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FIGURE 6.12 Relative Young’s modulus (E), fracture toughness (KIC), and strength (σ) of single and polycrystalline Al2O3 versus test temperature (normalized by taking the property value at 22°C = 1). X following the property designation (E, KIC, and σ) designates single crystal values (followed by the crystal orientation in ( ) if known). Numbers following the property and crystal designations give the source of the data (from listing, upper right). For polycrystalline values, grain sizes are shown in ( ) where pertinent and available. Curves designated σt are for true tensile testing of fibers (FP, a coarser grain pure alumina and PDR, a finer grain alumina-zirconia fiber). While most tests were in air, some were in vacuum or liquid N2. Note the change in scale between relative values of 0.8 and 1.1 in order better to differentiate the data there, and that E–T trends, especially for single crystals, are a key basis of comparison. (From Rice [1], published with the permission of the Journal of Materials Science.)

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800°C indicate a strength minimum at 400–600°C, and these and higher temperature tests showed little or no relative strength decrease from 22°C levels until 800°C and may often show a limited maximum at 600–800°C (also observed for some fibers, tested in true tension, designated by σt in Figure 6.12, or flexure).

Typical ice, i.e. solid H2O, has several properties, including strength, similar to Al2O3. This includes their single crystal basal slip and associated large strain rate sensitive yield drops, and scaling with the fraction of absolute melting point (i.e. homologous temperature), e.g. compare Higashi’s [121] and Kronberg’s [122] data and effects of solid solution species (e.g. Jones and Glen [123]). Thus Schulson et al.’s [124] strength for ice at –10°C ( 96% of the absolute melting temperature) provides not only information for ice but also some guidance for Al2O3. Their results showed a Petch-type relation for samples with and without purposely introduced sharp cracks (Fig. 6.13), implying similar behavior at similar relative strain rates for Al2O3 without other significant effects,

FIGURE 6.13 Tensile strength of ice at – 10°C with a strain rate of 10–3/s. Note the Petch behavior despite the testing being at > 96% of the absolute melting temperature, implying analogous behavior in Al2O3. (From Ref. 124.)

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e.g. from grain boundary phases. Thus their results indicate that Al2O3 can have brittle, Petch-type behavior at very high temperatures. Similarly, Dykins’ [125] results show the ratio of tensile strengths of ice stressed parallel or perpendicular with growth dendrites to be 3; with the latter strength decreasing from 1.4 to 0.9 MPa as the test temperature increased from –27 to –3°C which implies that similar grain orientation effects can substantially impact the high temperature strength of polycrystalline Al2O3.

C.Effects of Grain Size on Strength of BeO at Elevated Temperatures

Bentle and Kneifel [126] showed polycrystalline BeO strength averaging 10% greater at –196° than at 22°C in vacuum, suggesting a possible 15–30% increase for grain sizes > 40 m and a possible 5–10% decrease at grain sizes of 20–40 m. They also showed that testing in air or water vs. vacuum at 22°C reduced strengths of BeO (G 20 m) 8–10% and 15–20% respectively. Similarly, Rotsey et al. [94] showed a strain-rate dependence of BeO (G ≤ 3 m, P0.04) indicating 30% strength decrease in water vs. air at 22°C for circumferential ground (pressed) rods. Slightly higher strength but similar relative changes were found in air but no change in silicone oil. Annealed samples had higher strength and somewhat greater decreases ( 40%) for testing in air but decreased nearly 10% for tests in silicone oil.

