Comprehensive nuclear materials 2 10 graphite properties and characteristics

Comprehensive nuclear materials 2 10 graphite properties and characteristics Comprehensive nuclear materials 2 10 graphite properties and characteristics Comprehensive nuclear materials 2 10 graphite properties and characteristics Comprehensive nuclear materials 2 10 graphite properties and characteristics Comprehensive nuclear materials 2 10 graphite properties and characteristics

2.10 Graphite: Properties and Characteristics T D Burchell Oak Ridge National Laboratory, Oak Ridge, TN, USA Published by Elsevier Ltd 2.10.1 2.10.2 2.10.3 2.10.3.1 2.10.3.2 2.10.4 2.10.4.1 2.10.4.2 2.10.4.3 2.10.4.3.1 2.10.4.3.2 2.10.4.3.3 2.10.4.4 2.10.5 2.10.6 References Introduction Manufacture Physical Properties Thermal Properties Electrical Properties Mechanical Properties Density Elastic Behavior Strength and Fracture Porosity The binder phase Filler particles Thermal Shock Nuclear Applications Summary and Conclusions Abbreviations AE AG AGR CTE FoM RMS WG Acoustic emission Against-grain Advanced gas-cooled reactor Coefficient of thermal expansion Figure of merit Root mean square With-grain Symbols a b c C C Cp E G h k KIc KT la Crystallographic a-direction (within the basal plane) Empirical constant Crystallographic c-direction Elastic moduli Specific heat Specific heat at constant pressure Young’s modulus Shear modulus Plank’s constant Boltzmann’s constant Critical stress-intensity factor Thermal conductivity at temperature T Mean graphite crystal dimensions in the a-direction 286 286 290 290 293 294 294 295 297 300 301 301 303 303 304 304 lc m N P q R S T T a a aa ac ak a? Dth g uD l Mean graphite crystal dimensions in the c-direction Charge carrier effective mass Charge carrier density Fractional porosity Electric charge Gas constant Elastic compliance (1/C) Stress Temperature Coefficient of thermal expansion Thermal diffusivity Crystal coefficient of thermal expansion in the a-direction Crystal coefficient of thermal expansion in the c-direction Synthetic graphite coefficient of thermal expansion parallel to the molding or extrusion direction Synthetic graphite coefficient of thermal expansion perpendicular to the molding or extrusion direction Thermal shock figure of merit Cosine of the angle of orientation with respect to the c-axis of the crystal Debye temperature Charge carrier mean-free path 285 286 m n nf r s s sy t v Graphite: Properties and Characteristics Charge carrier mobility Poisson’s ratio Charge carrier velocity at the Fermi surface Bulk density Electrical conductivity Strength Yield strength Relaxation time Frequency of vibrational oscillations A B c 0.670 nm A 2.10.1 Introduction Graphite occurs naturally as a black lustrous mineral and is mined in many places worldwide This natural form is most commonly found as natural flake graphite and significant deposits have been found and mined in Sri Lanka, Germany, Ukraine, Russia, China, Africa, the United States of America, Central America, South America, and Canada However, artificial or synthetic graphite is the subject of this chapter The electronic hybridization of carbon atoms (1s2, 2s , 2p2) allows several types of covalent-bonded structures In graphite, we observe sp2 hybridization in a planar network in which the carbon atom is bound to three equidistant nearest neighbors 120 apart in a given plane to form the hexagonal graphene structure Covalent double bonds of both s-type and p-type are present, causing a shorter bond length than that in the case of the tetrahedral bonding (s-type sp3 orbital hybridization only) observed in diamond Thus, in its perfect form, the crystal structure of graphite (Figure 1) consists of tightly bonded (covalent) sheets of carbon atoms in a hexagonal lattice network.1 The sheets are weakly bound with van der Waals type bonds in an ABAB stacking sequence with a separation of 0.335 nm The invention of an electric furnace2,3, capable of reaching temperatures approaching 3000  C, by Acheson in 1895 facilitated the development of the process for the manufacture of artificial (synthetic) polygranular graphite Excellent accounts of the properties and application of graphite may be found elsewhere.4–6 2.10.2 Manufacture Detailed accounts of the manufacture of polygranular synthetic graphite may be found elsewhere.2,4,7 Figure summarizes the major processing steps in a 0.246 nm Figure The crystal structure of graphite showing the ABAB stacking sequence of graphene planes in which the carbon atoms have threefold coordination Reproduced from Burchell, T D In Carbon Materials for Advanced Technologies; Burchell, T D., Ed.; Elsevier Science: Oxford, 1999 the manufacture of synthetic graphite Synthetic graphite consists of two phases: a filler material and a binder phase The predominant filler materials are petroleum cokes made by the delayed coking process or coal–tar pitch-derived cokes The structure, shape, and size distribution of the