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The marked EA of ZrO2 may correlate with the occurrence of grain boundary fracture origins in larger grain bodies, fully and partially stabilized ZrO2 [197]. The temperature rise of ZrO2 EA may also contribute significantly to its higher temperature grain boundary sliding. Further, since EA increasing with temperature is very broad if not universal, its rise may be a factor in the E–T and σ–T jogs of MgAl2O4 noted earlier (at 500–700°C), similar to, but less pronounced than, for ZrO2. While the EA of MgO [197,207,208] is relatively low at 22°C, hence much less likely to be a factor at moderate temperature, its substantial EA levels at higher temperature [197], e.g. 1200°C, may be related to increased fracture initiation from even relatively clean (i.e. recrystallized) grain boundaries at > 1200°C [139,140]. Thus EA needs to be considered as another broad factor besides, or in addition to, grain boundary impurities in increasing intergranular failure with increasing temperature.

Other materials show little or no initial strength decrease until temperatures of 1000°C or higher. Thus ThO2 and UO2 show higher strength at 1,000 vs. 22°C (Figs. 6.16 and 6.17). Whether such effects in ThO2 are related to mechanical and electrical relaxation in the temperature range are unknown. Further, as noted earlier, nonoxides such as B4C, SiC, and TiC, show limited, or possibly no, initial strength decrease, and in some cases possibly a slight increase with initial temperature increases, in contrast to the E–T decrease (typically a few to 10% to 1000°C). Some of these differences could reflect reduction of TEA stresses, e.g. in B4C, but in the case of B4C, effects of substantial twinning, and in α-SiC of polytypes, are unknown. While oxidation and relief of surface compressive stresses from machining may also be factors, tests in neutral or reducing atmospheres show that these are, at best, partial factors.

The changes in strength with temperature, environment, and grain size of most ceramics are overall consistent with flaw induced failure. Thus slow crack growth is a well established adjunct to normal flaw failure, and microplastic nucleation of cracks, or assisting their growth, are accepted mechanisms interacting, and consistent, with conventional flaw failure. The same is true of changes in single crystal strengths and changes in grain boundary effects whether intrinsic, e.g. due to changes in TEA or EA stresses, or extrinsic, e.g. due to impurities. However, while the above concepts are known, fully effective quantification of the contributions to failure is generally not available.

Bridging, widely cited as an important factor in behavior of many ceramics, e.g. suggested [209] and questioned [210] in Al2O3 at lower temperatures, might be seen as enhanced at elevated temperatures due to increased intergranular fracture, but the issue of bridging effects at higher temperatures is at least as uncertain. This is due again to issues of observing bridging via arrested cracks along specimen surfaces, incompatible G dependences of large crack toughnesses and normal small crack strengths at lower temperatures applying at higher temperatures, as do effects of material and microstructural parameters effecting flaws, es-

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pecially from machining, controlling strength as discussed in Chaps. 3 and 4 for room temperature behavior of monolithic ceramics and in Chaps. 8 and 9 for ceramic composites. Further, while increased intergranular fracture at higher test temperatures would be consistent with increased crack bridging, this corresponds to grain boundary weakening and associated decreased, not increased, strengths and toughnesses, which in fact may be responsible for some reduction of tough- ness–strength discrepancies. Though variability in brittle–ductile transitions and higher temperature strain-rate-dependent plastic deformation result in further toughness–strength differences at higher temperatures, there are other mechanisms that can dominate strengths of materials where bridging might occur.

Thus the strength minima and maxima observed with sapphire, as well as a number of (mainly larger grain) polycrystalline Al2O3 bodies, raise questions of how a single crystal mechanism, e.g. possibly twinning in sapphire as was noted earlier, impacts a polycrystalline body. Clearly, this can be the case if flaws causing failure are on the scale of one or a few grains, as was indicated earlier, but it seems unlikely that twinning could impact failure with flaw propagation over several to many grains, as is implied by crack scales needed for bridging, as is also implied by the absence of strength minima and maxima in finer grain Al2O3 bodies where cracks cover a number of grains. Again, the increased intergranular fracture with increased temperature over much of this range also raises questions about bridging in view of the strength decreases that occur [211].

The behavior of other materials also raises serious question regarding the role, if any, of bridging on their normal strength behavior. Thus BeO generally shows the opposite strength–temperature trend to 1000°C but has similar Young’s modulus, TEA, and slow crack growth to Al2O3, so at least one of these two materials would appear to be inconsistent with bridging. MgO shows similar though more moderate trends than BeO, but not greatly less, as would be expected if TEA stresses (absent in MgO) were a major factor in bridging, as is commonly proposed. ZrO2 shows substantial strength decrease with initial temperature increases, which is accompanied by some increase in intergranular failure, which should aid bridging and hence limit strength decrease, i.e. the opposite of what appears to happen. Also, the decrease in Young’s modulus, which appears to be due to lattice defects, raises further questions of how bridging could be a factor in associated strength changes.

