Mechanical Properties of Ceramics and Composites

46.K. F. H. Ahlborn, Y. Kagawa, and A. Okura. Observation of the Influence of Mi-

crocracks on the Crack Propagation Inside of Transparent ZrO2. Ceramics To- day—Tomorrow’s Ceramics 66C (P. Vincenzini, ed.). Elsevier Science Publishers B.V., 1991, pp. 1857–1864.

47.Y. Akimune and R. C. Bradt. Knoop Microhardness Anisotropy of Single-Crystal Stoichiometric MgAl2O4 Spinel. J. Am. Ceram. Soc. 70(4):C-84–86, 1987.

48.W. H. Rhodes, P. L. Berneburg, and J. E. Niesse. Development of Transparent Spinel (MgAl2O4). Avco Corp. Report for Army Contract AMMRC-CR-70-19, 10/1970.

49.P. P. Budnikov, F. Kerbe, and F. J. Charitonov. The Hot Pressing of AluminumMagnesium Spinel (MgAl2O4). Sci. Cer. 4:69–78, 1968.

50.K. Okazaki and K. Nagata. Effects of Density and Grain Size on the Elastic and

Piezoelectric Properties of Pb(Zr-Ti)O3 Ceramics. Mechanical Behavior of Materials, Proc. Intl. Conf. on Mechanical Behavior of Materials 4, Kyoto, 8/15–20/1971. Soc. Matls. Sci., Kyoto, Japan, 1972, pp. 404–412.

51.P. D. Zavitsanos and J. R. Morris, Jr. Synthesis of Titanium Diboride by a SelfPropagating Reaction. Cer. Eng. Sci. Proc. 4(7–8):624–633, 1983.

52.R. D. Koester and D. P. Moak. Hot Hardness of Selected Borides, Oxides and Carbides to 1900°C. J. Am. Cer. Soc. 6:290–296, 1967.

53.F. W. Vahldiek and S. A. Mersol. Slip and Microhardness of IVa to VIa Refractory Materials. J. Less Com. Met. 55:265–278, 1977.

54.D. R. Flinn, J. A. Kirk, M. J. Lynch, and B. G. Van Steatum. Wear Properties of Electrodeposited Titanium Diboride Coatings. US Dept. of the Interior, Report of Investigations, 1981.

55.F. X. McCawley, D. Schlain, and G. R. Smith. Electrodeposition of Titanium Diboride. Am. Cer. Soc. Bull. 5(4):349, 1972.

56.K. Nakano, H. Matsubara, and T. Imura. High Temperature Hardness of Titanium Diboride Single Crystal. Jp. J. Appl. Phys. 13(6):1005–1006, 1974.

57.Y. Miyamoto and M. Koizumi. High Pressure Self-Combustion Sintering for Ceramics. J. Am. Cer. Soc. 67(11):C-224–223, 1984.

58.T. Watanabe and S. Kouno. Mechanical Properties of TiB2-CoB-Metall Boride Alloys. Am. Cer. Soc. Bul. 61(9):970–973, 1982.

59.D. Kalish, E. V. Clougherty, and J. Ryan. Fabrication of Dense Fine Grained Ceramic Materials. ManLabs, Inc. Final Report for US Army Materials Research Laboratory, 11/1966.

60.Z. A. Munir and G. R. Veerkamp. An Investigation of the Parameters Influencing the Microstructure of Hot-Pressed Boron Carbide. Univ. of Calif. Dept. Mechan. Eng., Davis, CA, Progress Report, 11/1975.

61.K. Niihara. Slip Systems and Plastic Deformation of Silicon Carbide Single Crystals at High Temperatures. J. Less Com. Met. 65:155–166, 1979.

62.G. R. Sawyer, P. M. Sargent, and T. F. Page. Microhardness Anisotropy of Silicon Carbide. J. Mat. Sci. 15:1001–1013, 1980.

63.O. O. Adewoye and T. F. Page. Anisotropic Behavior of Etched Hardness Indentations. J. Mat. Sci. 11:981–984, 1976.

64.S. Fujita, K. Maeda, and S. Hyodo. Anisotropy of High-Temperature Hardness in 6H Silicon Carbide. J. Mat. Sci. Lett. 5:450-452, 1986.