filler particles are major variables in the manufacturing process Thus, the properties are greatly influenced by coke morphology For example, the needle coke used in arc furnace electrode graphite imparts low electrical resistivity and low coefficient of thermal expansion (CTE), resulting in anisotropic graphite with high thermal shock resistance and high electrical conductivity, which is ideally suited for the application Such needle-coke materials would, however, be wholly unsuited for nuclear graphite applications, where a premium is placed upon isotropic behavior (see Chapter 4.10, Radiation Effects in Graphite) The coke is usually calcined (thermally processed) at $1300  C prior to being crushed and blended The calcined filler, once it has been crushed, milled, and sized, is mixed with the binder (typically a coal–tar pitch) in heated mixers, along with certain additives to improve processing (e.g., extrusion oils) The formulations (i.e., the amounts of specific ingredients to make a specified grade) are carefully followed to ensure that the desired properties are attained in the final products The warm mix is transferred to the mix cylinder of an extrusion press, and Graphite: Properties and Characteristics Raw petroleum or pitch coke Calcined at 1300 ЊC Calcined coke Crushed, ground, and blended Blended particles Coal tar binder pitch Mixed Cooled Extruded, molded, or isostatically pressed Green artifact Baked at 800–1000 ЊC Baked artifact Impregnated to densify (petroleum pitch) Rebaked and reimpregnated artifact Graphitized 2500–2800 ЊC Graphite Purified Purified graphite Figure The major processing steps in the manufacture of nuclear graphite the mix is extruded to the desired diameter and length Alternately, the green mix may be molded into the desired form using large steel molds on a vertical press Vibrational molding and isostatic pressing may also be used to form the green body The green body is air- or water-cooled and then baked to completely pyrolyze the binder Baking is considered the most important step in the manufacture of carbon and graphite The pitch binder softens upon heating and goes through a liquid phase before irreversibly converting into a solid carbon Consequently, the green articles can distort or slump in baking if they are not properly packed in the furnace If the furnace-heating rate is too rapid, the volatile gases evolved during pyrolysis cannot easily diffuse out of the green body, and it may crack If a sufficiently high temperature is not achieved, the baked carbon will not attain the desired density and physical properties Finally, if the baked artifact is cooled too rapidly after baking, thermal gradients may cause the carbon blocks to crack For all of these reasons, utmost care is taken over the baking process Bake furnaces are usually directly heated (electric elements or gas burning) and are of the pit design The furnaces may be in the form of a ring so that the waste heat from one furnace may be used to preheat the adjacent furnace The basic operational steps include (1) loading, (2) preheating (on waste gas), (3) gas heating (on fire), (4) cooling (on air), and (5) unloading Typical cycle times are of the order of hundreds of hours (Figure 3) The green bodies are stacked into the furnace and the interstices filled with pack materials (coke and/or sand) Thermocouples are placed at set locations within the furnace to allow Furnace temperature (ЊC) 3000 Graphitization Baking 2500 Cool 2000 1500 Power on 1000 Cool Unpack Unpack Load furnace 500 Repair Reload Reload 0 10 15 287 20 25 Time (days) 30 35 40 45 Figure Typical time versus temperature cycles for baking and graphitizing steps in the manufacture of graphite 288 Graphite: Properties and Characteristics direct monitoring and control of the furnace temperature More modern furnaces may be of the carbottom type, in which the green bodies are packed into saggers (steel containers) with ‘pack’ filling the space between the green body and the saggers The saggers are loaded onto an insulated rail car and rolled into a furnace The rail car is essentially the bottom of the furnace Thermocouples are placed within the furnace to allow direct monitoring and control of the baking temperature The furnaces are unpacked when the product has cooled to a sufficiently low temperature to prevent damage Following unloading, the baked carbons are cleaned, inspected, and certain physical properties determined The carbon products are inspected, usually on a sampling basis, and their dimensions, bulk density, and specific resistivity are determined Measurement of the specific electrical resistivity is of special significance since the electrical resistivity correlates with the maximum temperature attained during baking Minimum values of bulk density and maximum values of electrical resistivity are specified for each grade of carbon/graphite that is manufactured Certain baked carbon products (those to be further processed