procedure of the analysis, the irradiation swelling, irradiation creep, temperature distribution, etc. in the fuel and cladding of the oxide fuel elements during the reactor in operation are studied. Some theoretical models and empirical relations (on the basis of accepted experimental data) for irradiation swelling and creep in the fuel and irradiation creep in cladding materials are postulated and developed. Some analytical and empirical relations (based on test results) for heat generation and temperature distribution in the fuel during fuel restructuring are derived. The fuel restructure is, in general, divided into the central void, columnar grain, equiaxed grain, and unaffected grain zones (or regions) after a sufficiently long period for the fuel elements to be irradiated (or operated). From these relations derived for irradiation swelling, irradiation creep, and temperature distribution in the fuel and cladding, together with the well-known strain-stress, incompressibility, compatibility, and stress equilibrium equations, the irradiation swelling, creep, and thermal-stress analysis for the LWR fuel elements can be carried out.From the analytical results obtained, a computer code, ISUNE-2 (which is in the sequence of computer code ISUNE-1 and -1A developed and used previously for liquid-metal fast breeder reactor fuel element design and safety and economic analysis), can be developed. With some reliable experimental data (measured during fuel elements in operation) as input, the computer code may predict various cases of LWR (oxide or carbide) fuel elements in operation. The general scope and resulting contribution of this paper is to provide a realistic analysis and a reliable operating LWR fuel element code for use by nuclear power utilities to predict the fuel element behavior in power reactors. The fuel element design, safety analysis, and economic optimization depend largely on the fuel element behavior in the power reactors.     

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。     

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.     

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.     

He implantation induced microstructure- and hardness-modification of the intermetallic γ-TiAl

TiAl is a well known high temperature material with good creep properties. It is investigated as a potential structural material for Generation IV high temperature gas cooled nuclear reactors. The tests are performed with the ABB-2 (Ti-rich TiAl with 2 at.% W) developed by ASEA Brown Boveri Ltd. (ABB). Thin samples are irradiated throughout with 24 MeV ⁴He²⁺ ions; the irradiated material is then investigated towards its microstructure and its hardness. The microstructure is studied by transmission electron microscopy and the hardness is investigated using a micro-hardness tester and a nano-indenter. Different effects can be identified. From room to moderate irradiation temperatures, the radiation induced hardening of the material slowly vanishes until the material completely recovers at about 943 K. Beyond this temperature, He-bubble formation seems to harden the material again, until beyond 1200 K a steep increase in hardening is detected. This effect can be correlated with bubbles being identified in the micrographs. The results are consistent and give strong indications to a microstructural development as a function of temperature.     

The relationship between irradiation induced dimensional change and the coefficient of thermal expansion: a modified Simmons relationship

In the 1960s, a theoretical relationship between the dimensional changes and the coefficient of thermal expansion of irradiated graphite was derived by J.H.W. Simmons. The theory was shown to be comparable with experimental observations at low irradiation doses, but shown to diverge at higher irradiation doses. However, various modified versions of this theory have been used as the foundation of design and life prediction calculations for graphite-moderated reactors.This paper re-examines the Simmons relationship, summarising its derivation and assumptions. The relationship was then modified to incorporate the high dose, high strain changes that were assumed to be represented in the changes in Young’s modulus with irradiation dose. By scrutinising the behaviour of finite element analyses, it was possible to use a modified Simmons relationship to predict the dimensional changes of an isotropic and anisotropic graphite to high irradiation doses.These issues are important to present high-temperature reactors (HTRs) as the life of HTR graphite components is dependent upon their dimensional change behaviour. A greater understanding of this behaviour will help in the selection and development of graphite materials.     

