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boundary phases, and test conditions, to some extent test atmosphere, but especially on strain rate. Again this higher temperature transition occurs due to opposite G dependences, i.e. finer grains result in easier grain boundary sliding and deformation and hence lower strengths as opposed to higher strengths at lower temperatures, i.e. indicated per Eq. (6.2), with strengths tending to be inversely proportional to the deformation strain rate. Greater deformation at finer G is shown by the occurrence of superplastic deformation in fine G ceramics similar to such behavior in metals [176,177].

The details of this transition, from lower temperature strengths being proportional to G–1/2 and higher temperature strengths to various powers of G ≥ 1, are complex and poorly defined. The general transition is fairly well indicated for several specific bodies, e.g. as reviewed by Quinn [178] and illustrated in Figure 6.24. However, what is almost totally missing is, especially quantitative, documentation of how such transitions depend on changes in grain size, shape,

FIGURE 6.24 Plot of flexure stress versus test temperature for a specific commercial hot pressed Si3N4 for various strain rates, thus forming a useful failure mechanism map for such test variables. Unfortunately, detailed information on the effects of grain structure and differing amounts and types of grain boundary phases is not available. (From Ref. 178, published with the permission of the

Journal of Materials Science.)

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or orientation, as well as on the amount and character of grain boundary phases. The lack of such information arises from both the lack of adequate data as a function of T and the complexity of high-temperature behavior and the transition between this and lower temperature behavior. The complexity stems substantially from other changes and transitions in behavior that occur over intermediate temperature ranges. Unfortunately, many have focused on only the basic lower to higher temperature failure changes and thus do not begin higher temperature measurements till ≥ 1000°C, thus missing changes that often occur at lower temperatures. Frequent modest and sometimes extreme changes occur from the simple trend for toughnesses and especially strengths to decrease in proportion to the decreases in E till temperatures ≥ 1000°C, where grain boundary sliding or other deformation processes begin to occur depending on material and strain rates. Thus minima, maxima, or both of toughness, strength, or both commonly occur at T ≤ 1200°C (e.g. Figs. 6.12, 6.14, 6.15, and 6.18) before continuous and accelerating decreases in strengths and polycrystalline toughnesses (disparities for single crystal toughnesses will be discussed later).

B.Property Changes Impacting Strength and Its Grain Size Dependence as a Function of Temperature

Young’s modulus decrease with temperature again provides a baseline comparision of strength–temperature behavior, since it is a basic factor in strength changes with temperature. Such E–T trends, while not directly revealing grain structure dependence, can aid in this by considering other possible superimposed strength changes, especially those that are known or expected to depend on grain structure. Such comparison is the purpose of this section given the limited amount of experimental data reviewed earlier, starting with changes in slow crack growth.

The substantial occurrence of SCG due to environmental species, especially H2O, clearly disappears as T decreases below 22°C for tests in liquid nitrogen at –196°C (Fig. 6.25). Thus if strengths and Young’s moduli are plotted versus T starting well below room temperature, those materials experiencing SCG at modest T, e.g. due to H2O, would show a deviation below strengths paralleling the decreases of E as T increases. However, such materials should also show a positive deviation of strengths versus T back toward the T dependence of E as T increases above 22°C due to reduced SCG from H2O and other fluid species due to increased temperature reducing the amount of such species at the crack tip. Though not studied in detail, such a change was shown by Evans and Lange’s [53] n values for SiC hot pressed with Al2O3 additions increasing with T, i.e. 80 at 22°C and > 200 at 600°C. However, as temperature increases, other mechanisms of SCG can come into play, commonly due to grain boundary sliding, especially due to boundary phases. Again, Evans and Lange’s [53] study of

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FIGURE 6.25 Schematic plot of the impact of various mechanisms for deviations from the overall temperature dependence of tensile strength from the inherent dependence of Young’s modulus. Note that besides basic dependence on temperature (T), (1) the SCG deviations depend on test environment, strain rate, material, and often the amount and character of grain boundary phases, and also probably also on G (Fig. 2.8), (2) surface annealing and especially surface oxidation effects are respectively body and material and atmosphere specific, (3) TEA effects are material specific and clearly depend on grain structure, (4) higher temperature plastic effects are very strain rate dependent and may depend substantially on grain structure and boundary phases, and (5) effects of EA (not shown) are probably either positive or negative depending on their character and that of TEA and possibly plastic anisotropy and grain structure and boundary phases.

