Mechanical Properties of Ceramics and Composites

aHH and LH are respectively the high and low, i.e maximum and minimum, values for different Knoop indenter orientations on differing crystal surfaces; values in GPa. A range of values reflects two or more differing sets of data.

bMost values 2.4–3.0.

Source: Ref. 3.

HV was independent of aspect ratio at 20.5 GPa. Another complication, as in hardness itself, is load dependence of H anisotropy. Though not extensively documented, Pajarec et al.’s data for the HK anisotropy of cubic ZrO2 crystals shows the maximum anisotropy decreasing from 1.31 with a 0.5 N load to 1.12 at a 2 N load, indicating an increased role of slip requiring higher stress activation [36].

Note first additional sources of H anisotropy data and second studies of Westbrook and Jorgensen [117]. The latter not only are an additional source of data on H anisotropy of ceramic crystals but also showed that adsorbed moisture on crystal surfaces can measurably alter their hardness values and thus also the measured anisotropy (see also Chap. 7, Sec. II). Finally note that, besides effects of electric fields and poling on cracks and related effects in ferroelectric and piezoelectric materials (Chap. 2, Sec. III.I), hardness can also be affected. Thus Park et al. [118] showed that while HK (0.25–1 N) was isotropic for both single-

and dense polycrystals (G 60 m), HK with the long axis of the Knoop indentation normal to the poling direction resulted in lower H and that parallel to the poling direction higher H (i.e. 4.42 and 4.69 GPa, which approximately straddle the unpoled, isotropic value of 4.53 GPa). A similar anisotropy was found in single crystals, i.e. respectively 4.06 and 4.35 GPa. Note that single crystal value is somewhat higher than the large G polycrystalline body, which indicates that H of BaTiO3 may not have a minimum, e.g. suggesting effects of twinning.

III.GENERAL DISCUSSION

A.Variations, Uncertainties, Consistency, and G Range of Data

The substantial data reviewed earlier clearly shows that a Petch-type, i.e. a G-1/2, dependence of ceramic hardness occurs over the entire, or more commonly the finer, portion of the grain size range. The deviation from a pure Petch relation (i.e where all H values increase from those of the average crystal values in a linear fashion as a function of G-1/2) is associated with the extensive trend for a hardness minimum at some intermediate grain size due to cracking. However, before discussing such cracking it is useful to note variations commonly impacting data, which arise to some extent from test method or more extensively from the character of the specimen, its preparation, and its characterization.

The primary test factors, indenter type (i.e. shape) and load, which can significantly impact H values (e.g. especially for < 500 gm loads, as is well documented), are respectively usually and commonly given, making substantial data useful, but some of limited or no value. Loading (and unloading) rate, time, and environment, which can have some, often varying effects, are widely neglected, as is resultant indent character, e.g., symmetry and cracking. The latter can be a particular problem, since irregular indents are typically discarded rather than being seen as an indication of irregularities in the sample, especially locally around and under the indents. Such neglect can bias results toward a more favorable rather than a true hardness evaluation. Use of recording indenters [111] should be valuable to determine the nature and extent of effects of loading (and unloading) rates, times, environment, and local variations, especially for better documentation and understanding of indent associated cracking, as was indicated earlier. A specimen preparation factor impacting test factors is the load dependence of H not only on the final surface finish but also on earlier surface finish steps if the extent of cracking and especially surface work hardening of earlier finishing steps are not fully removed by subsequent finishing steps [19].

The first of the more extensive specimen factors impacting hardness is composition. Beyond the fundamental factor of the basic chemical composition of the body, e.g. NaCl versus TiC, are variations in composition, due both to stoichiometry and to other (added or accidental) constituents. Though commonly

neglected, it was shown earlier that variations in stoichiometry often have their major effects via impacts on G, e.g. B4C (Fig. 4.11). However, it appears there is also an intrinsic effect of stoichiometry beyond that via effects on G. This is more strongly indicated in TiC, where there is again some tendency for G to decrease with increasing C/Ti ratio [74]. A related compositional factor is phase content, which can be quite important (e.g. in Si3N4, Fig. 4.13), but substantially less in other materials, e.g. SiC.

