Comprehensive nuclear materials 4 11 graphite in gas cooled reactors

Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors Comprehensive nuclear materials 4 11 graphite in gas cooled reactors

4.11 Graphite in Gas-Cooled Reactors B J Marsden and G N Hall The University of Manchester, Manchester, UK ß 2012 Elsevier Ltd All rights reserved 4.11.1 4.11.2 4.11.2.1 4.11.2.2 4.11.2.3 4.11.2.4 4.11.2.5 4.11.3 4.11.3.1 4.11.4 4.11.5 4.11.5.1 4.11.5.2 4.11.5.2.1 4.11.5.3 4.11.5.4 4.11.5.4.1 4.11.5.5 4.11.5.6 4.11.5.7 4.11.5.8 4.11.5.9 4.11.6 4.11.6.1 4.11.7 4.11.7.1 4.11.7.2 4.11.7.2.1 4.11.7.3 4.11.7.4 4.11.7.5 4.11.7.6 4.11.7.7 4.11.8 4.11.9 4.11.9.1 4.11.9.2 4.11.10 4.11.11 4.11.11.1 4.11.11.2 4.11.11.3 4.11.11.4 4.11.11.5 4.11.11.6 4.11.12 Introduction Graphite Crystal Structures Graphite Crystal Atomic Structure and Properties Coefficient of Thermal Expansion Modulus Thermal Conductivity Microcracking (Mrozowski Cracks) Artificial Nuclear Graphite Microstructure/Property Relationships Graphite Core Fast Neutron Fluence, Energy Deposition, and Temperatures Dosimetry (Graphite Damage Dose or Fluence) Early Activation Measurements on Foils Reactor Design and Assessment Methodology: Fuel Burnup Calder effective dose Equivalent Nickel Flux Integrated Flux and Displacements per Atom DIDO equivalent flux Energy Above 0.18 MeV Equivalent Fission Flux (IAEA) Fluence Conversion Factors Irradiation Annealing and EDT Summary of Fast Neutron Dose (Fluence) Graphite ‘Energy Deposition’ (Nuclear Heating) The Use of Titanium for Installed Sample Holders Radiolytic Oxidation Introduction Ionizing Radiation Energy deposition Radiolytic Oxidation Mechanism Inhibition Internal Porosity Prediction of Weight Loss in Graphite Components Weight Loss Prediction in Inhibited Coolant Graphite Temperatures Variation of Fluence, Temperature, and Weight Loss in a Reactor Core Fuel End Effects Temperature and Weight Loss Distribution of Fluence Within an Individual Moderator Brick Fast Neutron Damage in Graphite Crystal Structures Stored Energy Crystal Dimensional Change Coefficient of Thermal Expansion Modulus Thermal Conductivity Raman Property Changes in Irradiated Polycrystalline Graphite 327 327 327 328 328 329 329 329 330 332 333 334 335 335 336 336 337 338 339 339 339 339 340 341 341 341 341 341 341 342 342 343 343 346 346 347 347 347 348 348 352 353 354 354 354 355 325 326 Graphite in Gas-Cooled Reactors 4.11.13 4.11.14 4.11.14.1 4.11.14.2 4.11.14.3 4.11.14.4 4.11.15 4.11.15.1 4.11.15.2 4.11.15.3 4.11.15.4 4.11.16 4.11.16.1 4.11.16.2 4.11.16.3 4.11.16.4 4.11.17 4.11.17.1 4.11.17.2 4.11.17.3 4.11.17.4 4.11.17.5 4.11.17.6 4.11.18 4.11.19 4.11.20 4.11.20.1 4.11.20.2 4.11.20.3 4.11.20.4 4.11.20.4.1 4.11.20.4.2 4.11.20.5 4.11.20.6 4.11.20.6.1 4.11.20.6.2 4.11.20.6.3 4.11.20.6.4 4.11.20.7 4.11.21 References Averaging Relationships Dimensional Change Pile Grade A Gilsocarbon Effect of Radiolytic Oxidation on Dimensional Change Dimensional Change Rate Coefficient of Thermal Expansion Pile Grade A Gilsocarbon Methodology for Converting Between Temperature Ranges Effect of Radiolytic Oxidation on CTE Thermal Conductivity Pile Grade A Gilsocarbon Thermal Conductivity Temperature Dependence of Irradiated Graphite Predicting the Thermal Conductivity of Irradiated Graphite for Reactor Core Assessments Young’s Modulus Relationship Between Static and Dynamic Young’s Modulus Pile Grade A Gilsocarbon Separation of Structure and Pinning Terms Effect of Radiolytic Weight Loss on Dimensional Change and Young’s Modulus Small Specimen Strength Effect of Radiolytic Oxidation on Thermal Conductivity, Young’s Modulus, and Strength The Use of the Product Rule Irradiation Creep in Nuclear Graphite Dimensional Change and Irradiation Creep Under Load Types of Irradiation Creep Experiments The UKAEA Creep Law Observed Changes to Other Properties Coefficient of thermal expansion Young’s modulus Lateral Changes Creep Models and Theories UKAEA creep law German and US creep model Further modifications to the UKAEA creep law: interaction strain Recent nuclear industry model Final Thoughts on Irradiation Creep Mechanisms Concluding Remark Abbreviations AG AGR BAF BEPO CPV Against grain Advanced gas-cooled reactor Bacon anisotropy factor British Experimental Pile Zero Closed pore volume CTE DFR DSC DYM EDND EDNF Coefficient of thermal expansion Dounreay Fast Reactor Differential scanning calorimeter Dynamic Young’s modulus Equivalent DIDO nickel dose Equivalent DIDO nickel flux 357 359 360 363 364 366 366 366 367 367 368 368 369 369 369 370 371 372 372 372 374 374 375 375 375 376 378 378 378 380 380 381 381 381 383 385 385 387 387 387 388 Graphite in Gas-Cooled Reactors EDT FWHM HFR HOPG HRTEM Equivalent DIDO temperature Full-width, half-maximum High Flux Reactor Highly oriented pyrolytic graphite High-resolution transmission electron microscopy HTR High temperature reactor IAEA International Atomic Energy Agency MTR Materials test reactor NDT Nondestructive testing OPV Open pore volume PGA Pile Grade A RBMK Reaktor Bolshoy Moshchnosti Kanalniy (there are other quoted translations) RPV Reactive pore volume SEM Scanning electron microscopy SYM Static Young’s modulus TEM Transmission electron microscopy TPV Total pore volume UKAEA United Kingdom Atomic Energy Authority WG With grain 327 This chapter aims to address that need by explaining the influence of microstructure on the properties of nuclear graphite and how irradiation-induced changes to that microstructure influence the behavior of graphite components in reactor Nuclear graphite is manufactured from coke, usually a by-product of the oil or coal industry (Some cokes are a by-product of refining naturally occurring pitch such as Gilsonite.9) Thus, nuclear graphite is a porous, polycrystalline, artificially produced material, the properties of which are dependent on the selection of raw materials and manufacturing route In this chapter, the properties of the graphite crystal structures that make up the bulk polycrystalline graphite product are first described and then the various methods of manufacture and resultant properties of the many grades of artificial nuclear graphite are discussed This is followed by a description of the irradiation damage to the crystal structure, and hence the polycrystalline structure, and the implication of graphite behavior The influence of radiolytic oxidation on component behavior is also discussed as this is of interest to operators or designers of graphitemoderated, carbon dioxide-cooled reactors, many of which are still operating 4.11.1 Introduction Nuclear graphite has, and still continues, to act as a major component in many reactor systems In practice, nuclear graphite not only acts as a moderator but also provides major structural support which, in many cases, is expected to last the life of the reactor The main texts on the topic were written in the 1960s and 1970s by Delle et al.,1 Nightingale,2 Reynolds,3 Simmons,4 in German, and Pacault5 Tome I and II, in French with more recent reviews on works by Kelly6,7 and Burchell.8 This text is mainly on the basis of the UK graphite reactor research and operating experience, but it draws on international research where necessary During reactor operation, fast neutron irradiation, and in the case of carbon dioxide-cooled systems radiolytic oxidation, significantly changes the graphite component’s dimensions and properties These changes lead to the generation of significant graphite