Mechanical Properties of Ceramics and Composites

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FIGURE 7.8 Compilation of some tensile and compressive strength versus G–1/2 for dense Al2O3 at 1600°C. Note both strengths extrapolate to a common value at G–1/2 = 0, i.e. to the compressive strength of one orientation of sapphire. (From Ref. 28, published with permission of Academic Press.)

failure stress [37] (Fig. 7.10). This again shows progressive reduction of strength with increasing G (linearly with decreasing with G–1/2) and T, as well as the advantage of evaluating the self-consistency of different data sets. Langdon and Pask [37] also noted two other trends consistent with increased plasticity as T increased. The first was the change from mainly a single axial macrocrack for the macroscopic mode of compressive failure at lower temperatures to a more complex mode of conical fracture from the loading platens and lateral barreling as T increased. However, the general onset of bulk deformation at 800–1200°C depending on material and microstructure did not mean the immediate cessation of cracking, which first generally became more complex in terms of character and spatial character and then overall less in extent as T increased further. Second, transgranular fracture was dominant to 1000°C, except for much more intergranular fracture in material made with LiF additions, again indicating effects of residual grain boundary phases. While attributed to somewhat greater CaO and SiO2 impurity levels, the continued transgranular fracture may reflect more ef-

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FIGURE 7.9 Ref. 34 ice compressive strength versus (A) G–1/2 at two temperatures and two strain rates, and (B) test and homologous temperatures (Tm) (G 1.3 mm, strain rate 10–3/s). (Published with permission of Philosophical Magazine.)

fect of the modest amount and size of residual pores along grain boundaries, and possibly the smaller ratio of such pore sizes to G, indicating the need for more detailed study. Thus while macroscopic ductility was generally substantial by 1200°C and further increased as T increased, there was still some cracking to at least 1400°C, again with some of it transgranular (in a body made without LiF additions).

Data of Ünal and Akinc [38] for one body of dense sintered Y2O3 (cubic, with G 5–40, average 25 m) showed similar results at a low strain rate ( 610-6/s). Thus bulk deformation, which occurred at 1200 but not at 1000°C, while terminating the axial macrofracture mode, did not immediately eliminate macrofracture; incompletely developed and connected axial cracks still formed, but they became progressively less extensive as temperature further increased. Both the compressive yield stress decreased more rapidly and true plastic deformation increased above 1200°C in comparison to brittle fracture at lower temperatures. While much of the fracture was intergranular, some transgranular fracture was observed to at least 1200°C.

Comparison of H/3 values and G–1/2 = 0 intercepts for compressive strengths of Al2O3 and MgO (Figs. 7.7 and 7.10) in Figure 7.11 shows that they

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FIGURE 7.10 Compilation of compressive strength data for MgO versus G–1/2 at various temperatures, data mainly from Evans [32] and Coply and Pask [36], after Rice [28]. However, data of Ref. 37 for the yield stress of MgO crystals stressed along <111> axes, which is at or somewhat above polycrystalline yield stresses, is shown by arrows at the left axis (top to bottom) for 1000, 1300, and 1600°C. Slopes for the different test temperatures have been adjusted modestly to account for the single crystal data. Note the designation of whether a data point represents fracture (F) or yield (Y). (Published with the permission of Academic Press.)

generally parallel each other, as expected. However, H/3 for each material is higher, with the difference possibly increasing as T increases. This indicates the need for further evaluation of H–yield relations as discussed later. Also shown in Figure 7.11 is the tensile yield stress for MgO crystals as a function of T from Day and Stokes [39]. This again shows the convergence of tensile and compressive behavior, especially in single crystals, as plasticity becomes more extensive as T increases, i.e similar to data for Al2O3 (Fig. 7.7), as was also suggested above for ice.