SiC hot pressed with Al2O3 additions showing SCG with n 21 at T = 1400°C illustrates this point.

Consider other changes as T increases that impact toughness and especially strength. Intrinsic changes include decreasing TEA as T increases, with such effects clearly being material and grain structure dependent (Chap. 2, Sec. II.C), and probably also by grain boundary phases. Thus increases in strengths of ZrB2, HfB2, and TiB2 to maxima at intermediate T are probably due to reduction of TEA stresses as T increases. The increase in the relative strength changes as G increases in TiB2 (while the overall strength decreased), as indicated by Baumgartner and Steiger [74]. Matsushita’s [159] data also ap-

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pears to be generally consistent with this, considering uncertainties in G and boundary phases. Such effects can be much more pronounced in very anisotropic materials, e.g. in BN and more extensively shown in graphites, where strengths can peak at 50% to threefold increases over those at 22°C at temperature of the order of 2500°C, e.g. Rice [8]. Strength increases in bodies with TEA can occur due to closing of microcracks from TEA as T increases, as appears to be at least part, if not all, of the cause of changes in larger G TiB2. However, strengths can also increase due to increased T reducing the opportunuty for microcracks to develop due to the combination of TEA and applied stresses. This is indicated by the absence of pronounced effects of increasing temperature on conductivity of graphites, i.e. if the strength increases with increasing temperature in graphites were due mainly to closure of microcracks, similar effects would be expected on thermal conductivity. The absence of a large effect on thermal conductivity of graphites indicates that much of the strength effects occur due to reduced opportunity for stress-induced microcracking, which would be consistent with the conductivity results, sine there would be limited microcracking to affect conductivity as observed.

EA should also have some similar effects as TEA, including grain effects, but there are three sets of complications. The first is that EA stresses depend on both the extent and nature of the EA as well as on the stresses in the body, i.e. EA varies the stress in the body but does not generate stresses as TEA does. Thus EA effects would be expected to increase with increasing G similar to those for TEA, but the tensile stresses that can be sustained by larger G bodies are inherently limited by G as reviewed in this chapter and in Chapter 3. The second set of complications is that, as will be discussed in more detail later (e.g. Fig. 7.13), EA can increase or decrease with, or be independent of, temperature, depending on the material and the temperature range considered. Thus while there is a consistent trend for a given material and temperature range, there is no general trend for all materials and temperatures as there is for TEA. The third complication is that EA effects are interactive with other anisotropies, i.e. of plastic deformation and resultant stress concentrations, of TEA, and of the grain shape and its orientation relative to the stress axes as a function of the nature of the EA, as modeled by Hasselman [179]. Thus while it is important to consider EA in evaluating mechanical behavior, its effects can be much more variable and complicated, e.g. since EA may vary in its crystallograpic dependence from the other anisotropies.

Other changes with increasing test temperature include reduction of residual (e.g. machining) stress, oxidation, and increasing plastic deformation. Residual stress changes are typically small and may often be more compressive from machining, so that their removal may give a limited decrease in strength. Oxidation of surfaces can consume and thus eliminate surface flaws, e.g. from machining, and thus increase strengths as indicated for TiB2 [159]. However, such

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effects are complicated and limited by various factors such as the nature of the oxide coating (material and body dependent), the formation of bubbles or other defects, and residual stresses in the coating, effects of the latter depending on coating character and thickness.

