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both exhibited SCG, via respectively 30 ± 10% and 50% increased strengths in liquid N2, while ZrO2 crystals partially stabilized with 5 w/o Y2O3 only increased strength 9%. However, DCB tests by Wu et al. [74, 75] of SCG of stoichiometric MgAl2O4 crystals oriented for {110} <110> crack propagation instead showed a zigzag {100} fracture at lower crack velocities that transitioned to the planned {110} <110> fracture at higher crack velocities (Fig. 2.7). Similarly, DCB tests of other orientations, e.g. where (100) and (110) or (111) planes were parallel to the specimen axes, but at different angles to the specimen surfaces, always resulted in crack propagation on (100) planes, despite this requiring 30% or more fracture area to be generated. However, flexure tests of bars oriented for fracture on (100) or (110) planes did so from machining flaws formed on these planes (including the typical strength anisotropy as a function of machining direction relative to the stress axis). Thus despite a strong preference for (100) fracture with large, low-ve- locity cracks in DCB tests, flexure tests showed no significant preference of (100) over (110) planes for formation of machining flaws and subsequent failure. Crack propagation studies of quartz crystals by Ball and Payne [76] showed the opposite type of crack propagation variation on some fracture planes, namely an increasing amplitude of zigzag crack propagation at high crack veocities, due to mist and hackle formation as a precursor to crack branching in quartz. Thus the spinel results show that important changes in

FIGURE 2.7 Change from {100} zigzag to planar {110} crack propagation in stoichiometric MgAl2O4 crystals oriented for {110}<110> fracture in DCB SCG tests.

(A) Schematic of low-velocity fracture. (B) and (C) Lower magnification SEMs of fractures with lower velocity (e.g. 2–50 m/s) crack propagation at the left and higher velocity (including catastrophic) propagation to the right. (After Wu et al. [74], published with the permission of the Journal of Materials Science.)

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crack propagation, and thus presumably in fracture toughness, can occur as crack velocity changes.

The above tests at -196 versus 22°C of polycrystalline cubic ZrO2 (6.5 mol-% Y2O3 bodies, G 20 µm) also showed that SCG with the same or very similar strength increases as the cubic stabilized crystal specimens. Polycrystalline bodies of stoichiometric MgAl2O4 with the same surface finishing as the above MgAl2O4 crystals, showed decreasing strength increases in liquid nitrogen versus air at 22°C. Bodies with G 100 µm showed the same or similar strength increases as the single crystals did, i.e. 35%. On the other hand, bodies with G20, 8, and 3 µm gave respectively decreasing strength increases of 31%, 27%, and 16%, i.e. the latter 1/2 the single crystal and large grain increases, indicating reduced SCG as grain size decreases (but still with predominant transgranular fracture) [72]. This G dependence is similar to that of alumina (Figure 8A). Polycrystalline bodies of CeO2, Y2O3, and TiO2 (with 1 of 4 1/4% oxide additions) having respective grain sizes of 20, 100, and 5–10 µm showed respective strength increases of 12%, 25%, and 40–75% [72]. All exhibited predominant or exclusive transgranular fracture at the fracture origin (and elsewhere), implying that SCG occurs in single crystals of these materials.

Similar strength tests of nonoxide materials in air (22°C) and liquid N2 corroborated and extended results, e.g. showing that very limited (e.g. 5%) or no strength increase in liquid N2 occurred, indicating little or no SCG in ZrB, B4C, TiC, ZrC, and Si3N4(CVD) bodies made without additives [73]. This was corroborated by the predominate or exclusive transgranular fracture of grains (typically 20–50 µm) at the fracture origins and over the total fracture. Bodies such as TiB2, SiC, and Si3N4 (commonly, especially the latter two, made with oxide additions) exhibited some to substantial strength increase, hence SCG, with mixed to substantial intergranular fracture at origins, and often across the fracture. Similarly, comparative tests of a silicate glass, and finer grain bodies of Al2O3, and MgF2 were consistent with other tests, i.e. substantial strength increases in liquid N2 and mainly or exclusively intergranular fracture in the SCG region of polycrystalline fractures.