to produce synthetic graphite) will be densified by impregnation with a petroleum pitch, followed by rebaking to pyrolyze the impregnant pitch Depending upon the desired final density, products may be reimpregnated several times Useful increases in density and strength are obtained with up to six impregnations, but two or three are more common The final step in the production of graphite is a thermal treatment that involves heating the carbons to temperatures in excess of 2500  C Graphitization is achieved in an Acheson furnace in which heating occurs by passing an electric current throughout the baked products and the coke pack that surrounds them The entire furnace is covered with sand to exclude air during operation Longitudinal graphitization is increasingly used in the industry today In this process, the baked forms are laid end to end and covered with sand to exclude air The current is carried in the product itself rather than through the furnace coke pack During the process of graphitization (2500–3000  C), in simplistic terms, carbon atoms in the baked material migrate to form the thermodynamically more stable graphite lattice Certain graphite require high chemical purity This is achieved by selecting very pure cokes, utilizing a high graphitization temperature (>2800  C), or by including a halogen purification stage in the manufacture of the cokes or graphite, either during graphitization or as a postprocessing step Graphite manufacture is a lengthy process, typically 6–9 months in duration Graphite structure is largely dependent upon the manufacturing process Graphites are classified according to their ‘grain’ size8 from coarse-grained (containing grains in the starting mix that are generally >4 mm) to microfine-grained (containing grains in the starting mix that are generally 1000 W mÀ1 K, whereas perpendicular to the basal planes, the room-temperature thermal conductivity PCEA WG PCEA AG 0.3 0.2 0.1 0 100 200 300 (a) 400 500 600 700 800 900 1000 Temperature (ЊC) Poco Average CTE (ϫ10–6 ЊC) IG-110 PCEA WG PCEA AG (b) 100 200 300 400 500 600 700 800 900 1000 Temperature (ЊC) Figure 12 Thermal expansion behavior of various graphite grades (a) thermal expansion versus measurement temperature and (b) average coefficient of thermal expansion verses temperature Graphite: Properties and Characteristics is typically 80 MPa for some isostatically molded, ultra-fine-grain and micro-fine-grain synthetic graphite Compressive strengths range from 140 MPa and typically, the ratio of compressive strength to tensile strength is in the range 2–4 Kelly12 reports that there are two major factors that control the stress–strain behavior of synthetic graphite, namely, the magnitude of the constant C44, which dictates how the crystals respond to an applied stress, and the defect/ crack morphology and distribution, which controls ½12Š where P is the fractional porosity, b is an empirical constant, and s0 represents the strength at zero porosity Figure 21 shows the correlation between flexure strength and fractional porosity for a wide range of synthetic graphite27 varying from finegrain, high-density, isomolded grades to large-grain, low-density, extruded grades The data are fitted to an equation of the form of eqn [12] with s0 ¼ 179 MPa and b ¼ 9.62 The correlation coefficient, R2 ¼ 0.80 Significantly, the same flexure strength data (Figure 22) is better fitted when plotted against the mean filler-particle size27 (R2 ¼ 0.87) In synthetic graphite, the filler-particle size is indicative of the defect size, that is, larger filler-particle graphite contains larger inherent defects Thus, the correlation in Figure 22 is essentially one between critical defect size and strength The importance of defects in controlling fracture behavior and strength in synthetic polygranular graphite is well understood, and despite the pseudoplasticity displayed by graphite, it is best characterized as a brittle material with its fracture behavior described in terms of linear elastic fracture mechanics.28 Synthetic graphite critical stress-intensity factor, KIc, values are between 0.8 and 1.3 MPa mÀ1/2 dependent upon their texture Graphite: Properties and Characteristics Mean 3-pt flexure strength (MPa) 50 y = 179.18e–9.623x R2 = 0.8042 45 40 35 30 25 20 15 10 0.12 0.16 0.20 0.24 Fractional porosity 0.28 0.32 Mean 3-pt flexure strength (MPa) Figure 21 The correlation between mean 3-pt flexure strength and fractional porosity for a wide range of synthetic graphite representing the variation of textures Reproduced from Burchell, T D Ph.D Thesis, University of Bath, 1986 50 y = 44.385e–0.765x R2 = 0.8655 45 40 35 30 25 20 15 10 0 0.5 1.5 Mean filler particle size (mm) Figure 22 The correlation between mean 3-pt flexure strength and mean filler-coke particle size for a wide range of synthetic graphite representing the variation of textures Reproduced from Burchell, T D Ph.D Thesis, University of Bath, 1986 and the method of