Thermal shock has been evaluated qualitatively for ZrC by various means. Susceptibility to failure by thermal shock is lowered in materials with high tensile strength, low elastic modulus, low thermal expansion coefficient, and high thermal conductivity. Gangler’s71 test involved cyclic heating and quenching of hot-pressed ZrC0.83-o.85 between a 1255 K furnace and 300 K air stream. ZrC withstood 22 cycles, though excessive oxidation was noted. Shaffer and Hasselman54 subjected hot-pressed ZrC spheres to thermal shock on heating: room — temperature specimens were drawn rapidly into the hot zone of a tube furnace at a temperature sufficiently high to cause fracture. For ZrC this was determined to be 1725 K, and free carbon was found to improve thermal shock resistance. Lepie96 subjected a pyrolytic ZrC-C alloy to firing in the nozzle-throat section of a solid-fuel rocket; no ill effects from the sudden expo­sure to the 3894 K exhaust flame were reported, and firing for 30 s at 5.5 MPa caused little erosion.

2.13.5 Environmental Resistance

2.13.6.1 Oxidation

Despite excellent refractory properties, ZrC suffers from poor oxidation resistance, with oxidation initi­ating in the range of 500-900 K (Table 5). The kinet­ics and mechanism of ZrC oxidation have been assessed in several studies, between room tempera­ture and 2200 K, at oxygen partial pressures (P02) between 8 x 10~4 and 101 kPa (0.79 x 10~6 and 1 atm), with the oxidation products a function of both parameters.

2.13.6.1.1 Oxidation products

Oxidation resistance is imparted by the formation of a dense, adherent oxide scale which effectively restricts oxygen access to the carbide. Since the oxi­des of carbon are gaseous, protection is only afforded

aBartlett efa/.134

bShimada & Ishii,135 temperature at which sintered ZrC weight gain initiates.

cShimada,136 DTA peaks indicating onset of oxidation of Zr and

C in single crystal ZrC, respectively.

dRama Rao and Venugopal.137

eOpeka et a/.138

Voitovich and Pugach.139

9Shevchenko et a/. ,140 DTA peaks indicating onset of oxidation of Zr and C, respectively. hTamura et a/.141

‘Zhilyaev et a/. ,142 ZrCxOy (x = 0.7-0.85, y = 0.15-0.25). jZainulin et a/. ,143 ZrCxOy (x = 0.43-0.97, y = 0.09-0.36).

by the zirconium oxide. However, low temperatures (<973 K) and P02 insufficient to oxidize C result in preferential oxidation of Zr and precipitation of amorphous carbon at the oxide-carbide interface, as detected by TEM,144 Raman spectroscopy,145,146 and Auger electron spectroscopy.147 Nonisothermal oxi­dation of ZrC by DTA showed two peaks, indicating the onset of appreciable Zr and C oxidation, respec­tively: the peak associated with Zr oxidation appeared between 653 and 763 K, while the C peak appeared at a higher temperature of 773-973 K.136,140

Alternatively, the liberated C may be incorporated into the ZrO2 lattice, stabilizing the cubic fluorite structure of ZrO2, whereas the monoclinic structure is normally stable at room temperature. Cubic ZrO2 nuclei absent in X-ray diffraction (XRD) were iden­tified by electron diffraction and TEM lattice fringes by Shimada and Ishii135 at 653-743 K. Cubic Zr02, with or without trace monoclinic ZrO2, formed in the 723-1013 K range.134,135,143-146,148 Shimada and Ishii135 and Tamura eta/.141 also reported the meta­stable tetragonal ZrO2 phase, based on XRD analysis. While XRD easily distinguishes monoclinic from tetragonal or cubic ZrO2, the latter two are difficult to tell apart, and additional techniques such as Raman spectroscopy or electron diffraction are required for a conclusive identification.

