Relationship between nuclear graphite moderator brick bore profile measurement and irradiation-induced dimensional change

A stress analysis for a hypothetical nuclear graphite moderator brick is presented, considering dimensional and other property changes due to fast neutron irradiation, to illustrate the relationship between the change in moderator brick bore profile and dimensional change of the material. The results give the stresses and deformations of the brick during operation and at shutdown, with the effect of irradiation creep on the deformation of the brick also considered. The analyses provide information useful to reactor designers and operators for planning graphite monitoring campaigns.     

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.     

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.     

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。     

核石墨耐辐照性能的评价方法

在高温气冷堆运行过程中,作为堆内构件的石墨经受高温和快中子的辐照,会经历先收缩后膨胀的宏观尺寸形变,并在膨胀至原始尺寸时到达使用寿命。在石墨尺寸形变的过程中,石墨内部气孔的结构和数目均有明显变化。当辐照剂量接近使用寿命时,石墨内部气孔数目明显增加,导致其力学性能急剧下降而退出服役。He⁺、C⁺、Xe⁺离子辐照实验表明,在200keV10¹⁴cm^-2Xe⁺离子辐照下,石墨气孔形貌变化明显。这一结果可作为石墨辐照性能的评价方法。     

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.     

Lifetime evaluation of graphite components for HTGRs

The lifetime of material and/or components has been discussed individually from different concepts, and sometimes gives confusion to material researchers as well as designers. The lifetime of materials is determined based on the dimensional changes due to neutron irradiation, at which they return to their original dimensions after initially contracting. On the other hand, the lifetime of components for HTGRs is defined based on a margin of the specified minimum ultimate strengths of the graphite to the stresses induced in the components. As an example, the stresses induced in the graphite block for the HTTR were, then, compared with the limited stress value determined from the specified minimum ultimate strength, and the lifetime of the component was evaluated and compared with that defined as dimensional changes. As a result, it was found that the lifetime of components for HTGRs should be determined as the shorter one in the two lifetimes defined by the stress-strength relationship and by the dimensional changes.     

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.     

高温气冷堆石墨材料的疲劳裂纹扩展综述

迄今为止,各国的高温气冷堆均采用石墨作为其堆芯活性区及反射层的主要结构材料。由于堆内的高温高辐照环境,石墨构件一般承受较高的热应力及辐照应力,这些应力的循环变化将引起疲劳载荷。     

熔盐/辐照环境中细结构等静压石墨的结构和化学稳定性研究

熔盐堆以石墨作为反射体和慢化体,熔盐与石墨直接接触,石墨在熔盐中的腐蚀反应和辐照损伤是值得研究的问题。本文采用自主研发的细结构石墨,阻隔熔盐浸渗,采用30 MeV He+模拟中子辐照,研究不同温度及熔盐环境下石墨微观形貌、微结构和化学结构的变化。研究结果表明,高温环境下,由于高温的退火效应,石墨缺陷密度的增加及形貌的变化都远小于室温环境。辐照后的石墨与熔盐接触,其缺陷密度略微降低。这种微结构的改善与高温熔盐环境中的退火效应及熔盐固化引起内部微裂纹的闭合有关。辐照后的熔盐浸泡可在石墨C—C键结构中引入C—F键,且C—F键的形成与缺陷密度及缺陷类型密切相关。稳定的空位簇及间隙原子的迁移均会影响层间化合物的形成,从而产生限制C—F键形成的环境,进而降低由层间化合物的形成对石墨表面结构的破坏。     

孔隙率对核级石墨氧化的影响

核级石墨在高温气冷堆中作为结构材料、慢化材料和反射层材料等被广泛应用,其氧化性能对高温气冷堆在进水或进气事故下材料的腐蚀行为有重要影响。初始孔隙率分布及孔隙率在氧化过程中的变化均对石墨氧化造成影响。本文以核级石墨IG-110、H-451、NBG-18和A3-3为例,以直径为6 cm的石墨球为研究对象,在一维瞬态氧化模型的基础上,分析了初始孔隙率分别服从均匀分布、正态分布和对数正态分布时对石墨氧化的影响。从模型简化和高温气冷堆安全分析角度保守考虑,建立石墨氧化模型时,核级石墨初始孔隙率可取均匀分布,此时石墨的整体失重率最大。     

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.     

Three-dimensional transient thermal stresses of reactor graphite subjected to internal heat generation and asymmetric surface heating

The present paper is concerned with three-dimensional transient thermal stresses of graphite in a nuclear reactor. In analyzing this problem, reactor graphite may be approximated by a transversely isotropic finite circular cylinder subjected to internal heat generation and asymmetric heating on an end surface. Thermal stresses are analyzed by means of the transversely isotropic potential functions method proposed by Takeuti and Noda. Numerical calculations were carried out for a special type of heating conditions, and time variations of temperature and thermal stresses of graphite are shown in figures.     

