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 contraction of the filler-coke particles during the calcination process. Frequently, when a crack propa­gating through the binder phase encountered a well — aligned filler particle, it took advantage of the easy cleavage path and propagated through the particle. However, in contrast to the mechanism suggested by Ioka eta/.,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, Most recently, the model was successfully validated against experimental ten­sile strength data for three graphites of widely differ-

28,45,46

ent texture.

The model and code were successfully bench — marked28,46 against H-451 tensile strength data and

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 ofthe 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-p. m 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

Stress (MPa)

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

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

Vapor pressures have been established by Langmuir vaporization of C-saturated ZrC and by Knudsen effusion studies of ZrC in equilibrium with graphite. These are plotted in Figure 10. Langmuir studies are internally consistent, but give higher pressures than for the Knudsen method. Pollock37 and Coffman eta/.38 assumed the congruent evaporation composition
to be stoichiometric, that is, equal evaporation rates for Zr and C. However, Langmuir evaporation of ZrC0.74_0.96 by Nikol’skaya et a/.39 found the con­gruently evaporating composition to lie in the range ZrC0 8-087, decreasing with increasing temperature between 2300 and 3100 K. Vidale40 computed Zr and C vapor pressures from tabulated H and S functions for Zr and C, AHf for ZrC of —185.5 kJmoP1, and an estimated ASf for ZrC of —11.3 kJmol—1 K—1, and the trend is consistent with Langmuir data. Storms2 com­puted Zr vapor pressure over ZrC + C from thermo­dynamic functions derived by the author for ZrC0 96, values in the 1963 JANAF thermochemical tables for Zr^g) and C(s), AHf for ZrC of —196.6 kJ mol—1, and AH^ for ZrC of 608 kJ mol—1, with the prediction consistent with Knudsen data. Evaporation rate as a function of temperature is plotted in Figure 11. Stan­dard enthalpy of vaporization of ZrC at 298 K has been reported as —1520 kJ mol—1 for Langmuir studies and —805 kJ mol—1 for Knudsen studies.37,38

Storms and Griffin13 coupled Knudsen effusion from TaC cells with mass spectrometry between 1800 and 2500 K to determine the Zr activity of ZrC0 55-“197” by comparing ion currents from pure Zr with those of the carbide. Carbon activity was obtained via a Gibbs-Duhem integration; activity of both as a function of C/Zr ratio at 2100 K is plotted

Temperature (K)
3000 т	2800 Т	2600 Т
10-4

10-5

10-8

10-9

3.2 X 10-4 3.4X10-4 3.6 X 10-4 3.8 X 10-4 4.0X10-4 4.2X10-4 4.4 X 10-4

1/T (K-1)

Figure 11 Langmuir rate of evaporation of ZrCx as a function of temperature.

in Figure 12. Activity of Zr exceeds that of C for carbon-deficient compositions up to the cross-over composition at 2100 K of ZrC089. The change in Zr activity with C/Zr ratio is most rapid at high-carbon compositions and becomes near-constant as the com­position drops below approximately ZrC0.8. Partial standard molar enthalpies of vaporization for Zr and C as a function of C/Zr ratio are plotted in Figure 13. Total enthalpies obtained by Pollock37 and Coffman et al3 are consistent with the values of Storms and Griffin.1 Partial enthalpy of Zr decreases monotonically as C is removed from the lattice. Partial enthalpy of C exceeds that of Zr for most of the homogeneity range, approaching that of Zr at a composition of ZrC0.99.

2.15.3.2.1 PWR UO2 fuel assembly

Figure 432 shows an example of a PWR fuel assem­bly. PWRs have 197-230mm square, ductless assem­blies that traverse the full 2635-4550 mm height of the core. They comprise a basic support structure of unfueled zirconium alloy guide tubes attached to the top- and bottom-end fittings, an array of 14 x 14 to 18 x 18 fuel elements (minus the number of guide tubes), and several axially spaced grids that hold the array together. About half of the assemblies have rod control clusters attached at their upper end; these consist of 18-24 slender stainless-steel-clad absorber rods of AgInCd alloy or B4C, individually located in the guide tubes. The absorber rods are withdrawn for startup and are repositioned after

Control rod guide thimble

Instrumentation guide thimble

refueling; the reactor is controlled at power by altering the concentration of an absorber (boric acid) in the coolant. The bottom-end fitting is located on the core grid plate and the assembly is spring loaded against a hold-down system to compensate for differential expansion or growth during irradiation.