The presence of added constituents of the same or different species of the body can also be important, with the former being an important factor in stoichiometry. Greater effects are indicated when the added constituents result in a second phase versus being in solid solution. Thus modest effects are indicated by solid solutions with Al2O3 [95–98], and possible greater effects from precipitates [100], e.g. due to excess Al2O3 in MgAl2O4 precipitating out in single crystals [101]; but much more study is needed. Similarly, effects of grain boundary phases can be significant, e.g. as in Co bonded WC (Fig. 4.5). Note that precipitation may also preferentially occur at free surfaces, as indicated in MgAl2O4 [101] and can also preferentially occur at or near grain boundaries. The above phenomena may interact with the G dependence of H in different intrinsic and extrinsic fashions. Thus both stoichiometric variations and second phase versus solid solution are typically in part (nonuniquely) related to grain size due to interactive effects of starting particle size and temperature on G. Totally unexplored is these compositional effects on hardness-related cracking and its G dependence.

One of the major limitations of H–G data, as in all microstructural property dependence, is microstructural characterization beyond that of composition noted above. Basic to this is the measurement of G itself, which presents three problems: (1) considerable H data is limited in its use because no specific G values are given, (2) besides uncertainties of factors such as grain shape, difficulties arise due to different (often unspecified) measurement methods, and (3) conversions to a “true” grain size, with both the definition of “true” and the conversion factors commonly not being specified. A fundamental issue is that the slip aspect of the G dependence of H would indicate use of a true three-dimensional or volume measurement of G, while the associated cracking may be more consistent with a two-dimensional surface grain size, requiring more basic understanding. Whether G represents an average as-measured grain diameter or a linear intercept value, or such values multiplied by a factor to give a “true” three-dimen- sional G, G values commonly have differences of 50–100% and possibly as much as 200%. Further, some idea of the G variation, i.e., range or standard deviation, is not given. (Ideally, G would be measured where the indent is made.)

Similarly, limits in other microstructural characterization, e.g. of grain shape and orientation, and of porosity and other constituents, are a probable source of data variations. Porosity is clearly of importance (e.g. Figs. 4.2 and

4.5) [12,15,16] but again presents a number of problems of incomplete characterization. While the amount of porosity is often given, its homogeneity, size, and relation to the grain structure are often not given. These latter issues can be important, since indents cover small areas, so heterogeneities in porosity can give “bad” (typically discarded) indents, biasing results. Such problems are more likely to occur with limited levels of porosity and medium to larger pores.

Most data is in the conventional G range of 1 micron and larger. There can be contamination problems in obtaining dense bodies with nanoscale grains (e.g. Chap. 3, Sec. V.A), which often get more severe as G decreases, which may be the source of H decreasing with decreasing nanoscale G for TiAl (Fig. 4.5). However, other bodies with such fine G are reasonably consistent with larger G body data. This is clearly the case for WC+ 10% Co [80,81] with G down to 300 nm (Fig. 4.5) and appears consistent with TiO2 data [29,31] when corrected for porosity. More recent data of Vaßen and Stöver [119] for SiC (mainly β) with G down to 80 nm with limited oxide boundary impurities and > 95% theoretical density showed HV (10 N) increasing from 23–24 GPa at G 0.3–5 m to 24–27 GPa at G 100 nm (= 0.1 m) and also supports continuation of H–G trends to finer G with suitable purity and density. Their earlier data [120] covered a broader range and clearly followed a G-1/2 dependence.

