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Fe, Si, and P. Dynamic fatigue tests conducted on higher purity TiB2 [74] as a function of a wider range of G showed limited intergranular penetration of molten Al into the TiB2, but no intergranular crack growth, i.e. transgranular fracture from surface connected, e.g. processing, flaws. However, dynamic fatigue tests were consistent with changing behavior as a function of G, showing generally increasing negative n values [i.e. of Eq. (2.3)] of 30–80–100 as G increased from 1–3 m and then becoming increasingly positive values of 44 and 53 as G increased to 10 and then 17 m. Baumgartner argued that the failure process was liquid metal embrittlement, i.e. a lowering of strength due to lowered toughness from the presence of liquid Al at the crack tips, instead of stress corrosion, which entails lowering of strength due to SCG. He also suggested that the trend in n values could be explained by possible competition of plastic blunting of cracks decreasing as G increased, i.e. mainly in finer G, stronger bodies, versus liquid metal embrittlement via reduced toughness at the crack tip. Thus the latter would be mainly operative in the absence of crack tip blunting in larger G bodies, where microcracking from TEA stresses was also present and probably contributing, especially in the largest G body.

Of the few studies of crack propagation and fracture energy and toughness in graphite, one examined crack propagation as a function of temperature and environment (e.g. atmospheres of H2O, CO, or He). Thus Freiman and Mecholsky [75] showed that both an isotropic (POCO-AXF-5Q) and an anisotropic (ATJ-S) graphite exhibited stable crack propagation to respectively 800 and 1600°C in H2O, CO, or He atmospheres. Above these temperatures crack propagation was catastrophic. They attributed the stable crack propagation to stress corrosion due to H2O in the pores (hence explaining no influence of the external test atmosphere, and consistent with strength results). They showed fracture energies in both materials increasing by of the order of 50% and fracture toughnesses by about 20% from 22 to 1400–1600°C. Similarly Sato et al. [76] showed fracture toughnesses of their three isotropic (molded) and one anisotropic (extruded) graphites increasing by respectively 50 (for the anisotropic, extruded material) and > 80% to maxima at 2100°C or at, or beyond, their maximum test temperature of 2600°C. These changes are substantially more than they found for Young’s modulus of these same graphites (and about the same or intermediate for tensile strength), but similar in overall trend. Extruded material had the lowest toughness and the least increase, consistent with its measurement being with the oriented grains versus those of the molded graphites being across the grain orientation.

Turning to discussing the grain structure dependences of toughness and crack propagation as a function of temperature, there is limited data on the basic, intrinsic factors of this, namely grain size (G), as well as shape and orientation. Further, such possible grain effects are compromised by the frequent dominant effect of grain boundary effects, since small amounts of grain boundary phases

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can dominate higher temperature crack propagation and toughness, usually enhancing the former and limiting the latter. Such phase effects can readily mask effects of substantial changes in G since, for a fixed volume of grain boundary phase, its amount along an average grain boundary scales with the G, i.e. if G doubles so does the amount of the boundary phase along an average grain boundary. However, the first and clearest experimentally of four factors is that grain structure still has an important role in these processes and the substantial dependence of tensile strengths on basic grain parameters shown in the next section. This reflects both the more extensive strength data and the frequent differences, mainly due to crack scale effects, especially relative to the microstructure, between crack propagation and related measurements versus those in determining strengths. Second is the clear effects of different crystal planes, which, while often diminishing with temperature, are clearly significant, and sometimes complex (e.g. Fig. 6.1), which clearly imply basic effects of grain shape and especially orientation if not masked or overridden by grain boundary phase effects. Third are differences between the temperature dependences of E and K, which mainly aid confirmation of grain boundary effects. Fourth, and also basic, is expectations from other models and behavior, namely fracture at lower temperatures, e.g. 22°C, as is extensively discussed in Chap. 4, and high temperature behavior, e.g. as reflected in the G dependence in Eq. (6.2).