BeO shows a typical Young’s modulus decrease with increasing temperatures, e.g. 15% by 1200°C [118,119] (Fig. 6.14). Tests of (as-grown) single crystals in vacuum at 500°C and 1000–1800°C [127] showed slip only at ≥ 1000°C, with strengths following the decrease of Young’s modulus with temperature fairly closely. Carniglia’s earlier σ–G–1/2 surveys [105,106] of BeO showed moderate or no strength decreases at fine grain sizes until > 800°C, with strength possibly increasing at intermediate temperatures. Though there was less differentiation of strengths versus temperature at larger grain sizes, there was even greater indication of strength, first increasing with increasing temperature and then decreasing. Bentle and Kniefel’s [126] data for 500–1300°C almost always showed a strength maximum at 500–1200°C which was > strengths at 22°C (Fig. 6.14). Samples made with 1% MgO (G 60–150 m) showed substantially lower strength maxima. Such maxima were not seen for slightly less ( 99.3%) dense samples (e.g. G 45 and 60 m) or with greater impurity contents (mainly 5000–7000 ppm F) than those shown in Fig. 6.14 (99.7–99.8% dense); instead strength was constant (e.g. 400–800°C). The tests of Chandler et al. [129] at 300–1200°C in air showed moderate ( 15–25%) relative strength maxima at 500–1000°C for 99.9% pure (UOX and HPA) (P 0.02–0.03, G 20 m), while a less dense (99.7%) pure (AOX) BeO showed σ–T closely following E–T trends. However, the same AOX BeO with G 50 m (P 0.04) showed a strength max-

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FIGURE 6.14 Relative Young’s modulus (E) and flexure strength (σ) for (as-grown) single crystal and polycrystalline BeO (normalized by taking the value at 22°C = 1). Curve designations are analogous to those of Fig. 6.12. Note that Bentle and Miller’s [127] and Bentle and Kniefel’s [126] tests were in vacuum (G 60 and 154m is with 1% MgO). Data of Fryxell and Chandler [128] is for both unoriented (from AOX powder) and oriented grains (from UOX powder), 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.)

imum at 1000°C, 35% > at 22°C, and UOX BeO with 0.5% MgO rising to a slightly lower maximum. Fryxell and Chandler [128], using the same materials and process, showed all specimens having a relative strength maximum at 500–800°C with the level of the relative maximum increasing with increasing grain size from 7–10% (G 20 m) through 20% (>G 50) to 40–43% (G 90m). There was typically a tendency for lower relative strength maxima with

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AOX BeO (no additive) than with UOX BeO (+0.5% MgO); the latter also showed preferred orientation increasing with increasing grain size. The absolute strength values were highest ( 200 MPa) for G 20 m and intermediate for G 50 m bodies for both AOX and UOX, the latter showing 50 and 65% grain orientation for the two grain sizes respectively. The 90 m G bodies had strengths of 100–130 MPa for AOX and 130–175 MPa for UOX with 80% grain orientation. Relative strength maxima at intermediate temperatures were also reported by Stehsel et al. [130] for three commercial cold pressed and one commercial slip cast and fired BeO and two (both commercial) of four hot pressed BeO samples tested. While the latter tests and those of Chandler and colleagues were in air, those of Bentle and Kniefel were in vacuum, indicating that these trends (e.g. the maxima) are not due solely, if at all, to environmental (e.g. H2O) effects. On the other hand, Carniglia et al. [131] showed strengths (in vacuum) of dense hot pressed BeO being 12% higher at –200°C vs. in air at 22°C (σ270 MPa), and 45, 51, and 27% higher respectively at 550, 1000, and 1500°C.

D.Effects of G on Strength of CaO and MgO at Elevated Temperatures

As noted in Chap. 2, Sec. III.B, KIC of MgO crystals increased in H2O (but not DMF) [132]. Both Janowski and Rossi [133] and Rice [134] showed that MgO crystal yield stresses decreased 20% and strength 15% (but with greater ductility) in water versus in air at 22°C. Both showed that crystal pieces tested in water returned yield and fracture stresses back to their original air tested levels when retested (dried) in air. Thus SCG has not been observed in MgO single crystals, but yield and fracture stress reductions have been, indicating enhanced dislocation mobility (as does the increased toughness and ductility). On the other hand, similar CaO crystal tests showed yield and fracture stresses increasing respectively by 5–25% and 5–35% in water versus air at 22°C [134]. Testing MgO crystals in liquid N2 raised yield stresses 80–130%, consistent with Copley and Pask’s [135] (compression) and Thompson and Roberts’s [136] tests and fracture stresses 10–15% versus in air at 22°C. Corresponding CaO crystal increases were 105% and 90% respectively. However, long-term exposure of CaO crystals to liquid or vapor H2O results in propagation of cleavage cracks attributed to the wedging action of resultant Ca(OH)2 in preexisting cracks [134].

