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FIGURE 6.18 Relative Young’s modulus (E) and flexure strength (σ) of singleand polycrystalline ZrO2 versus test temperature (normalized by taking the property at 22°C = 1). Note the stabilizer in Neuber and Wimmer’s ZrO2 is not specified but is believed to be either CaO or MgO ( 5 wt%, P 0.13, 25 m) [81]. Note that curve designations are analogous to those of Fig. 6.12 (along with designation of some compositions) and that E–T trends, especially for single crystals, are a key basis of comparison. (From Ref. 1, published with the permission of the

Journal of Materials Science.)

an intermediate % [153] for the highest strength (410 MPa), vs. 90% at 370 MPa. Rice [156] observed fracture initiation from grain boundaries surrounded entirely by 100% transgranular fracture not only in MgO, CaO, and MgAl2O4 but also in ZrO2 (12.4 w/o MgO) and ZrO2 (+11 w/o Y2O3, from the same processing as specimens used by Adams et al.). The substantial intergranular fracture at higher temperatures correlates with substantial grain boundary sliding creep, and even superplasticity found at ≥ 1000°C in fine grain TZP [156].

F.Effects of Grain Size on Strength of Mixed Oxides at Elevated Temperatures

As noted in the previous section, MgAl2O4 toughness decreased ( 20%) to a minimum at 900°C for {100} fracture (and less for other orientations) [38].

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Toughness of hot pressed MgAl2O4 decreased slowly with increasing temperature (e.g. 10% by 900°C) for G = 5, 12, and 25 m (but possibly less for G = 40 m) and then much more rapidly [39], or was constant to 800°C and then increased for G 35 m [41]. Overall strength behaved similarly, being the same at 22 and 200°C; it dropped by 25% to a minimum at 600°C or a plateau at 400–800°C and then decreased slowly at higher temperature, i.e. similar to the temperature dependence of Young’s modulus [39].

Penty [157] prepared and tested hot pressed mullite bodies (P ≤ 0.01, G 0.75–1.5, mostly > 1 m) showing a strength minimum at 700°C and a maximum at 1200°C, with some variation with stoichiometry (Fig. 6.19). Mah and Mazdiyasni [48] reported flexure strengths increasing from 130 MPa at 22°C to 145 MPa at 1500°C in dense, transparent, hot pressed mullite (61.9 mol% Al2O3, G 3–9 m). However, measurements at only 22, 1000, and 1200–1500°C missed possible intervening strength changes. Their lower strengths appear to be consistent with their larger grain size, though specimen size and surface finish are probably also factors. Fracture toughness calculated from fractography gave 1.8 MPa·m1/2 at 22°C, decreasing 20% to a minimum

FIGURE 6.19 Mechanical properties of polycrystalline mullite versus test temperature for mullite. (A) Young’s modulus and toughness data of Baudin [47]; (B) strength data of Baudin (solid line) [47] and Mah and Mazdiyasni (dashed line) [48], with the former being nearly identical to that of Penty [157] (not shown for clarity). Note measurements only at 22, 1000, and 1300–1500°C by Mah and Mazdiyasni missed seeing possible changes at intervening temperatures and that their larger G is probably an important factor in their overall lower strengths, despite having residual P 0 versus 0.006 for Penty. Vertical bars = standard deviations. See also Figure 6.4.

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of 1.5 MPa·m1/2 at 1100°C and then increasing substantially as the temperature further increased, apparently due to slow crack growth that was observed beginning at 1300°C and was attributed to limited amounts of a glassy grain boundary phase observed in TEM. Ohnishi et al. [46] showed a similar toughness trend with temperature, i.e. initially decreasing similar to E but then increasing substantially at higher temperature. Their strengths for sintered mullite, though higher, clearly showed more complex changes than a simple linear trend with increasing temperature. Baudin [47] reported lower E values but with a similar relative decrease with increasing T and a similar range of toughnesses and strengths values but decreasing 10% to minima at 800°C and then increasing to maxima 20% > values at 22°C at 1400°C.

