Mechanical Properties of Ceramics and Composites

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Consider first hardness. For composites, especially of all crystalline constituents, a first approximation is the rule of mixtures, i.e.

where the subscripts C, M, and S refer respectively to the composite, matrix, and dispersed second (“particulate”) phase, and φ is the volume fraction second phase. For multiconstituent composites this Eq. (10.1) can be used repetitively to include each extra phase beyond the second, e.g. by first using the equation to predict the hardness behavior of the two phases present in the greatest amount and then treating that composite as one constituent with the next most prevalent phase, etc. until all phases are included. However, it must again be noted that Eq. (10.1) is an approximation; it is often a useful one, but it may not be feasible to adequately incorporate effects of particle and grain sizes, shapes, orientations, and changing contiguity of one or more of the composite phases as the percolation limits are reached for the various phases as φ changes. A modification of this equation was proposed by Lee and Gurland [1] to include the contiguity of each phase as a weighting factor for its volume fraction, which they showed agreed well with WC-Co data.

A special case that has received some consideration is that of partially crystallized glasses, where some glass matrices can undergo deformation required for indentation by densification as well as, or instead of, deformation by volume conserving processes that dominate deformation of crystalline materials. Miyata and Jinno [2] proposed a hardness theory for composites of crystalline or glass spherical particles of isotropic character dispersed in an isotropic glass matrix. They considered two cases where (1) the dispersed phase is harder than the glass matrix and (2) the matrix is harder than the dispersed particles, using Marsh’s theory of glass deformation. In case 1 the composite hardness depends on the matrix hardness and flow stress of the matrix, the elastic properties of both phases, and the volume fraction of dispersed phase, while in case 2 hardness and elastic properties vary in the same fashion with the volume fraction dispersed phase. In both cases particle size and spacing do not play a role other than via their variation as the volume fraction dispersed phase (φ) changes, i.e. the latter dominates. However, while they showed that the limited data was consistent with their two models, as noted later, whether there is a significant and reliable difference between the rule of mixtures relation Eq. (10.1) and their model is uncertain.

There do not appear to be any models for compressive strength, ballistic performance, wear, or erosion specifically for composites. Correlations of these properties with H and K can be a guide, e.g. per Eqs. (5.1) for erosion and (5.2) for crack sizes introduced by particle impacts and especially abrasive action. However, there are added uncertainties for composites in addition to those for monolithic ceramics (Chaps. 4 and 5). The primary added uncertainty is the pos-

sibility of preexisting, or especially stress generated, microcracks due to the twoor multiphase nature of composites, which respectively may not have the same effects on H as other properties or not be generated as extensively, or at all, in hardness testing. The latter is a concern in view of the extensive hydrostatic nature of much of the stress during indentation versus generally greater tensile stress generated in compression, wear, etc.

III.EXPERIMENTAL RESULTS

A.Hardness

Miyata and Jinno [2] showed that their HV (100 gm) data for phase separated PbO-B2O3 glasses supported their models for harder and for softer particles relative to the glass matrix, i.e. showing respectively H increases of 25% by φ= 0.25 and H decreases of 30% by φ= 0.3. Though the necessary property data was not available to make such specific quantitative comparisons in other systems, they noted that basic trends for phase separated sodium borosilicate glass and for crystallized Li2O2-SiO2 glass were consistent with their model, e.g. in the latter case H was independent of crystallite size. However, their plots are not far from linear, as was also noted by French et al. [3], raising the question of how significantly their model deviates from a rule of mixtures.

Some other data supports the dominance of φ on H, e.g. Roesky and Varner [4] and Stryjak and McMillan [5] for crystallized glasses in respectively the LiO2-Al2O3-SiO2 and ZnO-Al2O3-SiO2 systems, but they are not clear in differentiating between the rule of mixtures, Miyata and Jinno’s, or other mechanisms. Thus in the latter composition, H also increased linearly with D, but whether this is totally reflected in the φ dependence is uncertain. On the other hand, Tashiro and Sakka [6] reported HV (200 gm) data for a photosensitive LiO2-SiO2- based glass varying linearly with D-1, or D-1/2 (as also more clearly shown for flexure strength) for higher temperature crystallization (e.g. with D 0.8 to 2.3m), but a more complex, possibly reverse dependence on D from lower heat treatment and finer values (D 0.07–1 m). Further complicating the picture is data of Cook et al. [7] for crystallization of three nearly identical LiO2-SiO2- based glasses giving HV increasing with D and λ but not with φ Though not presenting detailed quantitative Hv– microstructure data, Donald and McCurrie [8] showed some complexities of crystallized glasses in their MgO-LiO2-Al2O3- SiO2-TiO2 systems, i.e., while having an overall trend for H to increase with heat treatment and extent of crystallization, they showed wide variations with heat treatment. Thus heat treatments at 800, 900, and 1000°C all gave rapid increases in H to a maximum, then a decrease to a minimum, followed by further increases as heat treatment time increased, but with substantial differences in H, e.g. of minima and maxima, values.