Two other factors show that the general correlation of compressive strength and hardness continues to high temperatures, but that the relationship

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FIGURE 7.11 Stress at the G –1/2 = 0 intercept, actual single crystal yield, or H/3 for Al2O3 and MgO as compiled by Rice [28]. Note the convergence of the tensile and compressive yield stresses of MgO by 1600°C, i.e. similar to Al2O3 data of Figure 7.7. (Published with permission of Academic Press.)

also must vary some from the simple H/3 correlation. The first is Lankford’s [27] measurements of both properties on the same bodies, showing that the two properties do not follow parallel paths as a function of T, but compressive strengths decrease more rapidly with T. Thus the ratio of hardness to compressive yield stress varies and is often higher at higher T (Fig. 7.6). Second, the G dependence of compressive strength appears to be substantially greater (e.g. nearly twofold in Fig. 7.12 for TiB2) than that of H at elevated T, as is also noted at room temperature. Kohlstedt [20] considered this issue in conjunction with his study of H of refractory NaCl structure carbide crystals discussed earlier, especially above the brittle–ductile transition where the discrepancy was greatest. He applied Marsh’s [40] theory of indentation deformation, obtaining H 4.5Y instead of 3Y (see Sec. IV), which was in the right direction but still too low in comparison to the data. He cited higher strains and strain rates in hardness versus strength testing as a probable important factor in this difference, but it is clear that more study is needed to refine understanding of H and yield relations beyond the approximate, but useful, correlations observed.

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FIGURE 7.12 Compressive yield strength of dense sintered TiB2 versus G–1/2 at 1750–2000°C ( 58–65% Tm) of Ref. 41. Their data and fitting the points for each temperature to a common activation energy of 0.8 eV/atom show a clear Hall–Petch relation. (Published with permission of the Journal of Materials Science.)

Ramberg and Williams’ [41] study of the compressive strength of dense sintered TiB2 in vacuum (5 10-4/s strain rate) showed that macroscopic plastic deformation was seen only above 1700°C, where a clear Hall–Petch relation was shown (Fig. 7.12). They attributed the plastic deformation to slip, consistent with their evaluation that five or more independent slip systems can operate in TiB2 at high T. Their tests of a single crystal at 2000°C gave a fourfold higher yield stress than indicated by projection of the polycrystalline data to G–1/2 = 0. This was attributed to the presence of laminar TiC precipitates hardening the single crystals.

The above studies, though useful and more substantial than most, reflect the common tendency to neglect measurements between 22 and 1000°C. Though Lankford’s studies of compressive strengths and hardness are for only one body (hence a given G) for each of three materials, Al2O3, SiC and Si3N4, his results (Fig. 7.6) are important for showing substantial changes at lower temperatures, direct correlations of H and σC for the same body versus temperature, and

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the impacts of test variables such as strain rate [42]. Consider first his Al2O3 data, which shows more extensive and complex changes, all of which are of some uncertainty in their origin but appear real and some related to other effects. Thus the initial increase in H to 200°C may reflect water desorption effects as shown by Westbrook’s results [11,14] of the previous section. The apparent H minimum at 250°C probably correlates with the more definitive σC minimum at 200°C, especially since the σC minimum shifts in temperature and magnitude with strain rate (Fig. 7.13), which increases its similarity to the larger, anomalous tensile strength minimum (Fig. 6.12). This correlation is further suggested by the fact that this minimum appears to be due to twinning, whose presence has been activated in (but not necessarily restricted to) compressive testing. Thus Lankford attributed the compressive strength peak at 300°C to enhanced twinning [27]. This is not necessarily inconsistent with twinning being the cause of the σC minima at modestly lower T, since the temperatures of these minimum and maximum strengths are dependent on test conditions, especially strain rate (Fig. 7.13), and Lankford notes that twin thickness increases substantially as T increases over this range {42–45]. This increased twin thickness could substan-

FIGURE 7.13 Compressive stress versus test temperature for a dense polycrystalline Al2O3 (G 25 m) for a wide range of strain rates. Note the designation of the general changes in fracture mode and in twinning and related acoustic emission. (From Ref. 42, published with permission of the Journal of Materials Science.)

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tially change its effects as indicated. The differences between the H and σC minima may reflect differences in stress state, i.e. much of the stress around an indent is hydrostatic, while that in compression is uniaxial, which is more effective for activating twinning.

