Mechanical Properties of Ceramics and Composites

FIGURE 8.8 Photomicrographs of composites with (A) 40 v/o spherical particles 25 m dia. and (B) 30 v/o of irregular particles 40 m dia. While the solid white lines indicate limited mean free path lengths between particles, i.e. high crack–particle interaction, the dashed white lines show that significantly reduced crack–particle interaction may occur with limited change in crack trace shape. The extent to which this occurs is unknown, but it probably depends on factors such as interactive stresses between particles and cracks (e.g. Fig. 8.9) and crack velocities. (From Ref. 13. Published with permission of Ceramic Engineering and Science Proceedings.)

FIGURE 8.9 Schematic of idealized interactions of a matrix crack with (A) a particle in hydrostatic tension (e.g. due to higher expansion than, and strong bonding to, the matrix), and (B) in hydrostatic compression (e.g. due to lower thermal expansion than the matrix). (From Ref. 13. Published with permission of Ceramic Engineering and Science Proceedings.)

FIGURE 8.10 Schematic of a serious heterogeneity (enclosed by dashed line) of toughening particles (open circles), which may result in this acting not only as a flaw but also often as one with less local toughening. (From Ref. 13. Published with permission of Ceramic Engineering and Science Proceedings.)

Finally, it is important to note two points. First, a few combinations of mechanisms have been suggested (e.g. Figs. 8.1B and 8.2C) and others have been discussed [13,14], but most evaluations continue to assume that only one mechanism need be considered, usually without any justification. Second, in part as a corollary problem, while observations and analysis of the crack wake bridging concept are an important component of research in this area, it is also important to note briefly two negative aspects of this on research. One is the focus on

wake bridging (enhanced by its ready observation) and an almost total lack of research on other mechanisms based on the premise that bridging is applicable and generally dominant, without clearly demonstrating its applicability to normal strength behavior. Another related negative effect is a common tendency simply to measure toughness and observe associated large-scale crack bridging, but to not measure strength, instead assuming that it follows the compostional, microstructural, and other dependences of toughness. As will be shown in Chap. 9, this assumption is often seriously incorrect, leaving the field with fragmented, incomplete, and uncertain data.

III.PARTICLE PARAMETER EFFECTS ON ELASTIC PROPERTIES

The primary parameters of the elastic properties of ceramic composites, as for any type of composites, are the composition, which determines the elastic properties of each of the constituents, and the volume fractions of the constituent phases. Secondary factors are the specific character of the second phase, such as its shape, orientation, and degree of interconnection (all of which are often related, e.g. interconnection of the second phase is related to volume fraction, size, and shape), and whether it occurs in the composite as a single crystal (hence being a second phase with elastic anisotropy that may be important). There is some, but not extensive, data on the elastic properties, most commonly Young’s modulus of ceramic composites. Useful compilations of data for particulate [27] and whisker composites [28] are available. However, little comparison of results to models, especially comparison to two or more different models, has been made. The focus here is a brief summary indicating the status and reasonable approaches as an aid in addressing other mechanical properties.

Hasselman and Fulrath [29] evaluated Young’s modulus of their composites of hot pressed sodium borosilicate glass with 10–50 v/o Al2O3 particles ( 50m). They showed that use of the rule of mixtures upper bound gave average values that typically exceeded measured values by 9–12%, while the average of the Hashin–Shtrikman bounds tended to fall below measured values by 0.5 to5% as the volume fraction alumina increased. Application of Eqs. (8.3) and (8.4) gave averages that ranged from 9% high to < 2% low using their stated value of E for the alumina (which probably presents some uncertainty). Lange’s [30] measured E values for 10, 25, and 40 v/o alumina particles (3.5, 11, 44 m), which all gave the same values for a given v/o, in a similar glass gave average values of the upper and lower bounds [Eqs. (8.1) and (8.2)] that were 8–14% higher than measured values (assuming E for the alumina to be ( 400 GPa). Use of Eqs. (8.3) and (8.4) gave averages that ranged 5–8% higher than measured, i.e. about half the difference for the rule of mixtures bounds. Frey and Mackenzie [31] found that predictions used by Hasselman and Fulrath above worked even better on their composites of glass with Al2O3 or ZrO2 spherical particles ( 125–150 m), i.e. accurate to ± < 4%, while for alumina particles in a glass

