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studied ceramic), BeO, and TiO2; some mixed oxides and Nb2O5 (some with phase transformations or extensive microcracking); TiB2,B4C, and Si3N4 (including some effects of grain elongation and boundary phases), and then TZP bodies with phase transformation and possible microcracking. A few more comments on the transition to single crystal and especially grain boundary values are made at the end. Again the following two sections address crack wake and R-curve effects and effects of preferred grain orientation, both particularly for noncubic ceramics.

Overall, the fracture energy and toughness of noncubic ceramics often show more pronounced grain size dependences as well as more variation with different materials, microstructures, and measurements (Fig. 2.16). While there are variations in the relative magnitude of the values with general agreement in the trends with grain size, there can also be significant differences in the trends

FIGURE 2.16 Summary of the fracture toughness versus grain size for various noncubic ceramics at 22°C by various tests (along with cubic material data from Figure 2.11). Note that while these are common trends shown by one or two techniques (mainly WOF or DCB) for some materials and several techniques for Al2O3, some investigators have obtained significantly different results, mainly for Al2O3 (the most extensively tested ceramic), as is discussed in the text, along with differences among these material results. Note representative single crystal values for some of the materials shown along the lower right scale.

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with G. These differences reflect incompletely documented and understood changes in mechanisms and their dependence on test effects. Thus per Fig. 2.16 and previous reviews [11, 60, 108] DCB and DT, and sometimes NB, tests show pronounced Al2O3 toughness maxima, e.g. at G between 50 and 150 µm, which as noted earlier correlates with stress-induced microcracking (Figs. 2.11 and 2.16). Such trends appear consistent with a transition from mainly or exclusively stress-induced microcracking at lower G and spontaneous microcracking at larger G. However, other studies, especially with NB tests, show toughness constant or decreasing slightly as G increases over the typical G range of 3–30 µm, with the more limited NB (and IF) data at G 40–50 µm showing further, often more pronounced, toughness decrease. Some NB tests also show marked increases below G 10 µm (which may reflect inadequate notch-crack effects), while other NB data shows toughness independent of G or slightly decreasing as G increases to the limits of much testing at 30 µm. Note that the overall NBAl2O3 data shows the typical toughness for it of 3–4 MPa·m1/2. Also, even tests designed to give toughness values without bridging done in Al2O3 (e.g. G 1–16 µm) give K0 (i.e. “crack tip”) values of 1.8–2.7 and values controlling strength failurenearer 3 MPa·m1/2 [157], but there are various uncertainties in such measurements. Further, much more limited data for BeO (Fig. 2.17) indicates a similar trend as for DCB Al2O3 data, consistent with the two materials having very similar Young’s moduli and TEA (hence microcracking).

FIGURE 2.17 Fracture energy versus grain size for several noncubic oxides, including DCB data for Al2O3 and TiO2 data in Figure 2.16 and for three titanates and Nb2O5 with higher TEA and thus more microcracking at finer G. (After Rice [60] published with the permission of the Journal of Materials Science.)

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More limited TiO2 DCB and WOF data (Figs. 2.16, and 2.17) shows some differences, but reasonable overall consistency. More recent data [60, 161, 162] also showed marked toughness decreases between G = 20–30 µm from higher values (e.g. 6+ down to 3–4 MPa·m1/2), and probable effects of stoichiometry. The TiO2 data thus also appears to reflect effects of microcracking, e.g. probably much of it stress induced, but also spontaneous cracking at the lower toughnesses at larger G (Fig. 2.10).

Consider now noncubic ceramics of more extreme TEA, e.g. titanates of MgO, Fe2O3, and Al2O3 along with Nb2O5, which have extensive microcracking at modest to fine G (Fig. 2.10). These also generally show, often pronounced, maxima of fracture energy and toughness versus G (Fig. 2.17), with overall trends generally consistent with those expected from Eq. (2.5), and the previously outlined microcracking model [43]. However, comparison of two groups of materials: (1) Al2O3 and TiO2 (as well as presumably BeO and BaTiO3), and

(2) MgTi2O5, Fe2TiO5, and Nb2O5 (and presumably also Al2TiO5) shows that fracture energy peaks of group 1 are narrower and occur at finer G, typically substantially so, than predicted for spontaneous fracture per Eq. (2.4) than those of group 2; the peaks of group 2 occur at G values at or beyond those predicted for spontaneous fracture. The former is consistent with the microcracking model, the latter is not. Second, the fracture mode of group 1 typically involves some to substantial transgranular fracture, while that of group 2 entails mainly intergranular fracture, e.g. for G above half the peak toughness value. Third, and particularly important, while the tensile (flexural) strengths of both groups decrease with increasing grain size (Chap. 3), those of group 2 do so at a faster initial rate as compared to group 1, as well as most ceramics of cubic or noncubic crystal structure (Figures 3.1 and 3.23). Fourth, dynamic E values are independent of G for group 1 but decrease with increasing G for group 2, and for the latter, along with tensile strength, increase with temperature [164] Hamano et al. [105] showed that as microcracking increased as G increased, the work of fracture more than doubled as E, flexure strength, and crack velocity decreased substantially. They attributed these effects to crack deflection and blunting due to the microcracks.