component shrinkage and thermal stresses Fortunately, graphite also exhibits ‘irradiation creep’ which acts to relieve these stresses ensuring, with the aid of good design practice, the structural integrity of the reactor graphite core for many years In order to achieve the optimum core design, it is important that the engineer has a fundamental understanding of the influence of irradiation on graphite dimensional stability and material property changes 4.11.2 Graphite Crystal Structures The properties and irradiation-induced changes in graphite crystals have been studied using both ‘naturally occurring’ graphite crystals and an artificial product referred to as highly orientated pyrolytic graphite (HOPG), formed by depositing a carbon substrate using hydrocarbon gas6 followed by compression annealing at around 3000  C HOPG is considered to be the most appropriate ‘model’ material that can be used to study the behavior of artificially produced polycrystalline nuclear graphite It has a density value near to that of a perfect graphite crystal structure, but perhaps more appropriately, it has imperfections similar to those found in the structures that make up artificial polycrystalline graphite A detailed description of the properties of graphite can be found in Chapter 2.10, Graphite: Properties and Characteristics 4.11.2.1 Graphite Crystal Atomic Structure and Properties In this section, the atomic structure of graphite crystal structures is discussed briefly, along with some of the properties relevant to the understanding of the 328 Graphite in Gas-Cooled Reactors irradiation behavior of graphite Graphite can be arranged in an ABAB stacking arrangement termed hexagonal graphite (see Figure 1) This is the most thermodynamically stable form of graphite and has a density of 2.266 g cmÀ3 The a-spacing is 1.415 A˚ and the c-spacing is 3.35 A˚ However, in both natural and artificial graphite stacking faults and dislocations abound.10 4.11.2.3 The crystal elastic moduli6 are C11 (parallel to the basal planes) ¼ 1060.0  109 N mÀ2, C12 ¼ 180.0  109 N mÀ2, C13 ¼ 15.0  109 N mÀ2, C33 (perpendicular to the basal planes) ¼ 34.6  109 N mÀ2, and C44 (shear of the basal planes) ¼ 4.5  109 N mÀ2 as defined by the orthogonal co-ordinates given below: 4.11.2.2 Modulus sxx C11 C12 C13 0 C11 C13 0 C13 C33 0 0 C44 0 B C B B syy C B C12 B C B B C B B szz C B C13 B C B Bt C ¼ B B zx C B B C B Bt C B @ zy A @ Coefficient of Thermal Expansion The coefficient of thermal expansion (CTE) as measured for natural graphite and HOPG is temperature dependent (Figure 2) and the data from a number of authors has been collated by Kelly.6 The room temperature values of CTE are about 27.5  10À6 KÀ1 and À1.5  10À6 KÀ1 in the ‘c’ and ‘a’ directions, respectively txy 0 0 C44 0 0 10 C C C C C C C C C C A 1ðC ÀC Þ 12 11 exx B C B eyy C B C B C B ezz C B C Be C B zx C B C Be C @ zy A exy ½1Š c c a a Upper layer (A) a Lower layer (B) 40 30 CTE ac (10−6 K−1) CTE aa (10−6 K−1) Figure The crystalline structure of graphite Bailey and Yates Steward et al Harrison Yates et al −1 −2 20 Bailey and Yates Steward et al Harrison Yates et al Nelson and Riley 10 0 500 1000 1500 2000 Temperature (K) ‘c’ direction 2500 3000 500 1000 1500 2000 Temperature (K) 2500 ‘a’ direction Figure Crystal coefficient of thermal expansion Modified from Kelly, B T Physics of Graphite; Applied Science: London, 1981 3000 Graphite in Gas-Cooled Reactors The strength of the crystallite is also directly related to the modulus, that is, the strength along the basal planes is higher than the strength perpendicular to the planes, and the shear strength between the basal panes is relatively weak 4.11.2.4 Thermal Conductivity The thermal conductivity of graphite along the basal plane ‘a’ direction is much greater than the thermal conductivity in the direction perpendicular to the basal plane ‘c.’ At the temperature of interest to the nuclear reactor engineer, graphite thermal conduction is due to phonon transport Increasing the temperature leads to phonon–phonon or Umklapp scattering (German for turn over/down) Imperfections in the lattice will lead to scattering at the boundaries 329 width and many micrometers in length (as seen in Figure 3(b)), appears to be counterintuitive and has led to speculation that these microcracks may contain some low-density carbonaceous structure The presence of these microcracks is very important in understanding the properties of nuclear graphite as they provide accommodation for thermal or irradiationinduced crystal expansion in the ‘c’ direction Therefore, two crystal structures are of interest; the ideal, ‘perfect’ structure and the nonperfect structures as may be defined with reference to HOPG It is of the latter that many of the crystal behaviors and properties have been studied Definition: In this chapter on nuclear graphite, ‘crystal’ refers to the perfect crystal structure and ‘crystallite’ refers to the nonperfect crystal structures containing Mrozowski-type microcracks (and nanocracks) 4.11.2.5 Microcracking (Mrozowski Cracks) 4.11.3 Artificial Nuclear Graphite During the manufacture of artificial graphite, very high temperatures (2800–3000  C) are required in the graphitization process On cooling from these high temperatures, thermoplastic deformation is possible until a temperature of $1800  C is reached Below this temperature, the large difference in thermal expansion coefficients between the ‘c’ and ‘a’ directions leads to the formation of long, thin microcracks parallel to the basal planes, often referred to as ‘Mrozowski’ cracks.11 These types of cracks are even observed in HOPG (Figure 3) The high density of HOPG when compared to the large number of microcracks, a few nanometers in The reactor designer requires a high-density, very pure graphite, with a high scattering cross-section, a low absorption cross-section, and good thermal and mechanical properties, both in the unirradiated and irradiated condition The purity is important to ensure not only a low absorption cross-section but also that during operation the radioactivity of the graphite remains as low as possible for waste disposal purposes Artificial graphite is manufactured from coke obtained either from the petroleum or coal industry, or in some special cases (such as Gilsocarbon, a UK grade of graphite) from a ‘graphitizable’ coke derived µm µm (a) (b) Figure Transmission electron microscopic images of highly orientated pyrolytic graphite (a) View into the ‘basal’ plane, ‘c’ direction, of HOPG (reproduced from Kelly, B T MSc thesis, University of Cardiff, Cardiff, Wales, 1966) and (b) Mrozowski cracks in HOPG as seen along the ‘basal’ planes, ‘a’ direction Courtesy of A Jones, University of Manchester 330 Graphite in Gas-Cooled Reactors from naturally occurring pitch deposits.9 The raw coke is first calcined to remove volatiles and then ground or crushed for uniformity, before being blended and mixed with a pitch binder (Crushed ‘scrap’ artificial graphite may be added to help with heat removal during the subsequent baking For nuclear graphite, this should be of the same grade as the final product.) This mixture is then formed into blocks using one of various techniques such as extrusion, pressing, hydrostatic molding, or vibration molding, to produce the so-called ‘green article.’ The ‘green’ blocks are then put into large ‘pit’ or ‘intermittent’ gas or oil-fired furnaces The blocks are usually arranged in staggers, covered by a metallurgic coke, and baked at around 800  C in a cycle lasting about month to produce carbon blocks These carbon blocks may be used for various industrial purposes such as blast furnace liners; it has even been used for neutron shielding in some nuclear reactors (Care must be taken as the carbon blocks are not as pure as graphite and may lead to waste disposal issues at the end of the reactor life.) To improve the properties of the graphite produced from the carbon block, the carbon block is often impregnated with a low-density pitch under vacuum in an autoclave To facilitate the entry of the pitch into the body of the block, the block surface may be broken by grinding After impregnation the blocks are then rebaked This process of impregnation and rebaking may be repeated 2, 3, or times However, the improvement in the properties by this process is subject to diminishing rewards The next process is graphitization at about 2800– 3000  C by passing a large electrical current at low voltage through the blocks either in an ‘Acheson furnace’ or using an ‘in-line furnace.’ In both cases, the blocks are covered by a metallurgical coke to prevent oxidation This graphitization cycle may take about month If necessary, there may be a final purification step This involves heating the graphite blocks to around 2400  C in a halogen gas atmosphere to remove impurities The final product can then be machined into the many intricate components required in a nuclear reactor For quality assurance purposes, during manufacture the blocks are numbered at an early stage and this number follows the block through the manufacturing process This is clearly an expensive manufacturing process and therefore, at each stage, quality control is very important Many samples will be taken from the blocks to ensure that the final batch (or heat) is of appropriate quality compared to previous heats It is important that the reactor operators retain this data in electronic form as it may be required to investigate any anomalous behavior as the reactor ages Samples of ‘virgin’ unirradiated graphite blocks should also be retained for future reference Records should include information on the batch or heat, property measurements, nondestructive testing (NDT) results, and measurements of impurities It is not enough just to have the ‘ash’ content after incineration and the ‘boron equivalent’ as some impurities, such as nitrogen, chlorine, and cobalt, will cause significant issues related to reactor operation and final waste disposal It is important that the reactor operator takes responsibility for these measurements as in the past it has been found that reactor designers and graphite manufacturers close down or merge, and records are lost Final inspection will uncover issues related to damage, imperfection, quality, etc Therefore, a ‘concessions’ policy is required to determine what is acceptable and where such components can be used in reactor Again, the reactor operator will require an electronic record of these concessions 4.11.3.1 Microstructure/Property Relationships The microstructure of a typical nuclear graphite is described with reference to Gilsocarbon This product was manufactured from coke obtained from a naturally occurring pitch found at Bonanza in Utah in the United States To understand the microstructural properties, one has to start with the raw coke The structure of Gilsonite coke is made of spherical particles about mm in diameter as shown in Figure This structure is retained throughout manufacture and into the final product In Figure 4(b), the spherical shaped cracks following the contours of the spherical particles are clearly visible This coke will be carefully crushed in order to keep the spherical structures that form the filler particles and help to give Gilsocarbon its (semi-) isotropic properties At a larger magnification in a scanning electron microscopy (SEM), the complexity of these cracks is clearly visible, Figure 4(c), and at an even larger magnification, a ‘swirling structure’ made up of graphite platelets stacked together is discernable between the cracks In essence, the whole structure contains a significant amount of porosity After graphitization, the Gilsonite coke filler particles are still recognizable (Figure 5(a) and 5(b)) From the polarizing colors, one can see that the main ‘a’ axis orientation of the crystallites follows the Graphite in Gas-Cooled Reactors (a) 331 (b) (c) (d) Figure Gilsonite raw-coke microstructure (a) Photograph of Gilsonite coke, (b) Scanning electron microscopy (SEM) image of polished Gilsonite coke, (c) detail in an SEM image showing the region around cracks that follow the spherical shape of the coke particles, and (d) a higher magnification SEM image showing the intricate, random arrangement of platelets Courtesy of W Bodel, University of Manchester (a) (c) 500 µm (b) 200 µm (d) Figure Polarized optical and scanning electron microscopic images of Gilsocarbon graphite (a) Optical image, (b) optical image, (c) SEM image, (d) SEM image Courtesy of A Jones, University of Manchester 332 Graphite in Gas-Cooled Reactors spherical particles circumferentially, as does the orientation of the large calcination cracks The crystallite structures in the binder phase are much more randomly oriented, and this phase contains significant amounts of gas-generated porosity There are also what appear to be broken pieces of Gilsonite filler particles contained within the binder phase The bulk properties of polycrystalline nuclear graphite strongly depend on the structure, distribution, and orientation of the filler particles.12 The spherical Gilsonite particles and molding technique give Gilsocarbon graphite semi-isotropic properties, whereas in the case of graphite grades such as the UK pile grade A (PGA), the extrusion process used during manufacture tends to align the ‘needle’ type coke particles Thus, the crystallite basal planes that make up the filler particles tend to align preferentially, with the ‘c’ axis parallel to the extrusion direction and the ‘a’ axis perpendicular to the extrusion direction The long microcracks are also aligned in the extrusion direction The terms ‘with grain (WG)’ and ‘against grain (AG)’ are used to describe this phenomenon, that is, WG is equivalent to the parallel direction and AG is equivalent to the perpendicular direction Thus, the highly anisotropic properties of the crystallite are reflected in the bulk properties of polycrystalline graphite (Table 1) A graphite anisotropy ratio is usually defined by the AG/WG ratio of CTE values For needle coke graphite, this ratio can be two or more, while for a more randomly orientated structure, values in the region of 1.05 can be achieved by careful selection of material and extrusion settings A more scientific way of defining anisotropy ratio is by use of the Bacon anisotropy factor (BAF).13 Other forming methods are usually used to produce isotropic graphite grades such as the Gilsocarbon grade described above In this case, it was found that Gilsocarbon graphite produced by extrusion was not isotropic enough to meet the advanced gascooled reactor (AGR) specifications Therefore, a Table Relative properties–grain direction relationships Property Coefficient of thermal expansion (CTE) Young’s modulus Strength Thermal conductivity Electrical resistivity With grain (WG) Against grain (AG) Lower Higher Higher Higher Higher Lower Lower Lower Lower Higher ‘molding’ method where the blocks were formed