E.Summary and Conclusions

Limited data on the grain dependence of thermal shock shows critical quench temperatures and retained strengths tending to increase some as G increases, but obviously at the expense of starting strength. Greater retained strengths may reflect benefits of possible crack bridging/R-curve effects, but this has not been investigated.

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Single crystal toughnesses, e.g. of Al2O3 (Fig. 6.1), MgAl2O4 (Fig. 6.3), SiC (Fig. 6.5), ZrO2 (Fig. 6.6), and MgO, while initially commonly decreasing with increasing temperature, typically exhibit a minimum, then a subsequent maximum, followed by a continued, probably accelerating, decrease. This reflects effects of overall increasing plastic deformation, primarily by slip, though in special cases, especially in sapphire, lower temperature twinning causes significant minima as a function of orientation, as implied by strength results (which implies a similar toughness maximum, probably due to increasing slip). However, while there is a corresponding minimum in the strength of sapphire, the temperature trends of toughnesses often do not correlate well with those of the corresponding polycrystals, due to grain boundary effects, which increase with temperature and many boundary phases.

Polycrystalline toughnesses, while sometimes showing minima and maxima (Fig. 6.4), which may not correlate well with those for single crystals, often show less variations from a continuous decrease as temperature increases (Fig. 6.3), especially at higher temperature, e.g ≥ 1000°C. R-curve effects are observed, e.g. due to glassy grain boundary ligaments, or more generally impurity enhanced or intrinsic increased intergranular failure as temperature increases. However, these are also often associated with lower toughness (Fig. 6.2), and especially lower strength, relative to purer bodies of the same material. While there continues to be some G dependence for some materials, this appears to diminish at higher, relative to lower, temperatures (Fig. 6.2).

Turning to σ–G–1/2 behavior, this overall typically follows a two-branch behavior as at 22°C, i.e. limited grain size dependence at finer grain size due to c < G, and a substantial G dependence at larger grain size due to c ≤ G. Such two-branch behavior occurrs at temperatures < 22°C (Fig. 6.9) and at higher temperatures, e.g. commonly to at least 1200–1300°C (Figs. 6.10, 6.22, and 6.23), though being material and strain rate dependent. An extreme of this in terms of the fraction of absolute melting temperature is indicated in ice (Fig. 6.13). All of this reinforces the dominance of flaw mechanisms of failure, as does the scaling with E (Figs. 6.22 and 6.23). Where microplastic failure occurs, mainly at medium and larger grain size, strength extrapolates to the stress for the easiest activated mode of single crystal microplasticity. Higher relative σ of materials such as ThO2 (Fig 6.16) and UO2 (Fig. 6.17) at higher temperature may indicate increasing effects of microplasticity. Where flaw failure occurs, strengths at large grain size generally extend well below strengths for the weakest crystal orientation. No clear differentiation between cubic and noncubic materials failing from flaws was found, i.e. the mechanisms of failure are not primarily determined by structurally related effects. There is some indication of nonoxides such as SiC and Si3N4 (i.e. more covalently bonded) materials having higher relative strength, but the relative balance of intrinsic versus extrinsic reasons (e.g. more successful development)

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for this is not clear, showing that much remains to be documented and understood about σ–G–T behavior.

The need for further documentation and understanding is also shown by the fact that while flaw failure predominates, substantial complexity exists as reflected in significant deviations, especially from E–T behavior. Though more limited, there is sufficient data to show that a number of variations occur in the above trends, such as shifts in singleversus polycrystal strengths and probably between strengths for different grain sizes due to SCG and other effects, mainly at > 22°C and ≤ 1000°C, where testing is often particularly neglected. These variations are best seen for Al2O3 (Fig. 6.12), BeO (Fig. 6.14), MgO (Fig. 6.15), and ZrO2 (Fig. 6.18) for which there is most data, including for E, whose general trends for different materials as well as for the specific material of interest is important.

Consider now a summary of the main variations, starting with sapphire, partly addressed earlier. Its strength drops rapidly from at least –196°C to a minimum at 400–800°C and then rises to a maximum at 900–1100°C, before steadily decreasing at higher temperature. Polycrystalline Al2O3 often shows a similar, though usually less drastic, initial strength drop and may exhibit (1) a strength minimum, a subsequent maximum (similar to but less extreme than for single crystals), or both, or (2) an approximate strength plateau at intermediate temperature (e.g. 400–800°C). Both these trends appear to require sufficiently large grains and may be overridden by the presence of other sources of failure, e.g. pores. Both are also in contrast to the simple, steady, moderate decrease of Young’s modulus (e.g. 10–15% by 1200°C), which would also be the expected strength trend if only simple flaw failure were occurring. In contrast to this, neither BeO singlenor polycrystals show similar rapid initial strength drops at > 22°C that Al2O3 does, but crystals show simple σ–T and E–T trends, while polycrystals often show significant strength maxima at intermediate temperatures, with impurities (or additives) again limiting these. MgO, while having overall σ–T dependence consistent with slip induced fracture, shows intermediate temperature polycrystalline strength maxima (less pronounced than in BeO) or plateaus similar to BeO and Al2O3, despite the differences in underlying mechanisms. ZrO2 shows polycrystalline E decreasing more rapidly with increasing temperature than single crystal Young’s moduli, and even greater polycrystalline strength decreases. Other limited oxide and nonoxide data indicate some strength increases, or no decrease form 22 to 1000°C (including in nonair atmospheres, ruling out surface oxidation effects), i.e. not following E–T decreases nor those expected due to relaxation of surface machining stresses.

