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= 0). Further, limited fractographic studies showed failure from larger, usually exaggerated grains [100, 239, 240], as has also been found in self-reinforced bodies, often associated with excess additive phase [241–244]. Again note that significant toughness maxima often seen with R-curve effects (Chap. 2, Sec. III.F) are inconsistent with σ – G-1/2 behavior.

Data on graphites and related carbon materials is limited by the extensive complications of the typical substantial porosity and local or global grain orientation and resultant anisotropy of properties reflecting the high crystalline anisotropy, as well as the coupling between these factors. However, limited attempts to sort out the grain size component have consistently shown that strength decreases with increasing G. Thus Brocklehurst’s review [245] notes such G dependence of graphites, citing in particular work of Knibbs [246]. Rice has also presented some analyzed data in a survey [11]. While details of this G dependence of strength such as finer and larger G branches are uncertain, they are not inconsistent with the basic model (Fig. 3.1).

V.COMPOSITIONAL, MICROSTRUCTURAL, AND SURFACE FINISH EFFECTS

A.Compositional and Nanoscale Grain Effects

A diversity of compositional effects can occur ranging from enhanced to reduced strength, which may involve a G dependence or obscure it, e.g. the latter via global effects of body composition on strength through changes in E, or more local changes. Effects mainly or exclusively via global changes in properties impacting strength are only outlined here, since they are a very diverse topic and often require large additions to have substantial effect. However, their effects must often be recognized in order to adequately identify and understand σ–G relations. Both local and global compositional effects on micro-, especially grain-, structure are addressed in more detail. An important separation of effects is in part associated with whether the other constituents are as a second phase or in solid solution.

Impurities or additives that end up in solid solution commonly increase strengths of materials in which microplasticity, especially slip, determines their strength, even at modest levels, e.g. CaO [46–48] (Fig. 3.4), MgO [48, 51, 52] (Fig. 3.5), and BaTiO3 [41] (Fig. 3.3). Such increased strength should be independent of G if a suitable solid solution is achieved, uniformly raising the σ–G-1/2 line. However, a decreased solid solution with reduced temperature–time exposure in obtaining finer G would reduce the σ–G-1/2 slope. Increased solid solution (and undissolved phase, typically at grain boundaries) would commonly result in transitioning from microplastically controlled strength at larger G values. For materials whose strength is controlled by brittle failure from flaws, constituents

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in solid solution may affect strength by altering properties such as E, or EA and especially TEA, but this typically requires substantial contents for significant effects. However, limited study of such possible effects is not definitive (e.g. for Cr2O3 in Al2O3 [10, 145].

While added constituents as second phases can influence microplastic behavior, e.g. via precipitation toughening, effects of such phases have more extensive effects on failure due to preexisting flaws, and some on failure from microcracks. Again, a general effect is via changes in properties affecting strength; a key example of this is effects on Young’s modulus, e.g. of SiO2 (Fig. 3.30), which can lower E substantially. This reduction may or may not depend on the degree of reaction and hence processing conditions that also affect grain structure (though this is often not much of a factor in the Al2O3-SiO2 system, since E is not greatly different for mixtures or compounds of these at a given constituent ratio). Another, though probably less common, property effect that is pertinent to the presence of lesser quantities of SiO2 is surface roughness of asfired surfaces. Some strength increase of alumina fibers containing or coated with SiO2 has been attributed to reduced surface roughness [159].

Other diverse compositional effects include effects on microcracking, either increasing this by forming phases with substantial expansion differences with themselves or the matrix, or decreasing this by reducing intergranular stresses, e.g. as some silica glass phases may. The latter often require less second phase and are often particularly dependent on wetting effects, which at elevated temperature can seriously reduce strengths with more extensively coated grain boundaries. However, serious effects can also occur at moderate temperatures, e.g. Wakamatsu et al. [247] recently showed lower strength in Al2O3 + V2O3 sintered in air due to formation of an AlVO4 grain boundary phase despite some inhibition of grain growth. On the other hand, firing in a reducing atmosphere, which also inhibited grain growth, resulted in solid solution of the V without significant strength degradation, but with a higher surface concentration of V4+.

