Mechanical Properties of Ceramics and Composites

depth of the wires below the tensile surface and not seeing near as much of the tensile stress in flexure [131,132]. The issue of cracking, especially due to expansion differences, is also indicated in work of Rice and Lewis [132]. They showed that though good strengths (and toughnesses) could be obtained in various composites of ceramics with uniaxial fine SiC-based (Nicalon) fibers in various ceramic matrices, highest values were obtained when the differences in fiber and matrix expansions were < 2–3 ppm/°C.

IV. CERAMIC COMPOSITE RELIABILITY, WEIBULL MODULI, STRENGTH VARIABILITY, AND FRACTOGRAPHY

A major motivation for developing ceramic composites, besides achieving better or unique levels or combinations of properties, has been to increase mechanical reliability. This latter motivation became closely related to study and evaluation of R-curve effects, since the increased toughness with increasing crack propagation was seen as reducing the dependence of strength on the starting flaw size and thus reducing the variability of strengths due to varying initial flaw sizes, hence increasing reliability. While issues of the large crack sizes commonly needed for most significant increases in toughness have been noted earlier and will be discussed further in the next section, the issue of reliability, as measured by Weibull moduli, is addressed in this section. Since most investigators have not directly measured Weibull moduli of their composites, values have been estimated by Eq. (3.4) and these estimates compared to other related mechanical properties, not just to strengths.

Rice [32] previously surveyed Weibull moduli of ceramics and ceramic composites, noting that composites of the type that are the focus of much of this book and this chapter typically had a Weibull modulus (m) in the range of 5–15, as did monolithic ceramic materials considered for mechanical applications. (Note that composites of continuous ceramic fibers in a ceramic matrix clearly provide increased reliability, since they result in lack of catastrophic failure and associated notch insensitivity, neither of which has been achieved in the composites addressed here.) Further evaluation of Weibull moduli of ceramic composites considered in this and the previous chapter are generally consistent with this range. This consistency is supported by the limited Weibull moduli reported by the few investigators addressing them. Thus Govila [133] reports m 7 for an Al2O3 and 10 for a similarly processed Al2O3-SiC whisker composite based on ten tests each. Similarly, Akimune et al. [68] report m = 6–13 for their Si3N4- SiC particulate composites. However, though based on limited tests, Baril et al. [113] report Weibull moduli increasing from 10 to 19–29 as the v/o of SiC platelets in a Si3N4 matrix increased from 0 to 30 v/o, with greater increases for smaller SiC platelets, and probably more of the increase occurring by 20 v/o platelets.

Some substantially higher moduli are calculated from some strength data

sets, typically for a data point for a fixed composition, but there is substantial uncertainty in their validity given the limited number of tests commonly involved (e.g. 4–10). Thus while some of these higher values may indicate real increases in reliability (which if real may be from other sources, as is noted below), many do not, so that broader trends are of primary interest. Two such trends stand out. The first is that the Weibull moduli for toughness values vary about as widely with similar values as for the corresponding strengths. This seriously questions either the occurrence or the effectiveness of R-curve effects, since these would imply decreased variability due to increased effects of the average material-mi- crostructure and less effects of local variations as crack sizes increased. The second, and not surprising, trend is for Weibull moduli for other properties such as E or H to be far higher, e.g. values of 50 to several hundred. Such high values, though they are few, since adequate data for calculating them is commonly not given, are at least approximately indicative of what the variation of material properties is for properties averaging material behavior over a longer range versus those reflecting a much more local property average. A third but much more uncertain trend is for some possible higher Weibull moduli for strengths and toughnesses for bodies in which the toughening microstructure is developed in situ. This includes crystallized glasses (though changing microstructures and mechanisms are probably an important complication in many of these) and especially in situ development of plateletor whiskerlike grains [134], with in situ toughened Si3N4, as was discussed in Chaps. 2 and 3.