Explanations for some, and known or probable factors for other, variations can be cited, the latter including environmental factors such as SCG, whose temperature dependence is poorly documented. At modest T, SCG effects (due often to H2O) apparently occur only during external stressing, either not occurring, or

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(more probably) fairly rapidly saturating due to internal (e.g. TEA) stresses alone, and can occur transgranularly (especially in larger grains), but also intergranularly in polycrystalline bodies with or without single crystal SCG, e.g. due to grain boundary phases. SCG is affected by temperature and may be interactive with microplasticity, TEA and EA, and surface machining stresses. However, though the balance between increased reactivity versus reduced content as T increases, must ultimately cease SCG, intermediate trends are uncertain, as is the case of corrosion effects such as H2O effects in some TZPs. Even less is known about high-temperature gas-driven SCG, e.g. as indicated in graphites, and liquid SCG, e.g. for TiB2 in molten Al, where grain boundary (especially O2) phases appear important. The second factor is changes of basic properties such as E, EA, and TEA as T increases. While TEA decreases with increasing T are fairly well known, its interactions with other factors such as grain orientation (e.g. in BeO, Chap. 2, Sec. III.H), boundary impurities, and EA are complications. EA has had much less attention, is probably dependent on grain shape and orientation and their changes with temperature, and varies widely with material, presenting difficulties of prediction. E normally decreases slowly, e.g. 1–2%/100°C, till 1000–1500°C, and hence individually and collectively E changes with T provide a useful reference point for comparing changes in other properties such as toughnes and strength. Some anomalous E changes do occur with increasing T, e.g. in MgAl2O4 and especially ZrO2, where defect effects are probable factors via, or in addition to, EA changes (both have higher EA). Such defect (and related internal friction) effects probably extend to several other materials, e.g., CeO2, ThO2, and UO2. Occasional phase transformations, e.g. at 1200°C for PSZ and > 2000°C for BeO, can also be important factors. More generally, higher temperature environmental factors such as oxidation of nonoxides, or reaction or reduction of oxides, can become a critical factor due to changed surface flaw populations and possible microstructural changes (including pores in surface reaction phases).

The third and most specific and pervasive is plastic deformation, with slip or twinning at lower T being more limited and material specific. As noted earlier, sapphire’s rapid strength drop with increasing T reflects failure from twin crack nucleation, and the subsequent strength maxima in Al2O3 (and BeO) probably reflect increased microplasticity to allow crack tip blunting. Other materials such as ThO2 and UO2 are probably more representative of typical effects of the onset of plastic deformation and CaO and MgO as examples of normal, gradual increases in deformation as T increases. The latter two clearly show effects of the deformation, including macroscopic deformation, but with brittle fracture (as for alkali halides), with these changes recognizable, but gradual, not nearly as spectacular as the onset of rhombohedral twinning failure in Al2O3 (which may be complicated by SCG from H2O) . The other, much more pervasive, type of deformation is that due to first grain boundary sliding and then more general creep

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mechanisms as T increases, especially above 1200–1500°C. These can be substantially affected by grain size, shape, orientation, and boundary phases, e.g. SiO2=based ones, but the latter effects can depend substantially on fabricationwetting effects as in some Al2O3 bodies.

While existing data provides some insight, much more information is needed. Not only is there very little SCG information on single crystals (including materials for which crystals are readily available, e.g. TiO2 and MgAl2O4), but the documentation in the most studied material, sapphire, is incomplete. Data for grain size effects in polycrystalline materials are even less well defined. There is reasonable evidence of TEA affecting strength, but specifics of this are still lacking, e.g., levels of these stresses, and how their effects depend on key parameters, e.g. flaw size. While significant EA increases with temperature in a number of, but not all, ceramics may cause increased grain boundary fracture initiation of many ceramics at higher temperatures, much less is known of its effects. Besides such direct polycrystalline studies, this also requires more single crystal elastic moduli–temperature data. Finally, an overall key need is for polycrystalline studies that explore enough variables, e.g. grain size, temperature, elastic moduli, and strength, that provide a reasonable opportunity of sorting out different factors. Narrow studies, focused on a single, often simplistic, approach or mechanism are of much less, if any, use.

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