65.I. J. McColm. Ceramic Hardness. Plenum Press, New York, 1990.

66.M. G. S. Naylor and T. F. Page. Microhardness, Friction and Wear of SiC and

Si3N4 Materials as a Function of Load, Temperature and Environment. First Annual Tech. Rept. US Army Grant DA-ERO-78-G-010, 10/1979.

67.T. F. Page, G. R. Sawyer, O. O. Adewoye, and J. J. Wert. Hardness and Wear Behavior of SiC and Si3N4. Proc. Brit. Cer. Soc. 26:193–208, 1978.

68.T. Hiari and K. Niihara. Hot Hardness of SiC Single Crystal. J. Mat. Sci. 14:2253–, 1979.

69.D. Chakraborty and J. Mukerji. Effect of Crystal Orientation, Structure and Di-

mension of Vickers Microhardness Anisotropy of β, α-Si3N4, α-SiO2 and α-SiC Single Crystals. Mat. Res. Bull. 17:843–849, 1982.

70.Y.-W. Kim, S.-W. Park, and J.-G. Lee. Composition and Hardness of Chemically Vapour-Deposited Silicon Carbide with Various Microstructures. J. Mat. Sci. Lett. 14:1201–1203, 1995.

71.D.-J. Kim and D.-J. Choi. Microstructure and Surface Roughness of Silicon Carbide by Chemical Vapour Deposition. J. Mat. Sci. Lett. 16: 286–289, 1997.

72.D. J. Rowcliffe and G. E. Hollox. Hardness Anisotropy, Deformation Mechanisms and Brittle-to-Ductile Transition in Carbides. J. Mat. Sci. 6:1270–1276, 1971.

73.R. H. J. Hannick, D. L. Kohlstedt, and M. J. Murray. Slip System Determination in Cubic Carbides by Hardness Anisotropy. Proc. Roy. Soc. Lond. A. 326:409–420, 1972.

74.D. B. Miricale and H. A. Lipsitt. Mechanical Properties of Fine-Grained Substoichiometric Titanium Carbide. J. Am. Cer. Soc. 66(8):592–597, 1983.

75.Y. Kumashiro, A. Itoh, T. Kinoshita, and M. Sobajima. The Micro-Vickers Hardness of TiC Single Crystals up to 1500°C. J. Mat. Sci. 12:595–601, 1977.

76.S. Shimada, J. Watanabe, and K. Kodaira. Flux Growth and Characterization of TiC Crystals. J. Mat. Sci. 24:2513–2515, 1989.

77.I. Cadoff, J. P. Nielsen, and E. Miller. Properties of Arc-Melted vs. Powder Metallurgy Titanium Carbide. Warmfeste und Karrosconfestandige Sinterwerkstoffe, Springer-Verlag, Vienna, Austria, 1956, p. 712.

78.O. Yamada, Y. Miyamoto, and M. Koizumi. High-Pressure Self-Combustion Sintering of Titanium Carbide. J. Am. Cer. Soc. 70(9):C-206–208, 1987.

79.A. Leonhardt, D. Schlafer, M. Seidler, D. Selbmann, and M. Schonherr. Microhardness and Texture of TiC Layers on Cemented Carbides. J. Less Com. Met. 87:63–69, 1982.

80.H. C. Lee and J. Gurland. Hardness and Deformation of Cemented Tungsten Carbide. Mat. Sci. Eng. 33:125–133, 1978.

81.L. E. McCandlish, B. H. Kear, and B. K. Kim. Processing and Properties of Nanostructured WC-Co. Nanostrucrured Matls. 1:119–122, 1992.

82.W. Rafaniello. Development of Aluminum Nitride: A New Low-Cost Armor. Dow Chem. Co. Final Report for US Army Research Office Contract DAAL03-88-C- 0012, 12/1992.

83.R. F. Coe, R. J. Lumby, and M. F. Pawson. Some Properties and Applications of Hot-Pressed Silicon Nitride. Properties and Applications of Silicon Nitride,

Special Ceramics No. 5 (P. Popper, ed.). British Ceramic Society, Stoke on Trent, UK, 1977, pp. 361–376.