Polycrystalline MgO tests by Janowski and Rossi [133] and Rice [134] showed strengths lower (e.g. 15%) in water than in air at 22°C; i.e. very similar to crystal tests. Both also showed recovery of the strength loss on drying and retesting in air. (Rice’s tests covered G 2–100 m, showing no grain size trend.) However, strength in air was only 10% lower than in liquid N2, i.e. only10% of the difference found for single crystals. On the other hand, Rhodes et al. [95] reported delayed failure in polycrystalline MgO [G 25–45 m, P

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0–0.007, and ≤ 0.02–0.6% impurities]. While the two finer grain bodies (G = 26 and 30 m) showed delayed failure at 50% of the inert strength (versus 80 and 70% for G = 46 and 43 m respectively), they were also the lowest purity (99.4 and 99.6 versus 99.98+ and 99.92% respectively). Thus they concluded that purity was the dominant variable in SCG, which is consistent with most of the impurities being at the grain boundaries with intergranular fracture (in contrast to mostly transgranular fracture in similar grain size bodies tested in air [137]). They also observed a possible fatigue limit ( 80%) in the highest purity body, which they postulated to be due to the absence of a continuous grain boundary impurity film.

Recrystallized CaO crystal bars at 1100 and 1300°C showed little or no strength decrease from 22°C. However, macroscopic yield frequently preceded brittle, almost exclusively transgranular fracture [134]. Limited polycrystalline MgO studies at moderate temperatures typically showed either an initial limited strength rise to a maximum at 400–700°C (especially as grain size increased) or a lower rate of decrease before more rapid strength decrease with increasing temperature. These polycrystalline strength trends are also supported by data of Evans et al. [138] (G 25 and 150 m, particularly for chemically polished samples). MgO single crystals recrystallized by pressed forging or hot extrusion [139,140] also showed little or no strength reduction with increasing temperature, some macroscopic yielding by 1300°C and extensively at 1500°C (but maintaining transparency and subsequent brittle, cleavage, fracture). While hot extruded MgO specimens from hot pressed and annealed billets showed similar strength for the same grain size as from recrystallized crystals at 22°C, the former showed a greater strength decrease at 1540°C, and the recrystallized crystals averaged twice the strength as hot extruded, hot pressed MgO. Similarly, while the latter showed somewhat greater occurrence of grain boundary fracture at 22°C, it showed much greater frequency and amounts of this at higher temperature than the recrystallized crystals [139,140]. The above trends (which are consistent with those of Day and Stokes [141], G 100 ± 50 m, T ≥ 1700°C) are put in better perspective by plotting properties normalized by their 22°C values (Fig. 6.15). This shows (1) a moderate Young’s modulus decrease of 10–15% by 1200°C, (2) substantially faster yield stress decrease (for <100> stressing), (3) strength constant or a strength maximum between 400 and 800°C, and (4) a trend for less strength decrease and higher relative maxima at higher temperature as grain size increases.

E.Effects of Grain Size on Strength of Other Cubic Single Oxides ThO2, UO2, Y2O3, and ZrO2 at Elevated Temperatures

ThO2 shows positive σ–G–1/2 slopes for finer grains at 22 and 1000°C but somewhat higher strength at 1000 vs. 22°C across the grain size range studied

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FIGURE 6.15 Relative Young’s modulus (E), yield stress (<100> single crystal, Y), and flexure strength (σ) of MgO versus test temperature (normalized by taking the property at 22°C = 1). Note that curve designations are analogous to those of Fig. 6.12, and that E–T trends, especially for single crystals, are a key basis of comparison. (After Rice [1], published with permission of Materials Science the Journal of).