matrix of the same expansion, Binns [32] found that elastic properties agreed with the mean of Eqs. (8.1) and (8.2). Freiman and Hench reported < 3% error in using the Hashin–Shtrikman approach for crystallized glasses in the LiO2·2SiO2 system [33]. Jessen et al. [34] reported that addition of spherical particles (44–75m dia.) of a Fe-Ni-Co alloy in a borosilicate glass matrix gave Young’s moduli increasing per Eq. (8.1) at < 10 v/o addition and then transitioning to E closer to, and at or slightly below, that given by Eq. (8.2) by respectively 25 and 50–65 v/o metal. See also the note at the end of this chapter.

Donald and McMillan [35] made composites with varying contents (mostly up to 30 v/o) of chopped Ni wires ( 3 mm long and 0.05, or mainly 0.125, mm dia.) by mixing them with powdered glasses and hot pressing. Composites with a glass matrix with an expansion 8.3 ppm/°C below that of Ni decreased from E 54 GPa at 0 Ni to 44 GPa at 20–30 v/o Ni, while glasses with the same expansion as Ni decreased from 68 GPa at 0 Ni to a minimum of 46 GPa at 20 v/o Ni and then rising to 64 GPa at 40 v/o Ni. A glass matrix with an expansion 1.7 ppm/°C > Ni showed a similar trend, i.e. a minimum of 50 GPa at 20 v/o Ni and then increasing with more Ni, but less so than with matched expansion. In contrast to this, Zwissler et al. [36] added chopped (1.6 mm long) 304 stainless steel (SS) wires (6, 12, and 25 m in dia.) to an FeO matrix by hot pressing and found E linearly increasing from 129 GPa for FeO in agreement with the rule of mixtures as the chopped wire content increased to the limits of their experiments of 10–15 v/o, depending on wire size. The lack of reductions in E, and hence apparently of microcracking, is attributed to the limited expansion difference (FeO2 ppm/°C > the SS) and the smaller sizes and lower v/o.

Turning to composites with crystalline matrices, Ono et al. [37] showed that the ratio of Young’s modulus and density (E/ρ) for the composite system Al2O3-ZrO2(+ 3 m/o Y2O3) was linear as a function of ZrO2 w/o over the whole composition range. However their data with unstabilized ZrO2, while starting with the same slope at low ZrO2 additions, deviated significantly below the linear trend, especially from 10 to 20 w/o and 90 to 100 w/o ZrO2, resulting in a value of 1/2 that of ZrO2 with 3 m/o Y2O3 for the completely unstabilized ZrO2, indicating serious microcracking. French et al. [38] similarly measured E across the complete range of Al2O3 and ZrO2 contents, but with fully stabilized cubic ZrO2 (with 8 m/o Y2O3). Their results showed a linear decrease of E between the two extremes of 400 to 240 GPa respectively for Al2O3 and ZrO2, but without the deviations of Ono et al. with unstabilized ZrO2.

Yuan et al's [39] E values decreasing by up to 25% for mullite +0-25 v/o ZrO2 (with varying Y2O3 levels) from the nearly identical values of mullite and ZrO2 illustrates challenges of sorting out composite behavior. Corrections for the generally increasing 2.6–8.7% porosity as ZrO2 levels increased via e–4P indicates bodies with 1 m ZrO2 particles had E values 5–10% lower only with 20–25 v/o ZrO2 additions, and those with 2 or 4 m ZrO2 particles had values ≥5% and 10–15% lower with respectively 5–10 v/o and 15–20 v/o

ZrO2. ZrO2 particle size dependences of E clearly indicate microcracking, as does effects of quenching, and data of Ishitsuka et al. [40] showing E for 50 v/o TZP in mullite being 150 GPa versus 235 and 215 GPa for the 2 constituents. Ruf and Evans [41] showed that additions of up to 40 v/o ZrO2 to ZnO followed a rule of mixtures very closely, and extensions of this to 60 v/o were still close to a rule of mixtures. Limited deviations to values a few percent lower than the rule of mixtures at 40–60 v/o were attributed to limited microcracking.