Noncubic (i.e. piezoelectric) BaTiO3 shows a more definite and pronounced fracture energy maximum, 2–3 times that found at the same G as cubic BaTiO3 (above the Curie temperature, 126–129). More limited data of Freiman et al. [163] on PZT as-fired or poled showed toughness increased from 1.3 to 1.55 MPa·m1/2 as G increased from 2 to 14 µm and was 1.7 MPa·m1/2 at G 100 µm. A toughness maximum was assumed between the finer and large G values, i.e. similar to BaTiO3, but much broader. Their data for pressure depoled samples indicated a similar trend but shifted upward to 2.2 to 2.5 MPa·m1/2 at the lower and large G values respectively, again consistent with a maximum at intermediated G. At least some of these toughness changes in the noncubic state

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are related to stresses from the transformation (and possible microcracking Fig. 2.10) and from poling (Sec. III.I).

Consider next nonoxides. The fairly definitive toughness decrease for TiB2 (Fig. 2.16) [60] as G increases from 5 to 25 µm may be in part due to stress-in- duced microcracking, consistent with strength changes, prompting Telle and Petzow [98] to suggest, probably incorrectly as noted in Sec. III.C, spontaneous microcracking. The general trend for KIC of TiB2 to decrease above G 5 µm and a maximum for B4C at G 8 µm is generally consistent with Eq. 2.4 and possibly also with the microcracking model for fracture energy and toughness versus G. Thus Skaar and Croft [165] give the maximum single crystal Δα of 3 10-6 C-1, and the maximum single crystal–polycrystal Δα of 2 10-6 C-1, giving grain sizes for microcracking of the order of those in Fig. 2.4.

Turning to hot pressed B4C, DCB data of Rice [60] is generally consistent with more extensive and definitive NB data of Korneev et al. [166] and agrees well with DCB data of Niihara et al. [167] on CVD material. All of these showed toughness rising from 2.5–4 MPa·m-1/2 at G 3 µm through a maximum of 5.5 MPa·m-1/2 at G 10 µm, then decreasing, to 2.5 MPa·m-1/2 at G 30 µm. This trend is consistent with data of Schwetz et al. [168] for sintered-HIPed B4C + 2, 3, 4, or 5 w/o carbon, which rose, rapidly initially, then at a diminishing rate, from 2.5 to 4 MPa·m1/2 as G increased from 1–2 to 10 µm. The only noticeable effect of the excess carbon was generally to give somewhat finer G. Thus, except for one data point of Rice at G 80 µm and 4 MPa·m1/2, the data sets are generally consistent. The occurrence and scale of the B4C toughness maxima is also consistent with it having nearly identical TEA and Young’s modulus as Al2O3 [60], thus also suggesting a microcracking effect. This would suggest that the G value for its KIC maximum would be similar to that of Al2O3. However, it clearly deviates significantly from this expectation and hence from Eq. 2.4 and the microcracking model for the grain size dependence of fracture energy and toughness, being about an order of magnitude too low. Two other deviations are the essentially 100% transgranular fracture and extensive twinning on the fracture surfaces of larger B4C grains in contrast to mixed to intergranular fracture mode of Al2O3 with little or no obvious twinning. Twinning in B4C may provide a mechanism of microstructural stress relief or redistributin to avoid microcracking at large G, but it leaves uncertain the reason for the toughness maxima at G 10 µm, where transgranular fracture still dominates, but twinning appears to be much less.

The substantial fracture energy and toughness data for various Si3N4 bodies is complicated by limited characterization, as well as microstructural complexities similar to and beyond those for most other ceramics. Complexities include the α versus β phase contents and residual additive-boundary phases and contents, a limited range of grain diameters achievable (commonly < 10 µm, but often with substantial grain elongation, e.g. aspect ratios to 10), often with

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considerable heterogeneity of grain structure, along with varying degrees of grain orientation. However, overall trends are indicated by individual and some collections of tests as follows, with effects of bridging and grain shape and orientation in Secs. III.G and H.