As the oxidation temperature increases, apprecia­ble oxidation of the precipitated or combined carbon occurs in addition to oxidation of Zr. Concurrently, the relative proportions of cubic and monoclinic ZrO2 in the scale shift in favor of monoclinic. As carbon is more readily oxidized at higher tempera­tures, less carbon is available to stabilize cubic ZrO2 and the more stable monoclinic structure forms instead. These transitions from carbon precipitation to oxidation and from cubic to monoclinic ZrO2 are reported at temperatures higher than about 1073 K, with carbon-free, fully monoclinic ZrO2 reported at

1473 1773 K 137,139—141,143,144,146,147

The transformation may be manifested by a carbon concentration gradient with depth, either by a gradual decrease in carbon from the oxide-carbide interface to the free surface, or by the formation of distinct layers in the scale. This is consistent with observations of cubic ZrO2 concentrated at the oxide-carbide interface and monoclinic ZrO2 concentrated at the free surface.139 Wavelength dispersive spectroscopy by Shimada eta/.146 detected 7-10 at.% C combined in an outer ZrO2 scale layer, following oxidation of single-crystal ZrC097 at 773-873 K, with an inner layer characterized by a steep decrease in C content with depth.

Some authors also report the formation of a ZrC^Oj, oxycarbide phase isostructural with ZrC. The ZrC^Oj, phase is reported to exist between ZrC098 on the oxygen-poor side and ZrC0 73O014 on the oxygen-rich side.149 Formation of the oxycar — bide may occur as an intermediate layer between the ZrO2 scale and carbide, by the dissolution of oxygen in ZrC,145,150 or by a reaction between the ZrO2 scale and CO or CO2 gas diffusing outward from the oxide-carbide interface.142 Limited thermodynamic data for the Zr-O-C system (see Quensanga and Dode149) has hindered more thorough assessment of these hypotheses. At high temperatures in air atmosphere, formation of ZrN or ZrCxOj, Nz com­pounds may occur,139 but thermodynamic data for this quaternary system is similarly limited (see Constant et a/.151).

In the beginning stages of R&D for MOX fuel pro­duction, many kinds of manufacturing techniques were investigated. In the 1960s, the pellet route was adopted for all the pilot plants in Belgium, France, Germany, the United Kingdom, and Japan.2, 8 The two types of MOX fuel for LWRs and FBRs have quite different characteristics, affecting both the fabrication process and the quality requirements. These characteristics are summarized in the following points6:

• The plutonium content of FBR fuel is several times higher than that of LWR fuel.

• The smear density of FBR fuel has to be lower than that of LWR fuel because the former has to be used at higher temperature and for higher burn-up.

• The higher plasticity of FBR fuel, resulting from the higher irradiation temperature, justifies less

restrictive specification tolerances and quality requirements, than for LWR fuel.

• The uniformity in plutonium isotopic composition within a batch of fuel assemblies is a key perfor­mance-related quality for LWR fuel, while it is rather unimportant for FBR fuel.

On the basis of these points, various kinds of processes were developed to fabricate MOX pellets for FBRs and LWRs. The MOX pellet fabrication processes that have been adopted in several countries are described below.

P. J. Maziasz and J. T. Busby

ile strength

YS Yield strength

2.09.1 Introduction

Austenitic stainless steels are a class of materials that are extremely important to conventional and advanced reactor technologies, as well as one of the most widely used kinds of engineering alloys. They are austenitic Fe-Cr-Ni alloys with 15-20Cr, 8-15Ni, and the balance Fe, because they have a face — centered-cubic (fcc) close-packed crystal structure, which imparts most of their physical and mechanical properties. They are steels because they contain dis­solved C, typically 0.03-0.15%, and more advanced steels can also contain similar or greater amounts of dissolved N. They are stainless because they con­tain >13%Cr and Cr provides surface passivation for corrosion-resistance in various aqueous or corrosive chemical environments from room temperature to about 400 °C. At elevated temperatures of 500 °C and above, Cr provides oxidation resistance by the forma­tion of protective Cr2O3 oxide scales. Commercial stainless steels are complex alloys, with varying addi­tions and combinations of Mo, Mn, Si, and Ti as well as Nb to enhance the properties and behavior of the austenite parent phase over a wide range of temperatures. They can also contain a host of minor or impurity elements, including Co, Cu, V, P, B, and S, which do not have significant effects within certain normal ranges.

