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II.GRAIN DEPENDENCE OF HARDNESS AS A FUNCTION OF TEMPERATURE

The unfortunate tendency of investigators to make measurements as a function of temperature on only a few bodies, often only one, with little or no indication of even G is particularly prevalent for hardness. Thus much of the G dependence of H as a function of T must be implied from the extensive demonstration of such dependence at 22°C (Chap. 4) and extrapolations of this to elevated temperatures. Such extrapolations are guided by the reasonable H–T data for one or a few bodies, usually of unspecified G, and single crystals as well as correlation with other related properties. The latter is a useful source of information given H–σC correlations, and more σC–T–G data in the next section. Thus the focus of this section is mainly on the T dependence of H for dense polycrystalline bodies, mostly of unknown or uncertain G, and of single crystals, as well as some comparison of the two, and in turn some comparison of these to E–T changes.

Consider first the issue of hardness anisotropy as a function of the crystallographic plane on which single crystal indents are made and the direction of the apexes of the indenter relative to the crystal directions on the indented plane. As shown in Chapter 4, there is frequently substantial hardness anisotropy at room temperature in many ceramics arising from activation of differing combinations of deformation modes, mainly slip systems, with anisotropy often nearly as, and in some cases more, in cubic versus noncubic crystal structures. Since anisotropy of hardness (or of any solid property) must disappear when the material melts, this suggests that the anisotropy may progressively decrease as temperatures increase. However, data for ice crystals [3,4], which have many similarities to α-Al2O3 on the basis of homologous temperatures, shows substantial relative H anisotropy, e.g. from –5 to –12°C a minimum 35% < maximum H values. Such levels of anisotropy within 2% of the absolute melting point clearly show that H anisotropy does not gradually decrease to zero as T increases toward the melting point.

Other data clearly shows that anisotropy of hardness can vary substantially as a function of temperature for a given material and between different materials. Thus Atkins’ review [5] showed that relative H anisotropy of TiC and VC, both cubic ceramics, respectively decreased substantially from 25 to 250°C (26% to 5%) and then increased some ( 10%) by 610°C; it increased from 5% at –196°C to 7% and then to 18% at 25 and 350°C (Fig. 7.1). Bsenko and Lundström [6] showed little or no change in the relative HV anisotropy of arc melted, noncubic, B rich HfB2, using a lower load (0.5 N) and the large G to make measurements within individual grains from 115 to 210°C, despite a nearly 20% decrease in average HV values. Nakano et al. [7] reported HK (0.1 kg load) for two directions on three planes of TiB2 crystals at 22, 250, 500, 750, and 1000°C showing anisotropy disappearing at 250°C and then increasing with further temperature increases (Fig. 7.2).

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FIGURE 7.1 Knoop hardness anisotropy of cubic TiC and VC shown at three temperatures each. Note that while H anisotropy can decrease as T increases, e.g. in TiC at 250°C, it can also increase as T increases, e.g. in TiC at 610°C and VC at 350°C. See also Figure 7.2. (From Ref. 5, published with permission of the ASM.)

Similar crossover of HK (0.1 kg) curves for differing planes and directions of α-SiC crystals, as shown above for TiB2, was shown by Niihara [8], again at modest T (300–400°C). Overall H decreases of 60–80% were reported for different planes and orientations between 22 and 1600°C, with varying, moderate, but definitive degrees of deviation from linear decreases due to curvatures or inflections in the H–T curves indicating changes in plastic flow as a function of T related to slip changes, e.g. indicating substantial increases in plasticity above 800°C. Similar changes were indicated in HK (0.5 kg load) tests of Fujita et al. [9] to 1400°C, again with crossover of H values for some planes at 300–500°C as well as at 1200°C. Hirai and Niihara [10] reported essentially linear decreases for their HV (0.1 kg load) tests of SiC crystals to 1500°C with less anisotropy (as expected for HV). However some clear changes, but no clear decreases, of H anisotropy were seen along with similar H decreases by 60% or

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FIGURE 7.2 HK (0.1 kg load) data as a function of the homologous temperature (i.e. fraction of the melting point taken as 2980°C) for two directions on three planes of TiB2 crystals at 22, 250, 500, 750, and 1000°C showing anisotropy disappearing at 250°C and then increasing with further temperature increases. (From Ref. 7, published with permission of the Japanese Journal of Applied Physics.)

more. Note that the lower temperature crossovers of H values for one crystal plane versus another commonly correspond to much less initial decrease in H on one plane. A frequent factor in this, besides differing changes in slip, can be desorption of moisture, as indicated by studies of Westbrook and Jorgensen [11] discussed below.