The above issue of whether higher fracture toughness from R-curve effects is generally applicable to improved strength and especially reliability is further addressed on the negative side by the results of fractography identifying fracture origins. While limited studies of fracture origins have been made, those that have been conducted all show similar processing defects at fracture origins of composites as for monolithic ceramics, as well as frequent origins from defects of the composite structure. Thus a key example of the former are frequent voids, e.g. as shown by Govila [133] in his study of Al2O3- 15 w/o SiC whisker composite, e.g. voids as a result of whisker clustering (i.e. due to whisker “nests” as also frequently seen by other investigators). Rice [32] also showed fracture origins in such whisker composites from matrix rich regions (e.g. Fig. 9.19). Watanabe and Fukuura [135] have shown Al2O3-TiC fracture initiation from normal processing defects such as pores, larger grains, etc. Similarly, Cameron et al. [136] showed initiation from heterogeneities, e.g. clusters of larger grains, in reaction hot pressed composites. Other fracture surface observations include frequent exposure, and often failure initiation from clusters of larger particles in particulate composites [54,74] and of larger platelets, with substantial fracture along much or all of one of the large plate faces [116].

Finally, note that other scale factors can be factors in other types of ceramic composites. Thus fibrous monoliths, composites made by introducing an

FIGURE 9.19 Fracture initiation from an elongated Al2O3 rich region from center right across much of the photo in an Al2O3-SiC whisker composite. (A) Lower magnification showing larger fracture area. (B) Higher magnification of specific origin. Note the much larger Al2O3 grain size in the matrix agglomerate acting as the fracture origin. (From Ref. 32. Published with permission of Ceramic Engineering and Science Proceedings.)

array of weak interfaces (e.g. of BN in Si3N4 via extrusion of an array of BN coated green rods of Si3N4), increase strengths as the “fiber” diameter decreases. Simpson [137] showed flexural strengths of ceramic–metal composites he made from particles obtained by consolidating and sintering composite particles made by tape casting multiple, alternating green layers of HfO2-CeO2+MgO and Mo increased 50–100% as the particle dimensions decreased from 800 to 70 m in lateral dimensions (and compressive strengths increased by 15–40%, Chap. 10, Sec. III). This is similar to effects of colony structures (e.g. Figs. 1.9, 1.10, 1.12) on fracture.

V.GENERAL DISCUSSION

A.Toughness–Strength Differences and Strength– Microstructure Mechanisms, Especially via Flaw Sizes

Three sets of issues that need to be discussed are the comparison of toughness and strength results, especially their often significant differences, the mechanisms responsible for toughness and especially strength in composites, and models and improved evaluation of such behavior. With regard to the strength–toughness results, it is important to note that there are broad and significant differences of two types. The first and less common, but still frequently substantial, difference is for opposite dependences on φ over at least part of the φ range. Thus toughness generally increases, usually to a maximum (that may or may not be in the range investigated), while strengths sometimes show the opposite trend, e.g. Fig. 9.12, or show greater decreases at higher φ. While most or all of the latter is due to processing heterogeneities, the former indicates basic differences in mechanisms that are probably related to the source of the other basic difference, namely crack size effects. Thus, as discussed in Chap. 2, Secs. II.A and IV, varying crack–particle interactions in glass–metal composites (Chap. 8, Sec. V.A) and lower toughness in WC-Co (Chap. 8, Sec. IV.F) at higher crack velocities [138] are another indication of basic differences that can occur between toughness and strength tests.

The other, more general and basic difference between strength and toughness behavior are their dependences on microstructure, first and foremost on the sizes of the dispersed second phase and secondarily on the grain size of the matrix. Thus increased toughness with increased matrix grain size often corresponds to decreased strength, i.e. as is also seen in monolithic ceramics. More significant is the same trend for effects of dispersed particle size, i.e. while toughness generally increases as the dimensions of the dispersed phase increase, strengths decrease, e.g. Figures 9.12 and 9.13, directly analogously to the frequent disparities between toughness and strength of monolithic ceramics as a function of G. This is attributed to the same cause, namely effects of crack size, since larger dispersed particles can contribute more toughening at larger crack sizes, e.g. due to

greater crack deflection or bridging, but strengths are typically determined by smaller flaws that provide fewer opportunities for such toughening effects as crack bridging with larger cracks. Thus toughness tests with arbitrarily introduced cracks will often reflect increased toughening with larger particles, while such larger particles are often fracture origins that control normal strength behavior. Toughness more closely reflects average body behavior due to the use of larger cracks, while strength reflects weak link behavior, generally on a much smaller scale of the microstructure.

