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resulted in lower strengths on separate branches, while in the larger G region coarser finishing also resulted in lower strengths, but in one basic larger G branch. The polishing results of Chantikul et al. [131], though also entailing some probable benefit from biaxial testing (i.e. no edge failures), is consistent with higher strengths with finer finishing. [Note that Tresssler et al.’s [24] data for Al2O3 hot pressed with MgO (Ga 2 µm) or without MgO (Ga 3, 12, or 18 µm) generally agreed with other data whether plotted vs. Ga or, as they did, vs. Gm (Gm 3.3 and 4.3 µm for the two finest G bodies, but 80 – 100 µm, due to scattered large platy grains found at fracture origins, in their two largest G bodies). However, their data is insufficient to prove their claim that the fine G slope = 0; it is at least as supportive of a positive slope (though complicated by their use of Gm, see Sec. V.B). Also note that (1) Chantikul et al.’s [131] model is not correct, since the σ–G-1/2 behavior is basically the same in cubic and noncubic ceramics and thus is not determined by TEA effects as they proposed, and (2) there are important machining effects when the flaw and grain sizes approach each other [142–144] (Fig. 3.33), as is discussed later.

Again an important component of the σ–G-1/2 model for understanding failure mechanisms is relating strength and fractography of single crystals of the same material with the same or similar surface finish, i.e. sapphire in this case, focusing on weaker single crystal orientations (which are also typically the ones tested), since these are likely to dominate failure in larger G polycrystals. Rice’s [15] data for Verneuil crystals of two different orientations and machining parallel with the tensile axis agrees well with earlier data of Wachtman and Maxwell [145] (σ 350–700 MPa) and of Heuer and Roberts [17, 146] (σ 450 MPa) for unspecified machining (presumably parallel to the tensile axis) of similar sapphire. Again, polycrystalline strengths are frequently below those for single crystals with similar finishing, and machining perpendicular to the tensile axis reduces most strengths [15], often substantially. Mechanical polishing also gave single crystal strengths of 450 MPa, which increased to 600–900 MPa with subsequent annealing [17, 146], consistent with no grain boundary grooving on crystal specimens.

Definitive fractography of polycrystalline Al2O3 is more difficult, especially as G increases, but machining flaws have been found in some finer G bodies, where they are > G as expected (Fig. 3.16). In single crystals, definitive machining flaws are frequently found and are of similar size and character to those in similarly finished polycrystalline bodies. For bodies of intervening G, definitive machining fracture origins are generally not found, but probable or certain origins from larger grains or clusters of them occur [3, 11–13, 138] (Figs. 1.2A,B, 1.3A,B, 1.4).

Next consider effects of phases added, usually in limited amounts, for limiting G. Such additions were an important factor in extending the G range, especially with low to 0 P, but raises questions of additive roles in σ – G behavior.

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FIGURE 3.16 Examples of machining flaw fracture origins from semielliptical machining flaws in alumina bodies ground perpendicular to the subsequent tensile axis.

(A) Flexure tested sapphire bar ( 300 MPa); flaw: semielliptical feature bottom center of photo. (B) Large tensile tested hot pressed Al2O3 round, dumbbell specimen (280 MPa); flaw: large semiellipse across bottom 1/3 of photo. Since these flaws are from different machining conditions, they cannot be directly compared quantitatively, but qualitatively they show overall similarity of flaw sizes given statistical variations of machining and testing, e.g. due to flat versus round machined surfaces and large differences in surface areas and resultant flaw population sampling.

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MgO, the most common additive (often at ≤ 1 %), can be very effective in controlling G with resultant strength increases mainly, or exclusively, as a result of the reduced G, as was indicated above (but local, substantial, excesses of it can be quite detrimental [16]. Several other additives also appear to have little or no effect on strength other than increasing it via resultant finer G. Thus McHugh et al. [140] showed that sintered Al2O3 strengths increased with additions of fine Mo particles up to 6 v/o due to reductions in G, then remained constant to the limits of their study of 16% addition. Similar improvements were noted in another study using diametral testing [141], and for addition of W or ZrO2, as is discussed below. While some negative effects of other constituents occur, as is noted later, specimens with up to several percent silicate phase [121–129], 30% AION [147], and 25% Cr2O3 [10, 148], indicate limited, or no, effect of these phases, other than via their effect on G.