Consider now general H–T data trends for ceramic crystals, starting with cubic oxides. Guillou et al. [12] showed HV of MgO crystals ({100} surfaces) and Ca-CZ (Berkovich hardness, HB, on {111} surfaces) both decreasing to 30–40% of their 22°C values at 800°C (Fig. 7.3A), i.e. an order of magnitude or more than expected E–T decreases. Their MgO data is consistent with the mutual indentation (HM) data for MgO crystals of Atkins and Tabor [13] and Westbrook’s [14] data for indentations within single grains of polycrystalline MgO. Turning to noncubic ceramics, Kollenberg [15] showed HV (2–3.9 N loads) for three sapphire orientations being similar to that of Alpert et al. [16] for 10 N load, showing similar decreases to 26% of their 22°C values by respectively 750 and 1000°C (Fig. 7.1B). Kollenberg [17] also showed HV ( 1–2 N loads) for five orientations of hematite (Fe2O3) crystals (isomorphous with sapphire) substantially ( 90%) decreasing with some variations in anisotropy and in overall H values with T in tests to 800°C ( 0.6 Tm). These H decreases in single oxides such as Al2O3 and Fe2O3 are in marked contrast to a decrease to 70% of their HV (2 N load) value at 22°C by 1000°C in Kollenberg and Schneider’s [18] measurements on (001) and (010) surfaces of mullite crystals. This decrease of <

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FIGURE 7.3 Hardness versus temperature for selected crystallographic surfaces on crystals of cubic ZrO2-CaO and MgO [12], and noncubic Al2O3 [15,16] and mullite [18]. All hardnesses are Vickers with similar loads, except Berkovich (HB) for the Ca-CZ and mutual indentation (HM) for the higher T tests of MgO. Note reasonable agreement for the different MgO tests. (Published with permission of the British Ceramic Society, the Journal of Materials Science, and the Journal of the American Ceramic Society.)

1/2 that of Al2O3 over the same temperature range, despite mullite having a lower melting point, is attributed to greater difficulty of plastic deformation in such multiple constituent materials due to the requirement of cooperative motion of the added atomic species. Such results are consistent with those for other multiconstituent materials, e.g. as shown by Westbrook [14], as discussed below. Note that while several of these materials show essentially linear decreases in H over the limited temperature range, this is often not the case, as indicated by MgO and Ca-CZ, as well as a number of nonoxides discussed below.

Turning to nonoxide ceramics, deviations, often substantial, from simple linear decreases in H as T increases occur for both cubic and noncubic ceramics.

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Thus, for example, Kumashiro et al. [19] demonstrated that their HV measurements to 1500°C on {100} surfaces of cubic NbC, TaC, and ZrC crystals, as well as measurements of others on other cubic carbide crystals, showed various, often substantial, inflections in their H–T plots. While plotting data as a function of homologous temperature did not necessarily bring such inflections into coincidence, H values commonly decreased to 25% of their values at 22°C by 1500°C. More extensive is earlier work of Kohlstedt [20] for his measurements on crystals of NbC, TiC, VC, and ZrC showing that all have overall linear H decreases as a function of the fractional Tm (to values of 0.4–0.6), often with reasonable parallelness of some data. However, there were variations such as significant deviations from linearity, parallelness, or both above a fractional Tm of 0.25. His measurements showed little or no deviations to less H increase as T approached 20°C, which probably reflects measurement in vacuum and thus removal of much of the adsorbed water, as is discussed below. Guillou et al. [12] showed the hardness of α-SiC crystals [Berkovich, HB, 2 N load on a (0001) surface] decreasing to 40% of their 22°C values at 800°C (Fig. 7.4A) with a significant inflection between 300 and 400°C. Fujita et al. [9] showed similar as well as different rates of decrease, but similar total decrease for three orientations of HK(500 gm) indents on 6H crystals (Fig. 7.4B). Sawyer et al. [21] showed decreases of 65% from 22 to 800°C. Hirai and Niihara [10] studied HV (100 gm) on three surfaces of 6H SiC crystals, showing modest separations (e.g. 10%) that decreased linearly by 75% to 1500°C. Bsenko and

FIGURE 7.4 Hardness versus test temperature for 6H α-SiC crystals. (A) Berkovich hardness (2 N). (From Ref. 12, published with permission of the British Ceramic Society.) (B) Knoop hardness (500 gm). (From Ref. 9, published with permission of the Journal of Materials Science.)