Besides more detailed study, e.g. of microstructures (including related stresses) and properties, to sort out the above complexities, more study of artificial glass–ceramic composites is needed, but such data is very limited. Wolf et al. [9] reported that HV values of their composites of 25 v/o of glasses of expansions varying from < to > that of the Al2O3 fine grain preforms into which the glasses were infiltrated all gave H 12 GPa, which was between the upper and lower bounds [Eqs. (8.1) and (8.2)], i.e. somewhat below the rule of mixtures [Eq. (10.1)].

Turning to all crystalline composites, French et al. [3] reported HV (10 N) for their Al2O3 ( 5 m) of 18.4 GPa decreasing linearly as cubic stabilized ZrO2 (+ 8 m/o Y2O3) content was increased, e.g. to 13.9 GPa for only ZrO2 (G 5+ m), which was 76% of the Al2O3 hardness. Similarly, Ruf and Evans [10] showed that their HV (200 N) data for ZnO with additions of ZrO2 of up to 60 v/o was consistent with a rule of mixtures, except for limited deviations to lower values at > 40 v/o, attributed to limited microcracking, i.e. the same behavior as for E (Chap. 8, Sec. 3). More recently Hirano and Inada [11] showed that additions of up to 40 v/o Al2O3 to either 4Ce-TZP or 3Y-TZP increased HV (9.8 N), at or close to a linear function of Al2O3 content. However, the trends for each processing temperature shifted downward with increasing temperature and coarsening of the microstructure, with substantially more effect of processing in the Ce-TZP system.

Hwang and Niihara’s [12] data for BaTiO3 with 1–5 v/o additions of nanosize SiC particles showed HV (apparently with 9.8 N) increasing significantly with v/o of SiC similar to flexure strength (Fig. 9.11), fracture toughness and Young’s modulus (Fig. 8.19), though complicated by reduced G at lower SiC contents and bimodal G at higher SiC contents and densification temperatures. Nakahira et al. [13] showed that HV (0.98 N) increased linearly from 19.5 GPa at 0 v/o of 2 m SiC particles to 25 GPa at 50 v/o in an Al2O3 matrix. While some of this increase must be due to the progressive reduction in the Al2O3 grain size from 20 m at 0 v/o SiC to 3 m at 50 v/o SiC, this contribution is limited, e.g. to 0.5 GPa per Figure 4.2, with which their data is reasonably consistent. Krell and Klaffke [14] showed that HV (10 kg) of Al2O3-35 v/o TiC (fine G) was 21 GPa versus 17–18 GPa for pure Al2O3 of the same G ( 2.5 m).

Turning to composites in which the matrix and the particulate phase are both nonoxides, the HV (500 gm) data of Endo et al. [15] for the SiC-TiC system showed more complex behavior (Fig. 10.1) in contrast to their linear trend for E versus composition (Fig. 8.11). This more complex behavior was attributed to probable effects of G and residual stress changes with composition, with support for the latter seen in substantial increases in tensile strengths for the SiC rich portion of the system at elevated versus room temperatures (Chap. 11, Sec. III.E). In contrast to this Sasaki et al. [16] showed HV (98 N) of Si3N4 first increasing slowly from 13 GPa with addition of 0 to 10 v/o of 0.3 m SiC particles and

FIGURE 10.1 Vickers hardness (HV, 500 gm) versus phase content in the SiC-TiC particulate composite system. (From Ref. 15. Published with permission of the

Journal of Materials Science.)