Another example of variations and complications is with TiO2 additions to Al2O3, which can substantially aid densification [248, 249]. However, net effects can again be dependent on processing and use details. Thus beyond the solubility limit in vacuum sintering, grain growth inhibition occurs [250], but subsequent air annealing can result in preferential diffusion to grain boundaries and the surface with some reduction in strength. Hot pressing with TiO2 + MgO additions has indicated loss of MgO inhibition of grain growth [251]. High-temperature air sintering with TiO2 additions results in large grains, substantial intragranular pores, very rough surfaces, and resultant low strengths. However, oxygen partial pressure can have substantial effects on TiO2 in Al2O3 [252]. Thus while extensive second phase precipitation can have various effects, including toughening, as is discussed for ceramic composites (Chaps. 8 and 9), second phase effects can be complex, varying, and direct or indirect.

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FIGURE 3.30 Effects of SiO2 content on Young’s modulus and tensile and flexure strengths of alumina bodies based on data for fibers and flexure bars. Such data is only a rough guide, since effects of different processing, wetting and reaction, and microstructure are not fully specified or investigated. Curves were obtained from analysis of Steele et al.’s [122] data for bulk alumina bodies and from data for alumina rich fibers [162] by using the experimental correction of σ for lower density, then subtracting the decreases due specifically to porosity, leaving the reductions due to reduced density from the SiO2 additions.

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Consider next effects of local compositional variations, which can cause microcracks, and especially larger local grains, by themselves, or with microcracks, the local phase itself, or both acting as fracture origins. While occurring in several materials, such origins are commonly observed, especially in larger grains, in Al2O3 and in situ toughened Si3N4. Thus formation of larger platelet beta alumina grains that act as origins have been noted in Al2O3 bodies with alkali [253], e.g. especially Na, impurities (e.g. in Bayer processed Al2O3) made without grain growth inhibitors [24] (Figure 1.3A). In Si3N4, large rod shaped grains singly or more commonly two or more in combination with excess additive phase are dominant fracture origins as grain sizes and the level of toughness increase [241–244]. While both the number of grains clustered and the extent of excess additive phase, as well as the location of these relative to flexure tensile surfaces, affect the resultant effective flaw size (Fig. 3.31), there has been little evaluation. Such evaluation is of uncertain relevance to basic σ–G-1/2 behavior, e.g. for projection of strengths to significantly larger or finer grain sizes, since such combinations often represent a significantly different flaw population. Clues to the validity of such extrapolations are the similarity of the larger grain shapes, phases, associated amount and character of matrix phase, and resultant fracture mode to the body matrix. However, the above questions are relevant for understanding strength behavior of such bodies better to control their microstructure and properties. Such cases of heterogeneous larger grains may also reflect some local preferred orientation due to interactions of possible relations of nuclei or the impurity distribution to fabrication effects. Further, impurities or additives can be interactive with each other, as well as with effects of environment on strength.

Consider now the more general case of more global, hence typically more uniform effects of other constituents on grain structure, which are often sought and used to reduce both average and maximum grain size to increase strength. Thus note that stoichiometry variations in spinel samples [84, 85] (Fig. 3.11) had their primary effects via grain size changes, with possible (but unidentified) secondary effects on physical properties such as Young’s modulus. Similar effects are shown with other mechanical properties in subsequent chapters. Other constituents (often nonreactive or nonsoluble ones) are also often added to control grain size, which typically greatly limits exaggerated gram growth and hence also commonly deviations from equiaxed grain shape. Key examples of these for Al2O3 are MgO, ZrO2, Mo, and W (Fig. 3.17). Effects of such additions are commonly primarily or exclusively directly related to the reduction in grain size, increasing strengths, so long as the level of addition is limited. At higher levels of additions such grain growth inhibitors can change effects, e.g. MgO may form larger spinel grains, hence possibly lowering strengths. Both average and maximum alumina strengths increased with increasing Mo additions to 6 vol% and then leveled off (or, especially