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Lundström [6] showed linear decreases in HV of arc melted ZrB2 and HfB2, using a lower load (0.5 N) and the large G to make measurements within individual grains, thus giving an single crystal value averaged over the random grain orientations.

Westbrook’s [14] extensive testing and review of ceramic hardness versus T provides useful guidance in considering H–T–G relations. His HV values were at low, 0.05–0.1 kg. loads so indents were typically small compared to the larger (unspecified) G values of his samples, so they are more representative of single crystal values averaged over all orientations. This correlation with single crystal data is shown by direct comparison. Westbrook’s data commonly showed deviations at various temperatures in various materials similar to those noted above, but three additional sources of variations were identified. The first and most general was a trend for an increasing rate of H decrease with increasing T starting at 1/2Tm. The second and fairly general variation was a common lowering of H values at modest temperatures due to adsorbed moisture. Removal of this by heating in vacuum could increase the apparent H values, e.g. by 20–50% over the range of 50–300°C [11,14], as shown by retention of most or all of the higher H values on cooling and testing under vacuum. Due to differing adsorption characteristics by different crystal surfaces, desorption can change H anisotropy and may be a factor in other single crystal measurements, as was noted earlier. The third and more specialized variation was the significant changes that occur in H due to thermally driven crystal structure changes, e.g. increases of up to severalfold in H when the low-to-high quartz structure transition occurs in SiO2 at 573°C [14,22]. This is accompanied by a change in the H anisotropy and a marked increase in the rate of H decrease with increasing T, with similar though less extreme effects of the same phase changes observed in isomorphous GeO2 and AlPO4 [22]. Additionally, Westbrook’s measurements and survey showed on a homologous temperature basis that while binary compounds, e.g. NaCl structure oxides or carbides, may frequently have higher H values at lower T, their rate of H decrease with increasing T is typically substantially higher than that for most or all refractory ternary compounds, e.g. for mullite, spinel, and beryllium aluminate.

Consider now the limited data specifically on the effects of T on the G dependence of H. Though direct comparisons of H values for singleand polycrystals is limited, some does exist to further indicate G dependence as a function of temperature. Thus Alpert et al. [16] showed little or no difference between HV for sapphire and two high-purity polycrystals (G 3 and 20 m), while showing expected progressively lower HV for 96 and 90% (G 11 and 4 m) versus 99+% alumina bodies at lower T, but all merging together by T 1000°C.

There is very limited polycrystalline data over substantial T ranges that can be directly compared with single crystal data, but a few possible comparisons are indicated. Thus Westbrook’s [14] data for Al2O3 shows a decrease from 20 to 6 GPa from 22 to 800°C, i.e. similar to Alpert et al., while his MgO data from 22 to

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900°C shows H decreasing from 8 to 1.1 GPa, i.e. somewhat faster than single crystal values (Fig. 7.3). Additional examples of polycrystalline H values versus T for mostly nonoxides are shown in Figures 7.5 and 7.6. The former shows data for some CVD materials. The latter is of interest because of the H data being on the same samples tested for compressive strength, as is discussed in the next section. Note that, despite the limited T range, there is some tendency for more complex T dependences of polycrystalline H values. While some of this may reflect variations discussed above, e.g. effects of adsorbed water, some of this reflects additional complexities of polycrystalline bodies, e.g. of Al2O3, as is discussed in conjunction with compressive strength in the next section.

Lankford’s [27] results for one dense body each of SiC, Si3N4, and Al2O3 are useful not only because they are better characterized (including G) but also

FIGURE 7.5 Temperature dependence of H of hot pressed B4C and SiB4 (9.8–19.6 N) (B6O falls halfway between these two) [23], CVD diamond (HV, 7 N load) [24], arc-cast UC [25] HV (5.5 kg load), and CVD SiC and Si3N4 [26].

FIGURE

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7.6 Hardness and compressive strength (σC) data of Lankford [27] versus test temperature for (A) Al2O3 and (B) SiC. (Published with permission of the

Journal of Materials Science.)

because of corresponding compressive strength measurements on these, as is discussed in the next section. His hardness results show substantial inflections and changes as T increases for these three materials (Fig. 7.6), which are discussed in more detail in the next section in conjunction with the corresponding changes in compressive strength. However, it should be noted here that while almost no observations have been made on indent cracking as a function of temperature, i.e. much less than the limited observations at room temperature, Lankford [27] has noted this. Thus he reported that Vickers indentation (0.6 kg) generally reflected substantial increases in intergranular fracture around indents with substantial decreases in H as T increased. This was specifically illustrated for dense sintered Al2O3 showing more intergranular and less transgranular fracture at 1000 versus 22°C.