Consider now data for specimens with as-fired surfaces, typically from extruded rods. Data of Charles [149] for (lamp envelope quality) Al2O3 extruded, as-fired rods ( 1.7 mm dia, noting inhomogeneous G only in the next- to-largest G body) clearly shows a two-branch curve with the finer G branch having a significant positive slope (Fig. 3.17). Alford et al.’s [27] extruded (< 1 mm dia., as-fired) rod strengths are much higher, presumably reflecting the small-size) high-quality as-fired finish, and possible (unexamined) preferred orientation (e.g. reflecting the 1.5 aspect ratio of their Al2O3 powder particles and the small rod diameter, implying a high reduction ratio). However, their data is at least, if not more, consistent with a positive finer G branch slope rather than their proposed slope of 0. Their one fractograph indicating fracture from a cluster of three larger grains raises issues of the rationale of using the large G in such cases, as is discussed later (Sec. IV.B). Note that their strengths of machined bars ( 2.5 mm thick of unreported orientation relative to the pressing direction for the original disks) made from the same Al2O3 powder are similar to those of others but tend to lower strengths, especially at finer G in view of their use of Gm ( 3 Ga). This lower σ is reasonable in view of the large (e.g. 100 µm) processing defects (e.g. laminar voids), and as-sawn surfaces. Alford et al.’s use of maximum σ (σm, i.e. the outer fiber stress) is inconsistent with their use of Gm, since such round rods have such a small σm region and thus a low probability of failure occurring at σm with significant microstructural heterogeneity. Their proposed 0 fine G slope for their extruded rods (though affected by use of Gm and probable orientation effects) is far less than for similar extruded Al2O3 rods. Baily and Barker’s [150] and Blakelock et al.’s [151] data for smaller (<1 mm dia.) extruded, sintered Al2O3 rods vs. Ga showed positive slopes, which are also supported by these data extrapolating to σ–G values for Al2O3-based fibers (Figs. 3.17, 3.18). Hing’s [152] data for as-fired Al2O3–W (isopressed) rods (Fig. 3.17) clearly showed a two-branch behavior with > 0 slopes for the fine G branches and agrees with other as-fired or machined Al2O3

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FIGURE 3.17 Strength–G-1/2 data for alumina bodies with primarily as-fired surfaces. Nominally pure alumina bodies of Charles [149], extruded 1.7 mm rods asfired, and Alford et al. [27], high strength extruded rods (< 1 mm dia.), both tested as-fired. The solid lines for Alford et al.’s data are their original lines; the dashed lines are an equal or more probable alternative. Bailey and Barker’s [150] data (vertical bars represent the range of data) for as-fired extruded rods (0.8 mm dia., with 0.25% MgO). The three lines (top to bottom) are for three-point and four-point flexure, then true tension of Blakelock et al.’s rod [151] with 6 to 15% porosity, correction for which would increase strength 15 to 50% (assuming similar correction to that shown by Bailey and Barker). Data of Rice [15] for Verneuil crystals ground parallel or perpendicular to the tensile axis (open and closed symbols respectively). Hing’s [152] data (vertical bars = standard deviation) for isopressed, as-fired ( 9 mm dia.) rods of Al2O3 with 1.9 to 7.6 v/o W, and data of Hori et al. [153] for sintered bars with up to 5% ZrO2; both additions for grain growth inhibition show the same σ–G-1/2 behavior as pure alumina, except for Alford et al.’s high strength Al2O3. Note designation of whether the bodies were conductive or nonconductive indicating the degree of contiguity of the W phase. (From Ref. 2, [2], published with the permission of the Journal of Materials Science.)

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data with or without Mo additions. Similarly, data of Hori et al. [153] for sintered Al2O3 bars with up to 5 wt% ZrO2 that were machined and then annealed (at near sintering conditions) showed strengths increasing (but toughness decreasing) due to reduced grain growth. Lange and Hirlinger showed similar results [154].

Data on Al2O3-based fibers (Fig. 3.18) [155–168] complements and extends Al2O3 data (especially for as-fired surfaces). The typical fine G and defects (e.g. pores and cracks) [3] that are the cause of failure in most fibers indicate that all of this data belongs on finer G branches, except probably for some of Simp-

FIGURE 3.18 Al2O3-based fiber σ–G-1/2, i.e. as-fired, data. Data of Nazarenko et al. [155] is shown as-measured and corrected to P = 0. Data of Simpson [156] Hamling [157], Birchall [158], Dupont FP and PRD [159, 160] as well as various Al2O3-SiO2 fibers [159–164, shown as-measured]. Note reduced σ for larger G (annealed) Dupont fibers and the σ of commercial single crystal (c-axis) filaments [165–168].

