Mechanical Properties of Ceramics and Composites

240

Chapter 3

230.G. A. Gogotsi, Y. A. L. Groushevsky, O. B. Dashevskaya, Y. U. G. Gogotsi, and V.

A.Laytenko. Complex Investigation of Hot-pressed Boron Carbide. J. Less Com. Met. 117:225–230, 1986.

231.D. Kalish, E. V. Clougherty, and J. Ryan. Fabrication of Dense Fine Grained Ceramic Materials. ManLabs, Inc. Final Report for US Army Materials Research Lab. Contract DA-19-066-AMC-283(x), 11/1966.

232.K. Niihara. Mechanical Properties of Chemically Vapor Deposited Nonoxide Ceramics. Am. Cer. Soc. Bul. 1160, 1983.

233.K. Niihara. A. Nakahira, and T. Hirai. The Effect of Stoichiometry on Mechanical Properties of Boron Carbide. J. Am. Cer. Soc. 67(1) C-13–14, 1984.

234.R. W. Rice. Effects of Thermal Expansion Mismatch Stresses on the Room-Tem- perature Fracture of Boron Carbide. J. Am. Cer. Soc. 73(10):3116–3118, 1990.

235.B. Roebuck and E. A. Almond. Deformation Fracture Processes and the Physical Metallurgy of WC-Co Hardmetals. Intl. Mats. Reviews 33(2):90–110, 1988.

236.B. Roebuck. The Tensile Strength of Hardmetals. J. Mat. Sci., 14:2837–2844, 1979.

237.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.

238.K. Hiruta, H. Hirotsuru, R. Terasaki, and Y. Nakajima. Influence of Powder Characteristics on Flexural Strength of Aluminum Nitride Ceramics. Intl. Conf. on Aluminum Nitride Ceramics, Le Maridien Pacific, Tokyo, Japan, 3/8–11/98.

239.A. K. Mukhopdhay, D. Chakarborty, and J. Mukerji. Fractographic Study of Sintered Si3N4 and RBSN. J. Mat. Sci. Lett. 6:1198–1200, 1987.

240.R. K. Govila. Fracture Phenomenology of a Sintered Silicon Nitride Containing Oxide Additives. J. Mat. Sci. 23:1141–1150, 1988.

241.E. Tani, S. Umebayashi, K. Kishi, K. Kobatashi, and M. Nishijima. Effect of Size

of Grains with Fiber-Like Structure of Si3N4 on Fracture Toughness. J. Mat. Sci. Lett. 4:1454–1456, 1985.

242.J. A. Salem, S. R. Choi, M. R. Freedman, and M. G. Jenkins. Mechanical Behavior and Failure Phenomena of an Insitu Toughened Silicon Nitride. J. Mat. Sci. 27:442l–4428, 1992.

243.A. J. Pyzik and D. F. Carroll. Technology of Self-Reinforced Silicon Nitride. Ann. Rev. Mater. Sci., Annual Reviews Inc. 24:189–214, 1994.

244.C.-W. Li, S.-C. Lui, and J. Goldacker. Relation Between Strength, Microstructure, and Grain-Bridging Characteristics in Insitu Reinforced Silicon Nitride. J. Am. Cer. Soc. 78(2):449–459, 1995.

245.J. E. Brocklehurst. Fracture in Polycrystalline Graphite. Chem. Phys. Carbon 13 (P.

L.Walker and P. A. Thrower, eds.). Marcel Dekker, New York, 1977, pp. 145–279.

246.R. H. Knibbs. Fracture in Polycrystalline Graphite. J. Nuc. Mat. 24:174–187, 1967.

247.M. Wakamatsu, S. Ishingo, N. Takeuchi, and T. Hattori. Effect of Firing Atmosphere on Sintered and Mechanical Properties of Vanadium-Doped Alumina. J. Am. Cer. Soc. 74(6):1308–1311, 1991.

248.R. D. Bagley, I. B. Cutler, and D. L. Johnson. Effect of TiO2 on Initial Sintering of Al2O3. J. Am. Cer. Soc. 53(3):136–141, 1970.

Grain Dependence of Ceramic Tensile Strengths at 22°C

241

249.F. A Kröger. Enrichment of Titanium at Grain Boundaries in Al2O3. J. Am. Cer. Soc. 58(7–8): 355–356, 1975.