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for the maxima, may decrease slightly) to the limits of investigation of 16 vol% [141]. This limitation on effects of Mo additions was attributed to coalescence of Mo particles limiting further alumina grain size reductions but may also reflect some reduced elastic moduli and possibly bonding. However, while increasing AlON additions to alumina (via reaction processing) from 0 to 40 vol% decreased toughness some, e.g. by 10–20%, it gave intermediate flexural strengths [147] (Fig. 3.17), consistent with the intermediate grain size constant over the range of AlON additions (but better retention of strengths at higher temperatures). On the other hand, increased ZrO2 additions enhancedstrength and toughness to the extent that transformation toughening occurs and increases with increasing ZrO2 additions, but at low addition levels (e.g. <6%), the primary benefits come from maintaining fine G [153, 154]. The above constituents, whether additives or impurities, are either metals or compounds with anions giving bond strengths and temperature capabilities similar to those of the matrix material. Significant reductions in strengths at finer grain sizes, attributed to impurities involving anions of much weaker, much less refractory compounds, are discussed below.

While examples of added phases inhibiting grain growth are particularly common in Al2O3, as was outlined above, it is demonstrated in other materials, e.g. BeO with SiC [174, 175] or Al2O3 [173] additions (Fig. 3.19). Though some nonoxide materials such as Si3N4 are less prone in their pure state to substantial grain growth, some important densification aids for nonoxides also significantly limit grain growth, contributing to improved strength via grain size limitations. Thus pure dense WC typically has G values ≥ 10 µm, while metal, e.g. Co, additions generally give dense bodies in which G = 1–3 µm, and pure TiB2 commonly has grains 10 to 20 µm, while densification with Ni reduces G’s to 5 to 10 µm (but again with diminishing returns with increasing Ni content) [212]. Certainly in such cermets and other composites there can be other important effects increasing strength over and above that due to G reduction, but the latter can be an important factor.

Consider now effects of impurities characterized by anions that severely limit refractoriness and other properties that can be pervasive and severe in obtaining much finer, especially nanoscale, grain structures in some materials. These impurities and their effects are almost universally neglected, despite there being both reasonable theoretical, and especially experimental, evidence of their occurrence and effects [254, 255]. They are primarily materials such as hydroxides, carbonates, sulfates, etc., e.g. often the sources of common oxide ceramics, or of impurities (e.g. of Ca), and can form on oxide and on some other material surfaces. They are neglected because it is commonly assumed that their normally low decomposition temperatures preclude their presence in a solid body due to densification temperatures. However, this neglects effects in densification that inhibit decomposition, hence allowing retention of limited quantities of these

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(e.g. from << 1 to a few percent). While there are some chemical interactions (e.g. with densification aids such as LiF) that limit decomposition, a major factor is the pressures commonly used to obtain high densities at low temperatures necessary to limit grain growth and hence retention of finer grains from fine particles. The higher surface areas and lower decomposition temperatures commonly used to obtain finer powders exacerbate the problem by leaving more of these impurities in higher surface area powders to be densified. While such impurities can cause various fabrication problems, they can also be an aid in densification, e.g. the ready direct hot pressing of magnesium hydroxides of bicarbonates to near theoretical density (transparent), high purity (≥ 99%) MgO [256].

There are clear, well documented manifestations of these impurities [254, 255]. A simple direct one is IR transmission of frequently transparent or translucent specimens that commonly clearly show anion species discussed above via their IR absorption bands. More general methods are based on heating, with weight losses, though commonly limited, often being definitive, as is identification of the evolved species, e.g. by mass spectrometry. Particularly demonstrative are clouding, blistering, gross bloating, and in the extreme, crumbling back to powder (e.g. for MgO and Al2O3) pressed to full density at room temperature with GPa) [254, 255, 257] due to the large, 104 leverage in the expansion of the gaseous species released in solid state thermal decomposition on heating.