First, the absence or presence, amount, and character of residual boundary phases play a key role, since, while varying with the additive chemistry, fracture energy and toughness generally increase with oxide additive content, as shown for a variety of types and amounts of additive contents by Rice et al. [169], and more recently in a narrower study by Choi et al. [170]. Extrapolation of such trends to zero additive levels gives KIC 4 MPa·m1/2, i.e. below levels with oxide additives, which is consistent with extrapolation of fracture toughness data of RSSN (i.e without additives) to P = 0 [169]. It is also consistent with data for Si3N4 bodies: (1) hot pressed with nonoxide additives (BeSiN2) by Palm and Greskovitch [171], giving no significant residual boundary phases, (2) hot pressed or HIPed at high pressures without additives of Shimada et al. [172] and Tanaka et al. [173], and (3) from CVD Si3N4, as shown by Rice et al. [169] and Niihara [130, 174]. The latter CVD bodies (G 1, 4, and 10 µm) give KIC respectively of 5, 4, and 3.5 MPa·m1/2 (indentation), while the former CVD body with G 100 µm also gives KIC 4 MPa·m1/2. Bodies made without additives commonly have G of the order of 1 µm, as did those made with BeSiN2. Thus these results show little or no G dependence of KIC, or it is decreasing some with increasing G (e.g. from Niihara’s data), either of which is in contrast to results for bodies made with oxide additives (discussed below). Another important aspect of the above bodies is their predominately transgranular fracture mode (and in those tested, no SCG, Sec. III.B) across the complete range of G values, even with substantial to complete β phase content and grain elongation. This is in ontrast to substantial intergranular fracture in Si3N4 bodies made with oxide additives. The frequent absence of significant, if any, effects of β phase content in RSSN [175] is attributed to their smaller grain size, less elongation, and especially common transgranular fracture.

The toughness of Si3N4 bodies made with oxide additives, while generally increasing with additive content, also generally increases with grain size and grain elongation, the latter typically arising from α to β transformation with increased temperature exposure (mainly in processing). Studies show KIC increasing over part or all of the limited practical G range, e.g. Tani et al. [176], Matsuhiro and Takahashi [177], and especially Kawashima et al. [178]. The latter data (Fig. 2.16) implies a probable KIC maximum at G of the order of 10+ µm based on the high KIC level, as well as on strengths (Chap. 3), but such a maximum is at an order of magnitude or more lower G than expected from the TEA of

Si3N4, i.e. for α Si3N4, αa = 3.7, and αc = 3.8 10-6 C-1 and for β Si3N4 (i.e. the larger, elongated grains in most sintered bodies) αa = 3.3 and αc = 3.8 10-6 °C-1

[179] are both too small for microcracking in the grain size of such a KIC maxi-

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mum. On the other hand, Si2ON2 [179] and most oxide boundary phases would have expansion differences that could give microcracking closer to the indicated G range for the probable KIC maximum. Though specific grain sizes were not given, Himsolt et al. [180] showed a toughness maximum of 8 MPa·m1/2 at similar G values, correlating with nearly complete α to β conversion and increased grain growth (e.g. due to less inhibition by diminishing α content). This evaluation is consistent with that of others as summarized in the review of Pyzik and Carroll [181] showing projected toughness mxima at G 14 and 20 µm respectively for Y2O3-MgO and Y2O3-Al2O3 additives. Such additive effects are consistent with Peterson and Tien [182] correlating increased toughness and related crack tortuosity (and bridging) with increasing thermal expansion of the oxynitride boundary phase. Correlation of KIC with G is complicated by the extent of grain elongation, the volume fraction of such grains, and their orientation, but reasonable overall understanding and corroboration of the expected trends has been established. Sajgalik et al. [183] showed toughness increasing as the volume fraction of grains with larger aspect ratios increases (e.g. 4), and Ohji et al. [184] (Sec. III.E) showed substantially higher toughness (and bridging) with crack propagation normal to aligned tabular β grains, and much less for crack propagation parallel with such elongated grains.