by pressing in two directions was used This had the effect of slightly aligning the grains such that the AG direction was parallel to the pressing direction and the WG was perpendicular to the pressing direction However, Gilsocarbon has proved to be one of the most isotropic graphite grades ever produced, even in its irradiated condition Another approach is to choose an ‘isotropic coke’ crushed into fine particles and then produce blocks using ‘isostatic molding’ process The isostatic molding method involves loading the fine-grained coke binder mixture into a rubber bag which is then put under pressure in a water bath In this way, high quality graphite can be produced mainly for use for specialist industries such as the production of electronic components This type of graphite (such as IG110 and IG-11) has been used for high-temperature reactor (HTR) moderator blocks, fuel matrix, and reflector blocks in both Japan and China However, even these grades exhibit slight anisotropy The final polycrystalline product contains many long ‘thin’ (and not so ‘thin’) microcracks within the crystallite structures that make up the coke particles Similar, but much smaller, cracked structures are to be found in the ‘crushed filler flour’ used in the binder, and in well-graphitized parts of the binder itself It is these microcracks that are responsible for the excellent thermal shock resistance of artificial polycrystalline graphite They also provide ‘accommodation,’ which further modifies the response of bulk properties to the crystal behavior in both the unirradiated and irradiated polycrystalline graphite Typical properties of several nuclear graphite grades are given in Table One can see that polycrystalline graphite has about 20% porosity by comparing the bulk density with the theoretical density for graphite crystals (2.26 g cmÀ3) About 10% of this is open porosity, the other 10% being closed 4.11.4 Graphite Core Fast Neutron Fluence, Energy Deposition, and Temperatures Since the late 1940s, many journal papers, conference papers, and reports have been published on the change in properties in graphite due to fast neutron damage Many different units have been used to define graphite damage dose (or fluence) It is important to understand the basis of these units because historic data are still being used to justify models Graphite in Gas-Cooled Reactors Table 333 Typical properties of several well-known grades of nuclear graphite Property PGA CSF Gilsocarbon IG-110 H451 Production method Direction Density (g cmÀ3) Thermal conductivity (W mÀ1 K) CTE, 20–120  C (10À6 KÀ1) CTE, 350–450  C (10À6 KÀ1) CTE, 500  C (10À6 KÀ1) Young’s modulus (GPa) Poisson’s ratio Strength, tensile (MPa) Strength, flexural (MPa) Strength, compressive (MPa) Extruded WG AG 1.74 200 109 Extruded WG AG 1.66 155 97 Press-molded WG AG 1.81 131 Iso-molded WG AG 1.77 116 Extruded WG AG 1.76 158 137 0.9 1.2 3.1 1.5 8.0 3.5 4.8 2.8 4.3 4.5 11.7 5.4 $0.07 17 11 19 12 27 27 used in assessments for component behavior in reactors Indeed, some of these historic data, for example, stored energy and strength, will also be used to support decommissioning safety assessments Early estimations of ‘graphite damage’ were based on the activation of metallic foils such as cobalt, cadmium, and nickel Later, to account for damage in different reactors, equivalent units, such as BEPO or DIDO equivalent dose, were used where the damage is referred to damage at a standard position in the BEPO, Calder Hall, or DIDO reactors The designers of plutonium production reactors preferred to use a more practical unit related to fuel burnup (megawatts per adjacent tonne of uranium, MW/Atu) Researchers also found that the calculation of a flux unit, based on an integral of energies above a certain value, was relatively invariant to the reactor system and used the unit En > 0.18 MeV and other variants of this Today, the favored option is to calculate the fluence using a reactor physics code to calculate the displacements per atom (dpa) However, in the field of nuclear graphite technology historic units are still widely used in the literature For example, reactor operators have access to individual channel burnup which, with the aid of axial ‘form factors,’ can be used to give a measure of average damage along the individual channel length Fortunately, most, but not all, of these units can be related by simple conversion factors However, care must be taken; for example, the unit of megawatt days per tonne of uranium (MWd tÀ1) is not necessarily equivalent in different reactor systems When assessing the analysis of a particular component in a reactor, one must be aware that a single detailed calculation of a peak rated component in the 3.6 10.9 0.21 17.5 23.0 70.0 9.8 0.14 24.5 39.2 78.5 4.0 4.4 8.51 5.1 7.38 0.15 15.2 13.7 55.3 52.7 center of the core may have been carried out to give spatial, and maybe temporal, distribution of that component’s fluence (and possibly temperature and weight loss) These profiles may have then been extrapolated to all of the other components in the core using the core axial and radial ‘form factors.’ In doing this, some uncertainty will be introduced and clearly, some checks and balances will be required to check the validity of such an approach 4.11.5 Dosimetry (Graphite Damage Dose or Fluence) In a nuclear reactor, high energy, fast neutron flux leads to the displacement of carbon atoms in the graphite crystallites via a ‘cascade.’ Many of these atoms will find vacant positions, while others will form small interstitial clusters that may diffuse to form larger clusters (loops in the case of graphite) depending upon the irradiation temperature Conversely, vacancy loops will be formed causing the lattice structure to collapse These vacancy loops will only become mobile at relatively high temperatures The production of transmutation gas from impurities is not an issue for highly pure nuclear graphite, as the quantities of gas involved will be negligible and the graphitic structure is porous The change in graphite properties is a function of the displacement of carbon atoms The nature and amount of damage to graphite depends on the particular reactor flux spectrum, which is dependent on the reactor design and position, as illustrated in Figure It is impractical to relate a spectrum of neutron energies to a dimensional or property change at a 334 Graphite in Gas-Cooled Reactors 1800 TE rig in BEPO Hollow fuel element in BEPO Empty fuel channel in BEPO Empty lattice position in PLUTO 1600 Flux per unit lethargy f (v) 1400 Hollow fuel element in PLUTO 1200 1000 800 600 400 200 10 100 1000 Energy (keV) 10000 100000 Figure Flux spectrums for various reactor positions used in graphite irradiation programs Modified from Simmons, J Radiation Damage in Graphite; Pergamon: London, 1965 single point in a material such as graphite Therefore, an ‘integrated flux’ is used and is discussed later Table Relationship for BEPO equivalent flux (thermal) at a central lattice position to other positions in BEPO and other irradiation facilities 4.11.5.1 Early Activation Measurements on Foils Position Factor BEPO lattice BEPO hollow slug BEPO empty fuel channel Windscale Piles Windscale Piles thermostats NRX fast neutron plug MWHs American data MWd/CT 2.27 0.63 1.29 1.29 1.54  1015 5.5  1017 Although one cannot directly measure the damage to graphite itself, it is possible to measure the activation of another material, because of nuclear