Typical commercial steel grades relevant to nuclear reactor applications include types 304, 316, 321, and 347. They can be fashioned into a wide range of thick or thin components by hot or cold rolling, bending, forging, or extrusion, and many are also available as casting grades as well (i. e., 304 as CF8, 316 as CF8M, and 347 as CF8C). These steels all have good combinations of strength and ductility at both high and low temperatures, with excellent fatigue resistance, and are most often used in the solution-annealed (SA) condition, with the alloying elements fully dissolved in the parent austenite phase and little or no precipitation. The steels with added Mo (316) or stabilized with Ti (321) or Nb (347) also have reasonably good elevated temperature strength and creep resistance. Additions of nitrogen (i. e., 316LN or 316N) provide higher strength and stability of the austenite parent phase to the embrit­tling effects of thermal — or strain-induced martensite formation and allow this grade of steel to be used at cryogenic temperatures. It is beyond the scope of this chapter to describe in detail the physical metallurgy of austenitic stainless steels, and adequate descriptions are found elsewhere.1,2 The remainder of this chapter focuses on the factors that broadly affect the properties of austenitic stainless steels in specific reactor environments, and highlights efforts to develop modified steels that perform significantly better in such reactor systems. These will likely be important in enabling materials for any new applica­tions of nuclear power.

An interface material is deposited on the fibers. This interphase acts as a deflection layer for the matrix cracks. It consists essentially of PyC, boron nitride, or a multilayer ((PyC/SiC)n or (BN/SiC)n sequences). PyC-based interphases have been the subject of extensive studies and have been shown to be the most appropriate with respect to controlling crack deflection and mechanical properties. With the CVI process, the gas precursor is CH4 for carbon, and BCl3 and NH3 for boron nitride. Multilayered inter­phases may be deposited via pulsed CVI.

2.12.3.2 Infiltration of the SiC Matrix:

The CVI Process

The basic chemistry of making a coating and a matrix by CVI is the same as that of depositing a ceramic on a substrate by CVD.13-15 The reactions consist of crack­ing a hydrocarbon for deposition of carbon and crack­ing of methylchlorosilane for deposition of SiC. In the I-CVI process (isobaric isothermal CVI) the preform is kept in a uniformly heated chamber. Temperature and pressure are relatively low (<1200 °C, <0.5 atm).

A few alternative CVI techniques have been pro­posed to increase the infiltration rate.15,28,29 These techniques require more complicated CVI chambers and are not appropriate to the production of large or complex shapes or a large number of pieces.

The forced CVI (F-CVI) technique was proposed in the mid-1980s.29 The precursor gas is forced through the bottom surface of the preform under a pressure P1, and the exhaust gases are pumped from the opposite face under a pressure P2 < P1. The fibrous preform is heated from the top surface and sides, and cooled from the bottom (cold) surface. The densification times are significantly shorter when compared to I-CVI (10-24 h for a SiC matrix, a few hours for carbon), and the conversion efficiency of the precursor is relatively high. However, the technique is not appropriate for complex shapes. Only one preform per run can be processed, and complex graphite fixtures are required to generate the temperature and pressure gradients.

In order to overcome the aforementioned limita­tions of the F-CVI technique, alternative techniques using thermal gradients or pressure gradients have been examined for many years.15 In the thermal gradient process, the core of the fibrous preform is heated in a cold-wall reactor. The heat loss by radia­tion is favorable to get a lower temperature in the external surface. The densification front advances progressively from the internal hot zone toward the cold side of the preform. In the P-CVI process, the source gases are introduced during short pulses.15 The P-CVI process is appropriate for the deposition of thin films or multilayers.