[142,143] (Fig. 6.16). Collectively, UO2 flexure data [144–148] is consistent with the basic σ–G–1/2 model at 22 and 1000°C and indicates probable increased strength at 1000°C (Fig. 6.17). Diametral compression data [149] at 22°C also agrees with these trends. Individual data sets more clearly show strength increasing with temperature. Thus Burdick and Parker [144] showed UO2 strength increased to a maximum at 700–1100°C with net increases of 20–35% for G 20m (P 0.15–0.22) and 50–70% at > G 40 m (P 0.08–0.12). Knudsen et al. [145] showed 20% strength decrease for > G 45 m (P 0.1) and a 5 to 75%

FIGURE

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6.16 ThO2 σ versus G–1/2 at 22 and 1000°C. Data of Knudsen [142] corrected for variable porosity (superscripts in %) using b = 4.2 and 6.6 at 22 and 1000°C respectively per his analysis. Numbers with high temperature data points and below the error bars for tests at 22°C are the numbers of values averaged. Note the consistency of resultant corrected data despite quite variable P levels for different G bodies, and one data point of Curtis and Johnson [143]. (From Ref. 1, published with the permission of the Journal of Materials Science.)

increase for G = 20–25 m (P 0.08–0.24) between 22 and 1000°C. Evans and Davidge [146] showed no strength increase with initial temperature increase for their G = 8 m UO2 till 500°C, and then a significant rise, peaking at 800°C (a 35% total increase) before decreasing again. Their 25 m G body showed a longer, slower strength rise, peaking at 1100°C with a similar net increase before decreasing. Beals et al. [147] showed a similar σ–T increase and maximum strength (G 25 m, P 0.03). Canon et al. [148] showed that strength increased slowly to a maximum (about 20% higher than at 22°C) at 1400°C and then dropped sharply, for bodies with G = 8, 15, and 31 m.

While ZrO2 single crystals (11.1 m/o, 18.5 w/o Y2O3) show a typical Young’s modulus decrease (e.g. 1–2%/100°C) with increasing temperature to the limit of testing (700°C), polycrystalline behavior is more complex [150]. Polycrystalline ZrO2 (CaO or MgO) stabilized showed somewhat greater Young’s modulus decreases to 400°C and then transitions to an extrapolation of the above single crystal data [81,150]. Wachtman and Corwin [151] showed an internal friction peak in ZrO2, generally in the 300–400°C range but decreasing some

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FIGURE 6.17 UO2 σ vs. G–1/2 at 22 and 1000°C. Data of Burdick and Parker [144], Knudsen et al. [145], Evans and Davidge [146], and Canon et al. [148] are for flexure at both temperatures. (Data of Kennedy and Bandyopandhyay [149], only at 22°C and from diametral compression, is not plotted, but showed a similar, lower trend.) Note data plotted as-measured with P 0.02 for Canon et al. and 0.03 for Evans and Davidge, while Knudsen et al’s. data was corrected for P (= 0.05–0.24, mostly 0.05–0.1) and Burdick and Parker (P = 0.08–0.12) using b = 3 (a 2 next to some data points indicates two identical points). Kennedy and Bandyopandhyay’s data are plotted as-measured for P = 0.03–0.09 (shown next to data points). Note there is no trend for strength to decrease from 22 to 1000°C, and in fact strength appears to be greater at 1000 than at 22°C.