Another important system is that of Al2O3-TiC, where while there is limited difference of constituent E values, E has been reported to increase linearly from 393 to 415 GPa as the TiC content increased from 0 to 40 w/o (35 v/o) [42]. Small (1–5 v/o) additions of submicron particles of high modulus βSiC to lower modulus BaTiO3 (Fig. 8.19) substantially increased the modulus, though there are some effects of a BaTiO3 phase change [43]. Similarly, adding nanoscale βSiC particles to βSi3N4, while not increasing E at the 5 v/o level, linearly increased it over the 5–20 v/o range, approaching the investigators’ (apparently rule of mixtures) expectations at the higher levels [44].

Other systems offering opportunities for evaluation are those where the second constituent may be present in solution or as a second phase, e.g. as for crystallized glasses and a few all crystalline constituent composites. AlN-SiC composites are an example of the latter, since the two end phases can form extensive solid solutions depending on particle sizes and times at temperatures of densification or post treatment; otherwise they yield two-phase bodies. Ruh et al. [45] showed that solid solution bodies had somewhat higher moduli over most of the composite range (and the Hashin–Shtriktman bounds following at or slightly above their solid solution trend) (Fig. 8.11). Estimating the moduli of their composites using 1/2 the sum of values from Eqs. (8.3) and (8.4) and their values for pure AlN and SiC agrees fairly well with their solid solution data, adding to the question of the specific sources of differences between the two-phase and solid solution bodies. Comparison of this data with other data for composites having one constituent in common shows variation in the moduli for the same material, as is also common in the literature for ceramics in general. Thus Ruh et al. give E of dense SiC as 347 GPa, while Mah et al. [46] give it as 427 GPa and the latter give E 290 GPa for their Si3N4 matrix while Baril et al. [25] give this as 313 GPa. While these differences are not large and are generally representative, they illustrate an important problem in predicting moduli of composites, since such values of constituents vary, and it is uncertain how much of such variation is due to measurement or material issues (and their interrelation, e.g. due to heterogeneities in the bodies).

Another type of composite of interest is one where the second phase is produced by an in situ reaction as was used by Chen and Chen [47] to produce La hexaluminate platelets in an Al2O3 matrix. They report E decreasing from 420 GPa for pure Al2O3 to 230 GPa for the pure aluminate, with greater decreases occurring from 80 to 100 v/o aluminate.

FIGURE 8.11 Young’s modulus of SiC-AlN solid solutions or particulate composites versus AlN content. Note reduced Young’s modulus of the particulate composite versus the solid solution. (From Ref. 44. Published with permission of the American Ceramic Society.)

Turning to two-phase crystalline composites of all nonoxide constituents, the most extensive data from a volume fraction standpoint (φ= 0 to 1) is that of Endo et al. [48] for SiC-TiC particulate composites, which they noted followed a linear relation as a function of weight fraction (Fig. 8.12). Taking half the sum of Eqs. (8.3) and (8.4) (using their values for the two end points of pure SiC and TiC) results in very good agreement with the mean of Endo et al.’s results. Similar comparison of values for Si3N4-TiC composites (φ= 0 to 0.5) of Mah et al. [46] shows more scatter. How much of this reflects inaccuracies in Eqs. (8.3) and (8.4), measurement variations, and actual material variations, e.g. due to heterogeneities of distribution of the second phase or variations in possible degree of preferred orientation of the matrix grains, the dispersed particles, or both, in the composite, cannot be ascertained.