Increasing plastic deformation due to twinning, slip, or both, as well as grain boundary sliding, plays a complex and often incompletely addressed role in the changes of strengths as temperature increases. Plasticity due to boundary sliding often occurrs at modest temperatures, is both material and body specific, and depends substatnially on strain rate. While this may cause a very temporary, strain-rate-, body-, etc. dependent increase in toughness, strength, or both, it more broadly leads to greater than normal progressive decreases with increasing temperature. While increasing crystal plasticity with increasing temperature may lead to resultant polycrystalline plasticity, this is often not the case or requires temperature and body character that are of limited interest. This results from the fact that increased plasticity in crystals often still leaves substantial anisotropy in the plasticity, i.e. limited ability to relieve arbitrary stress concentrations as will occur at grain boundaries of grains undergoing shape changes from deformation. In other words, plasticity of single crystals and hence individual grains often increases much faster than the occurrence of sufficient, i.e. typically five independent, slip or deformation systems for general ductility. This disparity in amount of deformation versus its general stress-relieving ability can result in increased strength decreases, commonly via intergranular failure. This is probably at least part of the cause of the transition to intergranular fracture of CaO and MgO (Chap. 6, Sec. IV.D), but increasing EA with increasing temperature is also probably a factor in this. Thus it is common for single crystals to show markedly increasing strain-rate-dependent toughnesses (e.g. Figs. 6.1, 6.3, and 6.6), with limited, no, or opposite effects of the toughness and strength with temperature. A more spectacular example of this negative effect of increased deformation on strength as temperature increases is the often neglected marked strength decreases in Al2O3 at only a few hundred degrees, that appear to be due to increased twinning, as was discussed in Sec. V.C.

Finer grain branch(es) show limited, and larger grain branches show substantial, grain size dependence of strength. For microplastic controlled strength, the larger grain branch extrapolates to the single crystal strength, reflecting the easier modes of microplasticity activation [139–141]. For brittle fracture, the larger grain branch commonly extends, often substantially, below the lowest single crystal strength (as a function of orientation) for comparable surface finish. Where microplasticity occurs, it competes with flaw failure, with the balance between the two mechanisms often being shifted by specimen quality (i.e. processing defects), surface finish, temperature, and possibly test environment.

This survey shows that substantial strength changes can occur in the (often neglected) regime ≤ 1000°C. Thus significant changes of the relative singleand

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polycrystal strengths may occur, and there may also be variation of these changes with grain size. Parameters affecting such variations include not only environment (i.e. mainly H2O here) and temperature but also surface finish (especially machining effects). Further, possible effects of material parameters (e.g., TEA and elastic anisotropy, EA) vary with temperature, microstructure, and possibly environment, as do effects of surface finish (environmental effects are also a function of temperature). However, effects of environment and surface finish can be at least partly separated out, though studies have not often done this.

C.Temperature Effects on the Grain Size Dependence Al2O3 and BeO

That the temperature dependence of σ–G relations can be complex and involves other effects can be better seen from the relative temperature dependence of Al2O3, BeO, MgO, and ZrO2 (for which there is reasonable data, Figs. 6.12, 6.14, 6.15, and 6.18). Thus for T < 600–800°C, Al2O3 and BeO, both noncubic materials with similar, significant TEA, show opposite σ–T trends, i.e. BeO strength increases with temperature while Al2O3 strength decreases, especially for single crystals, and hence with no TEA.