Activation analyses for the IFMIF-Liquid Breeder Validation Module (LBVM)

The Liquid Breeder Validation Module (LBVM) will be one of the medium flux irradiation modules of the International Fusion Materials Irradiation Facility (IFMIF) neutron source. The objective of this module – presently under design – is the test of functional materials related to liquid breeders for future nuclear fusion power reactors (DEMO). This paper aims to describe the activation analyses performed to estimate the radioactive inventory and the expected contact dose from the activated materials of the module following a 345 day irradiation period. These calculations supply valuable information for different aspects related to the design of the module, such as the safety evaluation and the waste management and disassembly plan.The neutron transport calculations have been performed using the McDeLicious code. The ACAB nuclear inventory code, with the activation nuclear libraries EAF-2007, has been used for the activation analyses.The main results point out that the contact dose of the LBVM materials is much higher than the hands-on-limits, as expected. Therefore, remote handling operations are requested for disassembling the module. It is important to remark that after 8 h decay time, the contact dose rate of the LBVM decreases 76% for the EUROFER steel components and 46% for the 316 LN components. Regarding the isotopic inventory, although the main activation comes from the module steel structures, the production of tritium and Po-210 in the lithium lead inside the experimental capsules deserved a careful analysis.     

锆合金辐照蠕变和生长的宏介观模型研究进展

锆合金作为核反应堆堆芯的主要结构材料之一,在服役过程中会发生辐照蠕变和生长行为,严重影响其使用可靠性。预测锆合金的辐照蠕变和生长是保障反应堆安全运行的关键。本文聚焦于两类锆合金构件,包括压水堆用锆合金包壳管及重水堆用Zr-2.5Nb压力管,分别从宏介观尺度详细综述了其辐照变形预测模型。针对适用于包壳管的宏观经验模型及介观力学模型,分别描述了两类模型的特征,重点介绍了介观力学模型的研究现状及最新进展,并对其未来的发展方向提出建议;针对适用于压力管的宏观经验模型,包括加拿大CANDU压力管辐照变形计算方程(简称C6方程)及秦山重水堆压力管辐照变形计算方程(简称秦山方程),分别描述了两类方程的具体形式,并介绍了C6方程国产化的进展。     

MCNP5 modeling of the IPR-R1 TRIGA reactor for criticality calculation and reactivity determination

The IPR-R1 TRIGA is a research nuclear reactor managed and located at the Nuclear Technology Development Center (CDTN) a research institute of the Brazilian Nuclear Energy Commission (CNEN). It is mainly used to radioisotopes production, scientific experiments, training of nuclear engineers for research and nuclear power plant reactor operation, experiments with materials and minerals and neutron activation analysis. In this work, criticality calculation and reactivity changes are presented and discussed using two modelings of the IPR-R1 TRIGA in the MCNP5 code. The first model (Model 1) analyzes the criticality over the reactor. On the other hand, the second model (Model 2) includes the possibility of radial and axial neutron flux evaluation with different operation conditions. The calculated results are compared with experimental data in different situations. For the two models, the standard deviation and relative error presented values of around 4.9 × 10^?4. Both models present good agreement with respect to the experimental data. The goal is to validate the models that could be used to determine the neutron flux profiles to optimize the irradiation conditions, as well as to study reactivity insertion experiments and also to evaluate the fuel composition.     

Double differential neutron scattering cross sections of materials for ultra high temperature reactors

The five materials with the highest melting point are hafnium, tantalum, niobium and zirconium (ZrC) carbides and graphite (that sublimes). Graphite is the material of choice for very high temperature reactors (VHTR); ultra high temperature reactors (UHTR), like the thermal nuclear propulsion reactor NERVA use a dispersion of ZrC and UC in graphite as the material in the reactor core. Presently there are neither inelastic nor elastic double differential scattering data available that describe the thermalization process in ZrC. We therefore, calculated coherent elastic and incoherent inelastic cross sections for the ZrC crystal which has a face centered cubic (fcc) lattice. The phonon spectrum for the ZrC lattice was calculated with the computer code PHONON using the Hellman–Feynman forces computed with ab-initio methods [Jochyn, P.T., Parlinski, K., 2000. Ab initio lattice dynamics and elastic constants of ZrC. Eur. Phys. J. B 15, 265–268]. This phonon spectrum was then used to compute the S(α, β, T) matrices for the inelastic scattering cross sections for C and Zr in the ZrC lattice using modified versions of the computer codes GASKET, HEXSCAT and NJOY. The results were applied to calculate, with the proper S(α, β, T), criticality and reactivity coefficients of temperate of reactor systems containing ZrC and UC. For comparisons, these parameters were also calculated with approximations of S(α, β, T), i.e. the gas or the graphite scattering kernels. Depending on the degree of thermalization, k_eff is underestimated between 0.6% and 1%, and the values and the shape of the reactivity coefficients as a function of temperature change by substantial amounts.     