Fine control is obtained by incorporating a burn­able poison like Gd2O3 in some of the elements, in which it is admixed with UO2 in the core region, and with the upper and lower sections of natural UO2. By minimizing power changes in this manner, the inci­dence of pellet-clad interaction (PCI) failures can be kept to very low, acceptable values. Various improve­ments in fuel assembly design have been adopted. To improve reliability, for instance, debris filtering was adopted in the structural design of the bottom part of the fuel assembly, the grid structure design was mod­ified against fretting corrosion, and an intermediate flow mixer grid was added to enhance the margin to depart from nucleate boiling (DNB). Zirconium alloy grids for better neutronics, optimized distribu­tion of fissile and fertile materials, and a burnable poison to improve fuel cycle economy and to extend reactor cycle length were all introduced for econ­omy in the current assembly designs, as also the removable top nozzle to reduce operation and main­tenance costs.

The perturbations of the crystal lattice due to the displacement of atoms, that is point defects (intersti­tials, vacancies) and extended defects (defects clusters, dislocations, voids), contribute to the degradation of the thermal conductivity by scattering or limiting the mean free path of the phonons. This perturbation at the atomic scale is of the same nature as for soluble fission products and is also interpreted in terms of phonon scattering centers. Two aspects introduce uncertainties into the prediction of the effect of radia­tion damage: the concentration is difficult to calculate as a function of the irradiation conditions and the effect on the thermal conductivity is nonlinear (satu­ration occurs). Because of the large number of displa­cements produced by fission, the point defect concentration is expected to saturate early, probably before a burnup of 1 MWd kg HM~ , the saturation level depending on temperature. Supplementary radi­ation damage of a dynamical nature is present only in pile because of the fission spikes and its concentration depends on the fission rate; it disappears immediately when irradiation stops.

2.17.2.2.2 Stoichiometry

Stoichiometry has a major effect on the thermal conductivity of fresh fuels.19 UO2 is generally stoi­chiometric when introduced in pile and the O/U ratio of UO2 irradiated under LWR conditions remains close to 2.00 up to a burnup of 100 MWd kg HM~120-22 This parameter is, however, difficult to define for an irradiated fuel because of the complex chemical composition. Also, the effect of the oxygen defects due to the nonstoichiometry can be expected to be reduced because of the large number of oxygen defects created by irradiation.

2.17.2.2.3 Additives in UO2 (Pu, Gd, Cr)

The addition of Pu, Gd, or Cr to UO2 reduces the thermal conductivity of the fresh fuel. These addi­tives may form solid solutions with UO2 or be present as precipitates. The perturbation decreases with burnup because of the other burnup effects, as observed for (U, Gd)O2 by Sonoda et a/.,23 for (U, Pu) O2 by Fujii et a/.24 and Staicu et a/.,25 and for Cr by Caillot et a/.26

Here, we reviewed the fundamental properties of metal hydrides, focusing on zirconium hydride, which is a material used to make the neutron reflec­tors of fast nuclear reactors, as well as titanium hydride and yttrium hydride. We discussed the hydrogen content and temperature dependence of
the elastic modulus, hardness, electrical conductivity, heat capacity, and thermal conductivity of zirconium hydride. Values of the physical properties of zirco­nium hydride (8-ZrH166) are summarized in Table 3. Such data are very important and valuable for the utilization of metal hydrides as materials for neutron reflectors in fast reactors.

References

The data for the lattice parameter, Young’s modulus, shear modulus, bulk modulus, and Vickers hardness were obtained at room temperature.

2.11.4 Summary

This chapter has provided a basic outline of neutron reflectors for nuclear reactors from the perspective of materials science, beginning with an overview of the properties required for neutron reflectors, proceeding to an outline of the production and processing methods for Be and metal hydrides as representative reflector materials, and then to a description of their basic properties. The outline of metal hydrides has focused on zirconium hydride, which is currently used mainly in fast reactors, and has described the influence of temperature and hydrogen concentration on the basic properties of zirconium hydride. The data provided in this chapter are considered to be extremely important and valuable in regard to the use of Be and zirconium hydride as neutron reflectors.

