Mechanical Properties of Ceramics and Composites

Figure 4.11 HK vs. G -1/2 for polycrystalline B4C at 22°C. Data of Rice et al. [7] (100 and 500 gm loads) and Kalish et al. [59] (200 gm load giving a typical indent diagonal of 11 m; numbers above and below this data give the B/C ratio). Vertical bars = standard deviations. (From Ref. 7, published with the permission of the

Journal of the American Ceramic Society.)

corrected to 0 porosity) for G 2–7 m giving values of 21–23 GPa, with a limited decrease as G increases, is in good agreement with data of Fig. 4.10.

Kalish et al.’s [59] HK (200 gm) data for hot pressed B4C with B/C carbon ratios ranging from 3.7 to 5.5 is consistent with that of Rice et al. [7], i.e., lying in the appropriate range between the 100 gm and 500 gm load (Fig. 4.11). Their data show a general decrease in HK with increasing G over the range observed ( 2 to 23 m), indicating that G was a more important factor in changing H than was the B/C ratio itself (though G was probably highly influenced by the B/C ratio). This data does not show a clear H minimum, but data for B/C = 3.7–3.8 may indicate one at G 20 m. The limited data of Rice et al. [7] would not indicate an HK minimum at 100 gm load (in fact, if taken literally, it would imply a maximum) but would indicate an HK minimum at G 25 m (500 gm load). Data of

Munir and Veerkamp [60] on their hot pressed B4C showed HV (unspecified load) decreasing from 48.5 GPa at G 2 m to a minimum of 42 GPa at G 17 m in reasonable agreement with HK data of Fig. 4.11.

Niihara’s [61] substantial tests of 6H SiC crystals shows 100 gm HK 24–27.8 GPa as a function of orientation on (0001), 26.9–31.5 GPa on {1010}, and 21.9–29.8 GPa on {1120} planes, in good agreement with Sawyer et al.’s

[62]data for the same α crystal planes of respectively 29.5, 21.3–27.6, and 23.9–27.6 GPa at 100 gm and more limited 300 gm data of Adewoye and Page

[63]of 27.8–31.3 GPa and of Fujita et al.’s [64] 500 gm values of 20–28 GPa (see also McColm [65] for some values). Page and colleagues’ 1 kg polycrys-

talline SiC data [62,63,66,67] by itself suggests HK first decreases and then increases as G decreases, i.e., an HK minimum at G 10 m (Fig. 4.12). The limited (500 gm) data is consistent with Page’s 1 kg data. While the limited 100

FIGURE 4.12 HK–G -1/2 data for single and polycrystalline SiC at 22°C. Data of Rice et al. [7] (100 and 500 gm loads, giving typical diagonals respectively of 7 and 20 m) and of Page et al. [62,63,66,67] (1 kg). Vertical bars = standard deviations. (From Ref. 7, published with the permission of the Journal of the American Ceramic Society.)

gm SiC HV data is insufficient to show any trend, higher load data of Rice et al. [7] and the literature [7,23,62] suggest an HV minimum e.g. at G 30 m (500 gm). The phase content of some of the polycrystalline bodies varies or is not specified for some bodies, so some of the variation probably reflects varying α and β contents, which does not appear to have near as marked H impact as for

Si3N4.

HV SiC data shows similar trends, e.g. 100 gm values on the same crystal planes of 27–32 GPa of [68], and 500 gm values of 30.2–32.5 and 37.7–46.7 GPa at 100 gm [69]. The limited 100 gm polycrystalline data of Rice et al. [7] was again scattered (but in a different fashion from the HK data on the same specimens indicating specimen variations), but their 500 gm load data indicates a probable HV minimum, as did data of Page et al., but at uncertain G values. More recent data on CVD SiC of Kim et al. [70] and Kim and Choi [71], though complicated by incomplete grain characterization, e.g. of varying degrees and types of grain orientation and colony structure, supports H increasing as G decreases at finer G. Again, more limited effects of α and β contents is indicated. More recent data at nanoscale G is generally consistent with H for normal G values (see Sec. III.A).

While TiC data is generally limited in the G range, especially for any one investigator, collectively there is considerable data (mostly for G ≥ 10 m), which is generally reasonably consistent for a given load range and indenter between different investigators. Collectively, this data is consistent with an HK, and especially an HV minimum at G 20 m). The single crystal HK data of Rice et al. [7] (for material believed to have a Ti/C ratio of 1) and the single crystal data of Rowcliffe and Hollox [72] and Hannick et al. [73] agree fairly well. Also, the highest Ti stoichiometry (0.93) data point of Miracle and Lipsitt [74] (1 kg load) agrees reasonably well with the similar G data of Rice et al. [7]. Similarly, there is reasonable agreement of HV crystal data of Rice et al. with that of Kumashiro et al. [75] and that of Shimada et al. [76] (1 kg load) on {100}, which gave 26–28 GPa, as well as the large G ( 400 m) data of Cadoff et al. [77]. Data of Yamada et al. [78] also indicate H increasing with the C/Ti ratio and agrees with HV values of Rice et al. HV data of Yamada et al. and of Leonhardt et al. [79] both indicate H increasing at finer G, as overall does the other data.