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son’s [3, 156] data. Thus the Dupont fiber data by itself, as well as the other data collectively, show a substantial finer G slope. Addition of 20% ZrO2 maintains finer or more uniform G, while SiO2 additions reduce G and give non-α phases and smoother surfaces [159–161], the latter clearly shown to improve strengths. Note that single crystal sapphire filaments have higher strengths [165, 166] than many of the polycrystalline fibers, despite their generally >10-fold larger diameter and frequent failure from residual pores [168], and also fall below strengths of many polycrystalline fibers.

Note two important facts for later discussion. First, there are frequent significant discrepancies between the G dependence of toughness of Al2O3 (Figs. 2.16, 2.17) for many tests, especially those showing R-curve effects, and strength, which is true for much other data for noncubic ceramics. Second, strength data for Al2O3 as well as most other noncubic ceramics is consistent with the two branch model (Fig. 3.1).

B.Other Noncubic Oxide Ceramic

Individual BeO studies [169–175] and compilations by Cargniglia [8, 9] and Rice [11, 13] clearly show two σ–G-1/2 branches (Fig. 3.19). Again, (1) a few percent porosity present in some samples lowered σ, as did machining perpendicular (e.g., circumferentially for round rods) vs. parallel with their lengths (more so in the finer than in the larger G branch), and (2) the primary effect of a nonmiscible second phase (SiC) [175] or a reactive phase (Al2O3) [173] in increasing σ was via reduced G. The number of specimens (e.g. 50) per test and the demonstration of increasing preferred orientation (from extrusion) as G increased indicates that the negative finer G slope is real for UOX-derived BeO [169, 170] (Sec. III.N). Again, σ–G behavior is inconsistent with γ–(hence also K–) G behavior (Figure 2.17).

Machined TiO2 data of Kirchner and Gruver [176] (hot pressed, porosity ≤3%) vs. Ga, Alford et al.’s [27] (lower σ specimens from sintered, die pressed disks) are reasonably consistent regardless of whether Ga or Gm is used for Alford et al.’s data (Fig. 3.20). Alford et al.’s small (<1 mm dia) as-fired extruded rods with expected higher σ have a larger G slope < KIC, when it is recognized that c = G/2, not Gm as they used [27], and the zero σ intercept at G = ∞, finer G slopes = 0 are quite uncertain, and not supported by Kirchner and Gruver’s data. Additionally, all of the comments for Alford et al.’s extruded Al2O3 data apply to their extruded TiO2 data, since the processing (including a TiO2 powder aspect ratio of 1.5), testing, characterization, and analysis issues are the same. Again, some large G σ’s are below those of (Vernuil) crystals [13] (which may be weaker than Czchralsky crystals) with similar surface finishes. Again, γ–G and K–G behavior are inconsistent.

A previous σ–G-1/2 data compilation [74] for mainly PSZ ZrO2, and a more

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FIGURE 3.19 BeO σ – G-1/2 data of Chandler and colleagues [169, 170], Bentle and Kniefel [171], Veevers [172], Greenspan [173], and O’Neal and Livey [174] for relatively high-purity BeO with various processing and machining. Specimens of Greenspan and Hill et al. [175] with and without substantial levels of respectively Al2O3 and SiC additives.

recent survey [75] (especially for TZP bodies) with various types and levels of partial stabilization [177–185], show higher strengths but similar σ – G-1/2 behavior with transformation toughening from tetragonal ZrO2 as without (Fig. 3.21). PSZ bodies (some of which are conservatively corrected for porosity, Fig. 3.9A) lie along larger G branches whose slopes generally increase with decreasing stabilization (presumably to an optimum toughness, beyond which their slopes and other behavior should again decrease). Such PSZ strengths commonly extend well below the strengths of similarly machined PSZ crystal specimens of the

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FIGURE 3.20 TiO2 σ – G-1/2 data of Kirchner and Gruver [176] (hot-pressed and machined), machined single crystals (Verneuil) of Rice [13] and of Alford et al. [27] for extruded high strength (< 1 mm dia.) rods tested as-fired, and lower strength bars (tested as-sawn from die pressed and sintered disks). Solid lines are those proposed by Alford et al. [27] with equal or more probable dashed alternatives indicated.