250.V. Jayaram, B. J. Dalgleish, and A. G. Evans. Some Observations of Microstructural Changes in Alumina Induced by Ti Inhomogeneities. J. Mat. Res. 3(4):764-, 1988.

251.E. Ryshkewitch and D. W. Richardson. Oxide Ceramics, Physical Chemistry and Technology. General Ceramics, Inc., Haskell, NJ, 1985, p. 217.

252.T. M. Clarke, D. L. Johnson, and M. E. Fine. Effect of Oxygen Partial Pressure on Precipitation in Titanium-Doped Aluminum Oxide. J. Am. Cer. Soc. 53(7):419–420, 1970.

253.M. Blanc, A. Mocellin, and J. L. Strudel. Observation of Potassium β′′′ -Alumina in Sintered Alumina. J. Am. Cer. Soc. 60(9–10):403–409, 1977.

254.R. W. Rice. The Effect of Gaseous Impurities on the Hot Pressing and Behavior of MgO, CaO and Al2O3. Proc. Brit. Cer. Soc. 12:99–123, 1969.

255.R. W. Rice. Ceramic Processing: An Overview. AICHE J. 36(4):481–510, 1990.

256.T. A. Wheat and T. G. Carruthers. The Hot Pressing of Magnesium Hydroxide and Magnesium Carbonate. Science of Ceramics (G. H. Steward, ed.). Brit. Cer. Soc., 1968, pp. 33–51.

257.P. W. Montgomery, H. Stromberg, and G. Jura. Solid Surfaces and the Gas-Solid Interface. Am. Chem. Soc.: Advances in Chemistry Series 33, 1961, p. 18.

258.H. Kodama and T. Miyoshi. Study of Fracture Behavior of Very Fine-Grained Silicon Carbide Ceramics. J. Am. Cer. Soc. 73(10):3081–3082, 1990.

259.D. Stoyan and H.-D. Schnabel. Description of Relations Between Spatial Variability of Microstructure and Mechanical Strength of Alumina Ceramics. Cer. Int’l 16:11–18, 1990.

260.T. Sakai. Effect of Oxygen Composition on Flexural Strength of Hot-Pressed AIN.

J.Am. Cer. Soc. 61(9–10): 460–461, 1978.

261.K. Komeya and H. Inoue. The Influence of Fibrous Aluminum Nitride on the Strength of Sintered AIN-Y2O3). Trans. J. Brit. Cer. Soc. 70(3):107–114, 1971.

262.M. Yasuoka, K. Hirao, M. E. Brito, and S. Kanzaki. High-Strength and High-Frac-

ture-Toughness Ceramics in the Al2O3/LaAl11O18 Systems. J. Am. Cer. Soc. 78(7):1853–1856, 1995.

263.H.-D. Kim, I.-S. Lee, S.-W. Kang, and J.-W. Ko. The Formation of NaMg2Al15O25 in an α-Al2O3 Matrix and Its Effect on the Mechanical Properties of Alumina. J. Mat. Sci. 29:4119–4124, 1994.

264.J. A. Salem and J. L. Shannon, Jr. Crack Growth Resistance of Textured Alumina.

J.Am. Cer. Soc. 72(1): 20–27, 1989.

265.F. V. DiMarcello, P. L. Key, and J. C. Williams. Preferred Orientation in Al2O3 Substrates. J. Am. Cer. Soc. 55(10):509–514, 1972.

266.D. K. Smith, Jr., and S. Weissmann. Residual Stress and Grain Deformation in Extruded Polycrystalline BeO Ceramics. J. Am. Cer. Soc. 5(6):330–336, 1968.

267.H. Tagai, T. Zisner, T. Mori, and E. Yasuda. Preferred Orientation in Hot-Pressed Magnesia. J. Am. Cer. Soc. 50(10):550–551, 1967.

268.J. E. Dykins. Tensile Properties of Sea Ice Grown in a Confined System. Physics of Snow and Ice, International Conf. on Low Temperature Science, Vol. 1, Part 1 (H. Oura, ed.). Hokkaido University 1967, pp. 5–36.