Turning to the specific effect of such impurities on σ–G relations, it is important to note that such impurities will commonly be mostly or exclusively at grain boundaries, where they will typically have pronounced effects even for very modest quantities, due to their markedly different, usually much lower, properties than the ceramic itself. Thus strengths of MgO, while typically increasing with decreasing G, e.g. to G 10 µm or less [48, 50–54, 254, 255] start decreasing as G decreases further, often falling well below the generally expected strengths at finer G, especially with higher pressure processing to obtain finer G bodies with decreased grain size. The latter clearly show the presence of such anion species as hydroxides and can have their strengths markedly increased, e.g. doubled, by very slowly annealing such specimens to remove the impurity without serious disruption of the body structure. In such cases, the resultant strengths are those projected from larger grain bodies. Note that the decreased strengths of MgF2 at finer G (Fig. 3.24) were correlated with observed OH absorption bands in the transparent bodies [207]. Similarly, decreased Al2O3 strengths at finer G from higher pressure fabrication [64] and demonstrated high temperature outgassing of species from hydroxides, carbonates, and sulfates (e.g. from alum precursors) also strongly indicate the same effects [254, 255]. This is also true of similar reductions in strengths at finer G as higher pressures are used for processing NiO and Cr2O3 in view of their, and their precursor, chemical similarities respectively with those for MgO and Al2O3 [64]. A very important corroboration of these effects is the high strengths obtained in fibers of

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these or similar ceramics. The use of only temperature, not pressure for densification at low temperatures for fine G, along with very small cross ections of such fibers, means respectively that limited quantities of such anion impurity species will be in the fiber, and those there are much more likely to diffuse out of the fibers at their modest firing temperatures.

The above effects in a few common ceramic oxides and one related nonoxide, MgF2, probably reflect only a small fraction of the materials manifesting such anion impurity effects. Thus for example such effects have been indicated in Y2O3, manifesting themselves at higher temperatures (due to phosphate precursors) [255]. Also note that residues from the use of LiF additions that can be very beneficial to densification of several oxides, especially MgO and MgAl2O4, can also be detrimental to resultant strengths unless suitably removed by subsequent annealing, which is much more feasible in MgO than in MgAl2O4, as was discussed earlier (Figure 2.12).

Higher densification temperatures required for many other refractory ceramics such as borides, carbides, and nitrides indicate that such effects will be greatly reduced or not present in these materials from conventional powder processing. However, other low-temperature processing of nonoxides via preceramic polymers has similarities to processing of oxides from their common precursors and results in similar bulk body (Figure 2.14) [255] to fiber strength differences (Fig. 3.13). Whether such strength differences are related to similar impurity effects, residual stresses, or other effects, e.g. porosity, that would also be more serious in bulk bodies versus fibers is not established.

B.Grain Size Variation Effects, Especially Average Versus Maximum G

Even from a purely abstract standpoint, the issue of what G value to use for correlation with tensile strengths arises given any significant grain size distribution, strength being controlled by weak links. This issue is heightened by the frequent occurrence of fracture origins from larger grains or clusters of them, especially extremes of these from exaggerated grain growth in some materials such as Al2O3 (especially without grain growth inhibitors), beta aluminas, B4C, SiC, and Si3N4 (Figs. 1.2–1.5). However, the use of the maximum grain size (Gm), as proposed by some investigators, is a serious oversimplification whose use leads to serious problems for basic reasons. A fundamental reason from an experimental standpoint is that larger grains or clusters of them are not always fracture origins, even when in a region of high to maximum stress. Thus, though not seriously sought by most investigators (nor for a long time by this author), clear cases of large grains not being fracture origins have been observed (e.g. Fig. 3.27).