Fine-grain tetragonal ZrO2, i.e. TZP, bodies also show high maximum toughnesses at fine G (Fig. 2.18) with transformation toughening a major factor. Thus Wang et al. [185] showed a definite (NB) toughness maximum at G 1.2 µm for compositions with 2, 2.5, or 3 m/o Y2O3, and a similar result, but more differentiation of compositions and some differences in details of the G dependence, by indent methods (and overall similarity, but some variations in the G dependence of strength). Indent toughness of Cottom and Mayo [186] for 3 m/o Y2O3 ( 4 MPa·m1/2 at G 0.25 µm and 8 MPa·m1/2 at G 1.4 µm), while not inconsistent with the G dependence of Wang et al., are substantially lower in values, which are more consistent with indent values of Swain [187], which suggest a maximum at larger G. Data of Ruiz and Readey [188] on 2 m/o Y2O3 using the average of their four different calculations of indent toughness imply a possible toughness maximum at > 5 µm, but one set of calculations was reasonably consistent with a maximum at G 1–1.5 µm (respectively solid and dashed lines in Fig. 2.18). The three data points of Theunissen et al. [189] are in the same range, except shifted to finer G values than those of Ruiz and Readey. Indent results of Duran et al. [190] for two compositions of 3 m/o Y2O3 (with some Er2O3) showed modest toughness maxima of 5 and nearly 8 MPa·m1/2 at G 0.3 µm, which is clearly both different from, and similar to, data of Masaki [191] for 2, 2.5, 3, and 4 m/o Y2O3 for G = 0.2–0.6 µm showing no G dependence (but toughness of 15+ and 5 MPa·m1/2 for respectively 2 and 2.5–4 m/o Y2O3), consistent with some to substantially greater toughness with 2 m/o Y2O3. Combined indent data of Duh et al. [192] for 1 m/o YO1.5 + 11 mol% CeO2 and SENB data of

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FIGURE 2.18 Indent and SENB fracture toughness versus grain size for various TZP bodies, investigators, and tests [185–194]. Note clear or implied, pronounced toughness maxima, some similar and different, and a possible maximum for one of four indent calculations of Ruiz and Readey [188], respectively dashed and solid lines.

Wang et al. [193] for 12 m/o CeO2 indicate a pronounced maximum at G . 2–2.5 µm. While there are uncertainties in such combination, later indent results of Duh and Wan [194] for bodies with 5.2 m/o CeO2 and 2 m/o Y2O3 indicated a fairly broad toughness maximum of 19 MPa·m1/2 at G 1.5 µm. Thus, while there are considerable variation and differences, there is substantial evidence for often pronounced toughness maxima as a function of G. The indicated G values are approximately consistent with Eq. (2.4), and possibly (2.5), but other related effects of the transformation process and its effects need to be considered, e.g. as reviewed by Becher et al. [195].

Note the range of KIC values for some noncubic singleand polycrystals (Fig. 2.16, Table 2.1), mostly showing ratios of polycrystalline to single crystal KIC values of 2–3, as for cubic materials. This is not surprising, since cubic materials often have similar, sometimes more, anisotropy of elastic moduli [65] and cleavage and fracture as noncubic materials. Thus, except where TEA and other microstructural stresses are dominant, noncubic materials should show similar

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FIGURE 2.19 Schematic of local fracture modes (I, II, or III) of grain boundary facets for local microcracking (or crack propagation). (After Rice [39], published with the permission of the ASTM.)

transitions between polycrystalline and single crystal or grain boundary fracture energies or toughnesses as cubic materials do, e.g. as indicated for Si3N4 (Fig. 2.15). This is also indicated by indent tests of Liang et al. [80] of larger Al2O3 grains showing toughness decreasing from 2–4 MPa·m1/2 (G 50 µm) and 1.5–2.5 MPa·m1/2 (G 100 µm) (respectively for 5 and 10 N loads). Such a transition has also been outlined for CVD Si3N4 (Fig. 2.15), which has limited anisotropy and all transgranular fracture. However, it should again be noted that the combination of TEA and increasing G of many noncubic ceramics should result in increased intergranular fracture, which would shift the transition to grain boundary rather than single crystal values. While such grain boundary values will often be lower, they will often probably be more complex due to the local mixed mode fracture entailed when more than one grain boundary facet is involved (Fig. 2.19).

G.Grain Dependence of Crack Wake Bridging and Its Relation to Fracture Toughness

Crack bridging in the wake region is an established phenomenon based on direct observation in this region and is the source of increased toughness in R- curve effects. The latter was clearly shown by Knehans and Steinbrech [51] who first showed R-curve effects in NB tests of alumina. Then they extended the original sawn notch, removing the wake region generated from the initial

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crack propagation from the original notch. Upon retesting the specimen with the wake region from the original test removed, toughness returned to the initial level at the beginning of the first test but again increased in the same fashion as in the original test with subsequent crack propagation and new wake development.

Crack wake bridging observations are substantial, especially in Al2O3 and Si3N4 bodies, but have not been extensively reviewed. However, a review by Sakai and Bradt [196] is summarized and followed by a broader review, generally corroborating and extending key points in their review. These include bridging and resultant R-curve effects widely occurring and generally being more pronounced with increasing crystalline (grain) anisotropy. Thus R-curve effects are substantial in materials such as graphite (and especially in fiber reinforced ceramic composites), but results are probably not unique to a given material and microstructure. Further, while Weibull modulus may increase, the highest toughness does not necessarily yield the highest strength (Chap. 3), and there probably are crack geometry effects (e.g. along the lines depicted in Fig. 2.1).