Lankford [46,47] has also reported on the T dependence of compressive strengths of a Y-PSZ crystal and a commercial Y-TZP (fine grain) and Mg-PSZ (larger grain) to 800°C, with some observations on mechanisms, strain rate, orientation, and grain size effects. Thus crystals with 5 w/o Y2O3 stressed along <100> and <123> directions showed both differences in compressive ultimate strengths and deformation behavior at 22°C as well as in changes at higher T, e.g. 700°C. It was concluded that single crystals, which had ultimate strengths similar or > the polycrystals, reflected combinations of slip, transformation plasticity, and ferroelectric domain switching, while polycrystalline deformation at 22°C was by transformation plasticity and at 800°C by forming unstable shear bands with flow via grain boundary sliding and cavitation.

Briefly turning to his SiC and Si3N4 data, the initially flat H–T trend may again reflect, at least partly, water desorption, while the increase in σC may reflect reduced brittleness, i.e. some limited plastic accommodation. Lankford observed that the rapid decreases in both hardness and compressive strength for SiC and Si3N4 corresponded to transitions from substantial transgranular to substantial intergranular fracture, as he also observed for Al2O3 [27].

Finally, note that work on superplastic flow in compressive deformation of ceramics of sufficiently fine G [48] indicates increased deformation of finer G bodies, at least qualitatively consistent with the G dependence, e.g. Eq. (6.2).

IV. GRAIN DEPENDENCE OF EROSION AND WEAR AS A FUNCTION OF TEMPERATURE

A basic change in erosion and its effects on residual strength due to impact of particles on ceramic surfaces as a function of temperature is increasing plasticity. This results in a basic change from brittle to ductile erosion, which varies as a function of particulate and target character, and especially particle velocity, hence strain rate. As noted earlier, this transition changes the maximum erosion from particle impacts normal to the surface for brittle erosion to an angle 30° from the surface for ductile erosion [1,2].

Very few tests have been conducted as a function of temperature or at any elevated temperature, and there is thus little or no information on grain structure dependence. However, tests by Shockey et al. [49] on normal impact effects on dense Si3N4 (NC132, G 1 m) with either steel or WC spheres 2.4 mm dia. at 20 and 1400°C at velocities of 20 to 200 m/sec indicate changes and complexities that can occur at higher temperatures. While the WC spheres produced elastic fracture (ring and cone cracks) at room temperature, they produced

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elastic-plastic fracture (plastic impressions and radial cracks) at 1400°C. The type and extent of impact damage from WC spheres at 1400°C appeared to be more deleterious than at 20°C under equivalent impact. On the other hand there was no change in the fracture pattern for steel sphere impact at the two temperatures, showing the importance of the impacting material and its character versus that of the target. Though the effects of a cold particle hitting a hot surface is unknown (but is often a real engineering issue), these limited tests indicate complexities even in the absence of varying target microstructures, indicating the need for substantial further study.

The situation with regard to wear is very similar to that for erosion. Thus dry sliding wear tests of dense sintered Al2O3 (G 8 m) plates against themselves of Xiao et al. [50] at 800–1200°C at velocities of 0.002 to 0.2 m/s under applied loads of 107–320 N giving nominal contact pressures of 0.4 to 1.2 MPa showed an important added complication that occurs at high temperatures. This was the formation of a very fine (e.g. nm scale) grain layer within the wear track with the thickness of the layer varying inversely, while the grain size in the layer increased, with the test temperature, e.g. thicknesses of several and 1 m and G 0.1 and 1 m respectively for 800 and 1200°C. They concluded that this layer formed by dynamic recrystallization. While the effects of the starting body grain structure on such recrystallization is unknown, it serves as a signal of added complexity that needs to be addressed in the complexities of wear at elevated temperatures.