IV. EFFECTS OF GRAIN SIZE AND TEMPERATURE ON TENSILE (AND FLEXURE) STRENGTHS

A.Effects of Environment on the G and T Dependence of Strength, Including at T < 22°C

As discussed in Chap. 2, Sect. III.B, slow crack growth can occur at room temperature due to the effects of an active fluid, especially gaseous, species that alters or breaks crack tip bonds, with H2O being one of the most severe and prevalent of such species. Thus strength testing at lower temperatures reduces the activity and mobility of active species, especially if they are solidified, i.e. strength testing in liquid nitrogen, hence at its boiling point of –196°C, essentially halts most SCG, including that due to H2O. This allows a ready test for SCG and assessment of the extent of SCG by comparing strengths at –196°C and a higher temperature, usually 22 °C, since the 1–4 % increase in strength due to increases in E at –196 versus 22°C is negligible to most strength increases due to essentially eliminating SCG at –196°C which are typically 10 to > 50%. Further, such tests often allow changes in flaw sizes due to SCG to be observed by subsequent fractography or implied by changes in strengths and toughnesses. Such tests also indicate that the occurrence of SCG is either (1) intrinsic, if the failure initiating flaw (and usually also surrounding) fracture mode is mainly or

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exclusively transgranular, or (2) extrinsic, due to grain boundary character, usually phases, if the failure initiating flaw (and also possibly surrounding) fracture mode is mainly or exclusively intergranular as shown by Rice and Wu [77]. Thus they showed that such tests, while corroborating SCG in silicate glasses and Al2O3, showed increasing SCG in CeO2, Y2O3, ZrO2, and TiO2 respectively, while no SCG occurred in refractory borides, carbides, and nitrides such as TiB2, ZrB2, SiC, TiC, ZrC, AlN, and Si3N4, which in pure form (e.g. from CVD) exhibited more or exclusive transgranular fracture, unless there was sufficient oxide containing grain boundary phase and resultant substantial to exclusive intergranular fracture. There can also be special cases where there are environmental interactions with slip or twinning that may affect strengths, but these are mostly uncertain and limited.

Turning to specific σ–G–1/2 data, Figure 6.9 summarizes much alumina data at –196 versus 22°C [2,3,31,78–85], which while scattered shows a trend for higher strengths at –196°C, especially when data from the same investigators and bodies are compared, e.g. that of Charles [86] and Gruver et al. [84]. Overall this shows (1) the same two-branch σ–G–1/2 behavior, (2) both with finer grain size σ–G–1/2 slopes > 0. (3) single crystal strengths > many polycrystalline samples with similar surface finishing [2,78–82], and (4) greater singleand polycrystal strengths at –196°C versus 22°C. While some data, e.g. for press forged Al2O3 [3,83], does not clearly show increases at –196°C vs. 22°C due to scatter and the limited extent of the data, specific comparisons more clearly show single- and polycrystal strength increases. Thus Heuer and Roberts [80,87] showed sapphire strength increasing 35–50% in liquid N2 (–196°C) vs. 22°C in air for various surface finishes. Other investigators [89–91] showed similar increases, but Charles [86] showed a 75% increase. For dense hot pressed Al2O3 tested at –196°C, Rice [2] showed a 30% strength increase for most grain sizes but a 45% increase for G = 1–2 m. Similarly, Charles showed 20% strength increase for lamp envelope Al2O3 (G 6–150 m), Neuber and Wimmer [81] a 30% increase for 99.5% Al2O3 (porosity, P, 0.05, G 35 m), Davidge and Tappin [82] a 25% strength increase for 95% Al2O3, P 0.07, G 8 m, and Gruver et al. [84] a 30% increase for 96% Al2O3, P 0.05, G 7 m (Fig. 6.9) in liquid N2 vs. air at 22°C. Overall the polycrystalline strength increase is probably less than for sapphire (except possibly at G 1–2 m), reinforcing sapphire strengths being even > many polycrystalline values at –196°C versus 22°C. Tests in the absence of H2O at 22°C (e.g. in vacuum) showed that much, but not all, of the increase in strength at –196°C is due to the elimination of slow crack growth (SCG). Thus Charles showed sapphire strength increased only 17% at –196 vs. 22°C but decreased 50% in wet air vs. vacuum at 22°C, while lamp envelope Al2O3 (G 40 m) showed only about an 8% increase and an 44% decrease respectively; i.e. indicating less increase in liquid N2 but similar decrease in wet air to that of sapphire. He also showed an 20% increase in 22°C (air) strength for