Two specific evaluations using v–K or dynamic fatigue (DF) tests showed a grain size dependence of SCG in Al2O3. Gessing and Bradt [77] showed from their own studies as well as from a literature survey that the crack growth exponent, n [Eq. (2.3)] increased with decreasing alumina grain size (Fig. 2.8A), with this trend being fitted by

n 10 + 225G-1	from K–v data	and
n 20 + 114G-1	from DF data	(2.6)

Becher and Ferber [78] subsequently corroborated this v–K data trend for Al2O3 using some of the same and some of their own DCB data (Figure 8A) for high purity Al2O3 [79] e.g. giving n values of ≥ 110, 107, and 38 respectively for G =

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FIGURE 2.8 Grain size dependence of the exponential crack growth parameter n[Eq. (2.3)] from difference v–K studies of: (A) alumina of Gessing and Bradt [77] and Becher and Ferber [78, 79], and (B) BaTiO3 data from de With’s compilation [86].

4, 5, and 25 µm, corroborating the above trend. However, n = 22 for a body with bimodal grain size (averages 7 and 25 µm) indicates complexities of the G dependence. Liang et al. [80] obtained n 26 and 78 for two aluminas with G 20 and 2 µm, consistent with the above data. Despite higher scatter, n values of 26–38 for various alumina bodies (G 3–8 µm) with various SiO2 contents, while somewhat lower, are reasonably consistent with the trends of these more extensive studies [81–83]. Data of Ferber and Brown (n: 36–42, G: not given) [84] are also reasonably consistent with the above trends but clearly showed significant effects of variations in the water due to additives (as do other studies). However, data of Byrne et al. [85] for various commercial aluminas gave some results inconsistent with the above trend of n to increase with decreasing grain size (and again showed significant effects of pH). Some of these differences are probably due to varying degrees of chemical attack, e.g. dissolution of some of the boundary phase in some bodies (which is related to composition-pH effects discussed by them). Such effects of dissolution are probably consistent with differing effects of crack sharpening versus crack blunting in stress corrosion.

Three other data sets indicate decreasing n values as G increases. De With’s compilation of data on BaTiO3 for multilayer capacitors [86], though scattered (probably reflecting differing compositions), also shows a decrease in n values as grain size increases (Fig. 2.8B). Hecht et al.’s [87] data for various

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toughened zirconia bodies (G 0.3–45 µm), though widely scattered, again probably reflecting composition differences, also suggested a possible significant increase in n values at finer grain sizes. Becher and Ferber [79] obtained n values for two TiB2 bodies (G = 5 and 11 µm, hot pressed with 10 wt% Ni, resulting in 1.3–1.5 wt% NiB) respectively of 150 and 62, which again indicated a strong increase of n with decreasing grain size. Thus while there can be significant effects of compositional details of the bodies and the corrosion medium, there is substantial indication that n increases substantially with decreasing grain size, which is corroborated by results for strengths of MgAl2O4 in liquid nitrogen and in air at 22°C noted earlier. Therefore, much more attention to effects of grain size on SCG is needed than has been given. Considerably more SCG data exists, but often with only one, often unspecified, grain size, e.g. Yamade et al. [88] demonstrated SCG in dense sintered mullite (KIC 2 MPa·m1/2) due to H2O.

Gessing and Bradt [77] modeled the G dependence of n based on microcracking at the crack tip due to TEA stresses, i.e. in noncubic materials. Becher and Ferber [78] also presented a model, again based on TEA stresses in noncubic materials, but considering the superposition of TEA and applied stresses at finer grain sizes, and crack shielding from wake effects at larger grain sizes. However, the first and most fundamental of three points is that the focus on grain facet fracture due to TEA stresses neglects the frequent significant transgranular fracture of many of the materials, particularly at intermediate grain sizes, e.g. of aluminas at 5–20 µm, Figures 2.5 and 2.6. Second, the focus on TEA stresses and associated microcracking of grain boundary facets implies effects only in noncubic materials of sufficiently high (but unspecified) TEA, i.e. either neglecting, or assuming no, effects in cubic materials (as did much work on crack bridging and shielding). However, though limited and not directly giving n values, the data for MgAl2O4 implies a similar grain size effect in cubic materials (where bridging has also been found). Third, the form of Gessing and Bradts’ model [Eq. (2.6)] would be consistent with a crack pinning-bowing model (Figure 8.4), in this case crack pinning due to points of greater difficulty of SCG. Pinning points could be grain boundary facets with low tensile or especially substantial compressive TEA stresses between them, or simply grains unfavorably oriented for SCG around or through them. Such a model would be at least partially focused on impediments to propagation of the macrocrack rather than just on microcracks in advance of it and would be consistent with both inter- and transgranular fracture and grain size effects in not only all noncubic materials but also cubic ones.