impacts adjacent to the position of interest This activation may then be related to changes in graphite properties This was done in early experiments using cobalt foils and by measuring the activation arising from the 59Co(n,g)60Co reaction This reaction has a cross-section of 38 barns and 60Co has a half-life of 5.72 years, which need to be accounted for in the fluence calculations Such foils were included in graphite experiments in BEPO and the Windscale Piles, and are still used today for irradiation rig validation and calibration purposes In these early experiments, after removal from the reactor, cobalt foils were dissolved in acid, diluted, and the decay rate measured A measure of fluence could then be calculated from knowledge of the following:     the solution concentration the time in the reactor the decay rate the activation cross-section Source: Simmons, J H W The Effects of Irradiation on Graphite; AERE R R 1954; Atomic Energy Research Establishment, 1956 Unfortunately the 59Co(n,g)60Co reaction is mainly a measure of thermal flux and atomic displacements in graphite are due to fast neutrons An improvement was the use of cobalt/cadmium foils, but this was not really satisfactory Measurements made in this way are often given the unit, neutron velocity time (nvt) Table gives an example of thermal flux determined from cobalt foils defined at a standard position in the center of a lattice cell in BEPO Graphite damage at other positions in other reactors could then be related to the standard position in BEPO 376 Graphite in Gas-Cooled Reactors Dimensional change (%) −1 −2 −3 −4 0% weight loss 5.8% weight loss 13.4% weight loss 23.1% weight loss 38.4% weight loss Trend curve A Trend curve B −5 −6 −7 20 40 (a) 100 60 80 Fluence (1020 n cm−2 EDND) 120 140 160 Young’s modulus structure term 2.0 1.8 1.6 1.4 0% weight loss 5.8% weight loss 13.4% weight loss 23.1% weight loss 38.4% weight loss 1.2 1.0 0.8 (b) 20 40 60 80 100 120 140 160 Fluence (1020 n cm−2 EDND) Figure 51 Correlations between dimensional change and Young’s modulus structure term in Gilsocarbon (a) Dimensional changes in pre-oxidized Gilsocarbon and (b) Young’s modulus structure terms in pre-oxidized Gilsocarbon Modified from Schofield, P.; Brown, R G.; Daniels, P R C.; Brocklehurst, J E Fast neutron damage in Heysham II/Torness moderator graphites (final report on 3-temperature zone rig); UKAEA, NRL-M-2176(S); 1991     1 K0 30ị K0 ẳ ỵ dT ịf Sk ẵ52 K ox Kirr T ị K0 ð30Þ K0 ðT Þ In recent years, it has been realized that the use of the product rule is simplistic, and most probably, only applicable for low irradiation data, up to a fluence not far beyond dimensional change turnaround and only for relatively low weight loss Therefore, there has been a recent trend to use empirical fits to reactor or MTR data where available 4.11.20 Irradiation Creep in Nuclear Graphite By the late 1940s, it was known that graphite components, when subjected to fast neutron irradiation, suffered significant dimensional change It was thought that, because of the flux gradient across the brick section, these dimensional changes would generate significant stresses in hollow graphite moderator blocks and that this would lead to significant Graphite in Gas-Cooled Reactors 377 4.5 Fractional change in s/s0 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 50 100 150 200 250 300 350 Fluence (1020 n cm−2 EDND) Gilsocarbon (300–400 ЊC) Gilsocarbon (560 ЊC) Petroleum coke (300–440 ЊC) Petroleum coke (560 ЊC) Pitch coke (300–440 ЊC) Unidentified coke (300–440 ЊC) Unidentified coke (560 ЊC) E/E0 Ö(E/E0) Figure 52 Change in strength of irradiated Gilsocarbon graphite compared to change in modulus Modified from Brocklehurst, J E Chem Phys Carbon 1977, 13, 145–272 Thermal conductivity (k/ko) Young’s modulus (E/Eo) Relative change in property Tensile strength (s/so) Compressive strength (s/so) 0.5 e−2.8x e−3.8x e-5.1x 0.0 0.1 0.2 Porosity 0.3 0.4 Figure 53 Change in thermal conductivity, Young’s modulus, and strength due to radiolytic oxidation Modified from Adam, R W.; Brocklehurst, J E Mechanical tests on graphite with simulated radiolytic oxidation gradients; UKAEA, ND-R-853(S) (AB 7/26300); 1983 component failures within a few years of reactor operation Therefore, the fuel channels in the early reactors, such as the Windscale Piles, were designed to avoid the buildup of stress By the 1950s, it was realized that there was an irradiation-induced mechanism that was relieving stresses generated by dimensional change and the term ‘irradiation induced plasticity’85,86 was coined to describe this mechanism Later, around 1960, the term ‘irradiation creep’87 started to be used for the difference between dimensional change in loaded and unloaded graphite specimens irradiated to the same dose 378 Graphite in Gas-Cooled Reactors 4.11.20.1 Dimensional Change and Irradiation Creep Under Load Compressive stress increases, and tensile stress decreases, the irradiation-induced dimensional change of graphite as illustrated in Figure 54 In these experiments, two matching graphite samples, a loaded specimen and an unloaded ‘control’ specimen, were irradiated adjacent to each other in an MTR, and dimensional change in the direction of load was measured However, as well as change in dimension in the load direction, there are also dimensional changes perpendicular to the load direction as shown in Figure 55 An irradiation creep curve can be simply obtained by subtraction of the unloaded dimensional change curve from the crept dimensional change curve, as illustrated in Figure 56 However, for practical use in assessments, this would require data for a range of temperatures and fast neutron fluences covering all of the expected operating conditions Also, in the case of carbon dioxide-cooled reactors, the effect of Dimensional change (%) −1 −2 −3 Reference Loaded −4 50 100 150 200 250 Fluence (1020 n cm−2 EDND) (a) Dimensional change (%) −1 −2 4.11.20.2 Types of Irradiation Creep Experiments There are three categories of graphite creep experiments The first type was the restrained creep experiments In these experiments a graphite specimen, usually dumbbell in shape, is restrained from shrinkage by a tube or split collar manufactured from graphite that shrinks less than the specimen of interest In the case of anisotropic graphite, the tube or split collar could be manufactured with its longitudinal axis aligned with the more dimensionally stable grain direction; the specimen would be manufactured with its axis perpendicular to this These types of experiments are relatively easy to deploy but are difficult to assess as the load is not directly measured and a ‘creep law’ has to be assumed in the assessment of the results.88 A variation on these experiments was the graphite spring tests used in Calder Hall to define primary creep.86 A second important type of experiment was the ‘out-of-pile measurements’ technique.89,90 These experiments, importantly, give ‘real-time results.’ However, this type of experiment is difficult to install in a reactor and results are obtained only for one specimen The final type of experiment is the in-pile rig loading using a string of samples and usually taking advantage of the MTR flux gradient to obtain data on samples to various levels of fluence There have been various designs of simple strings of specimens loaded either in tension or in compression Tensile creep tests are vulnerable, that is, if one specimen fails, results for the whole string of specimens could be lost However, there have been various rig designs aimed at overcoming this problem −3 Reference Loaded −4 (b) the rate of radiolytic oxidation on creep rates would have to be quantified and understood In addition, changes to the CTE and Young’s modulus with irradiation creep have been observed, which further complicate assessment technology 50 100 150 200 250 Fluence (1020 n cm−2 EDND) Figure 54 Dimensional changes of loaded ATR-2E graphite (a) compression and (b) tension Modified from Haag, G Properties of ATR-2E Graphite and Property Changes due to Fast Neutron Irradiation; FZJ, Juăl-4183; 2005 4.11.20.3 The UKAEA Creep Law Irradiated creep experiments were carried out between 350 and 650  C on both PGA and Gilsocarbon graphite.91 Some low fluence experiments were also carried out in Calder Hall86 which were used to define the so-called ‘primary creep.’ Creep strain data ecr was normalized to elastic strain units (esu) by dividing by the applied stress (s) and multiplying by the Graphite in Gas-Cooled Reactors 379 Dimensional change (%) −1 Reference Loaded −2 50 100 Fluence 150 (1020 n cm−2 250 200 EDND) Figure 55 Lateral dimensional changes of loaded ATR-2E graphite Modified from Haag, G Properties of ATR-2E Graphite and Property Changes due to Fast Neutron Irradiation; FZJ, Juăl-4183; 2005 2.0 Creep strain (%) 1.5 1.0 0.5 Compressive Tensile 0.0 50 100 150 20 Fluence (10 −2 n cm 200 250 EDND)  Figure 56 Irradiation creep curves for ATR-2E at 500 C Modified from Haag, G Properties of ATR-2E Graphite and Property Changes due to Fast Neutron Irradiation; FZJ, Juăl-4183; 2005 unirradiated SYM (E0) as given below: esu ẳ E0 ecr s ẵ53 Surprisingly, they found that by doing this, the creep data for these two types of graphite, with very different microstructures, could be fitted to a simple ‘creep equation’ of the form s s ẵ54 ecr ẳ ẵexp4gị ỵ 0:23 g E0 E0 where g is the fast neutron dose This is illustrated in Figure 57 The primary creep strain is assumed to be recoverable on removal of the load while still under irradiation Some evidence for this came from out-of-pile measurement experiments such as the FLACH experiments.90 However, if the specimens had been left unloaded for longer duration, more than esu may have been recovered In addition to this, an experiment carried out on precrept samples, that is, 380 Graphite in Gas-Cooled Reactors 1.2 Creep strain (%) 1.0 0.8 0.6 BR–2 (300 – 650 ЊC, 900 psi) 0.4 Isotropic graphites (compressive) Isotropic graphites (tensile) PGA (perpendicular) PGA (parallel) Pyrolytic graphites 0.2 0.0 10 20 30 40 50 60 70 Fluence (1020 n cm−2) (a) 16 14 Elastic strain units 12 10 Isotropic graphites (BR-2, 300 – 650 ЊC) PGA (BR-2 (300 – 650 ЊC, perpendicular) PGA (BR-2 (300 – 650 ЊC, parallel) Pyrolytic graphites (BR-2, 300 - 650 ЊC) PGA graphites (PLUTO, 300 ЊC) Calder hall (140 – 350 ЊC) 0 10 20 (b) 30 40 50 60 70 Fluence (1020 n cm−2) Figure 57 UK creep data used to define the UK creep law (a) creep strain and (b) elastic strain units Modified from Brocklehurst, J E Irradiation Damage in CAGR Moderator Graphite; Northern Division, UKAEA, ND-R-1117(S); 1984 samples of PGA and Gilsocarbon irradiated in a creep experiment in the BR-2 reactor and then irradiated with the load removed in DIDO and DFR respectively, exhibited more than esu (a recovery in the region of esu in the case of Gilsocarbon in DFR) 4.11.20.4 Observed Changes to Other Properties 4.11.20.4.1 Coefficient of thermal expansion Significant differences have been observed between the unstressed CTE and stressed CTE, as illustrated in Figure 58 Compressive creep strain was found to increase the CTE, and tensile creep strain to decrease the CTE The changes in CTE caused by irradiation creep have similarities to those caused by the application of stress on unirradiated graphite Figure 59(a) shows the changes in CTE in irradiated, crept specimens plotted as a function of creep strain92 and Figure 59(b) gives the changes in CTE in unirradiated graphite due to stress.93 At room temperature, the average CTE of an isotropic graphite with no porosity should be the average of the crystallite CTEs, that is, the crystallite CTEs are $27.0  10À6 KÀ1 and À1.0  10À6 KÀ1 in the ‘c’ and ‘a’ directions respectively, giving an average Graphite in Gas-Cooled Reactors 381 CTE (10−6 K−1) Unstressed Compressive Tensile 10 20 30 40 50 60 Fluence (1020 n cm−2 EDN) (a) Change in CTE (10−6 K−1) IM1-24 (parallel) SM2-24 (parallel) SM2-24 (perpendicular) VNMC (parallel) VNMC (perpendicular) (b) 10 20 30 40 Creep strain(%) 50 60 Figure 58 Additional changes to the coefficient of thermal expansion in loaded materials test reactor specimens (a) Modified from Brocklehurst, J E.; Brown, R G Carbon 1969, 7(4), 487–497 and (b) Modified from Brocklehurst, J E.; Kelly, B T A review of irradiation induced creep in graphite under CAGR conditions; UKAEA, ND-R-1406(S); 1989 of 8.0  10À6 KÀ1 From Figure 59(a), which is for Gilsocarbon with an unirradiated CTE of 4.0  10À6 KÀ1, it is interesting to note that the increase in CTE in compression is approaching that value 4.11.20.4.2 Young’s modulus The early BR-2 experiments showed little evidence of change in modulus with irradiation creep However, other authors94 did find evidence of a change (Figure 60) Later, higher temperature creep experiments carried out in the United Kingdom92 also showed a change in Young’s modulus Figure 61(a) shows the fractional change in Young’s modulus E/E0, as a function of different compressive stresses In Figure 61(b), the data has been normalized by dividing the crept Young’s modulus Ec by the irradiated value of the unstressed specimen Ei 4.11.20.5 Lateral Changes Creep in metals is purported to be related to plastic flow occurring at constant volume However, artificial polycrystalline graphite is a porous material with a crystal structure considerably different from that of metals It is therefore not surprising that in irradiation creep, graphite does not deform with a constant volume As with much of the irradiation creep data, the quality of the transverse creep data is poor and inconsistent However, from the data that does exist, the irradiation creep ratio does appear not to be constant with creep strain (Figure 62) 4.11.20.6 Creep Models and Theories It is unfortunate that a validated set of graphite irradiation creep data covering the range of temperatures and fluences of interest for power producing reactors, as well as radiolytic oxidation in the case of carbon dioxide-cooled reactors, does not exist In addition, there are no microstructural studies available to give an insight into the mechanism involved in irradiation creep in graphite This has lead to much speculation and several model proposals 382 Graphite in Gas-Cooled Reactors Change in CTE (10−6 K−1) −5 −4 −3 −2 −1 −1 Compression (PLUTO) Compression (BR-2) Tension (BR-2) −2 Creep strain (%) (a) Change in CTE (10−6 K−1) Longitudinal stain gauge results −1 Longitudinal stain gauge results Transverse strain gauge results −60 −50 −40 −30 −20 −10 −2 10 20 Stress (MN m−2) (b) Figure 59 Synergy between changes in coefficient of thermal expansion in irradiation creep specimens and change in unirradiated, stressed graphite (a) additional change in CTE as a function of creep strain and (b) change in CTE in unirradiated stressed samples Change in Young’s modulus (E/E0) 2.0 1.6 1.2 SM1-24 (axial), irradiation temperature = 850- 920 