Toughness and strength behavior approach consistency with each other when the crack sizes are comparable either on an absolute scale or on a scale relative to the microstructure impacting mechanical properties. Thus large cracks used to determine toughness are pertinent when large cracks also determine strength, e.g. from serious thermal or impact stresses (Chap. 11, Sec. III.C). Alternatively, consistency occurs when smaller cracks are used for measuring toughness, e.g. via fractography from strength tests, or more generally when crack sizes controlling strength are sufficiently large relative to cracks for toughness measurement to reflect the same microstructural effects on both. This typically results with finer microstructutres, e.g. those of ZTA (Fig. 9.6), which have sufficient homogeneity so that there are not large differences in the statistical opportunities for toughening mechanisms to operate over the different crack scales used for much toughness testing versus those controlling strengths. Thus if grain and particle sizes are of the order of 1 m and flaws are 20 m in size, then there are 600+ grains in a halfpenny surface flaw and 60 grains along the crack periphery, but only 8 and 5 grains respectively if the grain size is 5 m. Clearly the former offers more statistical opportunities for toughening to approach the average toughening effects per area of large cracks, while the latter does not.

Turning to the issue of mechanisms, the past focus has been on resistance to crack propagation as typically measured with larger cracks where mechanisms such as crack deflection and especially branching and bridging can have significant effects. However, strength, while sometimes reflecting such toughening effects, commonly does not, as is shown in this chapter for composites and in Chaps. 3 and 6 for monolithic ceramics. The reality is that there are two other general mechanisms impacting strength. The first is the effect of composite character, especially composition, on Young’s modulus, which has received some attention, but substantial neglect, and which may or may not be reflected or recognized in toughness tests. The second, often more significant, mechanism is the effects of composite composition and microstructure on flaw character, especially size, typically from machining. These two broader mechanisms can occur in addition to or instead of more specialized mechanisms such as transformation toughening (from tetragonal ZrO2) or ductile inclusions (in some ceramic–metal composites) as well as more general large crack toughening such as crack deflec-

tion, bridging, and branching. Another mechanism that can result in significant strength and toughness differences is residual, especially microstructural, stresses resulting in pre-existing or stressing-induced microcracks or both. While microcracking in composites has been recognized and studied some, it has not been adequately evaluated, especially its effects on flaw size.

Consider the evidence for significant effects of machining flaws on composite strengths. The first and more widely used demonstration of this is flaw sizes calculated from strengths and toughnesses to be commonly a minimum at some intermediate volume fraction of dispersed phase, e.g. as extensively pointed out in Rice’s earlier review [32] and addressed in the previous sections. Since machining flaw sizes typically vary as inverse functions of K and H, each raised to different fractional powers [e.g. Eq. (3.2)], and toughness of composites typically passes through a maximum, flaw sizes would commonly pass through minima. Such flaw size minima have been widely indicated [32] (e.g. Figs. 9.10, 9.13, 9.16, 9.18), though not necessarily coincident with the toughness maxima, since the flaw size minima depend on composition and microstructural effects on H and E as well as on K variations with crack size. Thus H has different dependences of composite structure (Chap. 10, Sec. III.A), i.e. directly on φ and inversely on D as well as on the matrix G, which is a function of φ and dispersed particle powder and matrix powder particle sizes, as well as processing. E also varies with composition. Both H and E variations can shift the c minimum, as can the pertinent toughness controlling flaw formation, which may not be that obtained with large cracks. Thus reductions in matrix grain sizes as a function of composite composition and particle sizes, while possibly having other effects, can impact the sizes of machining-induced flaws due to similar effects. Such effects of limited second phase additions increasing strength via matrix grain size reduction were also shown for monolithic alumina bodies e.g. with limited Mo and W additions to alumina (Fig. 3.14). In addition to flaw size reduction effects, there can be residual surface, especially compressive, stresses from machining that will affect the flaw behavior, e.g. making flaws act as smaller than they really are. Such compressive surface stresses have been reported for machined TZP [139] and for nanocomposites of Al2O3-SiC [60].