The above indications of a G dependence of the slow crack growth parameter n are but one of many examples of the limited data directly showing substantial effects of G, hence putting much data not giving reasonable G characterization in question. Both the probability of effects of G on n and the un-

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certainties and complexities this introduces with inadequate documentation of results and microstructure is shown by work of Singh et al. [89]. They made differing measurements on two sintered β″ - alumina, both of which had mixtures of finer and larger (often more tabular) grains, which gave substantially different n values for the two bodies. For example, they obtained n values of 76 and 26 for the two respective bodies via dynamic fatigue tests, again indicating an important effect of grain structure like that noted earlier. However, there were two important variations indicating further complexities of test-grain structure interactions. First, they obtained different n values, e.g. 26 and 16 respectively, for the same larger G body via dynamic fatigue, depending on whether they used a diametrally loaded ring or flexure testing. Second, and more serious, they obtained an opposite trend, i.e. n = 64 and 96 respectively in the finer and coarser G bodies by DCB/DT stress relaxations tests. Both discussion and modeling indicated that these variations reflected combined effects of the crack-grain size and the microstructural variation in the bodies.

Consider briefly grain size dependence of other environmental, especially corrosion, effects on mechanical properties, which is a large and complex subject with limited attention to microstructural effects. Some TZP bodies partially stabilized with Y2O3 are subject to serious degradation, beginning with attack along grain boundaries and resultant microcracking from transformation of tetragonal to monoclinic ZrO2, which lowers crack resistance and strength, and in the extreme causes crumbling to a granular or powder character due to effects of water (Fig. 2.9). Degradation increases with the activity of the water (to an upper limit of 300–500°C), decreasing Y2O3 content, and increasing grain size (with the latter two generally being inversely related) [90]. More recent data corroborates this general trend but shows a more complex variation with G than a simple monotonic change for a two m/o Y2O3 TZP over the limited G range ( 0.5–1 µm) investigated [91]. Swab [92] has clearly outlined the composi- tion–grain size variations of such degradation.

More generally, ceramics, while being more chemically inert, can be subject to a variety of other corrosive attacks at modest to high temperatures that reduce strengths at all subsequent testing temperatures. Such attack is commonly most severe along grain boundaries, which introduces a grain size dependence from intrinsic and extrinsic sources such as TEA stresses and frequent greater accumulation of more corrosion susceptible species at grain boundaries as G increases. Some probable G dependence can also occur in lower, e.g. room, temperature corrosion of materials susceptible to H2O attack, e.g. CaO and MgO, where expansion of hydroxide products in pores or cracks causes failure as observed in CaO singleand polycrystals (e.g. over periods of weeks to months) [93] and in polycrystalline MgO (e.g. over years) [94, 95]. A G dependence of strength after corrosion is expected from the G dependence of tensile strength (Sec. 2.2).

FIGURE

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2.9 Example of gross degradation of a commercial Y2O3 TZP ball in 100 psi steam exposure for 30 hours at 200°C. (Photo courtesy of Dr. T. Quadir.)