84.K. Tsukuma, M. Shimada, and M. Koijumi. Thermal Conductivity and Microhardness of Si3N4 with and Without Additives. Am. Cer. Bull. 60(9):910–912, 1981.

85.Y. Miyamoto, M. Koizumi, and O. Yamada. High-Pressure Self-Combustion Sintering for Ceramics. J. Am. Cer. Soc. 67(11):C-224–233, 1984.

86.A. K. Mukhopadhyay, S. K. Datta, and D. Chakraborty. Hardness of Silicon Nitride and Sialon. Cer. Intl. 17:121–127, 1991.

87.A. K. Mukhopdhay, S. K. Dutta, and D. Chakrborty. On the Microhardness of Silicon Nitride and Sialon Ceramics. J. Eur. Cer. Soc. 6:303–311, 1990.

88.P. J. Burchill. Hardness Anisotropy of α-Si3N4 Single Crystal. J. Mat. Sci. 13:2276–2278, 1978.

89.D. Chakraborty and J. Mukerji. Characterization of Silicon Nitride Single Crystals and Polycrystalline Reaction Sintered Silicon Nitride by Microhardness Measurements. J. Mat. Sci. 15:3051–3056, 1980.

90.K. Ueno. Microstructure Dependence of Fracture Toughness and Hardness of Silicon Nitride. Yogyo-Kyokai-Shi 97(1):85–87, 1989.

91.M. C. Shaw. The Fundamental Basis of the Hardness Test. The Science of Hardness Testing and Its Research Applications (J. H. Westbrook and H. Conrad, eds.). Am. Soc. for Metals, Metals Park, OH, 1973, pp. 1–11.

92.R. F. Bunshah and R. W. Armstrong. Continuous Ball Indentation Test for Examining Hardness Dependence on Indentor Size, Indentation Size, and Material Grain Size. Am. Soc. for Metals, Metals Park, OH, 1973, pp. 318–328.

93.J. R. Floyd. Effects of Firing on the Properties of Dense High-Alumina Bodies. Trans. Brit. Cer. Soc. 64:251–265, 1965.

94.H. E. Exner and J. Gurland. A Review of Parameters Influencing Some Mechanical Properties of Tungsten Carbide Cobalt Alloys. Powder, Metallurgy 13(25):13031, 1970.

95.L. Belon, H. Forestier, and Y. Bigot. The Hardness of Some Solid Solutions of Alumina. Special Ceramics 4 (P. Popper, ed.). British Ceramic Research Association, Stoke on Trent, 1968, pp. 203–209.

96.F. Albrecht. Anisotropy of the Hardness of Synthetic Corundum. Z. Krist. 106:183–190, 1954.

97.R. C. Bradt. Cr2O3 Solid Solution Hardening of Al2O3. J. Am. Cer. Soc. 50(1):54–55, 1967.

98.K. Shinozaki, Y. Ishikura, K. Uematsu, N. Mozutani, and M. Kato. Vickers Micro-

Hardness of Solid Solution in the System Cr2O3- Al2O3. J. Mat. Sci. Lett. 15:1314–1316, 1980.

99.H. Chang, H. J. Höfler, C. J. Altstetter, and R. S. Averback. Synthesis, Processing and Properties of Nanophase TiAl. Scripta Met. Mat. 25:1161–1166, 1991.

100.R. J. Bratton. Precipitation and Hardening Behavior of Czochralski Star Sapphire. J. Appl. Phys. 42(1):211–216, 1971.

101.D. Lewis, B. A. Bender, R. W. Rice, J. Homeny, and T. Garino. Precipitation and Toughness in Alumina-Rich Spinel Crystals. Fracture Mechanics of Ceramics 8.

Microstructure, Methods, Design, and Fatigue (R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange, eds.). Plenum Press, New York, 1986, pp. 61–67.

102.W. F. Brace. Dependence of Fracture Strength of Rocks on Grain Size. Penn. State U. Mineral Experimental Station Bull. 76:99–103, 1963.

103.W. F. Brace. Brittle Fracture of Rocks. Intl. Conf. on States of Stress in the Earth’s Crust—Preprints of Papers (W. R. Judd, ed.). Rand Corp. Report, 1963.