1. Canel, J.; Zaman, J.; Bettembourg, J.; Flem, M. Le.; Poissonnet, S. Int. J. Appl. Ceram. Technol. 2006, 3, 23.

2. Han, B.; Kim, Y.; Kim, C. H. Fus. Eng. Des. 2006, 81, 729.

3. Beeston, J. M. Nucl. Eng. Des. 1970, 14, 445.

4. Genshiryoku Zairyou Handbook; The Nikkan Kogyo Shimbun: Tokyo, 1952.

5. Rare Metals Handbook, 2nd edn.; Reinhold: New York, NY, 19e1.

6. Chirkin, V. S. Trans. Atom. Ener. 1966, 20, 107.

7. Chakin, V. P.; Latypov, R. N.; Suslov, D. N.; Kupriyanov, I. B. JAERI-Conference 2004-2006, pp 119-127.

8. Syslov, D. N.; Chakin, V. P.; Latypov, R. N. J. Nucl. Mater. 2002, 307-311, 664.

9. Kleykamp, H. Thermochim. Acta 2000, 345, 179.

10. Tipton, C. R. Reactor Hand Book, 2nd edn.; Interscience: New York, 1960.

11. Gregg, S. J.; Hussey, R. J.; Jepson, W. B. J. Nucl. Mater.

1960, 3, 175.

12. Gregg, S. J.; Hussey, R. J.; Jepson, W. B. J. Nucl. Mater.

1961, 4, 46.

13. Kharlamov, A. G. Atomnaya Energiya 1963, 15(6), 517-519.

14. Manly, W. D. J. Nucl. Mater. 1964, 14, 3.

15. Keilholtz, G. W.; Lee, J. E. Jr.; Moore, R. E.; Hamner, R. L. J. Nucl. Mater. 1964, 14, 87.

16. Cooper, M. K.; Palmer, A. R.; Stolarski, G. Z. J. Nucl. Mater. 1963, 9, 320.

17. Pryor, A. W.; Tainsh, R. J.; White, G. K. J. Nucl. Mater. 1964, 14, 208.

18. Eisenbud, M. The Metal Beryllium; ASM, 1995, p 703.

19. Zuzek, E.; Abriata, J. P.; San-Martin, A.; Manchester, F. D. Bull. Alloy Phase Diagrams 1990, 11(4), 385-395.

20. Yamanaka, S.; Yoshioka, K.; Uno, M.; et al. J. Alloys Compd. 1999, 293-295, 908.

21. Ito, M.; Setoyama, D.; Matsunaga, J.; et al. J. Alloys Compd. 2006, 426, 67.

22. Yamanaka, S.; Yamada, K.; Kurosaki, K.; et al. J. Alloys Compd. 2002, 330-332, 99.

23. Yamanaka, S.; Yamada, K.; Kurosaki, K.; et al. J. Nucl. Mater. 2001, 294, 94.

24. Ito, M.; Setoyama, D.; Matsunaga, J.; et al. J. Alloys Compd. 2006, 420, 25.

25. Ito, M.; Matsunaga, J.; Setoyama, D.; etal. J. Nucl. Mater. 2005, 344, 295.

Heavy ion irradiation by Kr has been used to simu­late some aspects of fission neutron irradiation, such as high damage rate (up to 100 dpa). Gan et a/.173 irradiated TEM foils of commercial hot-pressed ZrC099 (the authors report a C/Zr ratio of 1.01, but the composition was corrected to reflect the impurity content of 1.9 wt% Hf, 0.19 wt% Ti, 0.21 wt% 0, and 0.61 wt% N, considering that the metals and nonmetals substitute for Zr and C on their respective sublattices). Irradiation was conducted at 298 or 1073 K to >1MeV Kr ions to a fluence of 2.5 x 1015—1.75 x 1016cm—2 (10-70dpa), with in situ TEM ofmicrostructural evolution during irradiation. Lattice parameter swelled by 0.6-0.7% (~2% volume increase) at 10 dpa (298 and 1073 K), 0.9% (~3% volume increase) at 298 K and 30 dpa, and 7% (21% volume expansion) at 1073 K and 70 dpa. Simulta­neously, precipitation of a fcc phase with 8% larger lattice parameter (5.09 A) than the matrix (4.71 A) was detected by ring patterns superimposed on the single-crystal ZrC electron diffraction pattern. Precipitate coarsening with temperature and fluence was observed. Energy-dispersive X-ray spectroscopy (EDX) detected no change in stoichiometry during irradiation. The authors linked the precipitate phase and the 7% lattice parameter increase at high tem­perature and fluence, but could not explain ade­quately its origin, hypothesizing that the expansion was related to Kr implantation. Cubic Zr02 formation is also plausible (a ~ 5.1 A). They acknowledged that the large ratio of surface area to volume in a TEM foil may permit larger lattice expansion than is possi­ble in the bulk. 0ther microstructural features noted were grain boundary cracking at high fluence, defect clusters at low temperatures and fluence, and dislo­cation segments at high temperatures. No irradiation — induced voids or amorphization were detected.