C.Grain Size and Other Dependence of Microcracking

Equations of the form of (2.2) with the same or similar numerical value give reasonable estimates of grain sizes for the onset of spontaneous microcracking due to microstructural stresses from phase transformation or TEA, as a function of material (mostly local) properties (Fig. 2.10), as is shown by the studies of Cleveland and Bradt [26, 27], Hunter et al. [35], Rice and Pohanka [29], and Yamai and Ota [96, 97]. Some of these evaluations have explicitly or implicitly used as a first approximation the γ/E ratio being constant, leaving Gs ( )-2, and for TEA-driven microcracking that Gs (Δα)-2, e.g. per a recent compilation [96], since T does not vary widely for most ceramics. Over a broad range such approximations give reasonable estimates, but these estimates can often be improved by using known or estimated values of E, γ, and T and adjustments of these. Note that Telle and Petzow’s designation of spontaneous microcracking at G 6 µm [98] is not consistent with the strength behavior they presented (Figure 3.25), other TiB2 data, or the general trends of Fig. 2.10, but may be consistent with decreasing toughness (Fig. 2.16) due to possible stress-induced microcracking.

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FIGURE 2.10 Log–log plot of the grain size for the onset of spontaneous microcracking as a function of (Δ)-2 for transformation (BaTiO3 and PbTiO3) and TEA derived strains. Note the general, but imperfect, correlation over a broad range and the use of the maximum minus either the minimum or the average grain (crystal) strain mismatch, with the latter indicating better correlation, as is discussed in the text. (Data from Rice and Pohanka [29], and from Yamai and Ota [96, 97], using respectively T values of 1200 and 1000°C [though the latter may be somewhat high].)

The first of two related sets of uncertainties in values used in Eq. (2.4) is its derivation, which, as noted earlier, entails either a two-dimensional approximation with more precise mechanical analysis or in one case a more appropriate three-dimensional model but with less precise mechanics analysis for idealized grains. Neglecting the ideal grain character still leaves uncertainty in the equation, e.g. in the numerical factor of 9, and adds to the second set of uncertainties of property values to use. Differing orientations of adjacent grains in quite anisotropic materials may vary the appropriate local E value, and varying grain shape may change the numerical factor. Greater uncertainty arises for γ, since

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this depends on the nature of the microcrack, e.g. transor more commonly intergranular fracture. The latter presents the greatest uncertainty, since γ for grain boundary fracture, commonly approximated as 1/2 of the lowest grain cleavage energy, is quite dependent on the character of specific boundaries involved and the resultant microcrack, e g. the number and spatial relation of grain boundary facets it encompasses. As much or more uncertainty arises for Δ, since it is commonly quite dependent on the specific crystallographic orientations of the grains involved, whether the strain mismatch arises from TEA or from phase transformations. For TEA, the T involved is often also uncertain since the temperature where stresses start to build up (commonly assumed to be1200°C, as used for all TEA-based calculations in Figure 10 except for the phosphates) depends on material and cooling rates, and the temperatures where the microcracks occur is often not known. Another uncertainty in Δ is associated with statistically significant microcracking. The maximum strain mismatch, e.g. due to the maximum–minimum single crystal thermal expansion msmatch, is often used, but typically pertains to only 1 grain facet of a limited number of grains. Limited microcracking probably commences when microcrack conditions are met with such a maximum grain (crystal) strain mismatch, but more should occur when conditions are met for a strain mismatch of the maximum minus the average grain (crystal) strain. Fig. 2.10 indicates better correlation with the latter, which can vary (Δ)-2 by a few, to nearly 10, fold, as well as a deviation at larger grain sizes and related lower anisotropy; but more evaluation is needed.

Equal or greater uncertainty is associated with reported or implied Gs values due in part to uncertainty in the measured grain size values, which as noted earlier can be a factor of 2 (and involve the issue twoversus threedimensional G values, the latter appearing more pertinent). Greater uncertainty often accompanies direct microscopic observations of microcracks on, or close to, free (mainly fracture) surfaces. Values from property measurements, e.g. expansion, elastic moduli (or damping), and thermal or electrical conductivities, and their temperature dependences and resultant hysteresis, are generally more valuable and offer important additional information (Chap. 3, Sec. III.D, Chap. 10, Sec. II.E, and Figure 9.3, Refs. 5,26–35,97,99). In particular, plotting of the temperature difference between the forming or opening of microcracks and their closing versus the inverse square root of G, as shown by Case et al. [30], is particularly effective. However, such information should be accompanied by data on grain size and shape, their distributions in the body, and the degree and character of preferred grain orientation. Of two bodies with the same average G, the one with the wider grain size and shape distributions, or both, is likely to have more microcracks, provided there is random orientation.