104.K. L. Lewis, J. A. Savage, K. J. Marsh, and A. P. C. Jones. Recent Developments in the Fabrication of Rare-Earth Chalcogenide Materials for Infrared Optical Applications. New Opt. Mat., SPIE Conf. Proc., 400, Soc. of Photo-Optical Instrumentation Enginers, Bellingham, WA, 1983.

105.K. L. Lewis, A. M. Pitt, J. A. Savage, J. E. Field, and D. Townsend. The Mechanical Properties of CVD-Grown Zinc Sulphide and Their Dependence on the Conditions of Growth. 9th Intl. Conf. on CVD, ECS Proc. 84(6):530–545, 1984.

106.D. Townsend and J. E. Field. Fracture Toughness and Hardness of Zinc Sulphide as a Function of Grain Size. J. Mat. Sci. 25:1347–1352, 1990.

107.E. Lendvay and M. V. Fock. Microhardness Anisotropy in Cubic and Hexagonal ZnS Single Crystals. J. Mat. Sci. 4:747–752, 1969.

108.A. W. Swanson and J. Pappis. Application of Polycrystalline ZnSe Prepared by Chemical Vapor Deposition to High Power IR Laser Windows. (Raytheon Co.) AFML Tech. Report TR-75-170, 1975.

109.J. Lankford. Comparative Study of the Temperature Dependence of Hardness and Compressive Strength in Ceramics. J. Mat. Sci. 18:1666–1674, 1983.

110.G. R. Anstis, P. Chantikul, B. R. Lawn, and D. R. Marshall. A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I. Direct Crack Measurements. J. Am. Cer. Soc. 64(9):533–538, 1981.

111.T. Sperisen, C. Carry, and A. Mocellin. Microfracture Behavior of Fine Grained Alumina Studied by Indentation and Acoustic Emission in Various Environments. Fracture Mechanics of Ceramics, Microstructure, Methods, Design, and Fatigue (R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange, eds.) 8. Plenum Press, New York, 1986, p. 69–83.

112.Y. Kumashiro and E. Sauma. The Vickers Micro-Hardness of Non-Stoichiometric Niobium Carbide and Vanadium Carbide Single Crystals up to 1500°C. J. Mat. Sci. 15:1321–1324, 1980.

113.J. Dusza, T. Eschner, and K. Rundgren. Hardness Anisotropy in Bimodal Grained Gas Pressure Sintered Si3N4. J. Mat. Sci. Lett. 16:1664–1667, 1997.

114.D. G. Rickerby. Observations of the Hardness Anisotropy in MgO and LiF. J. Am. Cer. Soc. 62(3–4):222, 1979.

115.T. W. Button, I. J. McColm, and S. J. Wilson. Hardness Anisotropy and its Dependence on Composition in Sodium Tungsten Bronzes and Rhenium Trioxide Single Crystals. J. Mat. Sci. 14:159–164, 1979.

116.A. M. Lejus, D. Ballutaud, C. R. Kha, and J. Solide. Microdureté de Monocristaux de V2O3. Mat. Res. Bull. 15:95–102, 1980.

117.J. H. Westbrook and P. J. Jorgensen. Effects of Water Desorption on Indentation Microhardness Anisotropy in Minerals. Am. Min. 53:1899–1909, 11–12/1968.

118.E. T. Park, J. L. Routbort, Z. Li, and P. Nash. Anisotropic Microhardness in SingleCrystal and Polycrystalline BaTiO3. J. Mat. Sci. 33:669–673, 1998.

119.R. Vaßen and D. Stöver. Manufacture and Properties of Nanophase SiC. J. Am. Cer. Soc. Submitted for publication.

120.R. Vaßen and D. Stöver. Properties of Silicon-Based Ceramics Produced by Hot Isostatic Pressing Ultrafine Powders. Phil. Mag. B 76(4):585–591, 1997.

121.G. R. Anstis, P. Chantikul, B. R. Lawn, and D. B. Marshall. A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I. Direct Crack Measurements. J. Am. Cer. Soc. 64(9):533–538, 1981.

122.C. Cm. Wu, R. W. Rice, and P. F. Becher. The Character of Cracks in Fracture Toughness Measurements of Ceramics. Fracture Mechanics Methods for Ceramics, Rocks and Concrete (S. W. Freiman and E. R. Fuller, Jr., eds.). ASTM STP 74, ASTM, Philadelphia, PA, 1982, pp. 127–140.