Because of very small irradiated volume (depth < 1 mm) produced by Kr ion irradiation, the authors later performed proton irradiation, asserting that protons provide a damage rate similar to the fast reactor core, with a more significant irradiated vol­ume (depth ~ 30 mm), though the achievable dose is limited (~10 dpa). Gan eta/.174 subjected the same commercial hot-pressed ZrC0.99 to irradiation at 1073 K by 2.6 MeV protons to a fluence of 2.75 x 1019cm—2 (1.8 dpa), subsequently preparing TEM foils. Lattice parameter change was assessed by higher order Laue zone (H0LZ) patterns in conver­gent beam electron diffraction, but no change within the uncertainty limit of 0.2% was detected. In con­trast, when the same material was irradiated by Yang et a/.175 at 1073 K in a 2.6 MeV proton fluence of 1 x 1019 or 2.3 x 1019cm—2 (0.7 or 1.5 dpa), XRD determined a lattice parameter expansion of 0.09% (0.27% volume expansion) for 0.7 dpa and 0.11% (0.33% volume expansion) for 1.5 dpa. Gan eta/.174 detected faulted dislocation loops on {111} planes, characteristic of irradiation of fcc metals, which were not seen for Kr irradiation. No ring pattern or pre­cipitation was detected, as in Kr irradiation.

Gosset et a/.176,177 irradiated commercial hot — pressed ZrC0.95 (containing <0.03 wt% 0) and sol-gel synthesized ZrC0.85O0.15 to irradiation at 298 K by 4MeV Au ions to a fluence of 1 x 1012—5 x 1015cm—2. In the carbide, XRD-determined lattice parameter expanded by 0.03-2% (0.09-6% volume expansion), increasing with fluence but saturating at about 1014cm—2, while the oxycarbide lattice param­eter expanded by 0.05% (0.15% volume expansion), independent of fluence. In both, fine precipitates formed, identified by electron diffraction as tetrago­nal ZrO2 (a~ 3.61 2A, c~ 5.19 A) and identified by tilting as adherent to the sample surface. The authors concluded that high oxygen content in ZrC did not modify the nature of the ion irradiation-induced defects. Faulted dislocation loops were identified in both. No amorphization was detected by XRD.

Early in the 1960s, comprehensive R&D programs concerning MOX fuel were started in Japan and they resulted in the JAEA process that was adopted by the Plutonium Fuel Fabrication Facility (PFFF) which started operation in 1972. The PFFF used local control equipment to fabricate MOX fuel for the advanced thermal reactor FUGEN,63 and the experimental fast reactor JOYO on an engineering scale. Following the completion of the Plutonium Fuel Production Facility (PFPF) in 1987, MOX fuel fabrications for JOYO and the prototype FBR MONJU have been conducted in PFPF since 1988. MOX fuel fabrication for FUGEN in PFFF was completed in 2001. Now, this plant is undergoing preparative work for its decommissioning.

Figure 18 shows the flow sheet of the JAEA pro­cess utilized in the PFPF. Two kinds of plutonium, either PuO2 powder prepared by the oxalate precipi­tation or the MH-MOX powder, can be used in the JAEA process to fabricate FBR MOX pellets.