determination.27–29 Such is the importance of the fracture behavior of synthetic graphite that there have been many studies of the fracture mechanisms and attempts to develop a predictive failure model An early model was developed by Buch30 for finegrain aerospace graphite The Buch model was further developed and applied to nuclear graphite by Rose and Tucker.31 The Rose and Tucker model assumed that graphite consisted of an array of cubic particles representative of the material’s fillerparticle size Within each block or particle, the graphite was assumed to have a randomly oriented crystalline structure, through which basal plane cleavage may occur When a load was applied, those cleavage planes on which the resolved shear stress exceeded a critical value were assumed to fail 299 If adjacent particles cleaved, the intervening boundary was regarded as having failed, so that a contiguous crack extending across both particles was formed Pickup et al.32 and Rose and Tucker31 equated the cleavage stress with the onset stress for acoustic emission (AE), that is, the stress at which AE was first detected In applying the model to a stressed component, such as a bar in tension, cracks were assumed to develop on planes normal to the axis of the principal stress The stressed component would thus be considered to have failed when sufficient particles on a plane have cleaved such that together they formed a defect large enough to cause such a fracture as the brittle Griffith crack Pores were treated in the Rose and Tucker model as particles with zero cleavage strength The graphite’s pore volume was used to calculate the correct number of zero cleavage strength particles in the model Hence, the Rose and Tucker model took into account the mean size of the filler particles, their orientation, and the amount of porosity but was relatively insensitive to the size and shape distributions of both microstructural features Rose and Tucker applied their fracture model to Sleeve graphite, an extruded, medium-grain, pitch-coke nuclear graphite used for fuel sleeves in the British AGR The performance of the model was disappointing; the predicted curve was a poor fit to the experimental failure probability data In an attempt to improve the performance of the Rose and Tucker model, experimentally determined filler-particle distributions were incorporated.33 The model’s predictions were improved as a result of this modification and the higher strength of one pitch-coke graphite compared with that of the other was correctly predicted Specifically, the predicted failure stress distribution was a better fit to the experimental data than the single grain size prediction, particularly at lower stresses However, to correctly predict the mean stress (50% failure probability), it was found necessary to increase the value of the model’s stressintensity factor (KIc) input to 1.4 MPa m1/2, a value far in excess of the actual measured KIc of this graphite (1.0 MPa m1/2) The inclusion of an artificially high value for KIc completely invalidates one of the Rose and Tucker model’s major attractions, that is, its inputs are all experimentally determined material parameters A further failing of the Rose and Tucker fracture model is its incorrect prediction of the buildup of AE counts Although the Rose and Tucker model considered the occurrence of subcritical damage when the applied stress lay between the cleavage 300 Graphite: Properties and Characteristics and failure stresses, the predicted buildup of AE was markedly different from that observed experimentally.34 First, the model failed to account for any AE at very low stresses Second, at loads immediately above the assumed cleavage stress, there was a rapid accumulation of damage (AE) according to the Rose and Tucker model but very little according to the AE data Moreover, the observation by Burchell et al.34 that AEs occur immediately upon loading graphite completely invalidated a fundamental assumption of the Rose and Tucker model, that is, the AE onset stress could be equated with the cleavage stress of the graphite filler particles Recognizing the need for an improved fracture model, Tucker et al.35 investigated the fracture of polygranular graphites and assessed the performance of several failure theories when applied to graphite These theories included the Weibull theory, the Rose and Tucker model, fracture mechanics, critical strain energy, critical stress, and critical strain theories While no single criteria could satisfactorily account for all the situations they examined, their review showed that a combination of the fracture mechanics and a microstructurally based fracture criteria might offer the most versatile approach to modeling fracture in graphite Evidently, a necessary precursor to a successful fracture model is a clear understanding of the graphite-fracture phenomena Several approaches have been applied to examine the mechanism of fracture in graphite, including