The second effect of composite character on flaw sizes is via the dependence of composite strength on particle size introduced here in this chapter (Figs. 9.2, 9.15, 9.16). Thus the mechanism is that finer particles are smaller than the flaw sizes induced by machining (or other surface abrasion) and thus have more limited effect on strength via their impact on resultant flaw character, especially size, via their impacts on local Young’s modulus, hardness, and toughness. Thus in this finer particle branch there is variable but a generally limited decrease in strength as D-1/2 decreases. On the other hand, as the sizes of particles approaches and then exceeds the flaw size, the particles (or larger particle clusters) become the sites for introduction of machining flaws controlling strength

with a resultant higher strength–D-1/2 dependence in this larger particle size branch. This is directly analogous to the mechanism for strength–grain size effects in monolithic ceramics, as was extensively discussed in Chapter 3, and will be some in Chapter 11. The direct parallel between these mechanisms for monolithic and composite ceramics (including accounting for the effects of matrix grain size in composites having similar effects on flaw generation and hence on strength) provides major corroboration for this mechanism in composites. Additionally, while the specific data base for this machining flaw–strength mechanism is limited, since most composite studies have been with finer particles, the empirical recognition that finer particles give higher strengths than coarser ones is added support for this mechanism, as is data showing limited effects of different finer particles on composite strengths in this chapter. This machining mechanism is also supported by the generally lower strengths of platelet composites, since the platelets often provide a larger, planar interface for preferential machining flaw formation (or microcrack or combined microand machining–crack formation).

A simple test of whether machining flaws are significant in controlling strength is to compare strengths for the same set of composite samples with either different machining abrasive grits or the machining direction parallel versus perpendicular to the stress axis in testing. Thus, as noted in Chapter 3, machining typically leaves two sets of flaws, one halfpenny shaped normal to the abrasive motion, hence machining direction, and one of more elongated flaws parallel with the abrasive motion [140]. Thus if machining flaws are controlling strengths, machining test bars parallel to the bar and stress axis thus causes failure from the former flaws, and machining test bars perpendicular to the bar and stress axis causes failure from the second set of flaws. Since both flaw populations are of the same depth [which is a function of the local material toughness, hardness, and elastic moduli, e.g. per Eq. (3.2)], there is strength anisotropy due to elongated flaws controlling failure for machining perpendicular versus machining parallel to the bar axes, the former having lower strengths than the latter. Thus the differences, or the ratios, of the average strengths for parallel and perpendicular machining show whether there is measurable strength anisotropy, and such anisotropy in turn is a clear indicator that machining flaws are controlling strength. In other words, if other sources of failure such as processing defects or microcracks dominate failure, then little or no anisotropy of strength will be found. Similarly, if crack wake toughening mechanisms are significant, so that the effects of the original flaws are limited or zero, there will be limited or no strength anisotropy as a function of machining direction. For reference, the ratios of strengths for typical perpendicular versus parallel diamond grinding of ceramics are 50–60% for grain sizes of 1 m and increase to 100% (i.e. no anisotropy) for G 50 m due to the flaw and grain sizes being equal (Fig. 3.1, and decrease again at larger G) [140]. Porosity

has little or no effect on such anisotropy unless there is substantial heterogeneity of large pores that control strength.

Rice [140] has measured strength anisotropies of a number of commercial and experimental ceramic composites showing that many have clear machining direction–strength anisotropy. Thus for example commercial crystallized cordierite (Pyroceram 9606), Al2O3-20 v/o TiC, and Al2O3-7 or 25 w/o SiC whiskers and grain sizes of a few microns had ratios of 70–85%, limited impacts of processing defects on strengths. Another 8 of 15 composites tested fell in the range of 86–96%, and only three did not show the indicated anisotropy. In both cases, especially in the latter group, either processing defects or microcracking (or both) were important sources of failure, thus limiting strength anisotropy as a function of machining direction. Thus, for example, three composites of aluminumand zirconium-titanate known to have substantial microcracking (e.g. as reflected in strengths of 65–100 MPa) showed anisotropy ratios of 89–96%, i.e. some limited anisotropy despite microcracks and heterogeneous porosity. Such machining evidence, especially on homogeneous composites, shows that machining plays an important role in the strengths of many ceramic composites. Thus the effect of composite character on machining flaws, especially on their depths, needs much more attention as a mechanism for their improved strengths.

