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.     

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.     

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.     

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.     

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.     

Joint programme of uni-axial creep measurements of htr compacts and matrix material under tensile load at 900°C

Three reactor creep machines with continuous in-pile dimensional measurement were fabricated and irradiated successively in the High Flux Reactor (HFR) of the Euratom Joint Nuclear Research Centre in Petten — Netherlands. Three different types of materials, of which two were dummy coated particle compacts and one pure matrix material, were tested in these machines. These dumbbell shaped material samples were delivered by Belgonucleaire S.A. — Brussels, the Kernforschungsanlage — Jülich and the Dragon Project; they were irradiated under constant uni-axial tensile load, at a constant temperature of 900°C and up to a peak fast neutron fluence of $\text{8.0 × 10}{}^{20}\text{n · cm}{}^{\mathrm{?2}}$(DNE). The main objectives of these experiments were the determination of the irradiation induced uni-axial primary and secondary creep behaviour, and the measurement of the creep strain limit of HTR matrix material and compacts. The design of these experiments, their irradiation histories and the analysis of the in-pile measurements are detailed and discussed in the paper.     

Electron induced irradiation creep and direct observation of the underlying dislocation processes involved

The dynamic behaviour of some of the lattice defects which current hypotheses assume to be responsible for irradiation enhanced creep has been studied using a high voltage electron microscope to concurrently generate displacement damage and image local deformations. Experimental techniques are outlined. Measurements on pyrolytic carbon, stainless steel, zirconium, and some alloys, are presented and discussed in terms of the revelation of physical processes underlying irradiation creep and the feasibility of simulating reactor induced behaviour by laboratory experiments.     

Thermally induced strain recovery in irradiated and unirradiated zirconium alloy stress-relaxation specimens

Thermally induced strain recovery has been measured in specimens which were stress relaxed at 570 K either in a reactor or in an autoclave. Strain recovery occurs in both unirradiated and irradiated specimens. Strain recovery in unirradiated specimens is attributed to unpinning of anelastically bowed dislocations. Strain recovery in irradiated specimens occurs in two stages; a rapid stage attributed to unpinning bowed dislocations and a slow stage attributed to annealing of irradiation defects. Assuming that mechanisms proposed for creep are applicable during stress-relaxation the complete recovery of irradiation-induced strains in annealed specimens and partial recovery in specimens with some cold-work agrees with expectations from models based on stress-induced alignment of dislocation loops and irradiation damage. Recovered strains in this experiment were small as were strains measured by others on irradiated specimens with larger deformation strains, thus annealing to reduce strains in reactor structures may not be useful.     

Behaviour of spent HTR fuel elements in aquatic phases of repository host rock formations

One back-end option for spent HTR fuel elements proposed for future HTR fuel cycles in the EC is an open fuel cycle with direct disposal of conditioned or non-conditioned fuel elements. This option has already been chosen in Germany due to the political decision to terminate the use of HTR technology. First integral leaching investigations at Research Centre Juelich on the behaviour of spent HTR fuel in salt brines, typical of accident scenarios in a repository in salt, proved that the main part of the radionuclide inventory cannot be mobilised as long as the coated particles do not fail. However, such experiments will not lead to a useful model for performance assessment calculations, because a failure of the coatings by corrosion will not occur during experimental times of a few years. In order to get a robust and realistic model for the long-term behaviour in aqueous phases of host rock systems, it is necessary to understand the barrier function of the different parts of an HTR fuel element, i.e. the matrix graphite, the different coating materials, and the fuel kernel.Therefore, our attention is focused on understanding and modelling the barrier performance of the different parts of an HTR fuel element with respect to their barrier function, and on the development of an overall model for performance assessment. In order to understand this behaviour, it is necessary to start with investigations of unirradiated material, and to proceed with experiments with external gamma irradiation to determine the effects of oxidising radiolysis species. Further experiments with irradiated material have to be performed to investigate the influence of the irradiation damage, and finally an investigation has to be made of the irradiated material plus additional gamma irradiation. Experimental data are now available for the diffusive transport of radionuclides in the water-saturated graphite pore system, the corrosion rates of unirradiated graphite with and without external gamma irradiation and unirradiated and irradiated silicon carbide, and for the dissolution rates of UO₂ and (Th,U)O₂ fuel kernels with and without external gamma irradiation. All investigations were performed in aquatic phases from salt, granite, and clay host rock.     

辐照用小尺寸样品力学性能表征技术研究进展

由于辐照空间尺寸限制、降低样品放射性和提高辐照参数精度等原因,小尺寸样品被广泛应用于核反应堆材料的辐照后力学性能表征。本文就国内外小尺寸拉伸、冲击、断裂韧性、疲劳、蠕变和小冲杆等测试表征技术的研究现状进行了综合论述,分析了小尺寸样品测试中的关键影响因素以及数据归一化方法,总结了小尺寸样品存在的问题,并结合我国需求对小尺寸样品技术的发展进行了分析和展望,以期为小尺寸样品技术及测试分析数据进一步规范化和工程应用发展提供参考。     

Irradiation creep of SA 304L and CW 316 stainless steels: Mechanical behaviour and microstructural aspects. Part I: Experimental results