ЊC 0.8 0.4 0.0 MPa (Capsule 76M-18A) 0.0 MPa (Capsule 77M-10A) 3.3 MPa (Capsule 76M-18A) 3.3 MPa (Capsule 77M-10A) 4.5 MPa (Capsule 76M-18A) 6.5 MPa (Capsule 76M-18A) 4.5 MPa (Capsule 77M-10A) 6.5 MPa (Capsule 77M-10A) 0.0 24 Fluence (10 10 12 14 16 −2 n cm , E > 29 fJ) Figure 60 Changes in Young’s modulus in tensile crept and uncrept specimens Reproduced from Oku, T.; Fujisaki, K.; Eto, M J Nucl Mater 1988, 152(2–3), 225–234 Graphite in Gas-Cooled Reactors Change in Young’s modulus (E/E0) 0.5 383 0.9 ϫ 1021 n cm−2 (1050 ЊC) 1.8 ϫ 1021 n cm−2 (1050 ЊC) ϫ 1021 n cm−2 (850 ЊC) ϫ 1021 n cm−2 (850 ЊC) 0.4 0.3 0.2 Fail 0.1 0.0 10 15 20 25 30 35 -2 Compressive stress (MN m ) (a) 40 45 50 Creep modulus/elastic modulus 1.1 1.0 1+3(creep modulus) 0.9 1050 ЊC 850 ЊC 0.8 -6 -5 -4 (b) -3 -2 -1 Compressive creep strain (%) Figure 61 Changes in Young’s modulus in irradiated-creep experiments (a) changes to Young’s modulus as a function of stress and fast neutron fluence and (b) normalized Young’s modulus as a function of creep strain Modified from Brocklehurst, J E.; Kelly, B T A review of irradiation induced creep in graphite under CAGR conditions; UKAEA, ND-R-1406(S); 1989 4.11.20.6.1 UKAEA creep law In the United Kingdom, to extend the creep law to higher fluence and to account for radiolytic oxidation, the following approach was taken by the UKAEA Creep strain, decr/dg, was assumed to be defined by decr s s ẳ aT ị ẵexpbgị ỵ bT ị dg Ec Ec ẵ55 where a(T), b(T ), and b are temperature-dependent functions equal to 1.0, 0.23, and 4.0, respectively in the AGR and Magnox temperature ranges, and s and g are stress and irradiation fluence, respectively The need for the temperature dependence outside this range was defined by data for HTRs obtained in the United States and Russia (Figure 63) The ‘creep modulus’ in the UKAEA model was defined as Ec ẳ E0 SEẵox ẵ56 where E0 is the unirradiated SYM and S is the irradiation temperature- and fluence-dependent structure term derived from the irradiated modulus data (Section 4.11.17.4) To account for radiolytic weight loss, E[ox] is a modulus weight loss term defined as E/E0 ¼ exp(Àlx) where l is an empirical constant equal to about 4.0 and x is the fractional weight loss There are no rigorous observational data to underpin this model other than a few data points for preoxidized graphite given in Figure 64 It should be noted that in Figure 64, the only two 384 Graphite in Gas-Cooled Reactors 0.6 Poisson’s ratio 0.5 0.4 0.3 0.2 SM2-24 VNMC IM1-24 0.1 0.0 (a) Longitudinal creep strain (%) Transverse creep strain (%) 0.4 0.0 −0.4 −0.8 −1.2 −1.6 0.0 ATR-2E (tension, 500 ЊC) ATR-2E (compression, 500 ЊC) H-337 (compression, 550 ЊC) H-337 (compression, 800 ЊC) AGOT (compression, 550 ЊC) AGOT (compression, 800 ЊC) H-451 (compression, 900 ЊC) 0.5 1.0 (b) 1.5 2.0 2.5 3.0 3.5 Longitudinal creep strain (%) Creep coefficient ( kg cm−2)−1 (neutron cm−2)−1 Figure 62 Various transverse irradiation creep data (a) UKAEA data and (b) US data Modified from Brocklehurst, J E.; Kelly, B T A review of irradiation induced creep in graphite under CAGR conditions; UKAEA, ND-R-1406(S); 1989 1E−24 1E−25 1E−26 Russian graphite American graphite (EGCR) American graphite (CGB) 1E−27 100 200 300 400 500 600 Temperature (ЊC) 700 800 900 1000 Figure 63 Temperature dependence of the secondary creep coefficient b(T) from US and Russian data Graphite in Gas-Cooled Reactors 385 12 Compressive Tensile Low density graphite (equivalent to 25% weight loss) UK creep law Elastic strain units (esu) 10 9.5% 9.8% 27.8% 25.5% 6% 0 10 15 20 25 30 35 40 45 50 Fluence (1020 n cm-2 EDND) Figure 64 Preoxidized irradiation creep data Modified from Brocklehurst, J E.; Kelly, B T A review of irradiation induced creep in graphite under CAGR conditions; UKAEA, ND-R-1406(S); 1989 samples with a significant amount of weight loss are irradiated to a relatively low fluence Similarly, there are some, even less convincing, data on creep samples initially irradiated to high fast neuron fluence before loading.92 The main criticisms of the UKAEA creep model, for inert conditions, is that it gives a very poor fit to the high fluence creep data obtained in Germany and the United States, as discussed in the next section 4.11.20.6.2 German and US creep model This model was devised for helium-cooled HTR applications where radiolytic oxidation was of no concern The form of some of the US and German data is given below (Figure 65) There appears to be a difference between tension and compression at high fluence However, this is the only data that shows this and it is not clear if it is a real effect It was assumed that microstructural changes at medium to high fluence would modify the creep rate and account for the shape of these curves It was assumed that this could be accounted for by modifying the secondary creep coefficient in the UK creep law by the following expression:   s ecrsecondaryị ẳ K E0   DV =V 0 ½57Š K ¼K 1Àm ðDV =V0 Þm where K0 is the UK creep coefficient, DV/V0 is the change in volume (which is a function of fluence and irradiation temperature), (DV/V0)m is the volume change at volumetric ‘turnaround,’ and m is a graphite grade and temperature-dependent variable 4.11.20.6.3 Further modifications to the UKAEA creep law: interaction strain The theory originally developed by Simmons in the 1960s reported in detail by Hall et al.61 relating the polycrystalline dimensional change rate and CTE with crystallite dimensional change rate, and CTE has been further developed95 in an attempt to explain the shape of the graphite irradiation creep behavior at high dose The proposed theory argues that if the dimensional change rate in polycrystalline graphite can be related to the CTE, and because irradiation creep has been observed to modify CTE of the loaded specimen differently to that seen in unloaded specimens, changing the CTE by creep would be expected to change the dimensional change rate and hence, the dimensional change in the loaded specimen This leads to the introduction of the so-called ‘interaction strain.’ The theory behind this methodology is described below Considering two specimens (a crept specimen and an unloaded control) being irradiated under identical conditions; in the unloaded control specimen, by applying the Simmons equations, the bulk dimensional change rate gx and bulk CTE ax can be defined by gx ¼ ð1 À Ax ịga ỵ Ax gc ax ẳ Ax ịaa þ Ax ac ½58Š 386 Graphite in Gas-Cooled Reactors 3.0 ATR-2E (stress = Mpa) Tension (900 ЊC) Tension (300 ЊC) Tension (500 ЊC) Compression (500 ЊC) Creep strain (%) 2.5 2.0 1.5 1.0 0.5 0.0 50 150 100 20 Fluence (10 –2 n cm 200 EDND) Figure 65 High-fluence German and US data where ga and gc are crystal dimensional change rate in the a and c directions, respectively, and aa and ac are the crystal CTE in the a and c directions, respectively Ax is referred to as the structure factor and by rearrangement ax À aa Ax ẳ ẵ59 ac aa Thus,  gx ẳ ga ỵ gT ax aa ac aa  ½60Š where gT is the crystal shape rate factor and is equal to gc À ga Similarly for the loaded specimen,   a aa ẵ61 gx0 ẳ ga ỵ gT x ac aa Therefore, the difference between the dimensional change rates of the unloaded and loaded specimen is   Da ẵ62 gx0 gx ẳ gT ac aa or gx0  ẳ gx ỵ gT Da ac À aa  ½63Š where Da is the change in CTE under load (a0x À ax) This leads to the following definitions:  The true dimensional change in the loaded specimen ¼ the dimensional change in the control ỵ the interaction term  True