then rising to 14.3 GPa at 20 v/o, similar to, but more extreme than, the behavior of E (Chap. 8, Sec. III). Bhattacharya and Petrovic [17] showed that HV (100 N) of MoSi2 increased rapidly from 9.3 to 12.3 GPa with addition of 5 v/o of 0.5 m SiC particles and then followed an linear trend parallel with, and slowly approaching, the rule of mixtures relation (with HV SiC 25 GPa), reaching nearly 18 GPa at 40 v/o SiC. The initial rapid rise of H correlates with reductions of the MoSi2 G from 28 to 11 m for 0 to 5 v/o SiC and the trend toward the rule of mixtures relation to further G reductions to 5 m at 40 v/0 SiC. Cameron et al. [18] reported HV (1 kg) of various reaction hot pressed, fine grain/particle (typically a few m) ceramic composites (Table 10.1) that were typically at least approximately consistent with the rule of mixtures. The H values were also typically close, e.g. within 5–15% of those of composites made by directly hot pressing the composites from mixtures of ceramic powders producing similar microstructures. Landon and Thevenot [19] reported that HV (1 kg) for AlN with SiC increased from 19 GPa with 30 w/o β-SiC to a possible maximum at 29 GPa at 75 w/o and from 21.5 GPa with 40 w/o α-SiC to a possible maximum or plateau of 28 GPa at 80 w/o. The maximum or plateau at 75–80

w/o SiC may reflect shifts in grain size and the degree of solid solution versus two-phase structure as composition changes.

Baril et al. [20] reported HV (20 kg) of composites of 0–30 v/o SiC platelets (11 or 17 m dia.) in a Si3N4 matrix modestly increased from 15.5 to 16 GPa over the range of additions for the finest platelets and 5% less for the larger platelets for measurement on planes parallel to the platelet orientation and5% higher on the normal plane.

Turning to whisker composites, Ashizuka et al. [21] showed HV (200 gm) of composites of SiC whiskers in a cordierite, anorthite, or diopside matrix increasing nearly linearly as whisker content increased to a maximum followed by significant decreases. This was overall similar to the trends for Young’s modulus, fracture toughness, and flexure strength, i.e. with the level of the maximum and the v/o at which it occurs increasing in the listed order of the matrices, e.g. respective maxima at 25, 30, and 40 v/o SiC whiskers. The maximum of H (and other properties) correlated with the maximum whisker content at which near zero porosity was achieved in fabrication. The data thus suggests a rule of mixtures trend, but densification, and especially lack of detailed quantitative information on the whisker orientation and hardness, prevents detailed evaluation.

Tamari et al. [22] showed HV (4.9 N) was independent of SiC whisker content (0–30 v/o) in B4C, in part reflecting limited hardness differences in the constituents. Dusza et al. [23] showed that HV (10 kg) of β-Si3N4 added to a S2N4 matrix decreased as the whisker content increased, presumably reflecting the lower H of β-Si3N4 versus that of α-Si3N4, the expected matrix and harder (Fig. 4.13) phase

The most extensive study of ceramic metal composites is of WC-Co bodies, which Lee and Gurland [1] showed agreed well with their modification of Eq. (10.1) to include the contiguity of each phase multiplying its volume fraction. Nawa et al.’s [24] composites of Al2O3 with 0 to 20 v/o Mo particles ( 0.65m) showed HV (9.8 N) decreasing linearly with increasing Mo content, indicating agreement with the rule of mixtures relation [Eq. (10.1)]. Both starting values at 0 v/o Mo of 18 GPa and significant (e.g. 20%) lower values due to increased Al2O3 G (from 0.4 to 2.8 m) are generally consistent with data of Figs. 4.1, 4.2. Chou et al. [25] showed HV (100 N) of Al2O3-NiAl particle (D 5.5 m) composites decreased linearly from 18.1 to 8 GPa as the volume fraction of NiAl increased from 0 to 50 v/o in fair agreement with Eq (10.1). However, there must be some other factor causing H to decrease more than just due to the much lower H of NiAl ( 0.3–0.45 GPa) as the v/o NiAl increases, since the Al2O3 matrix grain size was reduced with increasing NiAl addition, which would entail some increase in H above the expected rule of mixtures value of nearly 10 GPa. This greater decrease may reflect possible contraction of the NiAl away from the Al2O3 matrix or residual stresses in view of the NiAl thermal expansion just over twice that of Al2O3.