The initial, substantial strength decreases in sapphire and polycrystalline Al2O3 had been speculated to be due to increasing crack tip microplasticity, i.e. slip or twinning, but was questioned by crack tip dislocations or twins not being found by Wiederhorn et al. [29]. However, a number of earlier observations suggested a possible explanation for the sapphire σ–T minimum based on twinning as follows. Heuer [180] reported twins introduced in sapphire by either surface scratching or fracture (e.g. rhombohedral twins at least as low as –196°C), possible cracks following twins, possible crack nucleation by twin–twin and twin–grain boundary intersections, and twins being thicker and larger above 600°C. Becher [181] showed both rhombohedral and basal twins introduced by surface abrasion and frequent association with resultant surface cracks. He subsequently indicated probable cracks along basal twin-matrix interfaces [182]. Scott and Orr [183] showed the resolved shear stress for rhombohedrahl twinning dropping from 225 MPa at 320°C to 5 MPa by 600°C and remaining constant thereafter to ≥ 1500°C. Though Scott and Orr’s tests were in compression (requiring shortening of the specimen), thus not necessarily reflecting tensile behavior (requiring elongation), their changes closely mirrored the strength changes of sapphire, suggesting cause and effect i.e. similar twinning in tension. Alloying effects reported by Sayir [104] support this. KIC results of Iwasa and Bradt [26] might appear to question this, but being obtained by the (Knoop) indentation-fracture tests, they are thus essentially a strength test, and indents are common sources of twins [181,184]. (Twin-matrix interfaces could

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have lower KIC, and be preferred sites for SCG, e.g. be consistent with the marked strength drops in, at least machined, sapphire due to both increasing temperature and environment effects. Annealed surfaces may also have twin-flaw combinations, e.g. from previous machining or handling, but reduced in extent or severity, e.g. as possibly indicated by Charles’ [86] data for annealed sapphire.) There is also evidence that twinning is associated with tensile failure in BaTiO3 singleand polycrystals [185].

Recent research and development has confirmed that rhombohedral twinning is the source of the strength minimum in sapphire [186–192], despite the twinning being activitated in compression. Such confirmation resulted from both direct observation of the twinning and resultant failure as well as successful steps to suppress it and thus limit strength lossses. Both efforts were motivated by the severe weakening this mechanism causes in the use of sapphire as an irdome material for missiles, due to the resultant much easier thermal stress failure from aerodynamic heating. Thus Mecholsky’s [186] fractographic studies showed sapphire flexure bars failed from twin crack nucleation due to compressive under the flexure loading points. (This is an atypical but not unique example of failure from compressive stresses in flexure. Failure from compressive stresses in flexure also often occurs in fiber composites.) Subsequently Harris [187], Savrun et al. [188], and Schmid and Harris [189] showed that the orienta- tion–temperature dependence of sapphire flexure strength is due to rhombohedral twinning and resulatant crack nucleation, typically from twin–twin intersections. Such failure has been corroborated by reduction of failure of sapphire missile domes by minimizing compressive stresses on rhombohedral planes by orienting the domes relative to the asymmetrical aerodynamic heating. Corroboration is also supplied by both doping of sapphire [104,190,191] and especially a proprietary treatment [191,192] (speculated to be neutron irradiation), since both, especially the latter, reduce twinning. The doping (alloying) results are consistent with differing results cited for Cr2O3 doped sapphire, since such effects are a function of the dopant, its amount, test temperature, and sapphire orientation.

Twinning-induced fracture also appears consistent with Al2O3 σ–G effects via grain size limiting twin size less at moderate and large grain size, but more in the finer grain branch where too many grains are encompassed by the flaw size (c) for individual grain–twin interactions to be significant. Thus the substantial scatter of Kirchner and Gruver’s hot pressed Al2O3 strength minima and maxima [107,108] with C 20 m and G 2–5 m may reflect effects of known grain heterogeneity. Also, Mizuta et al.’s [109] lack of a strength minimum is consistent with their apparently uniform, fine grain size. Al2O3 fibers, while not being tested as low as 400–500°C, would be consistent with no minimum due to the fine grain size (but a maximum at 800–1100°C). Neuber and Wimmer’s [81] strength minima (and maxima) at intermediate grain size are consistent with

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such a twinning mechanism, as are Charles’ [86]. (His larger grain, lamp envelope Al2O3 showing less of a strength minimum and at higher temperature suggest that environmental factors may also play a role in these σ–T minima and maxima.) Only a suggestion of a strength minimum in tests of Jackman and Roberts [91] (G 50 m) may be due to the probable larger pore size of the residual ( 5%) porosity frequently being a key factor in failure. However, the role of TEA stresses cannot be neglected since, for example, large (e.g. isolated) grains are often preferred sources of failure in Al2O3 (and other ceramics) [78].