242

Chapter 3

269.K. Yon, M. Hahn, R. W. Rice, and J. R. Spann. Grain Size Dependence of SbSI with Oriented Grains. Adv. Cer. Mats. 1(1):64–67, 1986.

270.T. Ohji, K. Hirao, and S. Kanzaki. Fracture Resistance Behavior of Highly Anisotropic Silicon Nitride. J. Am. Cer. Soc. 78(11):3125–3128, 1995.

271.C. Cm. Wu, K. R. McKinney, and R. W. Rice. Strength and Toughness of Jade and Related Natural Fibrous Materials. J. Mat. Sci. 25:2170–2174, 1990.

272.J. S. Reed and A.-M. Lejus. Effect of Grinding and Polishing on Near-Surface Phase Transformations in Zirconia. Mat. Res. Bull. 12:949–954, 1977.

273.R. W. Rice. Effects of Ceramic Microstructural Character on Machining Direc- tion–Strength Anisotropy. Machining of Advanced Materials, (S. Johanmir, ed.). NIST Special Pub. 847, US Govt. Printing Office, Washington DC, 1993, pp. 185–204.

274.J. T. Chakraverti and R. W. Rice. Strengthening of Zirconia-Toughened Materials by Grit Blasting. J. Mat. Sci. 16: 404–405, 1997.

275.R. W. Rice and J. T. Chakravarti. Non-Machining Surface Strengthening of Transformation Toughened Materials. US Patent 5,228,245, 7/20/1993.

276.C. C. McMahon. Relative Humidity and Modulus of Rupture. Am. Cer. Soc. Bull. 58(9):873, 1979.

277.U. R. A. Lino and H. W. Hubner. Effect of Surface Condition on the Strength of Aluminum Oxide. Sci. Cer. 12:607–612, 1984.

278.A. Zimmermann, M. Hoffman, B. D. Flinn, R. K. Bordia, T.-J. Chuang, E. R. Fuller, Jr., and J. Rödel. Fracture of Alumina with Controlled Pores. J. Am. Cer. Soc. 81(9):2449–2457, 1998.

279.A. Zimmermann and J. Rödel. Generalized Orowin-Petch Plot for Brittle Fracture. J. Am. Cer. Soc. 81(10):2527–2532, 1998.

280.R. W. Rice. Pores as Fracture Origins in Ceramics. J. Mat. Sci. 19:895–914, 1954.

281.H. P. Kirchner and J. M. Ragosta. Crack Growth from Small Flaws in Larger Grains in Alumina. J. Am. Cer. Soc. 63(9–10):490–495, 1980.

282.R. W. Rice. Effects of Environment and Temperatures in Ceramic Tensile Strength–Grain Size Relations. J. Mat. Sci. 32:3071–3087, 1997.

283.S. L. Dole, O. Hunter, Jr., and D. J. Bray. Microcracking of Monoclinic HfO2. J. Am. Cer. Soc. 61(11–12):486–490, 1978.

284.O. Hunter, Jr., R. W. Scheidecker, and S. Tojo. Characterization of Metastable Tetragonal Hafnia. Ceramurgica, Intl. 5(4):137-, 1979.

285.D. Lewis and R. W. Rice. Comparison of Static, Cyclic, and Thermal-Shock Fatigue in Ceramic Composites. Cer. Eng. Sci. Proc. 3(9–10):714–721, 1982.

286.D. B. Marshall. Failure from Surface Flaws. Fracture in Ceramic Materials— Toughening Mechanisms, Machining Damage, Shock (A. G. Evans, ed.). Noyes, New York, 1984, pp. 190–220.

287.J. P. Singh, A. V. Kirkar, D. K. Shetty, and R. S. Gordon. Strength–Grain Size Relations in Polycrystalline Ceramics. J. Am. Cer. Soc. 62(3–4):179–182, 1979.

288.A. G. Evans. A Dimensional Analysis of the Grain-Size Dependence of Strength. J. Am. Cer. Soc. 63(1–2):115–116, 1980.

289.A. V. Virkar, D. K. Shetty, and A. G. Evans. Grain-Size Dependence of Strength. J. Am. Cer. Soc. 64(1):56–57, 1981.