核级石墨辐照变形对辐照应力和寿命的影响

石墨是高温气冷堆的堆芯关键结构材料,其机械性能,尤其是辐照后特性,对反应堆的运行安全至关重要.不同牌号的石墨在制备工艺上有较大差异,导致内部微观结构的不同,从而影响石墨的辐照变形.本工作通过对高温气冷堆堆芯侧反射层石墨砖的辐照行为进行数值仿真,分析不同石墨材料的辐照变形对石墨结构的辐照应力和辐照寿命的影响.结果表明,石墨结构的辐照应力和辐照寿命对石墨材料的辐照变形高度敏感.相关结论将为高温气冷堆堆芯石墨砖的结构设计提供重要的数值依据.     

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.     

FARST — A computer code for the evaluation of FBR fuel rod behavior under steady-state/transient conditions

FARST, a computer code for the evaluation of fuel rod thermal and mechanical behavior under steady-state/transient conditions has been developed. The code characteristics are summarized as follows:

1. (i) FARST evaluates the fuel rod behavior under the transient conditions. The code analyzes thermal and mechanical phenomena within a fuel rod, taking into account the temperature change in coolant surrounding the fuel rod.

2. (ii) Permanent strains such as plastic, creep and swelling strains as well as thermoelastic deformations can be analyzed by using the strain increment method.

3. (iii) Axial force and contact pressure which act on the fuel stack and cladding are analyzed based on the stick/slip conditions.

4. (iv) FARST used a pellet swelling model which depends on the contact pressure between pellet and cladding, and an empirical pellet relocation model, designated as “jump relocation model”.

The code was successfully applied to analyses of the fuel rod irradiation data from pulse reactor for nuclear safety research in Cadarache (CABRI) and pulse reactor for nuclear safety research in Japan Atomic Energy Research Institute (NSRR).The code was further applied to stress analysis of a 1000 MW class large FBR plant fuel rod during transient conditions. The steady-state model which was used so far gave the conservative results for cladding stress during overpower transient, but underestimated the results for cladding stress during a rapid temperature decrease of coolant.     

Effect of He-pre-injection on dislocation loop formation and irradiation-induced segregation of Fe–12%Cr–15%Mn austenitic steel

The effect of He-injection on irradiation-induced segregation of aging treated Fe–12%Cr–15%Mn austenitic steels, which are candidate materials as the reduced radio-activation of structure material for nuclear and/or fusion reactors was investigated by using the 1250 kV high voltage electron microscope (HVEM) connected with an ion accelerator. The Fe–Mn–Cr steel has been irradiated at 573 K by three irradiation modes of single electron-beam irradiation, electron-beam irradiation after He-injection and electron/He⁺-ion dual-beam irradiation in a HVEM. Irradiation-induced segregation analyses were carried out by an energy dispersive X-ray analyzer (EDX) in a 200 kV FE-TEM with beam diameter of about 0.5 nm. Dislocation loops with strain contrast were formed during irradiation and the loop numbers density increased rapidly with irradiation dose for He-pre-injected specimens. Voids were not observed after irradiations with three irradiation modes up to 5.4 dpa at 573 K. Irradiation-induced segregations of Cr and Mn near grain boundary were observed in each irradiation condition, but the amounts of Mn segregation decreased in the cases of electron/He⁺-ion dual-beam irradiation compared with single electron-beam and electron-beam irradiation after He-injection conditions.     

Probability assessment of graphite brick in the HTR-10

A probability finite element assessment program was developed to evaluate the security of graphite components in the HTR-10 (10 MW high temperature gas-cooled reactor-test module), based on the MARC non-linear finite element code and the strength uncertainty of the graphite material. Using user-defined subroutines (UDS), the irradiation thermal analysis subroutine, irradiation static analysis subroutine and probability assessment subroutine are embedded into the MARC program. The recompiled MARC program take into account irradiation-induced changes in graphite components such as the thermal conductivity coefficient, the thermal expansion coefficient, the creep coefficient, the elastic modulus, and the strength. The failure probabilities of the graphite components in the HTR-10, either under normal operating conditions or cold shutdown conditions, were evaluated. Additional analyses were done with the irradiation deformation increasing 20% and the creep coefficient decreasing 20%, to see the influence of irradiation deformation and the creep effect on the failure probability. The study showed that the probability finite element assessment method is an effective tool to assess the probability of structure failure.     