Earlier observations of Wu et al. [6] using DCB tests in an SEM as well as microradiographic and some optical observations of crack character in ceramics were made before wake bridging was recognized. Though their purpose was to demonstrate that the then common idealization of cracks in polycrystalline bodies as simple planar cracks as commonly found in glass was often not true, their results also clearly showed what is now recognized as crack wake bridging in both similar and different bodies (Fig. 2.4) from those subsequently investigated. Thus they showed via in situ SEM examination of Al2O3 of larger than normally investigated grain size (e.g. 30–50 µm) limited occurrence of bridges, which often consisted of several grains, and that some bridging in such bodies resulted in considerable local microcracking within bridges. Whether these reflect effects of larger grain sizes, as-fired, rather than the normal polished, surfaces, or both is not known, but they are one of many indicators of the need for wider study of surface and grain size effects on bridging. They also conducted microradiography of a commercial fused-cast alumina refractory sample (with machined surfaces, an average G 200 µm, with grains 50 to 2000 µm, and preexisting microcracks a few hundred µm in size). These microcracks, especially larger ones or clusters of them, interacted with the propagating macrocrack, e.g. each deflecting to join with each other (but not with isolated spherical pores, Fig. 2.4).

Other representative and important alumina observations for finer grain bodies with machined surfaces are outlined as follows. Swanson et al. [49, 50] showed a bridging zone length of 100 grains in a body with G 20 µm. Rodel et al. [55] also showed multigrain bridges, and their fracturing, i.e. microcracking along grain boundaries (G 11 µm). Vekins et al. [197] using DT tests of a commercial 96% alumina, some heat treated to extend the starting G from 4 to10 µm in several steps, showed progressively faster rises in toughnesses

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plateauing at higher values as grain size increased, distinguishing bodies of < 1 µm difference in G. They showed increasing reloading hysteresis as G increased in the R-curve region, and the ultimate fracture energy rose slightly faster than linearly with increasing G, while the length of the bridging zone behind the crack decreased nonlinearly with G from 11 to 6 mm, i.e. respectively 3000 and 600 grain diameters. Predominate transgranular fracture was observed, sometimes forming bridges a fraction of a grain in width and a substantial fraction to over a grain in length, i.e. similar to yttria and the ferrite noted above. However, the most significant bridging was attributed to intergranular fracture forming bridges of complete, often larger, grains or grain clusters. These were verified by locating the bridging grain on one half of the resultant fracture surface and the mating hole for it on the other fracture half along with wear markings from the pullout of the grain [197]. These observations are directly contrary to later claims that fractography can provide virtually no information on bridging [198]. Vekins et al. found no evidence of microcracking ahead of the crack or in its wake, other than that involved in forming the bridges. They concluded that, rather than bending of elastic ligaments, work expended in rotating and pulling bridged grains out of the mating fracture surface against friction was the main source of toughening, which they estimated entailed 10% of the grains in their case, but could be less if larger grains dominate the bridging process. They had no explanation for the large decrease, by 2, in the bridging zone length as grain size approximately doubled. Steinbrech et al. [199] showed a similar trend for greater toughness increases (but starting from lower initial values) for a 2 versus a 10 µm body. They also concluded that frictional effects were probably an important factor, that microcracks in the wake zone were mainly associated with debris, and that R-curves were not unique for a given body but depend on test parameters and microstructural variations. Thus crack wake bridging, extensively observed in Al2O3, may be an alternate explanation to microcracking for toughness maxima versus G (Fig. 2.16), but bridging-R-curve effects have been observed only over part of the G range (mostly G 1 to 10–20 µm) and may involve some microcracking and thus correlate with microcracking models.

Bridging and R-curve effects clearly occur in many Si3N4 bodies but are quite dependent on microstructural parameters, apparently occurring only in bodies with sufficient grain size, elongation, and amount and character of grain boundary phase. Such effects have not been observed in bodies without oxide additives due to resultant transgranular fracture (and no slow crack growth, Secs. III.A and B) in the absence of resultant grain boundary phases. Even with oxide additives, such effects are observed not to occur, or to occur only in very modest amounts, in finer grain, equiaxed bodies, e.g. as reported by Mizuno and Okuda in their evaluation of round robin KIC tests [13]. All observations of significant bridging in Si3N4 are with substantial amounts of oxide additives,