Grain Dependence of Ceramic Tensile Strengths at 22°C

243

290.H. Y. B. Mar and W. D. Scott. Fracture Induced in Al2O3 Bicrystals by Anisotropic Thermal Expansion. J. Am. Cer. Soc. 53(10):555–558, 1970.

291.R. W. Rice, R. C. Pohanka, and W. J. McDonough. Effect of Stresses from Thermal Expansion Anisotropy, Phase Transformations, and Second Phases on the Strength of Ceramics. J. Am. Cer. Soc. 63(11–12):703–710, 1980.

292.R. W. Rice, S. W. Freiman, R. C. Pohanka, J. J. Mecholsky, Jr., and C. Cm. Wu. Microstructural Dependence of Fracture Mechanics Parameters in Ceramics. Fracture Mechanics of Ceramics—Crack Growth and Microstructure 4 (R. C. Bradt, D.

P.H. Hasselman, and F. F. Lange, eds.). Plenum Press, New York, 1978, pp. 849–876.

293.R. W. Rice. Microstructural Dependence of Fracture Energy and Toughness of Ceramics and Ceramic Composites Versus That of Their Tensile Strengths at 22°C. J. Mat. Sci. 31:4503–4519, 1996.

294.R. W. Rice. Machining Flaw Size-Tensile Strength Dependence on Microstructure of Monolithic and Composite Ceramics. To be published.

295.R. W. Rice. Ceramic Fracture Mode-Intergranular vs. Transgranular Fracture. Ceramic Transactions 64: Fractography of Glasses and Ceramics 3 (J. R. Varner, V.

D.Frechette, and G. D. Quinn, eds.). Am. Cer. Soc., Westerville, OH, 1996, pp. 1–53.

296.M. S. Swain and L. R. F. Rose. Strength Limitations of Transformation-Toughened Zirconia Alloys. J. Am. Cer. Soc. 69(7):511, 1986.

297.K. Matsuhiro and T. Takahashi. The Effect of Grain Size on the Toughness of Sintered Si3N4. Cer. Eng. Sci. Proc. 10(7–8):807–816, 1989.

298.G. Himsolt, H. Knoch, H. Huebner, and F. W. Kleinlein. Mechanical Properties of Hot-Pressed Silicon Nitride with Different Grain Structures. J. Am. Cer. Soc. 62(1–2):29–32, 1979.

299.M. J. Hoffmann. Analysis of Microstructural Development and Mechanical Prop-

erties of Si3N4. Tailoring of Mechanical Properties of Si3N4 Ceramics (M. J. Hoffmann and G. Petzow, eds.). Kluwer Academic Publishers, The Netherlands, 1994, pp. 59–72.

300.Y.-W. Kim, M. Mitomo, and N. Hirosaki. R-Curve Behavior and Microstructure of Sinterted Silicon Nitride. J. Mat. Sci. 30:5178—5184, 1995.

301.P. F. Becher, E. Y. Sun, K. P. Plunckett, K. B. Waters, C. G. Westmoreland, E.-S. Kang, K. Hiro, and M. E. Brito. Microstructural Design of Silicon Nitride with Improved Fracture Toughness, Part I: Effects of Grain Shape and Size. J. Am. Cer. Soc. 81(11):2821–2830, 1998.

302.T. Masaki and K. Shinjo. Mechanical Behavior of ZrO2-Y2O3 Ceramics Formed by Hot Isostatic Pressing. Advs. Cer. 24: Sci. Tech. Zirconia III. Am. Cer. Soc., Westerville, OH, 1988, pp. 709–720.

303.G. S. A. M. Theunissen, J. S. Bouma, A. J. A. Winnubst, and A. J. Burggraaf. Mechanical Properties of Ultra—Fine Grained Zirconia Ceramics. J. Mat. Sci. 27:4429–4438, 1992.

304.L. Ruiz and M. J. Readey. Effect of Heat Treatment on Grain Size, Phase Assemblage, and Mechanical Properties of 3 mol% Y-TZP. J. Am. Cer. Soc. 79(9):2331–2340, 1996.

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Chapter 3

305.N. Hirosaki, Y. Akimune, and M. Mitomo. Effect of Grain Growth of β-Silicon Nitride on Strength, Weibull Modules, and Fracture Toughness. J. Am. Cer. Soc. 76(7):1892–1894, 1993.