B.Basic Mechanisms of Cracking

Two closely related key issues are the H minima and related indent cracking as a function of G. Materials of moderate to high hardness for which the most comprehensive range of H–G data are available, e.g. Al2O3, (Figs. 4.1 and 4.2), MgO (Fig. 4.4) , MgAl2O4 (Figs. 4.8 and 4.9), and ZnS (Fig. 4.15), almost always have an H minimum at intermediate G, e.g., in the 10–50 m range, especially as indent load increases. Despite more limited data, this trend for H is also indicated for hard nonoxides, e.g. TiB2 (Fig. 4.10), SiC (Fig. 4.12), and Si3N4 (Fig. 4.13) extending the H and bonding range of the minima. Thus as G decreases from single crystals (G = ∞), H first decreases (instead of a steady increase for a simple Petch relation) and then increases with further decreasing G. Single crystal or large G values are generally higher in comparison with intermediate and often some finer G values though the single crystal values are therefore typically obtained on only one or two low index crystallographic planes, which usually do not represent the highest crystal H values. Such minima tend to be more pronounced with higher loads, and probably Vickers vs. Knoop indents. The occurrence and nature of such minima thus explain what were previously seen as anomalous hardness dependence, e.g. of Armstrong, et al.’s [8] BeO data (Fig. 4.3).

The correlation of cracking with the H minima suggests it causes the minima, e.g. when G 1–3 times the indent diagonal (Table 4.2), superimposed on

the normal Hall–Petch H–G-1/2 relationship based on microplasticity. Though there is considerable variation in the scope and character of such cracking, grain boundary fracture is dominant whenever boundaries are near the indents indicating varying (statistical) grain misorientation, residual boundary porosity, and phases being factors. The importance of grain boundaries as well as of impurities is clearly shown by effects of grain boundary phases known to enhance intergranular fracture and lower fracture energy/toughness, i.e. residues from use of LiF in densifying some MgO and MgAl2O4 greatly enhance grain boundary fracturing around indents (Fig. 4.20). The broad ocurrence of such cracking over various material types and characters, e.g. from some softer oxides to much harder oxides and nonoxides, further reinforces the roll of cracking, again generally along grain boundaries. This correlation of cracking, especially along grain boundaries, is reinforced by such cracking being a maximum when the indent size is G, i.e. when indent stresses are high on local grain boundaries of larger grains. Limited other observations support such cracking, e.g. when the indent size was G in Al2O3 [121]. Very limited data indicates cracking occurs mainly on loading versus unloading, consistent with the former presumably having greater H effect; but this is another area for further research.

The importance of grain boundaries in such cracking suggests factors affecting grain boundary fracture as basic material properties impacting the process. In harder materials this suggests factors such as the degrees of elastic anisotropy (EA) and thermal expansion anisotropy (TEA), and deformation–boundary effects. Thus the apparent absence of such cracking in Y2O3 may reflect material property effects (e.g. as suggested by apparent avoidance of intergranular fracture in it, Chap. 2, Sec. II.D [122]), as does the apparent absence of such cracking in many softer materials. However, data indicates a probable absence of such cracking in less refractory, much softer materials such as some halides and chalcogenids, as might be expected from the easier and generally greater plastic flow in softer materials. While these cannot be fully sorted out, the following evaluation and summary in Table 4.5 provide some guidance.

Both TEA and EA are probable factors, since they can lead to considerably varying stress concentrations at grain boundaries. TEA clearly begins at mater- ial/body-dependent G values, and EA is believed to have similar dependences [123], explaining the apparent absence of indent-related cracking at fine G. TEA, which occurs only in noncubic materials and clearly commonly leads to grain boundary fracture (Chap. 2, Sec. II.C), is probably a factor in conjunction with local indent-induced stresses. Thus the more extreme H minima indicated for TiB2 versus Al2O3 and BeO, which have lower TEA, suggest TEA as a factor. However, αSiC (noncubic) has low TEA and β (cubic) SiC no TEA [121] but a substantial H minima. On the other hand, SiC and other cubic materials, e.g. MgO, MgAl2O4, and ZnS, all have substantial EA (as does TiB2) [124,125] and substantial H minima indicating a nonexclusive role of TEA due to EA impact.

aHardnesses of xl = single crystal and min. = polycrystalline minimum, both in GPa, from Figs. 4.1–4.15.

bValues from Refs. 124 and 125. cValues from Refs 123, 126, and 127.