same or similar composition and machining (e.g. > 1000 MPa [80], Fig. 3.21). On the other hand, TZP materials all appear to lie along finer G branches, again often at lower strength levels than strengths of PSZ crystals of similar finish and composition. Again there are some variations due to residual porosity, e.g. the slope of Wang et al.’s [180] data for ZrO2 fully stabilized with CeO2 (12 m/o, i.e.,16 w/o) would be decreased a limited amount since the limited porosity present (0.8–2.8%) tended to increase as G increased, so there would be greater correction of the larger G strengths. In either case, this data is approximately an extension to larger grain sizes of the data for similar compositions of Tsukuma and Shimada [177] and of Hecht el al. [182]. While it is possible that Wang et al.’s data reflects the large grain branch for such CeO2-based compositions, this seems unlikely based on (1) probable limited differences in slope between it and the other similar compositions, and (2) the fine G of such an intersection, in view

FIGURE 3.21 ZrO2 σ–G-1/2 data for machined bars with various stabilizers. Some PSZ data is shown from a previous survey [74] (Fig. 3.10) along with data for PSZ crystals of Ingel et al. [80]. Most data is for dense TZP bodies of Tsukuma and Shimada [177], Wang et al. [179, 180], Masaki [181], Hecht et al. [182], Tsukuma [183], and Puchner et al. [184]. Stabilizer contents (Y2O3 w/o shown next to data points of Masaki). Vertical bars = standard deviations, and numbers at bar bottoms the number of tests. Note (1) strengths of 1 GPa for Y-TZP of Kihara et al. [185] with finer G ( 0.5 µm) from modest additions of Al2O3 (to 1.5 m/o) agree well with other data, (2) TZP data appears mainly or exclusively as finer G branches for the larger G PSZ data, and (3) the general agreement of the bulk TZP data with that for ZrO2 fibers [74, 75, 186]. (From Ref. 75, published with the permission of the Journal of Materials Science.)

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of KIC of such material (5–19 MPa·m1/2) predicting intersecton per the model for c( G/2) at 50 – 400 µm. Note that while the Ce-PSZ materials varied in σ (as expected from variations in composition and processing, hence resultant quality), they all show (1) general consistency between data sets, (2) lower and moderate but definitely positive, finer G branch slopes, and (3) more definitive and extensive microplasticity.

The above trends show that toughened ZrO2 bodies follow very similar trends as normal ceramics, but with strength levels often increased substantially due to transformation toughening. Again, larger G branches extend to strengths considerably below those for single crystals of comparable composition and surface finish, and finer G branches have lower slopes than the larger G branches, but often substantial slopes. Although data to define intersection(s) of the larger and finer G branches is limited, there are indications that larger and finer G branches do intersect when c G (Table 3.1). Extrapolation of this data gives an intersection with the larger G PSZ data at G 10µm, which is consistent with the expected intersection at c G. Further, other miscellaneous TZP data, e.g., of Rice and McDonough [74], Jue and Virkar [82], Masaki [181], and Hecht el al. [182], would all be consistent with their being on the same or similar finer G branches, dependent upon their composition and processing. Note that primarily composition and secondarily processing are important factors in strength, and hence in determining the branches bodies appear on, especially in the finer G branch regime. Whether the finer G branches, especially for bodies (e.g. CePSZ) showing considerable plasticity, extrapolate, at least approximately, to single crystal yield stresses at G = ∞ (e.g. to 400 MPa) is not known. Such stress levels may not be unreasonable for a solid solution type system (versus compressive yield stresses in precipitate PSZ crystals, 1200 MPa for Mg-PSZ [187] and2800 MPa for Y-PSZ [188]). Again note that similar trends for machined and as-fired surfaces, including extrapolation to fiber strength–grain size trends, are also shown by ZrO2 data. There are again some uncertainties in correction for porosity (especially for Nazarenko et al.’s ZrO2 fibers [155], since the same or similar correction as for their Al2O3 fibers would imply a much greater Young’s modulus than for theoretically dense ZrO2. However, data for finer G TZP bodies overlaps with the data for ZrO2 fibers partially stabilized with CaO or Y2O3 [155, 186] (Fig. 3.21).

Collectively, these results show that grain size plays a major role in the mechanical behavior of partially stabilized ZrO2 materials, in essentially the same fashion as it does in other ceramics. The effect of toughening from transformation associated with partial stabilization appears to manifest itself primarily by effects of increased KIC increasing strengths by either allowing the introduction of smaller (e.g. machining) flaws or more difficult flaw propagation, or both, thus increasing σ over and above that for fully stabilized materials, but maintaining a similar G dependence. However, there is again a