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FIGURE 6.9 Comparison of σ–G–1/2 data, mainly for hot pressed and pressed forged, Al2O3, at (A) – 196°C and (B) 22°C. For reference, the range of data from an earlier survey [1] of data at 22°C is shown in (A) and the mean trend line for actual data at –196°C from (A) is shown in (B) as a dashed line. Note the (1) generally lower strengths of the author’s specimens made from Linde B versus Linde A powders, (2) greater scatter and possible lower strength level of the pressed forged vs. hot pressed Al2O3 , the latter mainly at finer G ( 10 m), (3) single crystal strengths being higher than much of the polycrystalline data at –196 and 22°C, and (4) direct comparison of Charles [86] and Gruver et al.’s [84] data (the latter labeled Kirchner) at both temperatures. (From Rice [1], published with permission of the Journal of Materials Science.)

a substantial G range ( 6–150 m) at a strain rate of 2.7 10–4 vs. 1.410–2/min. The lower strengths of bodies made from Linde B powder may reflect more anion impurities [1], while some lower strengths and greater scatter of press forged specimen strengths probably reflects more variation in grain size shape and orientation, and possibly of residual stresses.

Assessing whether the absence of SCG at –196°C shifts the G dependence of strength, e.g. due to possible effects of G on SCG (Fig. 2.8), is difficult due to the variations noted above, as well as complexities of the actual SCG. Thus the occurrence of SCG in single crystals, at rates generally similar to those of polycrystalline Al2O3 [92] (Chap. 2, Sec. III.B) indicates that transgranular

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SCG can occur in polycrystalline materials and thus may not impact the sin- gle–polycrystal strength balance. While SCG occurs in sapphire, the first of two complications is that sapphire SCG has been measured on only a few fracture planes, and the extent of less, or no, SCG on other planes is not known. Second and more basic is that SCG in polycrystalline Al2O3 is mainly or exclusively by intragranular fracture (which may reflect the preceding complication), especially at finer grain sizes (Fig. 2.6) in contrast to more transgranular fracture commonly observed in fast fracture, and may decrease with decreasing G (Fig. 2.8). Changing SCG as a function of G could change the intersection and slopes of the two branches of the σ–G–1/2 behavior.

McMahon [93] showed strength of sintered, high Al2O3 bars at 22°C being a function only of surface finish and relative humidity (to 70%) during the test, and not of prior humidity exposure. He showed that the relative level of strength and its decrease due to H2O varied as follows for different specimen surface conditions: (1) as-fired surfaces gave the lowest strength and the least ( 5%) strength decrease, (2) surfaces ground perpendicular to the specimen axis gave intermediate strengths and the greatest ( 15%) decrease, and (3) surfaces ground parallel with the specimen length gave the highest strength and an intermediate strength decrease with increasing relative humidity. Thus the relative strength decrease with increasing humidity was a function of surface finish as well as moisture content. Rice [80] showed that dense, hot pressed Al2O3 averaged 20% strength decrease on testing in distilled H2O vs. air at 22°C, but that retesting in air of bar sections previously tested in H2O (after drying) returned them to their original air strength. These two studies show that strength degradation due to SCG occurs during actual loading and is a function of the environment only during stressing. This implies that SCG either does not occur due to microstructural (e.g. thermal expansion anisotropy, TEA) stresses or that it saturates (at least for typical multigrain size flaws) after initial exposure.