V.DISCUSSION

A.Effects of Temperature and Elastic Anisotropy

The set of factors that may affect properties of this chapter are mainly those of the previous chapters, except that their temperature dependence must also be considered, as was partly done in the last chapter. Thus the temperature dependence of the various modes of plastic deformation, i.e. slip, twinning, grain boundary sliding, and diffusive creep, must be considered along with their strain rate dependences. A key example of this appears to be the probable contribution of twinning in Al2O3 to the significant flexure and tensile strength minima as discussed in Chap. 6 (e.g. Fig. 6.12). As noted earlier, the similar minima seen for H and σC in the present chapter (Fig. 7.6A) are probably due to the same cause, the differences arising from the differences in stress states and strain rates. The first of two important factors in the probable twinning effects in Al2O3 is the rapid reduction in the stress for twinning and then the thickening of the twins as T increases. The former appears to lead to the significant tensile strength and lesser compressive strength and especially hardness decreases as T increases, while the latter appears to be a factor in the subsequent property increases. The

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second factor is the indicated G dependence of these minima, i.e. the indicated diminution and then disappearance of them at finer G in flexure, which should be checked in hardness and compressive testing. Other more general changes in plastic deformation with increasing temperature are first the general increase in the extent of plastic deformation and the related reduction of stresses to activate it and second the changes in the anisotropy of such deformation, e.g. as revealed by hardness anisotropy and related wear anisotropy. However, such anisotropy clearly does not simply continuously decrease with increasing T; instead it often varies significantly (e.g. Figs. 7.1 and 7.2). While effects of this anisotropy are probably mitigated some by the increased plasticity as T increases, the issue of possible effects of variations in plastic anisotropy with T on other properties should not be neglected.

Two other anisotropies that need to be considered are TEA and EA along with their interactions with each other and with other factors such as anisotropies of plasticity and of single crystal (hence grain) fracture toughness. TEA stresses continuously decrease as T increases, going to zero at the stress relief or fabrication temperatures, and their effect becomes increasingly mitigated by increased plasticity. (Note that there can be some increasing TEA stress as T increases above the fabrication temperatures, where such temperatures are below stress relief temperatures, but this is limited to special low-temperature fabrication.) Further, effects of TEA stresses may be more limited in their effects on properties of this chapter, since they typically do not reflect failure from a single weakest link such as for tensile strength where TEA probably has more effect, as discussed in Chap. 6. However, TEA still probably plays an important role, e.g. in intergranular fracture in wear.

Turning to EA, its effects are probably more complex and pervasive, the latter arising from the fact that EA occurs in essentially all crystalline materials, frequently being as substantial or more in cubic versus noncubic materials, while TEA exists in only noncubic materials [51–53]. For cubic materials a common measure of EA is A :

	3(A − 1)			2		2C44
A* =					A =			(7.1)
	3(A − 1)	2	+ 25A
						C11 − C12

where the Cij are the crystalline elastic constants and A is usually given as a percentage [51,52]. For noncubic crystals two expressions are required to define EA, but the one for A shear is most closely related to the above expression. Among cubic ceramics, ZrO2, UO2, MgAl2O4, β-SiC, ZnS, and ZnSe have high EA (e.g. 5–10%, which means that the ratios of maximum to minimum Young’s moduli are 1.5–2), i.e. A of 8% means that the ratio of maximum to minimum Young’s modulus is 2 and that A 20% corresponds to a ratio of 3.

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The complexity of EA effects arises from several sources. One is that the local microstructural stresses due to EA depend directly on the EA and the applied stress and hence generate the highest stresses at and near stress concentrations such as crack tips. The second reason is that EA can increase or decrease substantially, or not change much, as T increases, depending on the material (Fig. 7.14) (and possibly on the temperature range). This behavior is in contrast to that of TEA, which decreases with increasing T, as was noted above, and whose stresses are independent of, and hence additive with, the applied stresses. The effects of TEA on properties clearly depend on grain size (G), and some on shape and orientation relative to the applied stress, as EA effects also appear to, but the latter depend on grain shape and orientation of grain elongation relative to the stress axis as a function of the stress character per modeling by Hasselman [53]. Another general complication for all the various anisotropies is that they can be interactive, but their dependences of crystal orientation, while often the same or similar, can differ substantially.

EA was indicated as a contributor to intergranular fracture (e.g. Fig. 2.3), especially at very large G, SCG, possibly some G dependence of fracture en-

FIGURE 7.14 Sample plots of EA versus test temperature for (A) some oxides, with some compositional effects shown for some ZrO2 and MgAl2O4 bodies (i.e. the latter designated in MgO/Al2O3 ratios) and (B) some halides and SiC. See also note on p. 253 of this book. (From Ref. 51, published with permission of the

Journal of Materials Science.)