306.Y. Ukyo and S. Wada. High Strength Si3N4 Ceramics. J. Cer. Soc. Jpn., Intl. Ed. 97:858–859, 1989.

307.S. Saito. Fine Ceramics. Elsevier, New York, 1988, pp. 182–183.

308.D. B. Price, R. E. Chinn, K. R. McNerney, T. K. Borg, C. Y. Kim, M. W. Krutyholowa, N. W. Chen, and M. J. Haun. Fracture Toughness and strength of 96% Alumina. Bul. Am. Cer. Soc. 76(5):47–51, 1997.

309.C. Zhang, W. Y. Sun, and D. S. Yan. Fabrication of Dy-—Sialon Ceramics. J. Mat. Sci. Lett. 17:583–586, 1998.

310.J. T. Neil. Calculating Weibull Modulus from Average and Standard Deviation. GTE Labs. Inc. Report TM-0135-07-89-066, 7/1989. See also J. Gong and Y. Li. Relationship Between the Estimated Weibull Modulus and the Coefficient of Variation of the Measured Strength of Ceramics. J. Am. Cer. Soc. 82(2):449–452, 1999 for a similar expression.

311.D.-H. Cho, Y.-W. Kim, and W. J. Kim. Strength and Fracture Toughness of In-Situ- Toughened Silicon Carbide. J. Mat. Sci. 32:4777–4782, 1997.

312.Y.-W. Kim, W. J. Kim, and D.-H. Cho. Effect of Additive Amount on Microstructure and Mechanical Properties of Self-Reinforced Silicon Carbide. J. Mat. Sci. Lett. 16:1384–1386, 1997.

313.H. P. Kirchner and R. M. Gruver. Fracture Mirrors in Alumina Ceramics. Phil. Mag. 27(6):1433–1446, 1973.

4

Grain Dependence of Indentation

Hardness at 22°C

I.INTRODUCTION

This chapter addresses the grain (mainly size) dependence of indentation hardness (H). Indenter geometries are either spherical or pyramidal, the latter primarily Vickers or Knoop (designated respectively by subscripts V and K), which are dominant in ceramic testing and the focus of this chapter. Scratch hardness is also used some, but primarily as a test to simulate machining or wear; hence it is covered in conjunction with these topics in Chapter 5. Though grain size (G) is commonly the dominant parameter, grain shape and orientation, and especially their combination, can be important, and while studied little, are noted and discussed to the extent that data allows.

The grain dependence of hardness arises primarily from its impact on plastic deformation, the primary mechanism of forming permanent indentations. While in the past there was substantial controversy about the mechanisms of indentation, especially in very hard ceramics, it is now accepted that such crystalline materials do undergo local deformation to form indents primarily by dislocation slip mechanisms, as in metals. Such deformation in ceramics, which is more restricted, approximately in inverse proportion to the material hardness, has been extensively verified by two sets of observations and their self-consis- tency. The first is direct observations of dislocations and slip by optical birefringence, etching, microradiography, and especially by direct transmission electron microscopy. The second is by hardness behavior itself, especially the relation of

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hardness anisotropy of single crystals as a function of crystal structure orientation relative to the indenter geometry as a function of the degrees of activation of differing slip systems [1–5] (Sec. II.E). (Note, in glasses, not addressed here, other deformation mechanisms, e.g. densification may occur—see Chap. 10.) The grain size, shape, and orientation dependence of hardness thus results from the same grain structure constraints on yield stress as given in Eq. (3.1), with two modifications. First, σf, which is usually slightly > the yield stress for the easiest activated slip system in testing the strengths of single crystals, and was used as a convenient approximation for the actual yield stress, is replaced by the yield stress, σy. Second, σy is the general yield stress for the required deformation and is not necessarily that for only the easiest activated slip system [6]. Thus a Hall–Petch type dependence on grain size, G (with some impacts of grain shape and orientation) is a major, or the total, factor in the G dependence of H. Although much hardness data is given with no grain (or other material or test) characterization, there is substantial data providing support for such an H–G-1/2 dependence, especially at mainly finer G [7], as will be extensively shown.