A more comprehensive, but still incomplete, characterization of microcracks and their effects is Tomaszewski’s [100] study of dense sintered Al2O3 (Fig. 2.11)

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FIGURE 2.11 Summary of Tomaszewski’s characterization of microcracks and resultant properties in a dense sintered alumina as a function of grain size [100]. Note general decreases, except for maxima in KIC and microcrack density at G 130 µm, and increasing microcrack length as G increases.

showing that while microcracks in finer G bodies were 5 times the grain size, this reduced to 1.2 at G 470 µm. (These results for stress generated microcracks in alumina are in contrast to the limited data of those from spontaneous microcracking.) Qualitative data indicates that spontaneously formed microcracks are more consistently similar in size to the grains. While the question of the effects of as-fired surfaces on such microcracking were not addressed, he showed that the general fracture mode decreased from 85% intergranualar fracture at the finest G to 5% at the largest G (i.e. generally consistent with Fig. 2.5). However, the 95% intergranular microcracking at the finest G initially decreased faster, then less rapidly, than the general fracture mode. The net effect was substantially more intergranular microcracking than for general fracture (i.e.50 versus 5% respectively), but still with substantial transgranular microcracking over most of the G range. He also showed that microcrack densities reached a maximum at G 130 µm. Calculations from his data indicate that the microcrack area per unit sample area reaches a maximum at this or larger G, e.g. 300 µm.

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Quantitative data of Kirchner and Gruver [101] for TiO2 shows microcrack size to average 1.5 to 2 times G, over the G range 5 to 150 µm; but much more documentation is needed.

Two sets of potentially related observations are important. First, as noted earlier, most observations of the cyclic change of microcrack dependent properties, while exhibiting hysteresis, are typically repeatable with multiple cycling. However, while such behavior was shown in evaluations of most HfO2 bodies, it ceased to be so in larger grain ( 17 µm) bodies, which showed serious progressive degradation of elastic moduli with thermal cycling [35, 36]. This clearly implied that microcracks no longer closed, or healed at such larger HfO2 grain sizes, since such closure and healing are basic to the observed recovery of the normal temperature dependence of properties in the absence of microcracking. The second observation is that while microcracking is commonly intergranular, some transgranular microcracking is observed, especially as grain size in a particular material increases sufficiently as found in TiO2 [29,101], and clearly shown in 2ZrO2 · P2O5 bodies [95], e.g. at G to 200 µm in the former and 10 to 20 µm in the latter as well as in Al2O3 [99] (Fig. 2.11). Such transgranular microcracking at larger (probably material dependent) grain sizes suggests an explanation for the progressive degradation of larger grain microcracking bodies on thermal cycling. While intergranular fracture results in well-defined fracture surfaces with potential for mating and possible healing due to sintering (especially with some boundary phase), transgranular fracture often generates more complex fracture surfaces that may be more difficult to close and heal. The occurrence of some transgranular microcracking at larger grain sizes may be consistent with general fracture mode trends, though probably shifted due to the TEA and other causes of the microcracking.

Another important aspect of microcracking is its occurrence due to the combination of microstructural stresses from phase transformation or TEA with applied stresses, either prior to or during measurement of crack propagation behavior. Limited investigations indicate that microcracks can be generated, enlarged, or both in some bodies and tests, e.g. E measured in flexure strength testing decreasing as G increased while dynamic measurements were independent of G at 393 GPa [99]. In more anisotropic graphite, Brocklehurst’s review [102] cited decreases in elastic moduli due to prior application of either a uniaxial tensile or compressive stress that varied with the microstructure and stress. The moduli decreases increased nonlinearly, and sometimes irregularly, as the stress level increased, e.g. reaching E reductions of > 30%, but could be fully or partially recovered by subsequent treatments, especially annealing. Greater decreases may occur from compressive stressing (possibly in part because of the greater stress levels achievable in compression) than with tensile stressing. Other differences occur, e.g. density and thermal expansion reduced from tensile, and increased from compressive, loading, and properties such as electrical