direct microstructural observations and AE monitoring.34,36–38 When graphite is stressed, micromechanical events such as slip, shear, cleavage, or microcracking may be detected in the form of AE In early work, Kaiser39 found that graphite emitted AE when stressed, and upon subsequent stressing, AE could only be detected when the previous maximum stress had been exceeded – a phenomenon named the Kaiser effect Kraus and Semmler40 investigated the AE response of industrial carbon and polygranular graphites subject to thermal and mechanical stresses They reported significant AE in the range 2000– 1500  C on cooling from graphitization temperatures, the amount of AE increasing with the cooling rate Although Kraus and Semmler offered no explanation for this, Burchell et al.34 postulated that it was associated with the formation of Mrozowski cracks.15 In an extensive study, Burchell et al.34 monitored the AE response of several polygranular graphites, ranging from a fine-textured, high-strength aerospace graphite to a coarse-textured, low-strength extruded graphite They confirmed the previous results of Pickup et al.,32 who had concluded that the pattern of AE was characteristic of the graphite microstructure Burchell et al.34 showed that the development of AE was clearly associated with the micromechanical events that cause nonlinear stress– strain behavior in graphites and that postfracture AE was indicative of the crack propagation mode at fracture For different graphites, both the total AE at fracture and the proportion of small amplitude events tended to increase with increasing filler-particle size (i.e., coarsening texture) Ioka et al.41 studied the behavior of AE caused by microfracture in polygranular graphites On the basis of their data, they described the fracture mechanism for graphite under tensile loading Filler particles, whose basal planes were inclined at 45 to the loading axis deformed plastically, even at low stresses Slip deformation along basal planes was detected by an increased root mean square (RMS) voltage of the AE event amplitude The number of filler particles that deform plastically increased with increasing applied tensile stress At higher applied stress, slip within filler particles was accompanied by shearing of the binder region Filler grains whose basal planes were perpendicular to the applied stress cleaved, and the surrounding binder sheared to accommodate the deformation At higher stress levels, microcracks propagated into the binder region, where they coalesced to form a critical defect leading to the eventual failure of the graphite The evidence produced through the numerous AE studies reviewed here suggests a fracture mechanism consisting of crack initiation, crack propagation, and subsequent coalescence to yield a critical defect resulting in fracture A microstructural study of fracture in graphite27,42 revealed the manner in which certain microstructural features influenced the process of crack initiation and propagation in nuclear graphites (Figure 23); the principal observations are summarized below 2.10.4.3.1 Porosity Two important roles of porosity in the fracture process were identified First, the interaction between the applied stress field and the pores caused localized stress intensification, promoting crack initiation from favorably oriented pores at low applied stresses Second, propagating cracks could be drawn toward pores in their vicinity, presumably under the influence of the stress field around the pore In some instances, such pore/crack encounters served to accelerate crack growth; however, occasionally, a crack was arrested by a pore and did not break free Graphite: Properties and Characteristics P P C F F 500 mm Figure 23 An optical photomicrograph of the microstructure of grade H-451 graphite revealing the presence of pores [P], coke filler particles [F], and cracks [C] that have propagated through the pores presumably under the influence of their stress fields until higher applied stresses were attained Pores of many shapes and sizes were observed in the graphite microstructure, but larger, more slit-shaped pores were more damaging to the graphite 2.10.4.3.2 The binder phase Two arbitrarily defined types of microstructure were identified in the binder phase: (1) domains, which were regions of common basal plane alignment extending over linear dimensions >100 mm and (2) mosaics, which were regions of small randomly oriented pseudocrystallites with linear dimensions of common basal plane orientation of less than about 10 mm Cleavage of domains occurred at stresses well below the fracture stress, and such regions acted as sites for crack initiation, particularly when in the vicinity of pores Fracture of mosaic regions was usually observed only at stresses close to the fracture stress At lower stresses, propagating cracks that encountered such regions were arrested or deflected 2.10.4.3.3 Filler particles Filler-coke particles with good basal