123.Z. Li and R. C. Bradt. Thermal Expansion and Thermal Expansion Anisotropy of SiC Polytypes. J. Am. Cer. Soc. 70(7):445–448, 1987.

124.R. W. Rice. Possible Effects of Elastic Anisotropy on Mechanical Properties of Ceramics. J. Mat. Sci. Lett. 13:1261–1266, 1994.

125.D. H. Chung and W. R. Bussem. The Elastic Anisotropy of Crystals. Anisotropy in Single-Crystal Refractory Compounds (F. W. Vahldiek and S. A. Merson, eds.). Plenum Press, New York, pp. 217–245, 1968.

126.R. W. Rice and R. C. Pohanka. Grain Size Dependence of Spontaneous Cracking in Ceramics. J. Am. Cer. Soc. 62(11–12):559–563, 1979.

127.E. C. Skaar and W. J. Croft. Thermal Expansion of TiB2. J. Am. Cer. Soc. 56(1):45, 1973.

load and configuration, it can also be an aid in sorting out similar dependences of wear, erosion, and machining.

Consider now the basic mechanism(s) of the grain dependence of these properties, i.e. in crystalline materials, since they are the ones having their volume nearly or fully occupied by grains. A key factor is again local plastic deformation as associated with hardness indentations (Chap. 4). While there is some uncertainty in the scope and specifics, e.g. changes and details of its occurrence in compressive strength, erosion, wear, and machining, local plastic flow is clearly a factor in all of these. While this is known empirically, it also stems from similar mechanisms of these properties and hardness, since erosion, most machining, and much wear entail particles or asperities penetrating surfaces. Such penetration causes local plastic flow and fracture similar to that involved in hardness indentation (Chap. 4), which thus entail local H values and E and K values respectively, as well as load dependence for both phenomena. While ballistic performance entails some penetration and compressive strength does not, both have some correlation with hardness [1–5] (hence also generally with elastic moduli [1,2]). The correlation of these properties, especially compressive strength, with hardness stems from the fact that hardness is a measure of the local yield stress (Y), which for many materials obeys the simple relation Y = H/C, where C is referred to as the constraint factor and is typically (for ceramics) 2.5 to 3 [2,6]. (Where there are significant differences in the yield stress for deformation, i.e. slip or twinning systems, that do not allow general deformation, e.g. do not represent five independent slip systems, then the values of C may be different [2], especially where stresses are limited, e.g. in tension. Also, in materials such as silicate glasses and polymers, where different deformation mechanisms may occur, their “yield” stresses also tend to scale with E [6–8]). Thus the H–σc correlation is attributed to the yield stress H/3 being the upper limit to the compressive strength of dense crystalline ceramics [3–5]. This correlation and that of other properties to H is a factor in their G dependence, but there are variations for each property.

While there is a basic correlation of σc with H, there are potential differences in their G dependence, as there are substantial differences and some similarities of σc with tensile strength, σT, as shown by the general character of the mechanisms involved. Though not documented or understood in detail, it is now generally recognized that in well conducted compressive tests, generation of substantial local tensile stresses occurs due to, and on the scale of, the microstructure, especially pores and probably grains, and second phase particles or regions. These local tensile stresses generate and grow cracks but at higher stresses than in tensile testing since the individual cracks are typically semistable in the macro compressive stress field. The high stresses reached allow microplastic processes to generate cracks, and possibly contribute some to their stability, growth, or both, thus providing the basis for correlation with H.

Further, while ultimate compressive failure is typically somewhat explosive due to the high stored elastic energy of the high stresses involved, the local, stable tensile cracking leads to cumulative failure, as opposed to much more immediate catastrophic failure from rapid growth of a single crack in tensile loading. Thus compressive failure is seen as the progressive generation, growth, and coalescence of small, initially micro, cracks, generated and grown by local tensile stresses due to stress heterogeneities, microplastic processes, or both, culminating in brittle failure, e.g. as indicated by acoustic emission [5,9–13]. These processes are the probable source of the G dependence of σc and the similarities and differences of its G dependence versus those of H and tensile strength, since these entail respectively more concentrated local deformation, cracking, or both and a lesser role of larger scale propagation of single cracks. Also, the load dependence of H and its local cracking appear to be sources of differences in the G dependences of H and σc, e.g. higher load H values are probably more pertinent, but H minima from local surface cracking probably have limited or no pertinence. Note also that there are various parasitic effects, e.g. end crushing or cracking due to end strain incompatibilities between loading and specimen surfaces, that can lead to premature compressive failure in testing and may vary with G.