2.12.3.3 Infiltration of the SiC Matrix:

The temperature and pressure dependence of density allows directly the construction of a thermal EOS. At normal atmospheric pressure, the density was measured better than other properties for all three liquid metal coolants of interest. For Na and Pb, the experimental data are available from normal melting point up to normal boiling point7-11,22-26 and even up to higher temperatures59; for Pb-Bi(e), the upper temperature limit is about 1300 K,24 that is more than 600 K below its normal boiling point.

At normal atmospheric pressure (p0), the tem­perature dependence of the density (p) of most of normal LM can be described with an uncertainty of 1-3% by a linear correlation:

p(T;p0) = pM,0 — ap,0(T — Tma) [4]

where pM;0 is the density at normal melting temper­ature and Ap,0 is a constant.

The isobaric volumetric coefficient of thermal expansion (CTE) is, by definition, expressed through the density as follows:

_J @P(T, p) p(T, p) дт

Substitution of p in eqn [5] by correlation [4] yields for CTE at normal atmospheric pressure:

a (T, p0)

p,0

Sometimes, more complicated correlations are used to estimate a liquid metal density on the saturation line at high temperatures in the region close to the

critical point.22,59

Recent reviews of literature data on the thermo­physical properties of liquid Na,22 Pb, and Pb-

Bi(e)24,26,34 show that the uncertainty of correlation

[4] at normal atmospheric pressure is about 0.3-3% for Na and 0.7-0.8% for Pb and Pb-Bi(e) in the aforementioned temperature ranges. The recom­mended coefficients34 of the correlations [4] and [6] are given in Table 7, and the density and the isobaric
volumetric CTE of Na, Pb, and Pb-Bi(e) are presented as a function of temperature in Figures 4 and 5, respectively.

Densities of the liquid metal coolants of interest monotonically decrease with temperature due to the increase of the interatomic distances caused by ther­mal expansion; the CTE increases with temperature due to reduction of the interatomic forces with the distance.

2.16.1 Introduction

Burnable poisons or burnable absorbers perform a very valuable function in nuclear fuels. They are materials, such as boron, gadolinium, erbium, or dys­prosium, which in their unirradiated state have a high propensity for neutron absorption, but which trans­form into ones that absorb very little after capturing a neutron. By this means, the neutron multiplication factor can be controlled in the reactor throughout the lifetime of the fuel with less reliance on insertion of neutron-absorbing control rods or other control mechanisms.

The first application of burnable poisons was actu­ally for an early submarine reactor design. It was discovered that control rods would be insufficient on their own to control the neutron multiplication factor for the specified refueling cycle time of the core and burnable poisons were used for supplementary control. Today, burnable poisons are used extensively in commercial light water reactors (LWRs), comprising western pressurized water reactors (PWRs) and the Russian equivalent denoted VVERs and boiling water reactors (BWRs). LWRs are by far the most numerous of the 436 commercial reactors currently (2009) in opera­tion. The UK’s advanced gas-cooled reactors (AGRs) also rely heavily on burnable poisons. The other reactor types in commercial operation (Canadian designed heavy water cooled and moderated reactor (CANDU), Russian designed graphite moderated water cooled reactors (RBMKs), and the UK Magnox reactors) do not normally use burnable poisons at present, though there is an advanced fuel bundle design available for CANDU reactors that do use them.

The response of synthetic graphite to a stress (its elastic behavior) is dominated by the bond anisotropy in the graphite single crystal lattice, the preferred crystal orientation, and the presence of defects (porosity) in the structure. The elastic response of the strong covalent in-plane bonds of the carbon atoms in the graphene sheets will be vastly different from the graphene sheets held in stacks with weak van der Waals forces. Definition of the stress-strain relationship for the hexagonal graphite crystal requires five independent elastic constants.23 These constants are identified as (using a Cartesian coordi­nate system with the z-axis parallel to the hexagonal axis of the crystal or c-axis):

Txx C11exx T C12eyy T C13ezz

Tyy C12exx T C11eyy T C13ezz

Tzz C13 exx T C13 eyy T C33ezz

Tzx C44ezx

Tzy C44ezy

Txy = 1/2(C11 — Cu)Sxy = C66£xy [9]

where the stresses T/m are defined as the force acting on the unit area parallel to the /th direction; the normal to the unit area is the mth direction. The parameters Cjare the elastic moduli and their inverse Sj are the elastic compliances. The various measure­ments of compliances made on single crystals and highly oriented pyrolytic graphites have been reviewed by Kelly12 and are reported to be the best available estimates (Table 2).