plane alignment were highly susceptible to microcracking along basal planes at low stresses This cleavage was facilitated by the needle-like cracks that lay parallel to the basal planes and which were formed by anisotropic 301 contraction of the filler-coke particles during the calcination process Frequently, when a crack propagating through the binder phase encountered a wellaligned filler particle, it took advantage of the easy cleavage path and propagated through the particle However, in contrast to the mechanism suggested by Ioka et al.,36 the reverse process, that is, propagation of a crack initiated in the filler particle into the binder phase, was much less commonly observed While some of the direct observations discussed above are not in total agreement with the mechanism postulated from AE data, there are a number of similarities Both AE and the microstructural study showed that failure was preceded by the propagation and coalescence of microcracks to yield a critical defect However, based on the foregoing discussion of graphite-fracture processes, it is evident that the microstructure plays a dominant role in controlling the fracture behavior of the material Therefore, any new fracture model should attempt to capture the essence of the microstructural processes influencing fracture Particularly, a fracture model should embody the following: (1) the distribution of pore sizes, (2) the initiation of fracture cracks from stress raising pores, and (3) the propagation of cracks to a critical length prior to catastrophic failure of the graphite (i.e., subcritical growth) The Burchell fracture model27,43–45 recognizes these aspects of graphite fracture and applies a fracture mechanics criterion to describe steps (2) and (3) The model was first postulated27 to describe the fracture behavior of AGR fuel sleeve pitch-coke graphite and was successfully applied to describe the tensile failure statistics Moreover, the model was shown to predict more closely the AE response of graphite than its forerunner, the Rose and Tucker model Subsequently, the model was extended and applied to two additional nuclear graphites.45 Again, the model performed well and was demonstrated to be capable of predicting the tensile failure probabilities of the two graphites (grades H-451 and IG-110) In an attempt to further strengthen the model,45 quantitative image analysis was used to determine the statistical distribution of pore sizes for grade H-451 graphite Moreover, a calibration exercise was performed to determine a single value of particle critical stress-intensity factor for the Burchell model.28,44 Most recently, the model was successfully validated against experimental tensile strength data for three graphites of widely different texture.28,45,46 The model and code were successfully benchmarked28,46 against H-451 tensile strength data and Graphite: Properties and Characteristics 100 Probability (%) validated against tensile strength data for grades IG-110 and AXF-5Q Two levels of verification were adopted Initially, the model’s predictions for the growth of a subcritical defect in H-451 as a function of applied stress was evaluated and found to be qualitatively correct.28,46 Both the initial and final defect length was found to decrease with increasing applied stress Moreover, the subcritical crack growth required prior to fracture was predicted to be substantially less at higher applied stresses Both of these observations are qualitatively correct and are readily explained in terms of linear elastic fracture mechanics The probability that a particular defect exists and will propagate through the material to cause failure was also predicted to increase with increasing applied stress Quantitative validation was achieved by successfully testing the model against an experimentally determined tensile strength distribution for grade H-451 Moreover, the model appeared to qualitatively predict the effect of textural changes on the strength of graphite This was subsequently investigated and the model further validated by testing against two additional graphites, namely grade IG-110 and AXF-5Q For each grade of graphite, the model accurately predicted the mean tensile strength In an appendant study, the Burchell28,46 fracture model was applied to a coarse-textured electrode graphite The microstructural input data obtained during the study was extremely limited and can only be considered to give a tentative indication of the real pore-size distribution Despite this limitation, however, the performance of the model was very good, extending the range of graphite grades successfully modeled from a 4-mm particle size, fine-textured graphite to a 6.35-mm particle size, coarse-textured graphite The versatility and excellent performance of the Burchell28,46 fracture model is attributed to its sound physical basis, which recognizes the dominant role of porosity in the graphite-fracture process (Figure 24) Kelly12 has reviewed