SCG also occurs in polycrystalline BeO [94] where the specifics of the SCG fracture mode are poorly documented (the overall fracture mode for tests in air at 22°C is predominantly transgranular). While SCG does not occur in some single crystals such as MgO and apparently ZrO2 [77], it can occur intergranularly in MgO, as shown by Rhodes et al. [95]. More SCG in finer versus larger grain MgO ( 25 m vs. 45 m) is uncertain because of impurity differences but may imply a grain size effect in view of there typically being thicker grain boundary phase as grain size increases. Whether there are intrinsic differences in SCG rates between materials exhibiting only intergranular versus at least some transgranular SCG is unknown. In contrast to the above oxides, fast fracture in a Mn-Zn ferrite [96] was mainly by intergranular fracture, while SCG occurred mostly by transgranular failure, especially with G 45 m and somewhat less with G 35 m with more grain boundary (e.g. Ca) phase, again suggesting possibly greater effects at finer grain size (Chap. 2, Sec. III.B and Chap. 2 end note).

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Li ferrites show SCG, which has also been reported to be sensitive to losses of Li on firing [97], which may imply gradients of stoichiometry between grain boundaries and the rest of the grain, which could be a factor in changing fracture modes and in possible grain size effects. Significant decreases in Young’s modulus and internal friction increases of HfO2 [98] occurred upon opening the vacuum furnace (after sintering or heat treating for grain growth), saturating after only 2 days; thus indicating microcracking from TEA stresses alone and SCG saturates in limited time in the absence of an applied stress.

Though noted in Chap. 2, Sec. III.B, it is again worth noting that corroding species which do not lead to SCG may also reduce strengths. Thus CaO and MgO crystals do not exhibit SCG due to H2O, which attacks them independent of stress to produce hydroxides, whose expanded volume, when this occurs in constrained locations, especially pores or cracks, results in fracture due to repeated stages of stress buildup and release by cracking over days to weeks for CaO and much longer for MgO. Similar effects occur in polycrystalline bodies, where pores accessible from the surface are also important sources of this hydration damage. Possibly more extreme is the substantial to complete degradation of some TZP bodies over certain ranges of Y2O3 contents and G (Fig. 2.9).

Regarding nonoxides, SCG has been shown in some halide single crystals, e.g., AgCl and CaF2, the latter also showing probable effects of slip limiting the extent of SCG, e.g. via easier arrest of cracks [92]. SCG in polycrystalline MgF2 and ZnSe being 100% intergranular (whereas fast fracture is essentially 100% transgranular) indicates grain boundary control of SCG in these materials. McKinney et al. [99] reported essentially no SCG with large-scale cracks, e.g. DCB or DT tests, in various Si3N4 materials and no small-scale SCG (i.e., no delayed failure in pure Si3N4, made by either CVD or reaction sintering), but clear delayed failure in Si3N4 made with oxide additives (with the extent of SCG generally increasing with the amount of oxide additive) via all intergranular fracture. They attributed this large vs. small crack behavior to oxide distribution along grain boundaries, i.e. maintaining that of the many flaws available on the surface for SCG, at least one could always be found that had sufficient contiguity of grain boundary oxides for sufficient SCG to lower strength. On the other hand, large cracks, as used in a DCB test, covered too broad a range of grain boundaries, many of which may not have sufficient contiguity of oxide content to allow continuous SCG. Recently SCG has been reported (via essentially 100% intergranular fracture) in AlN [100,101] on a similar or lower level than in Al2O3, with the extent of SCG apparently correlating with the residual oxide grain boundary content [92]. While there appears to be intrinsic SCG in carbon materials [75,92], SCG does not appear to occur in carbides, e.g. B4C, SiC, TiC, and ZrC (or borides, e.g., TiB2 and ZrB2) unless sufficient grain boundary phase (e.g. oxide) is present to provide the material and path for SCG [77,99]. Thus SiC made with oxide addi-

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tives shows SCG, but not SiC made with B-C additions or by CVD (i.e. without additives), i.e., paralleling the Si3N4 results. This is corroborated by such materials showing no SCG exhibiting predominant to exclusive.