The field of ballistic impact on ceramic materials is complicated first by complexities of the process and second by the fact that many of the test results are classified because of the important application to military armor [14,15]. Complexities of the process arise most fundamentally from the speed and resultant very high strain rates of the process that is typically controlled by shock wave phenomena that alter or preclude more normal mechanical behavior. Further complexities arise since there are various types of projectile threats that involve different degrees or types of various mechanisms, with each impacted by how well the ceramic is packaged in terms of both backing as well as, mainly for the most demanding applications, side and frontal containment of the ceramic. However, there is one basic aspect of the process that is clear, namely that there are two basic stages in what happens to the ceramic. The first stage, which is the key one in defeating the projectile, is the generation and initial propagation of a compressive shock wave from the projectile impact as both the projectile and the ceramic armor under it are shattered into fine fragments. The second stage is the propagation of the compressive stress wave through the ceramic to its boundaries where it reflects as a tensile stress wave that causes much further damage in the ceramic, which is a dominant factor in the extent to which there may be some second hit capability of the remaining ceramic in stopping a second projectile. Projectile penetration is defeated by erosion and fragmentation of the receding penetrator nose by the multitude of ceramic microfragments through which the projectile moves.

Erosive wear also generally correlates with hardness and its G dependence as well as via indentation cracking effects from the particle impacts. Though not

fixed surface for hardness measurements. Even greater uncertainty exists for the pertinent K values, since in wear, erosion, and machining, the crack scale will typically be much smaller than for normal fracture toughness testing, the larger scale of the latter being a major factor in significant variations in K–G relations (Chap. 2). Local temperature and environmental effects add further uncertainty.

While the diversity of wear presents challenges, it generally reflects important G dependences stemming from not only correlations with H but also in- dent-fracture and plastic deformation, as well as possible K–G dependence. Though such G dependence can depend on grain boundary character and grain size (and its distribution), shape, and orientation, it may aid in sorting out the varying mechanisms and is clearly important in developing, selecting, and applying wear resistant ceramics.

The subsequent sections review the G dependence of the above properties in the order: compressive strength, ballistic performance (briefly in view of very limited data) and erosion, wear, and machining. (No data on grain shape and orientation are known.) This review provides a more comprehensive data base and perspective on the G dependence of these properties (complementing and extending more limited earlier surveys of their G dependence [3,4,18]. This review also clearly shows the critical need for more study, especially of a more comprehensive nature.

II.GRAIN DEPENDENCE OF COMPRESSIVE STRENGTH

A.Grain Size Dependence

Four previous surveys of the G dependence of compressive strength of ceramics [3–5,18] provide the background for much of the following review, which addresses first compressive strength without superimposed confining stresses and then with such stresses. Much, especially earlier, data is for bodies with some to substantial porosity, especially at finer grain sizes, thus requiring correction of compressive strengths to P = 0, e.g. as extensively discussed elsewhere [1] to expand the limited data base. However, despite the limited data base, there is a fairly clear G dependence consistent with expectations based on earlier reviews.

Limited data of Alliegro [18,19] for hot pressed ZrB2 (P 0.01–0.09) clearly show, even with no or conservative P correction, substantial σc levels with a simple linear decrease as a function of G-1/2 extrapolating to substantial values at G-1/2 = 0, i.e. for single crystals (Fig. 5.1). Data for similarly hot pressed TiB2 of Alliegro [18,19], (corrected for P = 0–0.11, mostly ≤ 0.05), though of more limited G range, indicate similar G dependence, but at somewhat higher σc levels (> 2 GPa) and is consistent with the one data point of Mandorf and Hartwig (extrapolated to P = 0) [20]. Other data for TiB2 + 20%