multiaxial failure theories for synthetic graphite The fracture theory of Burchell28,46 has recently been extended to multiaxial stress failure conditions.47 The model’s predictions in the first and fourth quadrants are reported and compared with the experimental data in Figure 25 The performance was satisfactory, demonstrating the sound physical basis of the model and its versatility The model in combination with the Principal of Independent Action describes the experimental data in the first quadrant well The failure envelope 90 AGX 80 H-451 70 IG-110 AXF-5Q 60 50 40 30 Model predictions Experimental data 20 10 0 10 20 30 40 50 60 70 Stress (MPa) 80 90 100 Figure 24 A comparison of experimental and predicted tensile failure probabilities for graphite with widely different textures: AGX, H-451, IG-110, and AXF-5Q Reproduced from Burchell, T D Carbon 1996, 34, 297–316 25 Experimental data Mean stress Predicted failure Q1 20 15 10 Effective (net) stress (PR = 0.18) –5 Axial stress (MPa) 302 10 15 20 –10 –15 –20 –25 –30 –35 –40 –45 –50 –55 –60 –65 Hoop stress (MPa) Figure 25 A summary of the Burchell model’s predicted failure surface in the first (PIA) and fourth (effective stress) quadrants and the experimental data Reproduced from Burchell, T.; Yahr, T.; Battiste, R Carbon 2007, 45, 2570–2583 predicted by the fracture model for the first quadrant is a better fit to the experimental data than that of the maximum principal stress theory, which would be represented by two perpendicular lines through the Graphite: Properties and Characteristics 303 mean values of the uniaxial tensile and hoop strengths The failure surface predicted by the fracture model offers more conservatism at high combined stresses than the maximum principal stress criterion In the fourth quadrant, the fracture model predicts the failure envelope well (and conservatively) when the effective (net) stress is applied with the fracture model Again, as in the first quadrant, the maximum principal stress criteria would be extremely unconservative, especially at higher stress ratios Overall, the model’s predictions were satisfactory and reflect the sound physical basis of the fracture model.47 Fusion Plasma-Facing Material) Wrought beryllium has a value of $1  104, pure tungsten a value of $0.5  105, and carbon–carbon composite material $1  106 If the thermal shock is at very high temperature, the material’s melting temperature is a key factor Again, graphite materials well as they not exhibit a melting temperature; rather they progressively sublimate at a temperature higher than the sublimation point (3764 K) 2.10.4.4 Many of the properties that make graphite attractive for a particular application have been discussed above However, the following characteristics have been ascribed to synthetic, polygranular graphite6 and are those properties that make graphite suitable for its many applications: chemical stability; corrosion resistance (in a nonoxidizing atmosphere); nonreactive with many molten metals and salts; nontoxic; high electrical and thermal conductivity; small thermal expansion coefficient and consequently high thermal shock resistance; light weight (low bulk density); high strength at high temperature; high lubricity; easily dissolved in iron, and highly reductive; biocompatible; low neutron absorption cross-section and high neutron-moderating efficiency; resistance to radiation damage The latter properties are what make graphite an attractive choice for a solid moderator in nuclear reactor applications Nuclear applications, both fission and fusion (of keen interest the reader), are described in detail in Chapter 4.10, Radiation Effects in Graphite, and Chapter 4.18, Carbon as a Fusion PlasmaFacing Material Accounts of nuclear applications have also been published elsewhere.9,48–50 Graphite is used in fission reactors as a nuclear moderator because of its low neutron absorption cross-section and high neutron moderating efficiency, its resistance to radiation damage, and high-temperature properties In fusion reactors, where it has been used as plasma facing components, advantage is taken of its low atomic number and excellent thermal shock characteristics The largest applications of nuclear graphite involve its use as a moderator and in the fuel forms of many thermal reactor designs These have included the early, air-cooled experimental and weapons materials producing reactors; water-cooled graphite-moderated reactors of the former Soviet Union; the CO2-cooled reactors built predominantly in the United Kingdom, but also in Italy and Japan; and helium-cooled Thermal Shock Graphite can survive sudden thermally induced loads (thermal shock), such as those experienced when an arc is struck between the charge and the tip of a graphite electrode in an electric arc melting furnace, or on the first wall of a fusion reactor To provide a quantitative comparison of a material’s resistance to thermal shock loading, several thermal