G.Effects of Grain Size on Strength of Borides, Carbides, and Nitrides at Elevated Temperatures

While there is little or no σ–G data for most of these materials, there is some, as well as some other pertinent data on a few of them, e.g. TiB2. Thus σ–G–1/2 data for dense sintered TiB2 tested at 970°C in argon or molten Al by Baumgartner [73] both showed two-branch behavior typical of brittle failure from flaws, except the larger G branch and hence the branch intersection may occur at somewhat finer G due to effects of probable microcracks in the largest G body (Fig. 6.20). The presence and effects of microcracks was shown by direct observations of Baumgartner and Steiger [74] in the largest G ( 24 m, P= 0.004) body and effects on properties in such bodies and those with finer G. Thus at 22°C Young’s modulus of intermediate G ( 11 m) bodies was 6%< that of the finest G bodies ( 1 m), and that of the largest G bodies was typically 20% < the intermediate G bodies despite porosities of 2.4, 0.6, and 0.3% respectively in the finer through the largest G bodies. In the extreme, E of the largest G body at 22°C was as low as 270 versus 545 GPa for a finer G ( 4 m), and the thermal conductivity of the latter was 25% > the former. Finer and intermediate G bodies showed E decreasing by 24% from 22 to 1000°C, while the larger G bodies decreased by 14%. These trends are supported by their strengths increasing in inert atmosphere testing as temperature increased by 30 to 100% as G increased, with most (e.g. 80%) of the increase occurring by 1000°C. Further, the load–deflection curves for the finer G bodies were linear to at least 1250°C, while those for heavily microcracked larger G bodies were nonlinear prior to fracture, which was attributed to additional stress-induced microcracking. These observations are supported by results of Mandorf and Hartwig [158], who showed that while their Young’s moduli decreased less, e.g. by 4% to 1000°C (then accelerated in their decreases, especially with higher porosity), their flexure strengths increased more, e.g. by 25% on reaching a maximum of 305 GPa at 1400°C (for G estimated at 25 m with a few

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FIGURE 6.20 Flexure strength versus the inverse square root of grain size (G–1/2) for dense sintered TiB2 at 970°C in argon (Ar) and molten aluminum (Al) from Baumgartner [72]. Note that (1) the finest G body had residual porosity of 2.4% ( 3–8 times the other bodies) and that the second finest G body was tested at 1000°C, so correction for these further increases their strengths, (2) the largest G body was microcracked giving lower strength, and (3) the data of Matsushita et al. [159] at finer G and that of Mandorf and Hartwig [158] at larger G are consistent with the above plot, though the latter indicates less larger G strength decrease, consistent with less apparent microcracking. Baumgartner attributed strength reduction in molten aluminum to liquid metal embrittlement, i.e. a reduction of crack tip toughness, instead of SCG, since fractography showed Al had limited penetration along grain boundaries but good penetration into surface connected processing flaws, there was no evidence of SCG, and fracture was transgranular.

percent porosity) indicating substantial microcrack closure. Data of Matsushita et al. [159] for dense sintered TiB2 tested in Ar showed only a few % increase, mainly by 1000°C in testing to 1400°C (tests in air resulted in substantially greater increases, e.g. 50% at 1000°C and then decreasing back to inert atmosphere levels at 1200 and 1400°C due probably to oxidation effects). The lack of significant increase in inert atmosphere is attributed, at least in part, to their finer G, estimated at 5 m. Limited tests of ZrB2 at 1000°C showed no

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strength change from 22°C [160] or a maximum at 300°C ( 600°C for HfB2, both in inert atmosphere) [161].

Limited B4C data indicates limited changes from the σ–G–1/2 behavior at 22°C. Thus de With [162] showed that the strength of the commercial hot pressed B4C (G 10 m, P 0) in dry nitrogen decreased from 390 MPa at 22°C by only a few percent at 600°C and then more rapidly to a minimum of 300 MPa at 1000°C, then increasing back to its 22°C level at 1200°C. This was very similar in form, but larger in the extent of changes for toughness of the same material, with both strength and toughness tests giving 100% transgranular fracture across the temperature range. Gogotsi et al.’s [163] behavior of a commercial dense hot pressed B4C (G unspecified) showed very similar behavior in testing in Ar, except for starting from a strength of 300 MPa at 22°C (testing in air resulted in 10% strength reduction by 600°C and then dropping to 200 MPa at 1000 and 1200°C). Several investigations [164–166] showed strengths of B4C decreasing very little until 800°C (and limited decrease above 800°C) [162], which is consistent with KIC trends.