Table 2 reports the Young’s modulus parallel to the hexagonal axis of the crystal Ec = S—31 ~ 36.4GPa, the Young’s modulus parallel to the basal planes, Ea = S—11 ~ 1020 GPa, and the shear modulus paral­lel to the basal planes G = S—1 = C44 ~ 4.5 GPa. The very low value of Ec results from the very weak interlayer van der Waals bonding, while the value of Ea reflects the magnitude of the in-plane (sp2) C-C covalent bonds. Kelly12 reviewed the literature data for

Elastic moduli (GPa) Elastic compliances

(10-13 Pa-1)

experimental values of C44 and noted that while many reported values are lower than those reported in Table 2, the presence of glissile basal plane disloca­tions can reduce C44 by one or two orders of magnitude.

The Young’s modulus, E, of the single crystal will thus depend upon orientation of the crystal to the Measurements (stress) axis. Thus, E-1, may be writ­ten as a function of the angle, ‘, with respect to the crystal hexagonal axis as

E-1 = Sn(1 — g2)2 + S’33g4

+ (2S13 + S44)g2 (1 — g2) [10]

where g = cos’. Taking values for the elastic com­pliances from Table 2, and allowing S44 = 2.4 x 10- Pa-1, the variation of the reciprocal modulus with the angle between the measurement direction and the crystal c-axis, ‘, can be calculated using eqn [10] (Figure 16). Also plotted in Figure 16 is an approxi­mate value of E-1 calculated, allowing all Sj to be zero except S44. The agreement between the two is good over a wide range of values of ‘, clearly demon­strating the dominance of S44 in controlling the elastic modulus and other mechanical properties in polygranular (synthetic) graphites.

The graphite single crystal shear modulus, G (Pa-1), can also be calculated12 from the elastic compliances (Sj) given in Table 2 (allowing S44 = 2.4 x 10-10Pa-1) from eqn [11]:

G-1 = S44 + (s„ — S12 — (1 — g2)

+ 2(S11 + S33 — 2S13 — S44)g2 (1 — g2) [11]

Values of G-1 as a function of ‘ are plotted in Figure 17. The value of the crystal shear modulus at ‘ = 0, that is, parallel to the basal planes, is the smallest shear modulus and corresponds to C44 for crystal basal plane shear (weak van der Waals forces), again demonstrating the dominance of S44 in controlling the elastic moduli of the crystal. It is

interesting to note that while G-1 displays a mini­mum (largest G) at ~я/4, the reciprocal Young’s modulus value displays a maximum (smallest E) at ~я/4, reflecting the different modes of bond stretching and the different bonding nature in these cases.

The crystals in synthetic graphite are not as per­fect as discussed above. Moreover, while both the filler-coke and the binder phase exhibit crystallinity, the alignment of the crystallite regions within the filler and binder is not uniform, although it may display preferred orientation because of filler-coke calcination and the formation of the synthetic arti­fact. Texture also arises because of the alignment of the filler particle during formation. Consequently, the single crystal values of moduli are not realized in synthetic (polygranular) graphite. Typical values of Young’s modulus for synthetic graphite are given in Table 1. There is considerable variation ofYoung’s modulus with density. However, the effect of texture is clearly seen in the anisotropic values for grade AGX, 6.9 GPa (WG) and 4.1 GPa (AG), confirming the tendency of the filler grains to align on extrusion such that WG orientation displays more of the c-axis Young’s moduli (0 and p/2 in Figure 16) and is thus greater than the AG value. Grades with a greater density (^1.8gcm-) possess a Young’s modulus value, ~10 GPa, far less than the single crystal values (except C44). Measurements of the shear modulus derived from the velocity of shear (transverse) waves propagating through the graphite give values ranging from 3 to 4 GPa for various grades all with density ^1.8gcm- . The values of shear modulus (WG) were slightly greater than shear modulus (AG)