in magnitude and in the temperature of the maximum as the CaO content increased from 2 to 20%. Shimada et al. [152] showed an initial somewhat greater Young’s modulus decrease to 400°C and then (within the 650°C limit of testing) a similar transition as above for dense (P 0) sintered ZrO2 (+ 3 m/o, 5.5 w/o Y2O3), as have Adams et al. [153] for sintered (P 0.02–0.07, G = 15–50m) and hot pressed (P 0.005–0.02, G 1–3 m) ZrO2 (+ 6.5 m/o, 11 w/o, Y2O3). Adams et al. also showed that their ZrO2-Y2O3 and a commercial ZrO2- Y2O3 body (with 1 w/o SiO2) had a much greater Young’s modulus decrease from 100 to 400°C than three commercial ZrO2-MgO bodies tested. Rapid initial E–T decreases have also been more recently reported for (1) ZrO2 + 33m/o Tb4O7 between 200 and 500°C (but not with 33 m/o Pr6O11) [154], (2) 3 m/o

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Y2O3 between 22 and 300°C [9], and (3) 2 m/o Y2O3, + 8 m/o Y2O3, and 12 m/o CeO2 (with respectively similar, greater, and smaller decreases, the latter when the CeO2 was partly reduced, but no effect when it was fully oxidized) [10]. In the latter two cases, as well as that of Shimada et al., the anomalous Young’s modulus decreases were associated with maxima or high levels of internal friction. Nishiyama et al. [11] also recently reported an internal friction peak at 150°C in ZrO2-2.8 m/o Y2O3. These ZrO2 changes are corroborated by similar effects of Dole and colleagues [98] in HfO2, i.e. an internal friction peak in unstabilized (monoclinic) HfO2 at 400°C, and drops in both Young’s and shear moduli and an internal friction peak in HfO2-20 m/o Er2O3.

While fully stabilized ZrO2 crystals (22 w/o Y2O3) show essentially no strength changes till T 1500°C [64], polycrystalline strengths show similar but greater deviations from E–T trends (Fig. 6.18). Thus the lack of significant single crystal strength changes between –196 and 22°C indicates limited, or no, single crystal SCG. Partially stabilized (6 w/o Y2O3) crystals (which start from about fourfold higher strength than fully stabilized crystals) show an initial strength decrease much greater than that of Young’s modulus until 500°C; then it levels off (at twice the strength of fully stabilized crystals) until 1500°C. Adams et al.’s tests of sintered and hot pressed ZrO2 (+ 11 w/o Y2O3) [153], though scattered, showed an average initial trend similar to the PSZ (6% Y2O3) crystals but continued to have much greater strength decrease than Young’s modulus decrease, to a modest minimum at 700°C. Drachinskii et al. [155] showed a slightly greater strength decrease to the limit of their tests (500°C, Fig. 6.18) in ZrO2 + 4 m/o ( 7 w/o) Y2O3 sintered and then annealed substantially. However, specimens with limited annealing after sintering dropped to a strength minimum of 80% of their 22°C values at 100–200°C and then rose to a strength maximum at 300–400°C that could be similar or > (e.g. 35%) strengths at 22°C. Higher temperature tests of some of these lesser annealed samples showed first a strength minimum at 700°C (e.g. Adams et al.), but strength values ranged from 50% relative to 22°C down to 30% relative to their strength maxima at 300°C (i.e. in either case less relative decreases than for Adams et al.); then there was a strength maximum at 1000°C. Such greater strength deviations and complexities are apparently not limited to ZrO2-Y2O3 bodies, as shown by Neuber and Wimmer [81], who report greater strength decrease than of Young’s modulus with increasing temperature, and probable inflections at 300 and 800°C (Fig. 6.18) in ZrO2 (with 5 wt% CaO or MgO).

Fracture mode changes accompany the above ZrO2 strength decreases with increased temperature (Fig. 18), e.g. Adams et al. [153] saw mostly transgranular fracture at 22°C, mixed transand intergranular fracture at 1000°C, and 100% intergranular fracture by 1500°C in their ZrO2 ( 11 w/o Y2O3) bodies, similar to PSZ (2.4 w/o MgO) [64]. Drachinskii et al. [155] observed transgranular fracture varying from 40 to 90% for specimens of various annealing in tests at 100°C, with the least transgranular fracture being for the lowest strength (180 MPa), but