In this process, three feed powders, UO2 prepared by the ADU process, PuO2 or MH-MOX powder,

and dry recycled scrap powder, are prepared to get the plutonium concentration specified by the fuel specifications in the mixed powder. The feed powders are ball milled to get a homogeneous distribution of plutonium in the sintered MOX pellets. This mill pot has a silicon rubber lining on its inner surface to enhance the charging and discharging of powders by automated operation. About 40 kg of powder can be charged in this ball mill. A photograph of the ball mill is shown in Figure 19.

Similar to the milled powder in the SBR process (see Section 39.5.2.5), this powder must be granu­lated to provide a free-flowing property.51,52 After mixing zinc stearate (binder) and Avicel (microcrys­tal cellulose; pore former) with the milled powder, this powder mixture is roughly pressed into tablets at pressures of around 200 MPa and the tablets are then crushed into granules of sizes that make them free-flowing. These granules are pelletized into green pellets at pressures of around 500 MPa followed by the addition of zinc stearate as lubricant. Normally, these green pellets are sintered at about 1700 °C for 4 h under an atmosphere of Ar + 5% H2 mixed gas after dewaxing at about 800 °C for 2 h under the same atmo­sphere as used in the sintering.64 A ceramograph of a transverse section of a sintered MOX pellet prepared by the JAEA process is shown in Figure 20. This MOX pellet was fabricated under specifications for pellets to be loaded in the MONJU outer core.

After centerless grinding, the diameter, geometri­cal density, and appearance of each sintered pellet are inspected. An inspection device to check pellet den­sity and appearance is shown in Figure 21; it is installed in the PFPF. Details of the JAEA process

Figure 20 Ceramograph of a transverse section of a sintered mixed oxide of uranium and plutonium pellet for MONJU fuel prepared by the Japan Atomic Energy Agency process (plutonium content: 30.8 wt%, density: 84.84% theoretical density, mean grain size: 3.9 mm).

and its fuel fabrication technologies have been previ­ously reported in the literature.64,65

Generally, austenitic stainless steels that have no 8-ferrite stay austenitic from room temperature up to about 550 °C, at which temperature they can start to experience the effects of thermal aging. Aging causes the alloy to decompose from a solid solution into various carbide or intermetallic precipitate phases and a more stable austenite phase. The decomposition of a quaternary Fe-Cr-Ni-Mo alloy, typical of type 316 stainless steel at 650 °C, is shown in Figure 7, and

the time-temperature-precipitation (TTP) diagrams for aging of SA behavior of type 316 and 316L stainless steel at 500-900 °C are shown in Figures 8 and 9.12,13 For typical light water reactor (LWR) or fusion reactor applications, such high temperature aging behavior is not too important, but it does become important for understanding irradiation-induced or — produced precipitation behavior for FBR irradiation of compo­nents at temperatures 400-750 °C. As indicated in Figure 8, prolonged aging of 316 steel at 550 °C and above tend to produce precipitation of Cr-rich M23C6 in the matrix and along grain boundaries, while expo­sure at 600-750 °C eventually also produce precipita­tion of M6C, Laves (Fe2Mo), and s (FeCr) phases.12 Precipitation kinetics of these phases appears maxi­mum at 750-850 °C, and then at temperatures above 900-950 °C, none of these phases forms. The lower C content of 316L accelerates and shifts the formation of intermetallic phases relative to 316 steel, as indi­cated in Figure 9. Additions of Ti or Nb cause the formation of MC carbides at the expense of the Cr — rich M23C6 carbides, depending on whether the steel is fully stabilized or not, but can also accelerate the formation of intermetallic phases, such as s or Laves. If 8-ferrite is present in the alloy, it generally rapidly converts to s-phase during aging. CW effects tend to accelerate the formation and refine the dispersion of carbides, but they can also significantly enhance the formation of intermetallic phases at lower tempera­tures, particularly in 20% CW 316.12-15 However, careful alloy design and compositional modification

Time (h)

Figure 9 Time-temperature-precipitation diagram of solution-annealed 316L stainless steel during thermal aging. Dashed lines represent a lower solution anneal temperature (1090 °C vs. 1260 °C). Reproduced from Weiss, B.; Stickler, R. Metall. Trans. 1972, 4, 851-866.

of certain austenitic stainless steels, such as the HT — UPS steels, can result in alloys resistant to the forma­tion of а-phase during aging or creep for up to 60 000 h or more. The various precipitate phases that form in 300 series austenitic stainless steels during thermal aging or creep are listed below, with some information on their nature and characteristics.12,1 ,1

• M23C6 — fcc, Cr-rich carbide, that can also enrich Mo, W, and Mn, but is generally depleted in Fe, Si, and Ni relative to the 316 alloy matrix.