As test temperatures increase, e.g. to and beyond a few hundred degrees C, the amount of active species such as H2O is commonly reduced, reducing the amount of SCG. However, in some cases active species may be contained in pores, causing SCG at high temperatures independent of the external test environment, as was indicated earlier in graphites. On the other hand, at higher temperatures other species may cause corrosive damage or SCG, e.g. due to their liquefaction (hence mobility), increased reactivity, or both. As noted in the previous section, oxidation of nonoxide materials can be an important manifestation of this, especially if either there is a grain boundary phase that will combine with the oxidation product, e.g. to form a softer, more reactive glass, or the nonoxide produces oxide liquid or glassy phases, e.g. B2O3 or SiO2.

B.Effects of Grain Size on Strength of Al2O3 (and Ice) at Elevated Temperatures

Increasing temperatures above 22°C in air generally decreased sapphire strength [26,29,85–91,102–104] often drastically, e.g. losing 1/3 to 3/4 of its strength at 22°C upon reaching a minimum at 400–600°C depending on orientation (Fig.

6.1), surface finish, and test environment. Hurley [103] observed a rapid strength

° - < >

decrease from 22 to 400 C for both, <1120>and c-axis ( 0001 ) filaments and then a plateau to 700 and 900°C respectively before rapidly decreasing again. (However, compression testing of sapphire rods of the same orientations showed respectively a slow decrease, similar to that for Young’s modulus, and then a very rapid decrease starting at 800°C.) The level and especially the temperature of the strength minimum can be affected by other parameters. Charles [86] showed a strength minimum at 900°C for sapphire tested in air as-annealed (1200°C) vs. 400–600°C for mechanically finished surfaces. These tests in various atmospheres showed sapphire strength decreasing by 15% to a minimum at600°C in vacuum with less decrease in dry or wet H2 (but strength 20% lower in dry H2 than in vacuum and 20% lower for wet versus dry H2) before all merging together at 900°C. Iwasa and Bradt’s [26] (indentation-fracture) fracture toughness tests of sapphire oriented for basal or rhombohedral fracture showed similar trends; i.e. decreasing 25 and 75% to minima at 800 and 1000°C respectively (Fig. 6.1). (Their KIC tests of sapphire oriented for fracture on A or M planes follow the decreases of Young’s moduli with increasing temperature.) Less strength decrease, i.e. a higher minimum strength (but at a somewhat lower temperature) was indicated in one [89] but not another [91] test of Cr doped sapphire. However, Sayir et al. [104], who observed strength minima at 300°C and maxima at 900°C in undoped sapphire, reported that 500 ppm MgO

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or TiO2 (separately or combined) doping eliminated the minima and maxima. Carniglia’s surveys [105,106] of the σ–G–1/2 behavior of Al2O3 showed

strengths of finer grain size, dense bodies at 400°C the same as at 22°C and then decreasing at a moderate rate up to 1000–1200°C and more rapidly beyond 1200°C. Differentiation of strength as a function of temperature in the larger grain size region was even more moderate. (Correcting for Carniglia’s failure to plot all data at 22°C and erroneously plotting some data at higher strength reduces the limited differentiation his plot showed between fine grain bodies at 22 and 400°C.) Charles’ [86] testing of lamp envelope Al2O3 (G 40 m) showed strength constant from 200–600°C and then dropping gradually (e.g. 5%/100°C) in vacuum, while tests in dry and wet H2 (the latter again at lower strength levels as for sapphire) showed a strength minimum at 400°C and a maximum at 1100°C. Neuber and Wimmer’s [81] air testing of a ≥ 99.5% Al2O3 (P 0.05, G 35 m) showed distinct strength minima (at 400°C) and maxima (at 800°C, Fig. 6.12) for each of four sets of rods having diameters of 2–8 mm, with the strength levels slightly lower for each increase in diameter. Kirchner et al. [107,108] also showed a definite strength minimum at 400°C for their dense hot pressed Al2O3, tested as-polished, or strengthened by surface compression from quenching in silicone oil. The quenched material also showed a strength maximum at 800°C; however, there was substantial scatter in both the maxima and minima for their bodies. While Jackman and Roberts [91] clearly showed such maxima and minima for single crystals, their tests of a 99.3+% Al2O3 (P 0.05, G 50 m) showed only an uncertain indication of a strength minimum at 500°C. Mizuta et al.’s [109] HIPed, transparent Al2O3 (uniform G 1–2 m) showed no maxima or minima; instead strength was constant at 780 MPa to > 1000°C and then dropped to 700 MPa at 1100°C. Thus such minima, maxima, both, or a plateau at intermediate temperatures are shown in almost all [80,87,88,90,110] (Fig. 6.12) but not all [80,103] Al2O3 studies.