Limited data for pure WC of Lee and Gurland [80] clearly indicates a marked increase in HV (15 kg load) as G decreases from 4 to 1 m ( Fig. 4.5). Limited data of McCandlish et al. [81] (see Andrievski [30]) with somewhat smaller (nanoscale) grains in WC + 10 vol% Co also shows H markedly increasing with decreasing G, consistent with most other materials. Most, and probably all, of the lower H values for the WC-Co body versus those for pure WC of the same G are probably due to the effects of the Co, i.e. this data appears consistent with the model of Lee and Gurland [80] for effects of the Co boundary phase on the hardness of such bodies.

While there has been extensive development of AlN, hardness data is limited, especially over a reasonable G range. However, Rafaniello’s more extensive data clearly shows HV (9.8 N) decreasing with increasing G, e.g. decreasing 10% between G 2+ and 12 m from 10+ to 9- GPa [82] (Fig. 5.4).

McColm [65] has compiled much of the limited BN data, giving HV for hexagonal material 2 GPa versus 46 GPa for cubic material for loads of 0.25–1.5 N with unspecified G. He also reports values of 35 and 42 GPa for bodies with G 3 m with respectively 10 and 85% cubic content, thus providing extreme examples of the impact of phase content on H. He further compiled HK ( 4.9 N load) data on bodies of G = 1–3, 1–5, 3–9, and 10 m giving respectively 39, 34, 33, and 30 GPa, thus implying a typical H decrease with increasing G at finer G, but there are uncertainties due to differing binder compositions and amounts as well as probable variations in residual porosity. Single crystal values of 43 GPa at the same 4.9 N load again suggest an H minimum. [This HK value is consistent with another (1 kg load) of 45 GPa [3].]

Polycrystalline (mainly hot pressed) Si3N4 data of Rice et al. [7] is generally consistent with other data [13,14,23,65,83–85] for similar bodies, i.e. those with substantial β-Si3N4 content (Fig. 4.13). This data is also consistent with that of Mukhopadhyay et al. [86,87] (H 12–15 GPa for G 1–4 , data not shown in Fig. 4.13 to avoid confusion). Niihara and Hirai’s HV (100 gm) data for CVD (pyrolytic) polycrystalline SiC [11], along with (α) single crystals [62,63,66,88,89], is clearly above almost all hot pressed Si3N4 data. Grain boundary phases from additives and impurities in hot pressed samples probably contribute to their lower values. However, significantly lower β- versus α- Si3N4 polycrystalline or single crystal values are again shown, as previously reported [13], so variable β contents in hot pressed samples are an important reason for their lower and variable values. Distinctly lower H for β- vs. α- Si3N4 was shown by Greskovich and Yeh [13] and more recently by Ueno [90]. Both the hot pressed and especially the CVD (pyrolytic) data clearly suggests H first decreasing with increasing G (as also reported by Mukhopahyay et al. [86,87]) and then subsequently increasing, with single crystal values being higher than at least most of the range of polycrystalline values, i.e. a distinct HV minimum at G 20–100 m at 100 gm load for CVD material and also possibly for hot pressed material, since it typically contains considerable β-phase. This trend for an H minimum provides an alternate explanation for the failure of Niihara and Hirai’s data to extrapolate to single crystal values, which is consistent with a broad range of behavior of other materials, seriously questioning their proposed G –1 dependence of H. Note also that the data collectively indicates a probable H minimum at higher, e.g., 500–1000 gm, loads.

FIGURE 4.13 HV vs. G -1/2 for single and polycrystalline Si3N4 at 22°C. Data of Rice et al. [7] (100 and 500 gm loads) and other studies at 100, 500, and 1000 gm loads as shown. Note that P indicates pyrolytic, i.e., CVD, Si3N4, H hot pressed, and α and β the predominance of these respective phases. Where specific data on additive content for hot pressed material is available, it is shown next to the data point (one data point for 0% additives is the result of high pressure hot pressing [84]). Vertical bars = standard deviations. (From Ref. 7, published with the permission of the Journal of the American Ceramic Society.)