Irradiation creep in non-fissile metals and alloys

The principal methods used in measuring irradiation creep in non-fissile metals and alloys are described and the limitations of the techniques emphasised. The theoretical models of irradiation creep are surveyed and the experimental data on thermal and fast reactor core component materials, such as zirconium alloys and austenitic steels, are reviewed. In particular, the effects of compositional and metallurgical variables and irradiation parameters (temperature, dose and dose rate) on the magnitudes of the irradiation creep are assessed. Finally, the additional theoretical studies required to further the understanding of the phenomenon and the experimental work necessary for optimising the design and operation of thermal and fast reactors are summarised.     

THETRIS: A micro-scale temperature and gas release model for TRISO fuel

The dominating mechanism in the passive safety of gas-cooled, graphite-moderated, high-temperature reactors (HTRs) is the Doppler feedback effect. These reactor designs are fueled with submillimeter-sized kernels formed into tristructural-isotropic (TRISO) particles that are imbedded in a graphite matrix. The best spatial and temporal representation of the feedback effect is obtained from an accurate approximation of the fuel temperature. Micro-scale models of TRISO particles are necessary in order to obtain accurate predictions during fast transients or when parameters internal to the TRISO are needed. Most accident scenarios in HTRs are characterized by large time constants and slow changes in the fuel and moderator temperature fields. In these situations, a meso-scale, or pebble- and compact-scale, solution provides a good approximation of the fuel temperature as the fission thermal energy transports out of the kernel and into the surrounding matrix with a much shorter time constant. Therefore, in most cases, the matrix can be assumed to be in quasi-static equilibrium with the kernels. These models, however, fail to provide accurate information on the state of the various components of the TRISO during the early stages of transients. Since the coated particles constitute one of the fundamental design barriers for the release of fission products, it becomes important to understand the transient behavior inside this containment system. An explicit TRISO fuel temperature model named THETRIS has been developed and incorporated into the CYNOD–THERMIX-KONVEK suite of coupled codes. The code includes gas-release models that provide a simple predictive capability of the internal pressure during transients. The new model yields similar results to those obtained with other micro-scale fuel models of TRISO particles, but with the added capability to analyze gas release, internal pressure buildup, and effects of a gap in the TRISO. Analysis of bounding benchmark transients yield good agreement with other codes in which the TRISO particles are modeled explicitly. In addition, a sensitivity study of the potential effects on the transient behavior of high-temperature reactors due to the presence of an inter-layer gap is included. Although the formation of a gap occurs under special conditions, its consequences on the dynamic behavior of the reactor can yield responses during fast transients that depart significantly from those in which no gap is present in the model. The new model was applied to an extreme (beyond design basis) scenario in order to observe the behavior of the fuel during a large prompt critical reactivity insertion. Although a large amount of fission energy was deposited rapidly into the fuel, the kernel temperature is shown to stay well below the melting point and the silicon carbide layer remained well below the temperature above which failure is expected to occur. The explicit treatment of the TRISO particle geometry leads to much lower estimations of power peaking during the transient and a greater degree of negative Doppler feedback.     

Effects of dimensional change strain in nuclear graphite component stress analysis

Shrinkage and thermal stresses are induced into graphite components when they are irradiated in nuclear reactor cores. These stresses have to be taken into account in the reactor design and subsequent safety case assessments. This is usually done using graphite irradiation constitutive models programmed into a finite element code. The models use empirical data for the irradiation induced property and dimensional change, which are obtained from graphite material test reactor programmes. The dimensional change in nuclear graphite is one of the most important strains induced by the irradiation fluence. In this paper the effect of two different numerical methods to calculate the dimensional change strain is examined. Then the effect on the predicted stress using two different empirical models for dimensional change is studied. The solutions show that although the difference between two models is small, there are considerable differences in the stress profile.