for extruded and molded grades, as expected from the theory and textural effects. The measured values of shear modulus for synthetic graphites (3-4 GPa) are in reasonable agreement with the single crystal value of C44 (4-4.5 GPa) reported in Table 2. The presence of glissile basal plane dislocations would be expected to reduce the single crystal value of shear modulus substantially, but the defective nature of the crystals in synthetic graphite assures a high density of dislocation pinning sites, which will increase the value of shear modulus. For a wide range of synthetic graphites, the ratio of E/G ~ 3 is in agreement with previous observations.12 In addition to the effects of texture, such as the crystal/filler preferred orientation, on the elastic moduli of synthetic graphite, the existence of porosity with a wide size, shape, and orientation distribution (refer to Section 2.10.2) makes the interpretation of the elastic properties more complicated. Typical Young’s moduli for syn­thetic graphites range from 5 to 15 GPa (Table 1 ), with lower modulus being exhibited by coarser-grain graphite. The combined effect of porosity and texture in synthetic graphite causes anisotropy of the moduli, with the anisotropy ratio for Young’s modulus being as large as 2. Finer-grain graphites are far more isotropic with respect to Young’s modulus.

Various workers have studied the changes in the elastic compliances of single crystal graphite with temperature, as reviewed by Kelly.12 The single crystal elastic constants decrease with increasing temperature.2 The value of C33 decreases linearly
by more than a factor of 2 over the temperature range 0-2000 K.12 Synthetic polygranular graphite, because of the influence of texture and porosity, shows a completely different temperature depen­dence of their Young’s moduli. The thermal closure of cracks/pores aligned along the a-axis (between the basal planes — the ‘Mrozowski’ cracks15) will cause an increase4,21,24 in Young’s modulus of ^50% from room temperature to ^2300 K. Above this tempera­ture up to ^3000 K, Young’s modulus is reported to decrease slightly.21 Typical high-temperature behav­ior of Young’s modulus is shown in Figure 18 for pitch-coke and petroleum-coke graphite.

Poisson’s ratio for fine-grained isotropic graph­ite (ATJ) has been reported to be 0.1-0.16, and for coarser-grained extruded graphite (AGOT) 0.04-0.09, the value being dependent upon the mea­surement direction relative to the forming axis.21 In a large study of the room-temperature elastic proper­ties of 15 graphite grades measured using the velocity of sound waves (both longitudinal and transverse), the Poisson’s ratio value was seen to be between 0.17 and 0.24 for fine-grain, isotropic grades and between 0.28 and 0.32 for medium-grain, molded, or extruded grades.

2.10.4.2 Strength and Fracture

Typical compressive and tensile stress-strain curves for medium-grain, extruded graphite are shown in Figures 19 and 20, respectively. The stress-strain curve is nonlinear and typically shows hysteresis on

reloading after loading below the fracture stress, with a permanent set.12,23,25 The nonlinearity has been widely attributed to pseudo-plastic events such as basal plane shear and subcritical cracking.12,23-27 Table 1 reports the tensile, flexure, and compressive strength of a range of synthetic graphites. Tensile strengths vary with texture from as low as <5 MPa for coarser-grain, extruded grades to >60 MPa for fine-grain, isotropic grades and can be >80 MPa for some isostatically molded, ultra-fine-grain and micro-fine-grain synthetic graphite. Compressive strengths range from <20 MPa to >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

the distribution of stresses within the body and thus the stress that each crystallite experiences.