Thus an essential perspective for evaluating mechanisms controlling strengths of composites is to recognize that there are a variety of mechanisms that can be operative, and that while in some cases one mechanism may be a major factor, other mechanisms may also impact behavior. Further, there can be shifts in the mechanisms impacting behavior as composite parameters of composition and processing–microstructure change. Thus, for example, increasing the size, quantity, or both of the dispersed phase increases the opportunity and extent of spontaneous, i.e. preexisting, microcracking, e.g. with SiC platelet composites [105]. However, this should also be taken as a sign of possible stress-induced microcracking (which is far too often neglected) and that impacts of other mechanisms should be considered, including possible shifts in them precipitated by changes in microcracking.

Another factor consistent with the above flaw–particle size mechanism is the impact of matrix grain size in the same fashion as for monolithic ceramics, i.e. increasing the local hardness and probably the local toughness controlling machining flaw formation. Thus inhibition of matrix grain growth aids tensile strength, and mutual inhibition of grain and particle growth aids even more. However, the range of matrix grain sizes can vary widely for different types and amounts of additives and processing, e.g. as shown for TiB2-based bodies by Telle and Petzow [141]. Again, the consistency of data for TiB2 with different additives (Fig. 3.25) indicates consistency of composite and monolithic strength–microstructure dependence.

B.Probable Mechanisms Controlling Strengths of Specific Composite Types

As key illustrations of the above varying impacts of multiple mechanisms, consider first zirconia toughened materials. While transformation toughening is a dominant factor, this must often compensate for strength decreases due to reductions of E due to ZrO2 having a lower E than matrices such as Al2O3. However, such reductions are often counteracted in part by reductions in matrix grain size as well as of machining flaws, effects of surface compressive stresses from machining, or both. However, there are other mechanisms such as microcracking, e.g. as shown by the work of Claussen and colleagues [31,142] and Homeny and Nick [44], but often at strengths much below those implied by the toughness. Some other mechanism is also indicated by the unusual bridging of cracks by fine fracture or other filaments observed in eutectic Al2O3-ZrO2 bodies of Nick and Homeny. Thus models of transformation toughening are a useful guide but are uncertain in the degree of their quantitative predictions not only because of their idealization (especially assuming dilute, noninteracting transforming particles [143]) but also because of other varied contributions of uncertain quantification due to lack of accurate models and detailed characterization. While the finer microstructural scale of zirconia toughened composites often allows reasonable correspondence between toughness and strength behavior, this is not always so not only due to microstructural heterogeneities as indicated by comparison of Claussen’s and Becher’s original studies (Figs. 9.5, 9.6) but also due to flaw effects, since these are typically not reflected by most toughness tests.

Metal–ceramic composite toughness is often significantly impacted by ductile elongation of metal particles in the crack wake, but this again raises issues of the extent to which this can apply on the typically much finer scale of normal strength controlling flaws. Higher expansions of some metals relative to common ceramic matrices combined with metal particle size and the extent of metal–ceramic bonding can result in the metal addition often acting more as pores. On the other hand, when this does not occur, stresses may be generated by the particles that influence crack propagation directly, or by microcrack generation in response to a crack stress field or by spontaneous formation, each with some difference in effects on toughness and on strength. As with other composites, there may also be effects on matrix grain size as well as of flaw sizes and local stresses affecting them via effects on machining.

Ceramic particulate composites have much of the possible variations in mechanisms in ceramic–metal composites above, except for the general absence of the ductile toughening. Thus effects on matrix grain size have been noted, and stresses from mismatch in expansions (or altered by elastic property differences) between the dispersed phase and the matrix are clearly a factor. The highest strengths are generally obtained when such stresses are low or zero (see also