Similar tests of SiC showed strength and KIC maxima at 1400°C [167], and considerable investigation of dense sintered and hot pressed SiC for engine and other applications commonly showed strength at 1000°C similar to that at 22°C or somewhat (e.g. 20%) higher, typically for G 2–10 m [168]. Miracle and Lipsitt [169] showed limited (e.g. 10–20%) strength increases or decreases, or possibly no strength changes, in TiC from 22° to 600°C, and in some cases to 1000–1200°C depending on C/Ti ratios of 0.66, 0.75, 0.83, and 0.93 (G respectively 22, 21, 20, and 14 m). Substantial strength decreases occurred at higher temperatures, with the earliest and greatest strength decrease for the C/Ti = 0.66, G 22 m body. Thus the strength change with increasing temperature generally did not follow the 5% decrease of Young’s modulus in this temperature range [170]. More extensive testing of dense sintered or hot pressed Si3N4, as well as less dense RSSN, showed that some bodies had lower strengths by 800–1000°C vs. 22°C, many had no decrease, and several increased (again by up to 20%) [168]. This again shows strength not following the E–T trend (e.g. ≤ 5% decrease by 1000°C. Although such increases are most common for RSSN, they are not restricted to it (increases in strength can result from surface oxidation removing flaws in such nonoxides, especially RSSN).

V.GRAIN EFFECTS ON THERMAL SHOCK BEHAVIOR

Broader studies of thermal stress and shock resistance of ceramics support the general applicability of models discussed earlier, in particular confirming that fracture normally occurs on cooling rather than heating, since the former results in tensile stresses on the surface where fracture initiating flaws are typically much more prevalent. While such fracture thus occurs in material with less, pos-

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sibly no, increase over ambient temperature, the temperature exposure may have effects via the thermal gradient impacts on stresses and properties, e.g. Young’s modulus and thermal conductivity.

Data specifically on the grain, mainly size, dependence of thermal stress and shock resistance of ceramics, though quite limited, provides information to support the simple models, possible modification of them, and other insights to mechanical behavior, e.g. crack bridging effects. Gupta’s [171,172] study of thermal shock failure of various alumina bodies of differing G with little or no porosity using the typical water quench test provides some of the clearest data. In this test, bars are heated in a furnace to a fixed temperature and then quenched into a water bath and subsequently tested for their resultant strength. This is repeated with other specimens with the post quench strength plotted versus the quench temperatures, with particular attention to the critical quench temperature, i.e. TC, where strength decreases, often catastrophically. He showed that sapphire had the highest critical TC, 250°C (as well as the highest strength consistent with much data of Chap. 3, Sec. 1) but failed catastrophically, or nearly so, i.e. had zero or negligible strengths, after quenching at ≥ TC. Bodies with G of 10, 34, 40, and 85 m, which had initial strengths decreasing from 340 to 160 MPa, all had a TC of 200°C (Fig. 6.21). However, while the residual strengths after quenching well above TC were the same for all polycrystalline grain sizes, the strength retained for quenching at and somewhat above TC increased with increasing G, and more importantly the strength decrease above TC became gradual rather than abrupt (Fig. 6.21). Gupta [172] subsequently showed that plotting strength retained after quenching at TC linearly increased with G, reaching 1 at G80 m, consistent with his experimental results.

Tomaszeweski [173] conducted a more extensive study of G effects on thermal shock resistance of Al2O3 as an extension of his substantial study of effects of G on mechanical properties of Al2O3 (Fig. 2.11), covering the G range of4 to 600 m. He showed a similar TC of 200°C with the extent of abrupt strength decrease again decreasing as G increased, so that it disappeared by G 100 m, beyond which a gradual strength decrease with increasing quench T occurred with the starting strength level and the decrease diminished with further G increase, with a very low strength level of 10 MPa and no strength decreases occurring at G 570 m. These changes are related to linear reductions of the (static) Young’s modulus with increasing G, i.e. from 300+ to 150 GPa at G 100+ m and then to 100 GPa at G 460 m due to microcracking.

Seaton and Dutta [174] showed some similar and different results for G effects on thermal shock of B4C, which had very similar E, TEA, and toughness to Al2O3, but dominant transgranular rather than mixed or mainly intergranular fracture. They showed that, while starting strengths were somewhat higher for finer G, as was expected, the overall TC was the same for G = 2 and 16 m, as for Al2O3. However, the larger G showed strengths starting to decrease at < TC,

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FIGURE 6.21 Flexure strengths at 22°C for quenched Al2O3 [172] with G = 85 m and 10 m. Note the similarity that while starting strengths increase with decreasing G, the overall T values are independent of G, but residual strengths are somewhat higher, especially as a fraction of starting strengths at higher G for Al2O3, but not for B4C, which reflects differences between these two materials, e.g. possibly of crack–grain bridging. (Published with the permission of the Journal of the American Ceramic Society.)

and then were lower at and somewhat above T in contrast to the Al2O3 results (Fig. 6.21). The reasons for these differences are not known for certain, but they may reflect differing effects of crack–grain bridging effects. Thus as G increases in Al2O3, opportunity for such bridging increases and the resultant crack sizes involved in much of the thermal shock damage probably becomes large enough to involve a sufficient number of grains to limit strength loss. On the other hand, the predominant transgranular fracture in B4C appears to limit possible crack bridging and thus the opportunity to mitigate strength losses in thermal shock.