shock figures of merit (D) have been derived In its simplest form, the Figure of merit (FoM) may be expressed as K sy ½13Š aE where K is the thermal conductivity, sy the yield strength, a the thermal expansion coefficient, and E is the Young’s modulus Clearly, graphite with its unique combination of properties, that is, low thermal expansion coefficient, high thermal conductivity, and relatively high strain to failure (s/E), is well suited to applications involving high thermal shock loadings Taking property values from Table for Toyo Tanso IG-43 and for POCO AXF-5Q gives FoM values of D ¼ 99 923 and D ¼ 67 875, respectively (from eqn [13]) Another FoM takes account of the potential form of failure from thermally induced biaxial strains, Dth, and may be written as D¼ Dth ẳ K sy aE1 nị ẵ14 where K is the thermal conductivity, sy the yield strength, a the thermal expansion coefficient, E the Young’s modulus, and n is Poisson’s ratio Larger values of Dth indicate improved resistance to thermal shock Using the values above and dividing by (1 À n) from eqn [14] gives FoM values of Dth ¼ 124 904 and 84 844 for IG-11 and AXF-5Q , respectively The thermal shock FoM, Dth, has been reported48 for several candidate materials for fusion reactor first wall materials (see Chapter 4.18, Carbon as a 2.10.5 Nuclear Applications 304 Graphite: Properties and Characteristics high-temperature reactors, built by many nations, which are still being operated in Japan and designed and constructed in China and the United States All of the high-temperature reactor designs utilize the ceramic Tri-isotropic (TRISO) type fuel (see Chapter 3.07, TRISO-Coated Particle Fuel Performance), which incorporates two pyrolytic graphite layers in its form Graphite-moderated reactors that were molten-salt cooled have also been operated 2.10.6 Summary and Conclusions Synthetic graphite is a truly remarkable material whose unique properties have their origins in the material’s complex microstructure The bond anisotropy of the graphite single crystal (in-plane strong covalent bonds and weak interplanar van der Waals bonds) combined with the many possible structural variations, such as the filler-coke type, filler size and shape distribution, forming method, and the distribution of porosity from the nanometer to the millimeter scale, which together constitute the material’s ‘texture,’ make synthetic graphite a uniquely tailorable material The breadth of synthetic graphite properties is controlled by the diverse, yet tailorable, textures of synthetic graphite The physical and mechanical properties reflect both the single crystal bond anisotropy and the distribution of porosity within the material This porosity plays a pivotal role in controlling thermal expansivity and the temperature dependency of strength in polygranular synthetic graphite Electrical conduction is by electron transport, whereas graphite is a phonon conductor of heat This complex combination of microstructural features bestows many useful properties such as an increasing strength with temperature and the excellent thermal shock resistance and also some undesirable attributes such as a reduction in thermal conductivity with increasing temperature The chemical inertness and general unreactive nature of synthetic graphite allow applications in hostile chemical environments and at elevated temperatures, although its reactivity with oxygen at temperature above $300  C is perhaps graphite’s chief limitation Despite many years of research on the behavior of graphite, the details of the interactions between the graphite crystallites and porosity (pores/cracks within the filler coke or the binder and those associated with the coke/binder interface) have yet to be fully elucidated at all length scales There is more research to be done Acknowledgments This work is sponsored by the U.S Department of Energy, Office of Nuclear Energy Science and Technology under Contract No DE-AC05-00OR22725 with Oak Ridge National Laboratories managed by UT-Battelle, LLC This manuscript has been authored by UT-Battelle, LLC, under Contract No DE-AC0500OR22725 with the U.S Department of Energy The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to so, for US government purposes References 10 11 12 13 14 15 16 17 18 Ruland, W Chem Phys Carbon 1968, 4, 1–84 Eatherly, W P.; Piper, E L In Nuclear Graphite; Nightingale, R E., Ed.; Academic Press: New York, 1962; pp 21–51 A Pathfinder-Discovery, 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in Japan, and grade 20 20 graphite (Figures and 10) ... C33 C44 106 0 Ỉ 20 180 Ỉ 20 15 Ỉ 36.5 Ỉ 4.0–4.5 Elastic compliances (10 13 PaÀ1) S11 S 12 S13 S33 S44 9.8 Æ 0.3 À1.6 Æ 0.6 À3.3 Æ 0.8 27 5 Æ 10 22 22 25 00 Data from Kelly, B T Physics of Graphite; ... 179.18e–9. 623 x R2 = 0.80 42 45 40 35 30 25 20 15 10 0. 12 0.16 0 .20 0 .24 Fractional porosity 0 .28 0. 32 Mean 3-pt flexure strength (MPa) Figure 21 The correlation between mean 3-pt flexure strength and