The subsequent significant strength upturn and resultant relative σ–T maximum of much of the Al2O3 data (e.g. at 800–1,000°C) could reflect crack tip blunting due to plasticity in single crystals, since slip and twinning are clearly observed to occur to an increasing extent in this e.g. 600–1000°C, range, including at crack tips [29]. However, this is unlikely to be significant in polycrystalline Al2O3, especially as flaw size (c) becomes progressively > the grain size (c > G), since crack tip stress relief encompassing a number of grains is much less likely in view of the limited number of slip and twin systems. Instead of (or in addition to) such microplastic effects, reduction of TEA stresses [193] must be considered. The strength maximum occurs at, or close to, the temperature range at which such stresses are believed to disappear, e.g. based on spontaneous microcracking from such stresses. Evidence has been presented that such stresses increasingly directly contribute to failure at 22°C as the flaw size approaches the grain size [1,79,194] (Fig. 3.35), i.e. pertinent to much of the larger grain branch, with decreasing effects as grain size decreases along the fine grain branch. On the other hand, KIC at 22°C (measured with large cracks) commonly shows a maximum at intermediate grain size, originally attributed to microcracking from TEA stresses [193] but now attributed more to R-curve effects (Figs. 2.16, 2.17). The latter effects are believed generally not to be pertinent, since flaws controlling strength are commonly not on a sufficient scale in the pertinent grain size range. However, the specifics of both of these mechanisms, their possible interactions, and their actual temperature dependence are, at best, limited.

Reduction in TEA stresses with increasing temperature is a possible mechanism for the BeO σ–T maximum, as originally suggested by Bentle and Kniefel [126] and Clarke [195], e.g. the temperature range of the maximum (500–1000°C) approaches that estimated for the disappearance of TEA stresses based on microcracking from such stresses [193]. Also, other factors, such as greater grain boundary stress relief due to higher stress in testing than for spontaneous cracking (i.e., with no external stressing), could reduce the temperature for maximum strength. Particularly supportive of such a stress relief mechanism is the absence of any apparent single crystal complications as for Al2O3. Again, the stress-relief mechanism should be dependent on c not being >> G, since the effect of such stresses goes to zero when averaged over many grains [2,78–80,194]. The indicated grain size dependence of the σ–T maxima (e.g. at G 40–100 m) supports this postulate. However, note

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that reduction of TEA stresses as an explanation of the σ–T maxima also means that SCG effects may be underestimated by tests in liquid N2, since this increases TEA stresses, which would thus limit strength increases due to reduced SCG at T > 22°C.

Clearly grain boundary phases can play an important, but variable, role in the σ–T behavior, especially beyond 600°C. Thus SiO2-based grain boundary phases in Al2O3 can not only relieve TEA stresses but also lead to grain boundary sliding and attendant strain rate dependent maxima [82,110] (Fig. 6.11), as can grain boundary phases in other oxides and nonoxides (e.g. Si3N4). This is also shown by less pronounced maxima, or only an strength plateau in BeO with additives or impurities [126]. Such differences probably reflect interrelated effects of the boundary phase and its degree of wetting, which can also be a function of processing, e.g. less SiO2 wetting of Al2O3 under reducing condition [196], as indicated by differences between commercial (air) sintered 95% Al2O3 (Fig. 6.11) and Al2O3 hot pressed with 3% SiO2 [85].