Kennedy and Bandyopadhyay [149] conducted similar quench tests on four UO2 bodies with G 2–19 m and porosity of 9 to 3%, which generally decreased with increasing G. Again TC was independent of G (at 100°C), but

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there was no clear improvement of the residual strength as G increased. In fact, strengths after quenching the two finer grain bodies did not reach those of the two larger G bodies at TC until quench temperatures of 300–400°C.

Other tests show further complications and evaluation possibilities, e.g. in studies of Capolla and Bradt [175] of two recrystallized SiC refractory bodies with one having somewhat higher strength and WOF and somewhat lower thermal expansion with a substantial bimodal G distribution versus the other body with a grain structure of uniform grains of about the size of, or somewhat >, the larger grains in the first body. The former body had a TC of 350°C, slightly higher than the second body with its 325°C, but it had a substantially lower rate of strength decrease and a higher retained strength than the second body. The property best correlating with these differences in thermal shock behavior was the WOF, but the underlying microstructural reasons for this are not clear, e.g. the body with somewhat finer large grains in a matrix of substantially finer grains, hence a substantially smaller average G, had substantially better performance. While this difference in grain structure is probably a factor, interaction between the grain structure and the substantial and similar levels of porosity in both bodies may be important, since there is clear precedent for porosity critically interacting with other microstructural aspects significantly to improve thermal shock [8]. Finally, these investigators [175] and others [167,168] have shown the value of using damping as a tool to monitor thermal shock damage, i.e. showing substantial increases in damping below and beyond TC, then leveling off, with the overall levels being substantially higher with more thermal shock damage. Similarly, acoustic emission, though again used only a limited amount, can be a valuable indicator of thermal shock effects.

VI. DISCUSSION

A.Overall Strength–Grain Size Behavior as a Function of Temperature

As temperature increases, there must be a transition in the grain dependence of crack propogation and tensile strength, which is also significantly impacted by strain rate. This overall transition arises since the grain size dependence of these properties is fundamentally opposite at lower temperatures from what it is at sufficiently high temperatures, with the transition occurring at lower temperatures with lower strain rates and higher temperatures at higher strain rates. At lower temperatures, where brittle fracture initiation and propagation dominate, even where crack nucleation, growth, or both occur due to microplastic processes, strengths inherently increase with decreasing grain size, as was extensively shown in Chap. 3 and here. This chapter also clearly shows that such brittle fracture, most commonly manifested by the typical two-branch σ–G–1/2 behavior

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found at 22°C, commonly extends to ≥ 1000°C and sometimes to > 90% of the absolute melting point, as was shown for ice (Fig. 6.13). This is also supported by scaling of strengths with E commonly continuing to ≥ 1200°C (Figs. 6.22 and 6.23), similar to that found at 22°C (Fig. 3.37). This shows that while less σ–G–1/2 data exists at elevated temperature, sufficient does exist (mainly at 1000–1300°C) to show basic similarities with behavior at 22°C, i.e. the common occurrence of two-branch σ–G–1/2 curves, often higher strength levels for nonoxides, and limited differentiation of microplastic and flaw failure. It further indi-

FIGURE 6.22 σ–G–1/2 data for various ceramics at 1000°C normalized to the same Young’s modulus as Al2O3 (as in Chap. 3, Fig. 3.37 and Table 2). (From Ref. 1, published with the permission of the Journal of Materials Science.)

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FIGURE 6.23 σ–G-1/2 data for various ceramics at 1200°C normalized to the same Young’s modulus as Al2O3 (as in Figs. 3.37 and 6.22, and Table 3.2). (From Ref. 1, published with the permission of the Journal of Materials Science.)

cates that oxides tend to fall in a lower group and nonoxides such as SiC and Si3N4 in a higher group. This probably reflects some intrinsic as well as developmental effects. A possible difference is that oxides have more slip at elevated temperatures. Though this may temporarily increase strengths, e.g. as indicated for ThO2 and UO2, where strengths may become in part controlled by microplasticity (Figs. 6.16 and 6.17), much more study of dense quality bodies as a function of grain size and temperature is needed.

The extent to which brittle fracture extends to higher temperatures depends on the material, its microstructure, especially the amount and type of grain