creep ẳ dimensional change in loaded specimen À true dimensional change in loaded specimen  Apparent creep ¼ dimensional change in loaded specimen À dimensional change in control   Thus, the interaction term gT acDa Àaa is included in the finite element analysis of graphite components The limited data that exists on irradiated HOPG indicates that the dimensional change rate of graphite crystallites increases with increasing fluence in the ‘c’ direction and decreases in the ‘a’ direction for all measured irradiation temperatures and dose range For irradiation temperatures of 450 and 600  C, the data indicates that ac and aa remain invariant to fluence However, below 300  C the crystal CTE appears to change There are no crystal CTE data for higher temperatures It should also be noted that Simmons equations imply that Ax ¼ ax À aa g x À g a ¼ ac À aa g c À g a ½64Š Close examination of typical graphite irradiation data, say for Gilsocarbon irradiated in the temperature range where crystal data are available (450 and 600  C), shows that the relationship given above does not hold In fact, the Simmons relationship and measured data diverge at low dose This is attributed to Simmons assuming that polycrystalline graphite can be considered as a loose collection of crystallites with no mechanical interactions Others95 have added an extra ‘pore generation’ term to the Simmons dimensional change relationship to try and reconcile these issues, but again there is no real validation of these models Graphite in Gas-Cooled Reactors The use of this interaction term did not gain wide (international) acceptance as it appeared to be using the Simmons relationship beyond its applicability and did not explain the difference between compressive and tensile loading at high fluence 4.11.20.6.4 Recent nuclear industry model Recently Davies and Bradford96 have developed a far more complex creep model as given below: ðg ak1 Àk1 g s expk1 g dg0 exp ec ẳ E0 Sg; T ịW xị g0 ẳ0 g   b s dg0 þ À expÀk2 g E0 Sðg; T ÞW ðxÞ g0 ẳ0 ok3 k3 g ỵ exp E0 g g0 ¼0 s expk3 g dg0 Sðg; T ÞW ðxÞ ½65Š where a, esu (where this is defined by s/E0); k1, 0.0857e(1630.4/T); b, 0.15 esu per 1020 n cmÀ2 EDN; k2, 0.0128e(1270.8/T); o, esu; k3, 0.4066e(À1335.9/T); s, stress (P); E0, unirradiated SYM (Pa) appropriate to the stress applied (0.84  DYM); S(g, T), structure term representing structural induced changes to creep modulus (a function of fluence and temperature); W(x), oxidation term representing oxidation-induced changes to creep modulus (a function of weight loss, x, which is a function of fluence) The lateral strain ratio for the primary and recoverable terms is assumed to be equal to the elastic Poisson’s ratio The lateral strain ratio for secondary creep, nsc, is assumed to follow the relationship nsc ẳ 0:5ẵ1 3Sc ðgފ Sc is a structural connectivity term that the authors have used in model fits for other graphite property changes.57 This model certainly fits the available inert data better than the previous models, although it cannot be tested against radiolytically oxidizedgraphite data as there is none 4.11.20.7 Final Thoughts on Irradiation Creep Mechanisms Two main models for the mechanism of irradiation creep have been put forward but neither has any microstructural observations to support them The first suggestion is that a model by Roberts and Cottrell97 for a-uranium may be appropriate This model proposes that the graphite crystallite structures will yield and shear because of the generation 387 of stresses caused by dimensional change However, it is difficult to envisage such a yield and shear mechanism in crystalline graphite The second model98 suggests that under load, the crystallite basal planes will slide because of a pinning and unpinning mechanism during irradiation Such a mechanism is described in detail by Was99 with relation to metals and could explain primary creep and secondary linear creep However, if irradiation creep in graphite is associated with basal plane slip due to pinning–unpinning, it is surprising that in PGA, irradiation creep is less in the WG or parallel to the basal plane direction than it is in the AG or perpendicular to the basal plane direction (Figure 57) Another possibility is that stress modifies the crystal dimensional change rate itself In support of this are X-ray diffraction measurements100 that showed that the lattice spacing in compressive crept specimens is less than that in the unstressed control specimens (Figure 66) Such a mechanism would explain the PGA data and could be related to the change in CTE and the observed annealing behavior However, the data and experimental fluence and creep range given are very limited It is clear that changes to the lattice spacing in crept graphite would be an area worthy of further investigation in future irradiation creep programs Irradiation creep in the graphite crystallite will be reflected in the bulk deformations observed in creep specimens and in reactor components Changes to the bulk microstructure due to radiolytic oxidation would be expected to influence this bulk behavior, as would large crystal dimensional changes at very high fluence (past dimensional change turnaround) It would be expected that at very high fluence the behavior of graphites with differing microstructures would diverge; this appears to be the case from the limited high fluence data available 4.11.21 Concluding Remark Nuclear grade graphite has been used, and is still used, in many reactor systems Furthermore, it provides an essential moderator and reflector material for the next-generation high-temperature gas-cooled nuclear reactors that will be capable of supplying high-temperature process heat for the hydrogen economy Hence, nuclear graphite technology remains an important topic Although there is a wealth of data, knowledge, and experience on the design and operation of graphite-moderated reactors, 388 Graphite in Gas-Cooled Reactors 3.56 Unrestrained Restrained 3.54 Interlayer spacing (Å) 3.52 3.50 3.48 3.46 3.44 3.42 3.40 3.38 3.36 10 12 14 16 18 20 Fluence (GWd te−1) Figure 66 The effect of stress and irradiation on the interlayer spacing of graphite Modified from Francis, E L Progress Report for the JNPC-Materials Working Party: Graphite Physics Study Group; UKAEA, TRG-M-2854 (AB 7/17604); 1965 the need for present plants to extrapolate beyond current data and to predict the behavior of new graphite grades operating for longer lifetimes at higher temperatures than before means there is still a substantial amount of work for the graphite specialist Future understanding and validation of property/ microstructural change relationships that enable the prediction and interpolation of existing databases and the development 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...326 Graphite in Gas- Cooled Reactors 4. 11. 13 4. 11. 14 4 .11. 14. 1 4. 11. 14. 2 4. 11. 14. 3 4. 11. 14. 4 4. 11. 15 4. 11. 15.1 4. 11. 15.2 4. 11. 15.3 4. 11. 15 .4 4 .11. 16 4. 11. 16.1 4. 11. 16.2 4. 11. 16.3 4. 11. 16 .4 4 .11. 17... 4. 11. 17 4. 11. 17.1 4. 11. 17.2 4. 11. 17.3 4. 11. 17 .4 4 .11. 17.5 4. 11. 17.6 4. 11. 18 4. 11. 19 4. 11. 20 4. 11. 20.1 4. 11. 20.2 4. 11. 20.3 4. 11. 20 .4 4 .11. 20 .4. 1 4. 11. 20 .4. 2 4. 11. 20.5 4. 11. 20.6 4. 11. 20.6.1 4. 11. 20.6.2...  10À20 6.25  10À21 4. 7  10À 24 4.7  10À 24 4.6  10À 24 2.5  10À 24 1 .4  10À 24 1.6 1.9 2.3 2.5 4 5.5 4 5.5 4 6 4 6 4 5 4 6 4 6 4 6.5 4 5 4 6 4 6.5 4 6.5 2.83 28.3 280 48 0 500 Modified from