C.Effects of Indenter Geometry and Load, and Other Constituents and Materials

Pyramidal indenters such as Knoop and Vickers have planar sides that make uniformly shaped indentations that vary only in relative size with indent load. However, such indenters give different hardness values due to differences in interaction with differing surface layers and microstructures as well as their not being defined on the same basis, i.e. Knoop and Vickers hardnesses are defined respectively by the maximum cross-sectional area and the actual surface contact area of the indenter with the material [91]. Table 4.1 summarizes the approximate average hardness values for common ceramic materials with substantial data for Knoop and Vickers hardness for 100 and 500 gm loads. This shows that

while HK > HV at a 100 gm load, often substantially so, the reverse is generally true at 500 gm loads. Since indent dimensions are inversely related to H values, and the H minimums commonly observed are related to indent-to-grain-size ratios due to cracking, as discussed in the next section, this indicates some relative shifts in H minimum with indent geometry and load and related cracking and the grain sizes at which they occur.

While Knoop and Vickers indentations are dominant for ceramics, some, mostly older, ceramic data has been taken with spherical indenters due for example to wider use of such indenters for metals. Only a fraction of this limited ceramic data is available as a function of G, but spherical indenter tests are common in metals where a Petch-type relation is generally followed, e.g. Bunshah and Armstrong [92]. Floyd’s Rockwell 45N scale data for a 96% alumina composition with G varying from 6 to 25 m clearly also follows a Petch-type relation [93], as does the Rockwell A hardness of WC-12 wt% Co (G 1–6 m) [94]. Given the typical large size of such ball indenters, and the high loads commonly used, a possible H minimum could occur with such indents but would be expected at much larger grain sizes [i.e. use of different size indenters could be useful in better defining the occurrence and mechanism(s) of such H minima along with load dependences].

Consider next the effects of other constituents on H, a large subject that can be only outlined here, highlighting possible impacts on G dependence of H. (See also Chap. 7, Sec. II for data on temperature dependence of hardness and Chaps. 10 and 11 for hardness of ceramic composites.) Impurities or additives that are in solid solution can affect H values. While solid solutions can reduce H, e.g. as indicated in alumina rich MgAl2O4 crystals (Fig. 4.9), it often increases H, e.g. as illustrated by alumina data. Thus Belon et al. [95] showed that 2 mol% additions of isomorphous single (Cr2O3, Ti2O3,V2O3, or Ga2O3) or mixed oxides (MgTiO3) individually increased HK values (unspecified load) of A12O3 by 15–25%, while simultaneous additions of Cr2O3 with Ti2O3 or Ga2O3 increased H values 35–40%. All additions passed through H maxima at 1.5 (Cr2O3) to 3 (MgTiO3) m/o additions (in bodies made via vacuum melting, with additive levels determined after fusion). These A12O3 results are similar to those of Albrecht [96] showing an H maximum at 3 mol% Cr2O3. These Cr2O3 addition results are in contrast to those of Bradt [97] showing a linear HV (500 gm) increase of nearly 1% per m/o Cr2O3 to at least 12 m/o in samples hot pressed at various temperatures (but with the reduced surface layer removed). Shinozaki et al. [98] showed similar, but varying, results with HV (200 gm) increasing by 10–15%, peaking at 20 m/o (with higher H for firing at 1600°C and somewhat lower H peaking at 15 m/o for firing at 1700°C, both under reducing conditions). These different results probably reflect different rates and extents of Cr2O3 solution due to differing degrees of mixing, reduction, and firing, which have received little or no attention, but which may impact H directly or via G. However, Shinozaki et

al.’s results imply a lower H maximum at lower Cr2O3 levels with larger G expected from higher firing. Bradt clearly showed lower H due to larger G (e.g. 10 versus 2 m), but details of composition-processing-microstructure-hard- ness need further clarification.

The above variations in part indicate two sets of complexities of studying composition effects on H. The first set is due to additions of other materials impacting both sintering and grain growth, so truly valid comparisons can only be made by comparing bodies of sufficiently similar microstructures directly or by correcting results for such effects (e.g. using results of this chapter). These complexities are compounded by the extent of homogeneous mixing achieved, which is a complex function of the uniformity and scale of initial mixing and the tem- perature–time (and possibly atmosphere) of densification or additional heat treatment. The firing atmosphere can be important, since the stoichiometry of the additives, matrix, or both may be altered, impacting the extent and character of the solid solution. Such effects are closely related to those of stoichiometry of even a single constituent body, e.g. effects in bodies more susceptible to stoichiometric variations such as Cr, Ti (e.g. note effects on crack propagation, Fig. 2.5), and Zr oxides and B, Ti, and Zr carbides. Thus again note that major effects of stoichiometry are often primarily via effects on G, but there is some residual effect of the stoichiometry alone, e.g. B4C (Fig. 4.11) and TiC [7,74]. The second set of complexities, stoichiometry variations of the body, additive(s), or both, may often vary with depth from the surface, which may vary with grain size due to differing temperature giving different G values, and to effects of grain boundary diffusion, which may be dependent on G values. For the above reasons, especially the latter one, single crystal data for the stoichiometry or composition considered are a valuable guidepost to compare with polycrystalline results, e.g. as extensively shown by results reviewed in this chapter. Thus data for carbide crystals of differing stoichiometry clearly show differing H values.