D.Temperature Effects on the Grain Size Dependence on Other Ceramics, and Overall Mechanisms

The high EA of ZrO2 bodies at modest T and its increase with increasing T (Fig. 7.13) suggest that it may be a factor in the transition from transto intergranular fracture at modest T (Chap. 2, Sec. III). Similarly, such a fracture mode transition at higher T in MgO has been suggested as reflecting its more modest but increasing EA with increasing T [197]. However, again other mechanisms may be involved, e.g. as indicated by decreases in E of ZrO2 (Fig. 6.18), since this would presumably not occur due to EA unless it was causing microcracking (and then possibly only in tests with substantial applied stress, most likely static versus dynamic modulus measurements), but may be due to effects of lattice defect structures formed. Thus the often more extreme decrease of Young’s modulus (and strength) at modest temperature in fully or partially stabilized ZrO2, especially with Y2O3, also correlates with oxygen defects, e.g. forming anisotropic complexes as indicated by correlation of internal friction and other loss measurements via conductivity and dielectric tests [10,198]. This is corroborated by correlations of Young’s modulus decreases (especially with Y2O3 or reduced CeO2 additions) and variations with the stabilizer type and amount and reduction of CeO2 [10]. While such effects of reduction have been neglected or associated with darkening attributed to other effects [199,200], this is likely to be important due to reducing conditions in hot pressing or HIPing samples, and especially high-temperature heat treatment of PSZ [201] (usually achieved via induction heating of carbon). Such defect effects have been indicated in ThO2 [202] and are likely to occur in other materials, e.g. CeO2 and MgAl2O4 [i.e. the latter E–T (Fig. 7.13) and σ–T jog at 500–700°C, Fig. 6.18]. While Young’s modulus decreases would contribute to σ decreases, the latter are much larger, indicating an

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enhancement of the above oxygen defect mechanism or the addition of one or more other mechanisms.

Impurities, especially at grain boundaries, are a possible factor in the ZrO2 σ–T decreases, especially in view of observed increased intergranular fracture initiation with temperature vs. mostly transgranular at lower temperature. However, it is not clear why ZrO2 should be so much more sensitive to impurities, nor why they would be a factor at such low temperatures (e.g. 200–400°C). While, as noted earlier, SCG was not observed in Y2O3 fully stabilized ZrO2 crystals, polycrystalline SCG via grain boundaries may be a possibility, but extensive transgranular fracture at and near 22°C argues against this. Destabilization of partially stabilized ZrO2 by H2O has also been observed, but only for a modest range of temperature, grain size, and Y2O3 content, not explaining similar effects for CaO, MgO, or Tb4O7 stabilization or full stabilization with Y2O3. Further, this effect appears to be a corrosion phenomenon [203–206], not SCG; i.e. degradation over the exposed area, not just at tips of sufficiently stressed cracks. Attributing moderate temperature decreases in ZrO2 mechanical properties to attack of H2O (or other species such as HCl [204,206]) also appears inconsistent with some similar strength trends for both ZrO2 + Y2O3 singleand polycrystals (in view of probable association of this H2O effect with grain boundaries, hence not pertinent to single crystals). This would also possibly imply some opposite effects of H2O and boundary impurities, since the latter may often interfere with the reaction with H2O. H2O effects also appear to be inconsistent with many of the property changes continuing well beyond the temperature range of this destabilizing mechanism. Thus while H2O effects may contribute to the E–T and especially σ–T changes, they cannot be the fundamental cause of them.

While EA may decrease or not change much with increasing temperature for some materials, it shows considerable increase with temperature for several materials recently reviewed [197], e.g. CaO, MgO, and ZrO2. The latter shows EA increases significantly in the temperature range where Young’s modulus and strength show marked decreases (Figs. 6.18, 7.13) and shows substantial composition dependence, implying even higher EA for partially stabilized materials (e.g. those of Drachinskii et al. [155].

The similarity of TEA and EA providing local (grain boundary) stress concentrations (the latter, only with an external stress applied to the body) might suggest EA as an analogous possibility for some (e.g. MgO) σ–T maxima at intermediate temperature, i.e. as for TEA as a possible cause of such maxima in Al2O3 and BeO. However, the common continued rise of EA with temperature noted above would appear to rule this out [197] (TEA stresses decrease with increasing temperature). On the other hand, increasing deformation with temperature combined with EA-T changes might be a possible mechanism. Such EA contribution would probably increase with grain size, analogous to the grain size dependence of spontaneous cracking from TEA (Chap. 2).