Turning to ceramic eutectics, the most extensive data is from Bradt and colleagues [26–29], e.g. HK (300 gm) for directionally solidified MgOMgAl2O4 euctectic increased linearly with λ-1/2, exceeding values for the two constituents over the range of λ-1/2 investigated (0.3–0.7 ( m)-1/2). More extensive HK (500 gm) data for ZrC-ZrB2 showed H for both transverse and longitudinal sections increasing linearly as a function of λ-1/2 to a maximum at λ 1.85 m and then rapidly decreasing linearly with a further increase of λ-1/2, i.e. at finer spacing, which correlated with breakdown of the well-ordered microstructure. The peak H of 22.5 and 24 GPa respectively for longitudinal and transverse sections were substantially higher than for either constituent ( 13 and 17 GPa respectively). Stubican and Bradt [27] noted that eutectics of TiC-TiB2 and SiC-B4C both also showed H increasing with decreasing λ, but with the highest observed H values not exceeding those of the harder members (TiB2 and B4C). Echigoya et al. [30] reported that HV of longitudinal surfaces of directionally solidified Al2O3-ZrO2(Y2O3) eutectics were low ( 10 GPa) for 0 m/o Y2O3 due to cracking, but was 17 GPa at 3 m/o decreasing to 15 GPa at 13 m/o Y2O3.

B.Compressive Strength and Ballistic Performance

Very little compressive testing has been done on ceramic composites, presumably in part due to expectations that their strengths will typically be limited by substantial microstructural mismatch stresses, but we thus miss an opportunity to use such testing to help define such mechanisms of failure.

May and Obi [31] measured compressive strengths of crystallized SiO2- based glasses with 25–35 m/o LiO2 with 1–3% P2O5 for nucleation. While there were broad variations of compressive strengths, e.g. from 10 to 85 MPa, all compositions showed similar trends as a function of heat treatment, namely initial rises in strengths, e.g. to strength maxima a few to 150% that of the glass following early crystallization. These strength increases were followed by strength decreases to minima, e.g. similar to the starting strengths to 60% below them at intermediate heat treatment temperatures and then increases at higher heat treatment temperatures, commonly close to or higher than their initial maximum strengths (Fig. 10.2). Tests as a function of temperature, while all showing overall strength decreases, show substantial variations that should have the potential to allow improved understanding of behavior in these complex systems (Chap. 11, Sec. III.F).

Verma et al. [32] showed marked increases in the compressive strength of composites of SiC platelet ( 25–50 m dia., and 1–2 m thick) in a borosilicate glass matrix chosen for its thermal expansion match with SiC. Strength doubled from 160 MPa for 0 v/o SiC at 10 v/o, rose to 510 MPa at 40 v/o SiC, and then dropped greatly to 200 MPa at 50 v/o. The latter drop is

FIGURE 10.2 Compressive strengths versus heat treatment temperature (for 2 hr) for crystallization of Li2O-SiO2 glasses. This plot shows nearly half the curves generated and reflects the range and diversity of compressive strengths observed. Compare with Fig. 11.14. (Curves from Ref. 31. Published with permission of the Proceedings of the British Ceramic Society.)

attributed to substantial residual porosity at such high SiC loading. Fracture in such room temperature tests was totally brittle and catastrophic. Tests at elevated temperatures also showed strengths increasing with increasing platelet additions to 40 v/o, but at much reduced strength levels and with substantial plastic deformation.

Simpson [33] compression tested his ceramic–metal composites made from particles obtained by tape casting multiple, alternating green layers of HfO2-CeO2+MgO and Mo in his investigation of ceramic–metal composites (based on concepts of Knapp and Shanley [34]). Tapes with individual layers down to 20 m and total multilayer tape thicknesses of 25–450 m were cut into rectangular pieces from 800 to 70 m in lateral dimensions and consolidated and then sintered. Compressive strengths decreased faster initially and then more slowly from 1. 3 GPa with 30 v/o Mo to 650 MPa at 70 v/o Mo (while flexure strength increased from 175 to 400+ MPa). Both strengths increased as the size of laminated particles decreased, e.g. by 50–100% for flexure strengths, and for compressive strengths by 15–40%.

Another useful observation from compressive stressing is that of Suresh et al. [35] on Si3N4 with 0, 10, and 20 v/o SiC whiskers. They showed that while the threshold stress range for crack initiation in compressive fatigue testing of