However, some data did not necessarily show H decreasing with increasing G, mainly at intermediate G, and some results showed the opposite G dependence, i.e. H increasing with increasing G at larger G [7–10]. Thus Armstrong et al. [8] reported a reverse BeO HV–G dependence, i.e., decreasing from single crystal values (on {0001} and {10 10} planes) with decreasing G (Fig. 4.3). Similarly, Sargent and Page [9], though not giving specific H values, reported MgO single crystal HV higher (on {100} planes) than for dense, hot pressed polycrystalline MgO (G = 130 or 10 m). While not encompassing single crystal tests, Tani et al.’s [10] HV (2 N, 200 gm load) data for A12O3 shows a marked decrease in H with decreasing G (from 60 to 6 m, see Fig. 4.2) in contrast to the opposite trend for their Y2O3 data, thus showing that the different H–G trends are not due entirely to differing techniques of different investigators. Though these variations were limited, e.g. due to the frequently limited G range covered, especially at larger G, such variations are an underlying factor in H–G-1/2 data not necessarily extrapolating to single crystal values. Thus some, e.g. Niihara and Hirai [11], considered a G-1 dependence of H, since this resulted in their fine G polycrystalline values more closely extrapolating to single crystal data (Fig. 4.13).

A recent review [7] showed that the above variations are manifestations of a very common, but variable, indent associated deviation below a simple Petch relation at intermediate G whose recognition was typically seriously restricted by insufficient H–G data. Thus much more extensive H–G data presented previously [7] and here clearly shows frequent deviation through an indent-G dependent H minimum at intermediate G, which is attributed to observed indent associated cracking. While the cracking from indent vertices used for toughness and strength evaluations (mainly in finer G bodies) may be a factor in this, the

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observed indent associated cracking of interest here is more confined around the indent, consisting mostly of a number of spall-lateral cracks (Sec. II.D). Such cracking increases as the indent and grain dimensions approach one another and decreases as the indent size gets larger or smaller than the grain size. The result is a material-, body-, and test-dependent lowering of hardness values below those expected from the Hall–Petch relation as cracking increases, which thus typically occurs at varying intermediate G values that shift with indent size and hence material, grain structure, and indent types and loads. Thus hardness first commonly decreases from single crystal values as G decreases, reaches a minimum, and then progressively increases with further decreasing G at finer G, as the Hall–Petch relation at finer G. While there is no quantitative theory for these deviations, the substantial experimental data showing the trends for indent type, load, and material dependence is reviewed. Note that as the indent size approaches the grain size, increased scatter of hardness values is expected, since there is increased dependence of each value measured on the parameters of individual or adjoining grains indented.

The subsequent review of the grain dependence of hardness provides a more comprehensive data base and perspective than a more limited, earlier survey of the G dependence of H and related properties [12] by extensively drawing upon and extending a more recent and more extensive evaluation [7]. HK and HV data are reviewed first for single oxides, then for mixed oxides, then for borides, carbides, and nitrides, in alphabetical order, giving Knoop results first if sufficient data is available. Then limited data for spherical indenters and other materials is briefly addressed. Key trends to observe are that the more limited data for most softer, less refractory materials indicates a simple Hall–Petch relation, but almost all harder, more refractory materials (and a few softer, less refractory materials) have a superimposed indent–grain size dependent H minimum, mostly at intermediate G values. The limited data for bodies with nanoscale grains is shown to be generally consistent with data for bodies of the same composition but more normal G (i.e. ≥ 1 m), but some nanograin bodies are shown to have H decreasing as G decreases, i.e. opposite from the normal behavior at finer G.

This review of H–G-1/2 data is followed first by a review of indent character trends showing that the minimum in H values is associated with increasing local cracking, which is typically a maximum when the indent dimensions are those of the grains under and around the indentation. Then observations of extrinsic effects, mainly grain boundary phases or impurities and indent type and load on such cracking, are discussed and summarized followed by discussion of possible contributions of factors such as TEA and EA. [Note that data also shows the commonly observed load dependence of both HV and HK, and HV < HK at 100 gm, but the reverse tends to occur at 500 gm (Table 4.1).] This is followed by discussion of the limited data on effects of grain

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TABLE 4.1 Approximate Average Hardnesses
(GPa)a
	100 gm		500 gm
Material	HK	HV	HK	HV
Al2O3	26	23	18	19
MgO	10.5	9.5	8	7
ZrO2	15+	14	12-	13
MgAl2O4	18	17	13.5	15
SiC	37	34.5	23	27.5

aSource: After Rice et al. [7], published with the permission of the Journal of the American Ceramic Society.

shape and orientation, and especially implications on the latter from substantial single crystal data. Note that additional data on the room temperature hardness of both single and polycrystals is found in Chapter 7, Section II, on the temperature dependence of H.