A fundamental theoretical reason for larger grains or clusters of them not always being fracture origins, even when in a region of high or maximum stress,

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is that they may not be sufficiently serious flaws for either or both of two reasons. The first is that larger grains or clusters of them by themselves are not flaws; they must be associated with some other factor, a defect or stress, that causes the combination of it and the larger grain(s) to become a source of failure. Such a factor is typically an associated machining flaw (requiring the larger grains to be sufficiently near the finished surface), some other crack formed prior to testing or during testing in combination with the applied stress (e.g. from expansion differences between adjacent grains or second-phase regions or particles), or pores (e.g. Figure 1.4B). The second reason that larger grains or clusters of them are not always fracture origins is that they may not be of sufficient size. This is a particularly important problem for the finer G branches, which is also often the region where the difference between Ga and Gm has the greatest impact on the G-1/2 dependence of strength. Thus, for example, use of a Gm instead of a Ga value can significantly change (often increasing) the slope of the finer G, especially at very fine G (where use of Gm has less relevance), thus distorting the projections of strengths to finer grain sizes. Note that the suggestion of most using Gm that the slope of the finer G branches is zero is generally not supported by their own data and is inconsistent with the great bulk of other data.

The above observations imply a significant statistical variation in the occurrence of larger grains or clusters of them at fracture origins, e.g. due to the statistics of association of larger grains and other defects. These statistical effects are compounded by statistical variations in orientations of easier fracture planes nearly normal to the applied stress. That the statistics of the spatial distribution of larger grains is a factor was shown by Stoyan and Schnabel [259]. Using a pair correlation approach, they showed a higher correlation of the spatial distribution of larger grains with σ for nearly dense Al2O3 bodies than with variations of Ga over their limited G range ( 9 to 15 µm).

Larger grains or clusters of them frequently being fracture origins raises three broad questions concerning their (1) occurrence in terms of types of materials and body factors, (2) impact on σ–G-1/2 relations, and (3) impact on engineering development. With regard to their material occurrence, the preceding sections and a previous survey [2] clearly show larger grains as fracture origins mainly in some noncubic materials such as Al2O3, beta aluminas, B4C, and Si3N4, except for SiC where noncubic exaggerated tabular grains of α-SiC commonly form in β-SiC (e.g. above 2000°C). Similar large grain origins have been reported much less in cubic ceramics, since they typically do not exhibit as much exaggerated grain growth common to many noncubic materials. In fact in cubic ceramics cases are seen where some failure initiation occurs from smaller grains, though in such cases smaller grains at the origin commonly abut one or more somewhat larger (bur not unusually large) grains, e.g. Fig. 3.10B.

Fracture initiation arising from larger grains is of practical, e.g. engineering, importance in order to identify their cause(s) so they can be reduced or

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eliminated to improve strength and reliability. However, such cases may not be relevant to basic σ–G-1/2 relations or comparison of grain size dependences of strength and toughness to understand basic factors controlling fracture or projection of strength–grain size data to finer G as an indication of potential strength improvements by reducing grain size. Thus, three cases where larger G strengths may have limited relevance to basic σ–G-1/2 behavior [2] are where impurities (1) with a pore (and possibly causing the pore) cause large associated grains (e.g. Figure 1.4B), (2) cause platelet grains (Figure 1.3A), and (3) cause large grains that also have associated cracks (Figure 1.2D), or also cause cracks or reduced properties over the area affected by the impurity.