Ferrari and Fillipponi [50] reviewed the application of effective medium theories, specifically earlier self-consistent scheme (SCS) and Mori–Tanaka (M–T), as well as Hashin–Shtrikman (H–S) bounds to ceramic composites of nonspherical Al2O3 or spherical particles in glass matrices (discussed earlier), as well as to pores in glass. This shows some of the problems even for simpler, more ideal composites. They showed that the data for nonspherical Al2O3 particles (0–50 v/o) was fitted by the H–S lower bound, which is also the M–T

FIGURE 8.12 Young’s modulus versus volume fraction second phase for particulate composites of SiC-TiC by Endo et al. [48] (where both the range and the mean are shown by upper, lower, and intermediate lines), of Si3N4-TiC by Mah et al. [41], and of SiC-TiB2 by Pan et al. [49], as well as of Si3N4-SiC platelet composites by Baril et al. [25], Note that use of Eqs. (8.3) and (8.4) agrees almost identically with the mean trend for the data of Endo et al., while the data of Mah et al. shows measurable variations (scatter) between the data and such model predictions.

model for spherical particles, and the SCS model is also very close to the data. The dilute spherical particle models, while agreeing with data to 20 v/o, fell progressively below data as the Al2O3 content increased, e.g. being 10–15% low at 50 v/o. Overall the dilute concentration model fitted better, though it was high at lower v/o Al2O3, e.g. by 15% at 20 v/o, but it appears to be low at high v/o Al2O3. For glass with spherical W particles, the H–S lower bound and hence the M–T model for spherical particles were close, e.g. being 5% low at 50 v/o W particles, while the SCS model was a good fit. Again the dilute spherical inclusion model was low, e.g. 20% low at 50 v/o W. Their evaluations for voids in glass, being the extreme of low modulus inclusions, is indicative of problems for such composites, with a major one being the failure of the SCS and dilute concentration models, since they go to zero at 50 v/o pores. Data was close to the upper H–S bound, and still closer to the M–T model, but the latter fit was based on assuming an aspect ratio of 0.8 for the pores, which is

really a curve fitting approach, since there is no experimental or theoretical basis for this, i.e. equilibrium pores in glass are spherical. Such fitting and the lack of explanation why in some cases the H–S lower and in others the H–S upper bound fitted better are illustrative of the limitations of current models as well as of characterization of composites. This is very similar to the problems of effects of porosity on elastic properties which are impacted not by only pore shape but also by how they are arrayed in the body, i.e degree of randomness versus the degree and type of ordered stacking, orientation of nonspherical pores and their contact or intersection (which is impacted by volume fraction, shape, orientation, and size [51]).

Data for platelet and whisker composites is often more uncertain, since this invariably entails varying, generally incompletely characterized degrees of preferred orientation and its variations in the bodies. This also presents the challenges of first knowing the crystal structure–platelet or whisker morphology and resultant elastic properties as a function of orientation in the platelets or whiskers. Thus, for example, the Young’s modulus data for Si3N4-SiC platelet composite (φ= 0 to 0.3) of Baril et al. [25] (Fig. 8.12) faces these uncertainties for comparison to any model.

One set of platelet composites for which some limited, useful comparative data is available is those made with fine BN platelet particles dispersed in matrices of Al2O3 [52], mullite [52,53], SiC [54], and AlN [55]. Data for the relative Young’s modulus (measured parallel to the hot pressing axis) versus v/o of BN shows a common trend for all three composites except for two deviations, one at higher BN loadings in SiC and one data point for mullite-BN produced by in situ reactions of B2O3 and AlN or Si3N4 [53] (Fig. 8.13). Collectively these suggest a consistent pattern based on the substantial preferred orientation of the BN platelets normal to the hot pressing axis, as clearly shown for Al2O3 - [52] and mullite - [53] based composites made by hot pressing of the matrix and BN powders, while the platelets are essentially randomly oriented when produced in situ via reaction hot pressing (Fig 11.5). Bodies made by the former process are anisotropic, e.g. having E 35% higher in the plane of hot pressing versus normal to it [53], while the latter process gives essentially isotropic properties [54]. The high BN expansion of 25 ppm/°C in the c direction (i.e. normal to the plane of the platelets, but only 1 ppm/°C in the a direction) versus that of the alumina and mullite matrices (respectively 9 and 5 ppm/°C) strongly suggests that separations between the BN platelet faces should occur, which is also indicated in TEM studies [56]. Thus data for E normal to the plane of oriented BN platelets should approach that for platelet pores as suggested by Lewis et al. [52], with a common trend for relative moduli irrespective of matrix, while data for isotropic, unoriented bodies should be higher due to less alignment of platelet–matrix separations in the direction of measurement, as shown in Figure 8.13. The deviation at higher BN loadings in Si3N4 may reflect less creep-orientation accommodation in it during hot pressing.