• M6C — diamond-cubic phase that can be either a carbide (M6C — filled, M12C — half-filled) or a silicide phase (M5Si — unfilled), depending on how carbon fills the atomic structure. It is generally enriched in Si, Mo, Cr, and Ni relative to the 316 alloy matrix.

• MC — fcc Ti — or Nb-rich carbide. The Ti-rich MC phase can also be very rich in Mo, or V and Nb, and may contain some Cr, but tend to contain little or no Fe, Si, and Ni. The Nb-rich MC is a fairly pure carbide phase that can enrich in Ti, but does not usually contain any of the other alloying elements in the 347 or 316 alloy matrix.

• Laves — hexagonal Fe2Mo-type intermetallic phase. Fe2Nb and Fe2W can also be found in steels contain­ing those alloying additions. Phase tends to be highly enriched in Si and can contain some Cr but is generally low in Ni relative to the 316 alloy matrix.

• а — body-centered-tetragonal intermetallic phase, consisting of mainly Cr and Fe. It can be enriched
somewhat in Mo, but is depleted in Ni relative to the 316 alloy matrix.

• w — bcc intermetallic phase, enriched in Mo and Cr, and containing mainly Fe, and depleted in Ni relative to the 316 alloy matrix.

• FeTiP or Cr3P — hexagonal or tetragonal phos­phide compounds that can be found in stainless steels containing higher levels ofP. FeTiP is found in the HT-UPS steels during aging.

The basic damage phenomena in unidirectional com­posites under on-axis tensile loads involve multiple microcracks or cracks that form in the matrix perpen­dicular to fiber direction and that are arrested by the fibers by deflection in the fiber-matrix interface. In the composites reinforced with fabrics of fiber bundles, matrix damage is influenced by a multilength scale structure.39 Furthermore, 2D CVI SiC/SiC is ahetero — geneous medium because of the presence of fibers, large pores (referred to as macropores) located between the plies or at yarn intersections within the plies, and a uniform layer of matrix over the fiber preform (referred to as the intertow matrix) (Figure 5). Much smaller

Longitudinal tow

Transversal tow

Layer

0.5mm

Figure 5 Micrograph showing the microstructure of a 2D CVI SiC/SiC composite.

pores are also present within the tows. Under on-axis tension, damage in 2D CVI SiC/SiC occurs essentially in the formation of matrix cracks perpendicular to longitudinal fiber axis and their deflection either by the tows (first and second steps) or by the fibers within the tows (third step). These steps (Figure 6) correspond to deformation increments:

Step 1: cracks initiate at macropores where stress concentrations exist (deformations between 0.025% and 0.12%);

Step 2: cracks form in the transverse yarns and in the interply matrix (deformations between 0.12% and 0.2%);

Step 3: transverse microcracks initiate in the lon­gitudinal tows (deformations larger than 0.2%). These microcracks are confined within the lon­gitudinal tows. They do not propagate in the rest of the composite. The matrix in the longi­tudinal tows experiences a fragmentation pro­cess and the crack spacing decreases as the load increases.

As mentioned earlier, the directions of principal stresses are dictated by fiber orientation rather than by the loading direction. Thus, under on-axis condi­tions, all the matrix cracks are perpendicular to the loading direction. Then, under off-axis tension, matrix cracks that are located in the tows are
perpendicular to fiber direction, whereas those located between the tows are perpendicular to the load direction. On-axis loading conditions are dis­cussed later.

The resulting Young’s modulus decrease illustrates the importance of damage in the mechanical behavior (Figure 4). The major modulus loss (70%) is caused by both the first families of cracks located on the outside of the longitudinal tows (deformations <0.2%). By contrast, the microcracks within the longi­tudinal tows are responsible for only a 10% loss. The substantial modulus drop reflects important changes in load sharing: the load gets carried essentially by the matrix-coated longitudinal tows (tow reloading). During microcracking in the longitudinal tows, load sharing is affected further, and the load becomes carried essentially by the filaments (fiber reloading). The elastic modulus reaches a minimum described by the following equation (Figure 4):

Emin = 1/2Ef Vf [10]

where Vf is the volume fraction of fibers.