A fourth, more specialized question is the role of G variations on slip-in- duced or assisted failure. Theoretically, strength should still be controlled by the largest grain size, since this gives the longest slip source–barrier distance and thus the lowest back stress. However, there are the combined statistical effects of grain orientation on both the resolved shear stress on easily activated slip systems and the stress normal to the resultant initiated crack that may significantly affect which grains become fracture origins. There are also issues of effects of impurities on grain size, e.g. impurities might cause larger grains but increase their yield stress, thus partly or fully counteracting effects of their larger size in favoring their being origins. Experimentally it is observed that slip nucleated fracture does occur from some smaller grains [52], though again there are often one or more somewhat larger abutting gains. In some of these cases it is not clear whether the slip nucleated crack formed in the smaller grain with the slip band or in the abutting grain against which the slip band piled up. Note that slip band length should on average be controlled by the three-dimensional grain size, while the failure causing crack is more related to the grain dimensions on the fracture surface.

Consider now more specific experimental results based mainly on fractography, especially in alumina bodies, with some observations secondarily also from B4C [2]. As noted earlier, identification of specific fracture origins from larger grains showed plotting strengths versus the observed Gm shifted some data points from the finer to the larger G branches. However, this also left a number of data points still remaining on the finer G branch, indicating that the larger grains or clusters of them were not of sufficient size to be fracture origins by themselves. Larger grain origins frequently are from clusters of larger grains making them even more uncertain in their relation to σ – G-1/2 relations. Thus their frequently being shifted too far to the left, i.e. past the limiting larger G branch slope for data from failures from a single large or dominating grain, implying that the complete cluster was not the origin, or that the cluster origin was not directly pertinent to σ – G-1/2 relations, also usually indicated by abnormally low strengths (e.g. Figure 1.4B). However, use of Gm values transferring varying numbers of data points to the larger G branch made limited reductions of data

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scatter and increases in the larger G branch slope, and limited change in the finer G branch slopes, e.g. leaving them substantially positive. The number of data points affected by such evaluations varied substantially, from a high of 16 out of 40 data points (i.e. 40%) to much less (e.g. to 7%) [2, 17]. The extent and character of such Gm corrections increased with the size of the body and fabrication method, e.g. more for larger die pressed disks and less for smaller extruded rods. Similar evaluations of the much more limited data based on grain size averages and ranges (mostly observed on polished surfaces, thus not showing the full extreme of grain size range) ad much more limited impact on scatter and slopes of the larger and finer G branches. Thus sintered, machined Al2O3 data of Ting et al. (99+%) [133] and McNamee and Morrell (95%) [127] vs. Gm(from microstructural, not fractographic, studies) simply moved some data points leftward in the finer G regime or to the larger G branch. In either case their data agrees with the other data, as does Alford et al.’s [27] (99+%) machined data vs. Gm(the only values given).

Thus while there is scatter and uncertainty in many details, which can be improved some by more detailed evaluation such as of specific G values, there is a clear, very consistent overall pattern (Fig. 3.1). This pattern is observed despite the diversity of materials, test methods, especially characterization. The latter is often overlooked but in fact is probably one of the larger factors in variations, i.e., scatter, between different sets of σ–G data. The techniques of measuring G are often only partially given or not given at all. Thus while many investigators may state that they used a linear intercept, they frequently do not tell whether they used a factor, and if so what it was, to convert that linear intercept to a “true G value.” Such values are commonly of the order of 1.5 or more but can vary from <1 to >2, thus commonly giving at least a 50% variation in G values and possibly in excess of 100%. It was recommended (Chap. 1, Sec. IV.B) that the average diameters of grains be measured, e.g., along randomly selected lines with the average possibly being weighted based upon grain area considered for σ–G relations. It is important that the G measurement be compatible with measurement of individual grains, i.e. where they are fracture origins (which generally needs to be corroborated by fractographic analysis). It is also important that the σ and G measurements be self-consistent, i.e. use of Gmis often not consistent with use of the maximum flexure strength (= outer fiber stress at fracture, Sec. F).

C.Grain Shape Effects

Grain size effects and issues are often intimately related to various other grain factors, of which grain shape is the most immediate one. This affects σ–G-1/2 relations directly via effects on G measurements (Chap. 1, Sec. IV) as well as possible effects on failure causing flaw sizes and shapes. While, much, if not all, of