Generally, the strength increases as the modulus increases but is also greatly influenced by factors such as texture and density (total porosity). The strength (or Young’s moduli) is related to the frac­tional porosity through a relationship of the form

s = ff0e~bP [12]

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 fine — grain, 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 = 179 MPa and b = 9.62. The correlation coefficient, R2 = 0.80. Significantly, the same flexure strength data (Figure 22) is better fitted when plotted against the mean filler-particle size27 (R2 = 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 MPam~1/2 dependent upon their texture

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 fine — grain 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 filler — particle 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.

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 at32 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 stress — intensity factor (KIc) input to 1.4MPam1/2, a value far in excess of the actual measured KIc of this graph­ite (1.0MPam1/2). 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 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?5 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 2000­1500 °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?4 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?4 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 ofsmall 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.

2.13.1 Introduction

Zirconium carbide, like other carbides of the transi­tion metals of Groups IV, V, and VI, exhibits an

unusual combination of properties that are useful for refractory applications. These carbides combine the cohesive properties of covalently bonded ceramics (high melting point, high strength, and hardness) with the electronic properties of metals (high thermal and electrical conductivity). Comparative properties of the refractory transition metal carbides have been reviewed previously by Schwarzkopf and Kieffer,1

Storms,2 Toth,3 Kosolapova,4 and Upadhyaya.5 A thorough understanding of the thermodynamic and heat transport properties of carbides is limited by a paucity of experimental data as a function of composition.

2.15.3.1 Fuel Rod Design

2.15.3.1.1 Basic structural design

In LWRs and FBRs, a number of fuel rods are formed into a fuel assembly. The fuel rod is a barrier (con­tainment) for fission products; it has a circular cross­section that is suited for withstanding the primary pressure stress due to the external pressure of the coolant and the increase in internal pressure by fission gas release. An axial stack of cylindrical fuel pellets is encased in a cladding tube, both ends of which are welded shut with plugs. A gas plenum is located at the top part of the rod, in most cases, to form a free space volume that can accommodate internal gas. Helium gas fills the free space at atmospheric pressure or at a given pressure. A hold-down spring, located in the gas plenum, maintains the fuel stack in place during shipment and handling. UO2 insulator pellets are inserted at both ends of the fuel stack, in some fuel designs, to thermally isolate metallic parts such as the end plug and the hold-down spring.

2.15.3.1.2 Fuel rods for LWRs

Table 2 summarizes LWR fuel rod design speci­fications.30 LWR UO2 fuel rods contain dense low-enrichment UO2 pellets in a zirconium alloy cladding; they are operated at a low linear heat rate with centerline temperatures normally below 1400 °C. The fuel pellets of the VVER have a small central hole (1.2-1.4mm in diameter).

Fission gas release is low under these conditions and no large gas plenum is needed. Burnable absorber fuel rods containing UO2-Gd2O3 pellets are located in some part of the fuel assemblies of LWRs to flatten reactivity change throughout the reactor oper­ation cycle.

Great efforts have been made in LWR fuel rod design in order to achieve the following good perfor­mance features: high burn-up, long operation cycle, good economy, and high reliability. Toward achieving these ends, many modifications have been made, such as the development of high-density UO2 pellets, axial blankets for reducing neutron leakage, ZrB2 integral burnable absorber, high Gd content UO2- Gd2O3 pellets, corrosion-resistant cladding materials, and optimization of helium pressure and plenum length in the rod designs.

LWR MOX fuel rods contain MOX pellets that have a low plutonium content. As the plutonium concentration is low, their irradiation behavior is similar to that of LWR UO2 fuel rods. No additional

aPartial length rod.

Mitsubishi developed alloy.