However, a single direct correlation with EA is questioned by the apparent absence of an H minimum in ZnSe, which has one of the highest EA levels, e.g. 70% > than for ZnS. However, the lower hardness of ZnSe relative to ZnS may enhance plasticity in ZnSe relative to ZnS to the extent that it suppresses grain boundary cracking in ZnSe [whose strength may be controlled by microplasticity (Fig. 3.2)] but not in ZnS. One further factor that is likely to affect such local indent cracking is the anisotropy of slip itself, since fewer slip systems, i.e. greater slip anisotropy (e.g. in MgO [6]), usually result in more stress concentration at blocked slip bands at grain boundaries. This would also be another reason for reduced local cracking as G decreases below G values for the H minima. Thus four

factors are seen as probable material parameters in such local indent cracking. The first three are increased slip anisotropy and resultant boundary stress concentrations and the enhancement of these due to TEA in noncubic materials, and especially and more generally EA in all materials, but often more pronounced in cubic materials. Countering these three stress concentration factors is increased plastic flow to relax stress concentrations, with this generally correlating with lower hardness.

Again, both expectations and limited data indicate that much of the cracking occurs during the indent formation, rather than during or after unloading. However, this is an important area for further study, since understanding when cracking is occurring is important ultimately to fully interrelate H with other physical properties, and it may have important implications for wear, particle erosion, and machining phenomena in ceramics in view of their close relation to indentation effects. The H minimum due to local cracking clearly has important implications regarding use of indent flaws for fracture toughness testing, i.e., potentially precluding use of this over a range of intermediate grain sizes, and it may be related to changing flaw sizes from machining as grain size changes (Chaps. 3, 8, and 12).

IV. SUMMARY AND CONCLUSIONS

The room temperature HV–HK–G-1/2 trends of a variety of generally dense oxide and nonoxide ceramics covering considerable H and G ranges (including single crystals where feasible) show two related material trends. First is the expected basic Petch-type G-1/2 dependence that is commonly found mainly in softer materials, e.g. alkali halides. The other is a deviation from the Petch relation via a superimposed H minimum at intermediate grain sizes. Thus H instead initially decreases from single crystal or large G values with decreasing G vs. the generally accepted trend for H to increase continuously with decreasing G (e.g. a G-1/2 dependence), which is approached at finer grain sizes in this case. This second case is most commonly found in most, but not necessarily all, harder ceramics. The H minimum at intermediate G, which is dependent some on indent geometry and increases in extent and probably in the G at which it occurs with indent load, explains anomalous, non-Petch H–G trends previously observed. The overall H–G-1/2 dependence in all materials as well as single crystal hardness anisotropy are both consistent with plastic deformation by slip as the fundamental mechanism of forming hardness indents.

The H minimum at intermediate G is associated with a maximum of indent related cracking, often of a spalling character along grain boundaries, so the latter is the probable cause of the former. Such cracking tends toward a maximum, i.e. an H minimum, when the indent and grain sizes are similar. The extent of this H minimum tends to be greater for Vickers vs. Knoop indents and as the load increases. It

also shows considerable variability, e.g. a tendency to be exacerbated by residual grain boundary additives, impurities, and porosity, and a probable dependence on local statistical variations of grain orientations and factors such as elastic anisotropy (EA) and thermal expansion anisotropy (TEA). More fundamentally, the H minima and related local cracking are probably due to combinations of TEA, EA, and slip anisotropy driving the process (mainly via grain boundary stress concentrations), and the extent of deformation (generally inversely related to H) and related boundary stress relaxation limiting its occurrence. Other parameters such as stoichiometry may or may not be important; they cannot be sorted out without comparing microstructures, since compositional changes commonly change G, which can be the major mechanism of their affecting H.

Thus a variety of often incompletely determined factors impact H–G relations and need better definition and understanding. Effects of indent type are better, but not fully, understood. Load dependence and its relation to surface finish and subsurface effects (cracking and especially work hardening) need further attention. The mechanism of indent related cracking, i.e. both the issues of where it occurs in the indenting cycle and its intrinsic and extrinsic parameter dependence need much more attention. More thorough characterization of materials is clearly needed to assure full utility of H data and better understanding. Better G measurements are a key need, along with more attention to grain shape and orientation (though single crystal data provides important information on limits of the latter).

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