Equation [10] implies that the matrix contribution is negligible. At this stage, matrix damage and debonding are complete (saturation). The load is carried by fibers only. The mechanical behavior is controlled by the fiber tows oriented in the direction of loading.

The results presented earlier are valid only for the liquid phase and under condition that thermody­namic coefficients do not depend on pressure. In order to take into account the pressure dependence of the LM thermodynamic parameters, different thermal EOS were developed and applied to LM. Two main directions were followed with more suc­cess: the generalization of the well-known EOS of Van der Waals (VdW) and the use of statistical mechanics and intermolecular potentials for EOS development.

The generalized three-parameter VdW EOS was used by Martynyuk73 to find the critical parameters

of many pure metals (including Na and Pb). Morita and Fischer74 proposed a modification for the EOS of Redlich and Kwong75 to describe a metal vapor with dimer and monomer molecules and applied it for Na coolant. Later, this approach was extended by Morita et al. to Pb-Bi(e)52 and to Pb.56 A simple EOS for liquid phase was developed by Srinivasan and Ganesan76 based on the concept of the internal pres­sure of liquids and applied to sodium. Later, it was used by Azad58 for the calculation of the critical tem­peratures of Pb and Pb-Bi(e).

Eslami77 applied a perturbed hard-sphere-chain EOS developed by Song et a/.78 to calculate the den­sity of liquid Na and Pb on the saturation line up to very high pressures.

Comparison of different approaches shows that better results in large temperature and pressure ranges can be obtained with the modified Redlich and Kwong EOS74 and with the perturbed hard — sphere-chain EOS.78

2.14.5 Transport Properties

The most important transport properties of liquid metal coolants are viscosity, thermal conductivity, and electric resistance.

2.14.5.1 Viscosity

Accurate and reliable data on the viscosity of LM are not abundant. Some discrepancies between experi­mental data can be attributed to the high reactivity of metallic liquids, to the difficulty of taking
precise measurements at elevated temperatures. All three LM: Na, Pb, and Pb-Bi(e), are believed to be Newtonian liquids and the temperature depen­dence of their dynamic viscosity (q) is usually described by an Arrhenius-type equation:

V(T, p) = Viip) exp(Ev{p)/RT) [17]

where En is the activation energy of motion for nor­mal viscous flow and — the asymptotic value of q at T! 1 In a large temperature range, a more complicated formula is often used for more precise fitting of the experimental results on LM dynamic

viscosity: a

V(T; p)=TL exp(E, (p)/RT) [18]

where An and n are constants.

The viscosity of liquid Na at normal atmospheric pressure was well measured in the liquid range from normal melting point to normal boiling point at nor­mal atmospheric pressure3,6-8,11,22,26,79; the variation in the most reliable recommendations does not exceed ±5%.34

Data on the viscosity of Pb and Pb-Bi(e) were reviewed in Sobolev and Benamati24 and Imbeni et a/.48; it was measured up to about 1270 K for

lead79 and up to 1180 K for Pb-Bi(e).80 A good agree­ment exists among the different sets of experimental data and the values calculated by means of the empirical equations reported in different publica­tions. In the temperature range from TM,0 to 1270 K, the viscosity of liquid Pb can be described with the Arrhenius-type eqn [17] with uncertainty of ±5%. A higher variation (7-10%) exists between the values and recommendations given by different sources for Pb-Bi(e).

The recommended coefficients of correlation [17] are given in Table 11, and the calculated tempera­ture behavior of the dynamic viscosity of liquid Na, Pb, and Pb-Bi(e) is presented in Figure 11.

In engineering hydrodynamics, the kinematic vis­cosity (n) is also often used, which is a ratio of the liquid dynamic viscosity to the density:

The kinematic viscosities of liquid Na, Pb, and Bi versus temperature at normal atmospheric pressure, calculated with formula [19], and the recommended correlation for their dynamic viscosities and densities presented earlier, are presented in Figure 12.