FIGURE 8.13 Relative Young’s modulus at 22°C as a function of v/o fine BN platelet particles in composites with Al2O3 [52], mullite [52,53], SiC [54], and AlN [55] matrices. Measurements parallel to the hot pressing axis, hence normal to the plane of preferred orientation of the BN platelets, for composites made by simply hot pressing the composite ingredients [52,54], but not in the essentially isotropic bodies made by forming the BN platelets in situ by reaction processing (RP) of B2O3 with AlN or Si3N4 [53]. Note (1) data for Al2O3 and mullite matrices does not give values for the matrix alone, so values of 410 and 220 GPa were used respectively, (2) the common trend for all three composites with preferred platelet orientation regardless of matrix, and the higher value for the mullite-BN reaction processed composite without significant BN platelet preferred orientation, and (3) that the common slope of 3.5 is reasonably consistent with that for platelet pores oriented normal to the stress direction [52].

Turning to whisker composites, these offer all the complications of particulate and platelet composites, especially frequent substantial preferred orientation of the whiskers, though probably differing from the degree and character of orientation in platelet composites. No detailed studies of elastic properties of ceramic whisker composites have been made, but a few that are available indicate some of the variability and uncertainties. Consider first Ashizuka et al.’s [57] study of SiC whisker additions to cordierite-, anorthite-, and diopside-based glass systems, whose baseline E values were respectively 90, 130, and 160 GPa. All E values increased linearly by 40 GPa to reach maxima at φ respectively of 0.25, 0.3, and 0.4 and then dropped rapidly, with the extent of the decrease increasing in the reverse of the order listed. As expected, the percentage increase was greatest in the cordierite-based system having the lowest E value (Table 8.2). The decreases in E are attributed to microcracking, since anorthite has the closest thermal expansion to SiC, anorthite is higher, and cordierite is substantially lower, but the decrease is also dependent on φ, E, or both.

Consider next polycrystalline matrices for whisker composites, beginning with Wadsworth and Stevens’ [58] addition of 0.3 volume fraction SiC whiskers hot pressed in a lower modulus matrix (cordierite ) showing that E in the plane of pressing increased 24% from 140 to 192 GPa (Table 2). They showed that these results were nearly halfway between the bounds of Eqs. (8.1) and (8.2) using a value of E = 440 GPa for dense polycrystalline SiC as Yang and Stevens [59] did. Kumazawa et al. [60] showed that addition of 0–40 v/o of SiC whiskers to a mullite matrix increased E from 220 GPa at 0 SiC to 290 GPa, i.e by 30%. Tamari et al. [61] reported that the Young’s modulus of Al2O3 with mullite whiskers decreased linearly as φ increased from 0 to 0.3. Yang and Stevens’ study of Al2O3-SiC whisker composites is one of the most studied systems if not the most studied. They showed that E in the plane of hot pressing (i.e. parallel with the planar orientation of the whiskers) increased linearly as the volume fraction of SiC whiskers increased from 0 to 0.3. Correcting their results for limited porosity, they showed that E increased 10% from 397 to 408 GPa (Table 2) and that this trend was consistent with predictions from a rule of mixtures relation using the polycrystalline value of E for the SiC whiskers, a procedure of uncertain applicability to other bodies.

Fisher et al. [62] made a more detailed experimental and analytical study of elastic properties of composites of SiC whiskers in matrices of Al2O3 and Si3N4 with up to 30 v/o whiskers made via hot pressing. Although SEM examination showed considerable orientation of whiskers parallel to the plane of hot pressing, very little anisotropy in wave velocities was found. Thus while models for oriented whiskers were considered, behavior was nearly isotropic (which gave elastic moduli the same as for stressing normal to aligned whiskers, e.g. supporting a model of random three-dimensional arrays of whiskers giving isotropic behavior). Shalek et al. [63] similarly measured E as a function of SiC