Before proceeding to the data review, it is important to recall some of the factors that can impact hardness and thus potentially complicate accurate evaluation of its grain size dependence, considering first exclusively body aspects. Besides basic body chemistry, the presence of impurities or additives, as well as stoichiometry and varying crystal structure, and especially porosity, are commonly also important. While stoichiometry may often manifest much of its effects via its frequent impacts on grain parameters, especially size (as shown later), typically resultant lattice defects can directly impact dislocation motion to varying extents, hence directly impacting hardness in view of its basic dependence on local plastic deformation. Additionally, both stoichiometry and impurities or additives can change grain boundary strengths as well as stresses, e.g. those from TEA and EA, and thus the extent and impact of local cracking. Examples of enhanced local cracking due to grain boundary phases from (fluoride) additives are illustrated later, and possible impurity effects in some nanograin bodies are discussed. Changes in or mixes of different crystal structures of the same composition may have limited to substantial effects, e.g. by up to 25% in Si3N4 [13,14] (see Fig. 4.13). Porosity can have varying and substantial effects on hardness, as is extensively addressed elsewhere [7,15,16] with much of its effect being due to the amount and character of porosity, e.g. via the exponential, ebP, dependence of the ratio of H at some volume fraction porosity P to that at P = 0 over a reasonable fraction of the porosity range, e.g. to P = 0.2–0.5. The parameter b is commonly in the range of 3–7 for hardness, depending on the type of porosity.

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Factors dependent both on the body character and on test factors are grain and hardness measurements. As noted in Chapter 1, Section IV.B, measurement of grain size is complicated by several factors, including typically neglected and more difficult to quantify aspects of grain shape and orientation, but also by both actual measurement, including, even for random equiaxed grain structures, what the grain size should be, e.g. a two-dimensional one (i.e. the size of the grains at their intersection with a surface) or their “true” three-dimensional size. While the latter is probably more pertinent to H, there is no clear guidance, but these issues are commonly overridden by the very loose measurement of most G values, including specifics of the measurements and any factors to convert the common linear intercept values to some “true” G commonly not being given. These commonly result in uncertainties in G values of ± 50%, and sometimes substantially more. Actual hardness measurements for a given body also depend on indent load [7,17–19] and on surface character, with the two being partly interrelated [19]. Thus H values typically increase below indent loads of1 to a few kilograms (i.e. 10 or more N), with the increases being at first modest, but accelerating as the load decreases. Surface character is important for its impact on clarity of the indent dimensions, e.g. due to the degree of surface smoothness. However, mechanical surface finishing, which is almost exclusively used, also introduces surface cracks that may impact indent formation, and more fundamentally introduces extensive deformation in the surface [19,20]. The latter commonly is sufficient to work harden the surface, to depths dependent on the material, the grain structure and the nature of the final machining (commonly polishing), and commonly some on previous machining. Such surface work hardening is commonly a factor, often an important one, in the load dependence of H since higher loads cause more indent penetration into less work hardened material.

II.DATA REVIEW

A.Oxides

Brookes and Burnand’s [3] HK (500 gm load) data for the (1100) plane of sapphire averaging 16 ± 2 GPa is somewhat lower than Rice et al.’s data [7] (Fig. 4.1) and considerably lower, as expected, than Becher’s [19] HK (100 gm) values of 22–30 GPa for the (0001) basal plane [and 22–35 GPa on the (1120) plane] from the five-fold higher load. Becher’s data, where most of the variations are due to different surface finishes, is in good agreement with the current data. The substantial singleand polycrystal data of Rice et al. [7] suggests a limited minimum in HK (100 gm) at intermediate G ( 50 m) i.e., HK first decreases some, then increases with decreasing G. Their data shows a clearer and larger HK minimum at G 50 m for the 500 gm load. Al2O3 HK–G-1/2 (400 gm) data of Skrovanek and