The role of grain boundaries, as indicated by Lankford’s observations of increasing decreases in H with increasing T correlating with increased intergranular fracture, is supported by other observations. A basic one is generally less decrease in H at higher T for crystals versus polycrystalline bodies, e.g. as is indicated by the latter decreasing more rapidly near and above 1/2Tm, as noted by Westbrook [14]. This issue was also raised by Niihara’s observation that elevated T decreases of H are substantially higher in most polycrystalline SiC and Si3N4 than for example in single crystals [26]. However, he presented data for CVD SiC and Si3N4 as well as Si3N4 hot pressed without additives showing much less H decrease with increasing T at higher T, thus focusing on the issue of the character of the grain boundaries. This is also indicated by effects of grain

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boundary phases on high temperature SCG and tensile strengths (Chaps. 5 and 6), and in compressive strength (next section), e.g. residues from the use of LiF for MgO and MgAl2O4, and oxide additions for SiC and Si3N4. However, much remains to be established, including effects of possible preferred orientation and grain elongation, e.g. in many CVD bodies.

III.GRAIN DEPENDENCE OF COMPRESSIVE STRENGTH AS A FUNCTION OF TEMPERATURE

Data for the dependence of compressive strength on grain size and temperature is almost opposite that of hardness. Thus while there was very little actual data as a function of G and T, but considerable data for singleand polycrystals of one (often unspecified) G as a function of T for H, there is very little single crystal data, but reasonable polycrystalline data as a function of G and T. Much of the data available is from earlier studies and has been discussed in three previous reviews, which serve as an important source for this section [28–30].

Reasonable earlier data exists for Al2O3 [28], which, though some requires correction to zero porosity for finer G bodies, shows progressive reduction of strength with increasing G (linearly with decreasing G–1/2) and T (Fig. 7.7). This data also shows increasing indications of plastic deformation as T increases, e.g. above 1200°C, but dependent on strain rate as is shown and discussed further below. Another factor to note is that as T and resultant plastic deformation increase, the difference between compressive and tensile strengths decreases, especially in single crystals where there is no opportunity for differences in porosity generation from grain boundary sliding in tensile versus compressive stressing. Thus by or below 1600°C the G–1/2 = 0 intercept for dense Al2O3 is the same for tensile and compressive strengths at normal strain rates, but the σ–G–1/2 slope is still substantially greater for compressive versus tensile strength (Fig. 7.8).

Consider now ice, a noncubic material that often has similar properties to α-Al2O3 on a homologous temperature basis as noted earlier (Chap. 6, Sec. IV.B; Chap. 7, Sec. II). Schulson clearly showed the typical G–1/2 dependence of compressive strength to at least 96% Tm (Fig. 7.9) with no indication of bulk plastic deformation in stress–strain curves, but nevertheless with strain rate dependence [34]. While Schulson showed this data extrapolating to zero compressive strength at G–1/2 = 0, it could also be consistent with an intercept strength of 0.4 MPa, as found for tensile strengths in similar testing (Fig. 6.13), again indicating convergence of compressive and tensile strengths at higher temperatures, especially for single crystals, though again the strengths and slope of the compressive testing at the same temperature and strain rate are higher than for tensile strength. Gold’s [35] compressive creep studies of ice showed substantial cracking, with the amount of cracking as a function of strain showing maxima that increased in magnitude and occurred at lower strains as the test T increased.

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FIGURE 7.7 Compilation of compressive strength of Al2O3 versus G–1/2 at various temperatures, from limited data of Becher [31] and more data from Evans [32], where data for finer G bodies has been corrected for the volume fraction porosity

(P) to zero porosity per e–bP for the b values shown. The b values were selected to give linear extensions of the σC–G–1/2 for dense bodies at larger G and are consistent with other data and the expected increasing effect of porosity in limiting strength as T increases [33]. Note the consistency with other σC–G–1/2 data for dense Al2O3 at 1600°C in Fig. 7.8. (After Rice [28], published with the permission of Academic Press.)

Cracks were on the scale of 1–2 grains, transgranular, parallel to the compressive stress, and elongated in the direction of the substantial elongation of the columnar ice grains (oriented normal to the stress axis).

Turning to cubic oxides, there is a reasonable amount of data for dense MgO from Evans [32] and Copley and Pask [36] that shows similar behavior, especially when combined with each other and data for the yield stress of crystals stressed along a <111> axis, which is typically at or above the polycrystalline