Irradiation induced dimensional changes in graphite: The influence of sample size

Dimensional changes in irradiated anisotropic polycrystalline GR-280 graphite samples as measured in the parallel and perpendicular directions of extrusion revealed a mismatch between volume changes measured directly and those calculated using the generally accepted methodology based on length change measurements only. To explain this observation a model is proposed based on polycrystalline substructural elements – domains. Those domains are anisotropic, have different amplitudes of shape-changes with respect to the sample as a whole and are randomly orientated relative to the sample axes of symmetry. This domain model can explain the mismatch observed in experimental data. It is shown that the disoriented domain structure leads to the development of irradiation-induced stresses and to the dependence of the dimensional changes on the sizes of graphite samples chosen for the irradiation experiment. The authors derive the relationship between shape-changes in the finite size samples and the actual shape-changes observable on the macro-scale in irradiated graphite.     

Residual stresses associated with the hydraulic expansion of steam generator tubing into tubesheets

Various methods are being used to expand heat transfer tubes into the thick tubesheets of nuclear steam generators. The residual stresses in the as-expanded tubes and methods for reducing these stresses are important because of the role which residual stresses play in stress corrosion cracking and stress assisted corrosion of the tubing. Of the various expansion processes, the hydraulic expansion process is most amenable to analytical study. This paper presents results on the residual stresses and strains in hydraulically expanded tubes and the tubesheet as computed by two different finite element codes with three different finite element models and by a theoretical incremental analysis method. The calculations include a sensitivity analysis to assess the effects of the expansion variables and the effect of stress relief heat treatments.     

Magnetic measurements for evaluation of radiation damage on nuclear reactor materials

It is important for the plant lifetime management to estimate the loss of toughness and other effects, e.g. increase of yield strength and hardness, caused by irradiation. This paper deals with the use of magnetic measurements to determine the irradiation effects on nuclear reactor structural materials. Three types of nuclear reactor materials were studied. Samples of the materials were irradiated with different neutron fluences. The Magnetic Barkhausen Emission was measured using stabilised flux mode, i.e., control of the magnetic flux within the sample to compensate for leakage and variations on the flux. The samples were carefully identified according to position and the cutting direction within the steel forging block. Anisotropy effect due to sample cutting direction was observed and it masks the magnetic signal results induced by the irradiation effects. The results on the specimens cut in the same direction shows correlation with irradiation induced material hardening and its dependence on fluence. Different materials show different hardening levels. Barkhausen emission results were correlated to neutron fluence taking into account the cutting direction.     

高温气冷堆核级石墨相关问题研究

本文通过对石墨在高温气冷堆中的运行环境进行了分析,研究了在石墨堆内构件设计中的关键问题和在高温气冷堆单个模块及其未来发展中核级石墨的需求。从原料、成型及中子辐照等角度分析了核级石墨国产化研究方向。根据核级石墨目前的研发形势,进行了风险问题分析。     

Prediction of radiation induced hardening of reactor pressure vessel steels using artificial neural networks

In this paper, we use an artificial neural network approach to obtain predictions of neutron irradiation induced hardening, more precisely of the change in the yield stress, for reactor pressure vessel steels of pressurized water nuclear reactors. Different training algorithms are proposed and compared, with the goal of identifying the best procedure to follow depending on the needs of the user. The numerical importance of some input variables is also studied. Very accurate numerical regressions are obtained, by taking only four input variables into account: neutron fluence, irradiation temperature, and chemical composition (Cu and Ni content). Accurate extrapolations in term of neutron fluence are obtained.     

Modelling of the spatial distribution of the induced activities in the RBMK-1500 reactor graphite blocks and rings/sleeves

There is one nuclear power plant (NPP) in Lithuania – the Ignalina NPP – which is under decommissioning now. The Ignalina NPP has two units with RBMK-1500 reactors, which are the most powerful and the most advanced versions of RBMK-type reactor design. Unit 1 of the Ignalina NPP was shut down at the end of 2004 and Unit 2 was shut down at the end of 2009. RBMK is a water-cooled graphite-moderated channel-type power reactor and the decommissioning of these reactors faces specific challenges for proper characterisation and disposal of irradiated reactor graphite.Apart from radiological inventory, the spatial distribution of radionuclides in the reactor graphite is also very important because it could indicate the possibilities for decontamination/treatment of the irradiated graphite. This is important for consideration of the near surface disposal option for irradiated graphite, as without treatment it usually does not meet the waste acceptance criteria.Based on that, the work presented in this paper is focused on the modelling of the induced activity spatial distribution in the Ignalina NPP RBMK-1500 reactor graphite components: blocks and rings/sleeves. The modelling was performed with MCNP and SCALE computer codes and consisted of two mains stages: modelling of the neutron flux in the reactor graphite components, and then modelling of the neutron activation in them using the already modelled neutron flux. In such a way, the spatial induced activity distribution in the analysed reactor components was obtained. Modelling results show that the thermal neutron flux is more intensive in the outer radial regions of the graphite components and this, in general, results in higher induced activities there.