Solution annealed 304L (SA 304L) and cold work 316 (CW 316) austenitic stainless steel irradiation creep behaviour have been studied thoroughly. Irradiations were carried out in fast breeder reactors BOR-60 (at 330 °C, up to 120 dpa) and EBR-II (at 375 °C, up to 10.5 dpa), and in the OSIRIS mixed spectrum reactor (at 330 °C, up to 9.8 dpa). After an incubation threshold, the irradiation creep of the austenitic stainless steels is linear in stress and in dose. Creep appears to be athermal in this temperature range. A significant difference in the behaviour is measured between the creep of SA 304L and CW 316.In order to study the anisotropy of loop population, which would be the signature of a possible stress induced preferential absorption (SIPA) mechanism for irradiation creep, special attention was given to the measurement of anisotropy of loop distribution between the four families. The anisotropy induced by an applied stress has been shown to be in the range of the statistical scatter in the situation where no stress is applied. TEM microstructural analyses performed on this sample show slight difference between the microstructure of specimens deformed under irradiation and the microstructure of specimens irradiated without stress under the same irradiation conditions.     

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.     

Stress state dependence of in-reactor creep and swelling. Part 2: Experimental results

Irradiation creep constitutive equations, which were developed in Part I, are used here to analyze in-reactor creep and swelling data obtained ca. 1977-1979 as part of the US breeder reactor program. The equations were developed according to the principles of incremental continuum plasticity for the purpose of analyzing data obtained from a novel irradiation experiment that was conducted, in part, using Type 304 stainless steel that had been previously irradiated to significant levels of void swelling. Analyses of these data support an earlier observation that all stress states, whether tensile, compressive, shear or mixed, can affect both void swelling and interactions between irradiation creep and swelling. The data were obtained using a set of five unique multiaxial creep-test specimens that were designed and used for the first time in this study. The data analyses demonstrate that the constitutive equations derived in Part I provide an excellent phenomenological representation of the interactive creep and swelling phenomena. These equations provide nuclear power reactor designers and analysts with a first-of-its-kind structural analysis tool for evaluating irradiation damage-dependent distortion of complex structural components having gradients in neutron damage rate, temperature and stress state.     

Investigation of radiation creep of reactor graphite

The results of investigations of the radiation creep of GR-280 graphite under a high compression load (about 15 MPa) after irradiation in a BOR-60 reactor at 520°C to fast-neutron fluence 1.2·10²² cm⁻² are presented. It is shown that the fluence dependence of the creep deformation, calculated using the standard relation as the difference of the change in the dimensions of loaded and control samples, is anomalous. The linear thermal expansion coefficients of loaded and control samples are found as functions of the neutron fluence under the same conditions. It is noted that the linear thermal expansion coefficient of the samples irradiated under a load is much higher than that of the control samples. Simmons' theorem is used to take account of the effect of a load on the linear thermal expansion coefficient, and the dimensional changes of graphite exposed to radiation and the dependence of the true creep deformation on the neutron fluence are calculated. It is shown that these dependences are close to linear in the experimental fluence range (0.4–1.2)·10²² cm⁻². Translated from Atomnaya énergiya, Vol. 105, No. 2, pp. 83–87, August, 2008.     

Viscoelastic analysis of irradiated graphite with variable creep coefficient

This paper provides a refined analysis of a previous study concerning a method of stress analysis for irradiated graphite which may be used for molten salt breeder reactor (MSBR) core design. The present method includes the effect of a variable creep coefficient which is caused by the non-uniform temperature distribution. To facilitate a simple formulation, it is assumed that the temperature dependence of the elastic response of the material is approximated to be inversely proportional to the creep rate. It is shown that the problem reduces to the solution of several associated (fictitious) elastic problems which have a common elastic modulus inversely proportional to the creep rate of the irradiated graphite. Numerical examples in the previous paper were recalculated on the basis of the present theory. It shows, for large dose values, some small differences compared with the previous calculation. This method is expected to be more effective for higher dose values and more sensitive creep coefficients.     

Radiation creep of graphite. An introduction

Graphite, a class of materials with many unique and unusual properties, shows a remarkably high creep ductility under irradiation. As this behaviour compensates to some extent some of the more worrying radiation effects, such as dimensional changes and their strong temperature dependence, it is a property of large technological interest. There are various ways of observing and measuring in-pile creep of graphite, varying in degree of sophistication and in cost, in accuracy and in the type of data that is generated. This paper attempts to review briefly the various experimental methods, and the knowledge generated so far. An indication is given of the areas in which further knowledge is wanted.     

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.     

Microstructural examination of V-(Fe or Cr)-Ti alloys after thermal-creep or irradiation-creep tests

Microstructural examinations have been performed on irradiation-creep and thermal-creep pressurized tube specimens of V-3Fe-4Ti-0.1Si in order to understand failure and creep mechanisms. There are no typical microstructural differences between unstressed and pressurized creep tube specimens irradiated in ATR-A1 in the irradiation temperature regime from 212 to 300 °C. Failed thermal creep specimens show dislocation structures dependent on the tube specimen geometry. This can be interpreted in terms of a large number of slip dislocations oriented for optimum slip.