Al2O3 σ–G–1/2 data [84,85,88,89,111–113] at 1200–1315°C (Fig. 6.10) shows similar two-branch behavior but with lower strength (e.g. 50%, possibly more at fine grain size) than at 22°C, with reasonable agreement between different studies. Again, higher single crystal than many polycrystalline strengths are seen, as is a σ–G–1/2 slope > 0 at finer grain size. While strength–temperature data for bodies of various grain sizes shows the overall expected strength decrease with increasing grain size, there is commonly a limited maximum, or at least a strength plateau over a significant intermediate temperature range (Fig. 6.11).

Impurities or additives may or may not have significant effects in this temperature range. Thus there was no effect of AlON additions (other than via grain size) on strength (or KIC) to at least 800°C [114] nor of CaO [31]. Crandall et al. [85] showed similar trends for Al2O3 hot pressed with or without 3% SiO2 (Fig.

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FIGURE 6.10 σ–G–1/2 data, mainly for hot pressed and pressed forged Al2O3 , at 1200–1315°C. Note the general consistency of data from different sources and its indication of a two-branch σ–G–1/2 relationship with the finer G branch having positive slope, and the generally lower strengths relative to those for single crystals. (Published with permission of the Journal of Materials Science.)

6.11). However, typical commercial (sintered) Al2O3 having an SiO2-based (usually) glass phase commonly shows an intermediate (strain-rate-,composition- and possibly P-dependent) strength maximum at 700–1100°C, and then greater strength decreases [83,110] at higher temperature.

Al2O3 based polycrystalline fibers show similar strength–temperature trends. Tests of pure α–Al2O3 (Dupont FP) and Al2O3-SiO2 fibers show the same strengths at 22° and 800°C, only moderate ( 10%) decrease by 1000°C, and then a more rapid decrease [115-117] (Fig. 6.12). Al2O3-20% ZrO2 fibers show 10% higher strength at 800°C before dropping back to the same strength of 22°C at 1000°C (and more rapid decrease at higher temperatures. Neither set of fibers was tested at 22°C < T > 800°C).

The above strength changes with increasing temperature (T) are put in broader perspective by comparing singleand polycrystal Al2O3 (including fiber) strength normalized by their values at 22°C, along with similar Young’s modulus

(E) and KIC normalization (Fig. 6.12). This shows the well-known steady E–T

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FIGURE 6.11 Flexure strength versus test temperature for different Al2O3 bodies reflecting primarily different grain sizes and secondarily some composition and processing differences. Note that the solid symbol of Crandall et al. [84] is for Al2O3 + SiO2, and that the open symbol is for pure Al2O3, as is all other data except that of McLaren and Davidge [110]. (From Rice [1], published with permission of the Journal of Materials Science.)

decrease of 10–20% for both singleand polycrystals by 1200°C [108–120]. This is in marked contrast to a typically much faster initial decrease of both relative crystal KIC and strength (typically oriented for basal or rhombohedrahl fracture), toward minima at 400–800°C and then rising to pronounced strength maxima that can be ≥ to that at 22°C and then falling (rapidly). While absolute strength values vary as expected (e.g. with surface finish), these trends occur for crystals of various orientations [80,89,91] and machining [80,89], as well as asgrown (0°) crystal filaments [102]. Again, while sapphire strength values are higher when H2O is not present, or with reduced activity, the trends are also relatively independent of the environment, since the basic trends are similar, whether the testing is done in vacuum or in air. Most polycrystalline tests at T > 22°C, <