Effects of additives or impurities on H values as second phases may differ, often substantially, from those found with solid solution, with two extremes often having differing results. The first extreme, often with the greatest differences and variations, is formation of a second phase along grain boundaries. As briefly noted earlier (Fig. 4.5, see also Chap. 10), a softer bonding boundary phase such as Co for WC reduces hardness in proportion to both the hardnesses of the two phases, their volume fractions, and their microstructural character, i.e. grain size of the matrix and mean free path between binder phase boundary “sheets.” On the other hand, residuals from LiF additions in MgO (Fig. 4.21) and MgAl2O4 greatly exacerbate cracking around indents due to their enhancing intergranular fracture, i.e. local indent effects similar and related to the macrofracture and crack propagation effects noted for such additives (Fig. 2.12). Similarly, the significant decrease in H with decreasing G at fine G in the limited TiAl data of Chang et al. [99] (see Andrievski [30]) indicating opposite trends from almost all

other materials (Fig. 4.5) may reflect grain boundary impurities left from species absorbed on the nanoparticle similar to those indicated as sources of low strengths in nanoceramics (Chap. 3, Sec. IV.A).

The other extreme of second-phase distribution, which again reflects a composite structure (Chaps. 10 and 11), is homogeneous precipitation. Thus while effects will vary with the amount and the chemical and physical nature of the precipitate versus those of the matrix, precipitation commonly increases hardness values over those for solid solutions of the same composition. For example, studies of TiO2 precipitation in Al2O3 of Bratton [100], show that the precipitation of the modest levels of TiO2 solid solution achievable ( 0.1 wt%) increases HK values by 10–20%. Similarly, it is well known that precipitation in alumina rich MgAl2O4 crystals can increase H values, e.g. by 15%, but with varying dependence on heat treatments, e.g. Lewis et al. [101]. However, again note that in differing polycrystalline compositions varying spinel stoichiometry has much of its effects on H values via its impact on G.

ZrO2 bodies with varying additives for partial or full stabilization of the cubic or tetragonal phases can reflect various combinations of the above secondphase distributions. However, while such effects must be factors in the variations (and probably the indications of limited G dependence), the data, mainly for different types and levels of Y2O3 stabilization, does not appear to be a large factor in the H–G dependence, nor of ZrO2-Y2O3 crystals [7,39]. The consistency of the ZrO2 trends with other data, despite variable Y2O3 compositions, reinforces the limited effect of Y2O3 content.

Consider now other, primarily softer, less refractory materials, starting with limited halide data from a previous compilation [12] (Fig. 4.14), where, while not always specified, loads were commonly 100 gm. Both the KCl and the BaF2 HV data, while each consisting of one data set for single crystals and a few or one for the respective polycrystals (G 10 m), indicate little or no opportunity for an intervening H minimum. Such proscription of an H minimum is uncertain for the one HK data set for MgF2 crystals and two data sets for finegrain polycrystals.

HV and HK data on various rocks of nominally single-phase composition of Brace [102,103] all indicate that any intervening H minimum must be at G > several hundred microns (Fig. 4.14). However, the apparent high loads (to 150 kg) would indicate that any minimum would be at such high G values as would the lower hardness of most of these materials, especially the limestone. Note that the higher H values for dolomite in part reflect solid solution effects, since it is a solution of Mg and Ca carbonates. (Note also that Brace’s data is based on using the maximum G values (with measurement specifics not given), which increases the slopes on Petch plots to the extent of the average to maximum G ratio, which most likely varies some for the different rocks.)

Finally, consider data for cubic ZnS and ZnSe, which have been devel-

FIGURE 4.14 H vs. G -1/2 for KCl, MgF2, BaF2 [12] and PZT [12, 50], and for some nominally single-phase rocks after Brace [102] at 22°C. Note that the latter used the maximum G values, which increase the slopes by unknown and probably different amounts.

oped for IR window applications. Most extensive is HV (10 N, 1 kg and 100 N10 kg) data on CVD ZnS [104–106], covering a substantial G range, which clearly shows H first substantially decreasing with increasing G and then increasing again, so that projected single crystal values would be higher than a fair range of the polycrystalline values (Fig. 4.15). The projected HV value is in good agreement with HV values of 1.8 ± 0.3 GPa from studies of Lendvay and Fock [107] on single crystals with similar multikilogram loads. This data is also consistent with limited, previously compiled [12] polycrystalline data (apparently with low, e.g. 100 gm, loads) for G 3 and 0.8 m, giving respective HK values of 2 and 3 GPa. More limited HK (50 gm load) data for isostructural and similarly prepared CVD ZnSe of Swanson and Pappis [108] for G = 30–100