Source: Tarlton, S., Ed. Nucl. Eng. Int. 2008, 53, 26-36.

problems are apparent, with the possible exception of higher gas release and therefore an increase in rod internal pressure at high burn-up. Power degra­dation with burn-up is less in the MOX fuel than in UO2 fuel because of the neutronic properties of the plutonium isotopes and thus MOX fuel is irra­diated at higher power later in its life, releasing more fission gases. In addition, the slightly lower thermal conductivity of MOX may give rise to higher fuel temperatures, resulting in higher fission gas release. Design changes, such as lowering the helium filling pressure, increasing the plenum volume, and/or decreasing the fuel stack length in the rod, are applied to accommodate higher gas release in MOX fuel rods.

The effect ofthe parameters acting at the mesoscopic scale can be assessed using solutions of the heat equation obtained for particular microstructures, for instance, a matrix containing inclusions.

Interstitial

FP atom in solution in the lattice FP atom as interstitial in the lattice, or gas in solid Vacancy

Figure 3 Some parameters affecting thermal conductivity.

2.17.2.1.1 Porosity and grain boundaries

The porosity existing in fresh fuels evolves during irradiation and has a strong impact on the heat transfer in the pellet because of its low thermal conductivity as compared to the solid. The porosity is assumed to have identical effects on the fresh and irradiated fuels and therefore the same correction formulae are used. This assumption is valid when the shape of the pores is similar and the pore volume fractions are comparable (i. e., around 5 vol%). In order to analyze the effect of parameters other than the porosity, its effect is normal­ized to 0 or 5 vol% by converting the measurements obtained for samples with different porosity levels. Irradiation-induced pore-size distribution changes have a small effect, but the pore shape can play a larger role if the pores are not spherical and oriented. The correction formulae are derived from composite mate­rial formulae giving the effective conductivity of a matrix containing inclusions,4 often simplified by attri­buting zero conductivity to the pores. Loeb5 intro­duced the effect of temperature to take into account the radiative heat transfer in the pores. The influence of the complex pore shape observed in irradiated fuel was investigated by Bakker using the finite-elements technique applied to realistic microstructures obtained by image analysis.6 Limiting this presentation to a recent recommendation, the thermal conductivity can be normalized to 5% porosity using the formula of Brandt and Neuer as recommended by Fink7 (eqn [2]).

1 — 0.05f (T)

1 — Pf (T) where f(T) = 2.6-0.5T/1000 and P is the porosity fractional volume.

2.17.2.1.2 Precipitates of insoluble fission products

Precipitates are formed by fission products that are insoluble in the UO2 lattice (see Chapter 2.20,

Fission Product Chemistry in Oxide Fuels). They form oxide inclusions (such as BaZrO3 or SrZrO3) or metallic inclusions (Mo, Ru, Tc, Rh, Te, Pd, Sn, Cd, Sb, Ag, etc.) and their influence on the effective thermal conductivity can be evaluated by the formu­lae obtained for composite materials8: for instance, the Maxwell-Eucken equation.9 As the volume frac­tion of inclusions is small, this simple model gives results of sufficient accuracy. The inventory and vol­ume fraction of the precipitates can be calculated from the number of moles created at a given burnup. For illustration purposes, the Maxwell-Eucken formula was applied at a fixed temperature assuming a UO2 matrix with a thermal conductivity of 4Wm-1K — containing inclusions with thermal conductivities of 0 (pores), 2 and 10 (ceramic precipitates), and 100 (metallic precipitates) W m-1 K — . As shown in Figure 4, the effect of the precipitates on the thermal conductivity varies linearly with their volume frac­tion, which is proportional to the burnup, bu. If the coefficients a and b are used to describe this propor­tionality, we have k = a — b x bu; the negative burnup dependence is introduced because the fuel thermal conductivity globally decreases with burnup. Usually, the thermal conductivity is approximated by the 1/(A +BT) formula, where A and B describe the phonon scattering mechanisms. Therefore, one obtains the formula A +BT = (l/a)/(1 — b/a x bu) and if b/a x bu is small, we have A + BT = 1/a + (b/a2 x bu) — (b2/a3 x bu2) + ••• . At a fixed temperature T, the A and B coefficients depend in a linear or quadratic way on the burnup. This kind of dependence is often found in thermal conductivity correlations.