Mechanical Properties of Ceramics and Composites

section show that significant changes in mismatch stresses occur, impact toughness, and indicate that some parallel effects could occur in monolithic ceramics). However, data at higher temperatures, e.g > 800 to 1000°C, shows three sets of trends: (1) increasing intergranular fracture, which can aid crack bridging but is also commonly a precursor to high temperature SCG and resultant lower strengths, (2) lesser extremes of toughness variations, even before extensive high-temperature SCG or crack tip plasticity occurs, and (3) frequent but strain- rate-dependent increases in toughness at higher temperatures associated with plastic deformation, especially in single crystals. Note that the latter is another example of basic toughness–strength differences as shown by comparison to strength behavior in the following section.

B.Grain Size Dependence of Tensile Strength of Monolithic Ceramics

Turning to tensile or flexure strength at or near room temperature, the extensive focus to explain this has been by crack propagation studies, i.e. of SCG and especially toughness, with limited attention to the nature of flaws controlling strength. Clearly, both are important, but the perspective necessary to understand strength behavior of ceramics, especially its dependence on grain size, must start with the effects of body microstructure and properties impacting flaw populations introduced, which are a major factor in determining strength. The necessity of this perspective can be seen by noting inconsistencies of the toughness-based approach and the consistencies of the flaw-based approach.

Consider first failure from machining flaws, which is most common, and the inconsistencies that an approach based on the microstructural dependence of large crack toughness presents for explaining the microstructural dependence of small crack tensile strength. Strengths of dense machined ceramics show two fundamental aspects of strength–grain size behavior that must be satisfactorily explained in order to understand their strength behavior. The first, which is particularly extensively demonstrated, is the generally modest decrease of strengths as G increases at finer G, followed by a substantially faster strength decrease as G increases at larger G, with strengths at larger G often falling below those for single crystals of the weakest orientation with the same machining (Fig. 3.1). The other aspect of strength behavior of machined samples is the effect of machining variables on resultant strengths, especially increases as the grit size decreases and anisotropy of strength as a function of the machining direction relative to the uniaxial stress axis [33], which is zero when the grain and flaws are about the same actual size, and which increases as the grains decrease or increase in size relative to the flaws (Fig. 3.33). These strength trends, while varying in detail, are the same in overall character for both cubic and noncubic ceramics as well as transformation toughened ceramics (and other toughened ce-

ramic composites, see the next section). Such trends are clearly inconsistent with much data, especially large crack toughness–grain size data, which shows toughness increasing as G increases.

As was discussed extensively in Chapter 3, this strength–grain size behavior is explained by a primary effect and some secondary effects. The primary effect is that machining flaws are larger than finer grains and smaller than larger grains, and to a first approximation they are independent of G and hence are the size of the grains at an intermediate G. The specific flaw size and hence the G at which they are equal are a function of machining, so that the finer G branches shift as a function of machining. (Machining flaws for a given machining operation also do not vary widely for most ceramics, but clearly change some for different ceramics and machining parameters.) However, there can be some secondary dependence of machining flaw size on material parameters, primarily the local Young’s modulus, hardness, and toughness controlling formation of the flaws per Eq. (3.2). Note that these values, especially toughness, may be substantially lower than those commonly measured with large-scale cracks because of crack size effects [34], and they reflect local transient higher stress rates and temperatures; toughness and hardness can vary with G. Further, as the flaw and grain sizes approach each other, there can be increasing contributions of mismatch stresses between grains to failure, and the fracture toughness controlling failure is decreasing from polycrystalline to single crystal or grain boundary values (Fig. 2.15). Any or all of these three secondary effects result in strengths decreasing as G increases. Both the calculation of flaw sizes for different G bodies and direct fractographic observations corroborate that the larger and finer G branches intersect when the grain and flaw sizes are equal (recognizing that they are respectively measured by a diameter and a radius), with statistical effects resulting in some variation from absolute equality, as was discussed in Chapter 3.

Also note, first, that the slope of the larger G branch has been shown theoretically and experimentally to be variable and < the polycrystalline toughness due to varying transitions between polycrystalline and single crystal or grain boundary fracture toughnesses (Fig. 2.15). Second, while strengths typically extend below those for single crystals, they must ultimately reverse and approach lower single crystal values at very large G but may follow various paths depending on material, finishing, and especially specimen-grain parameters (Fig. 3.1). Third, as-fired surfaces show similar strength–grain size trends to those for machined surfaces, since the depth of grain boundary grooves increases with G, while the tortuosity of collections of grain boundary grooves to form a single flaw should decrease as G increases. Fourth, there are two variations on the above strength–grain size behavior due to either microplastically induced or grown flaws or for failure from microcracks, each having characteristics different from the above-normal G dependence of flaw failure. For microplastic-induced failure, the larger G strengths do not fall be-

low those for the weakest crystal orientation but instead extrapolate to the lowest single crystal yield stress, which is usually slightly below the crystal failure strength (Figs. 3.1). For microcrack failure, strengths decrease rapidly as G increases above the value where microcracking commences, but then the strength decrease begins to saturate as G increases further.

Another important source of information on strength behavior is the mirror, mist, hackle, and crack branching behavior widely observed on normal-strength fractures of monolithic ceramics, which, for example, reflects effects of TEA and related stresses [34]. While not quantitatively studied in larger grain ceramics where bridging and R-curves are greatest, these fracture patterns do not show deviations from normal patterns that would be expected if large increases in toughness accompanied crack propagation in normal strength failure. Further, data for intermediate G, e.g. < 10 m, in materials such as Al2O3, where measurable bridging and R-curve effects are reported, have fracture patterns consistent with those for finer G bodies where bridging and R-curve effects are not seen [35].

Though receiving very limited attention, especially for effects of microstructure, mechanical fatigue has been demonstrated under varying tensile loading. This has been shown to occur due to grain mismatch stresses, e.g. in larger grain Al2O3, and can be independent of environmental effects, since it can be more severe in liquid N2, rather than reduced or stopped by low temperatures. A mechanism was proposed based on microcracking during increasing tensile loading leading to local incompatibilities due to elastic relaxations around the microcracks preventing their closure (Fig.11.8). Thus microcracking further extends during unloading so that the local microcrack situation and stress state do not return to the situation at the start of the stress cycle.

Thermal shock generally shows different dependence on grain parameters than on strength. The critical quench temperature difference for serious loss of strength is independent of grain size, but the retained strength after damaging thermal shock generally increases as grain size increases and starting strength decreases. Toughening mechanisms such as crack bridging and R-curve effects may be operative in thermal shock to improve retained strengths, as is also suggested by composite effects in the next section. This is logical, because such damage generally involves larger scale cracks that form, but are arrested, thus allowing R-curve or other large crack toughening to be operative. Transformation toughening has limited benefit for thermal shock resistance, e.g. higher strengths from such toughening in TZP and PSZ bodies do not necessarily increase TC, but microcracking in such materials (associated with lower strengths and larger cracks) can significantly aid in retaining reasonable strengths after thermal shock. It is also expected that similar trends will occur from serious impact damage, i.e. impacts of larger or higher velocity particles may leave greater retained strength in bodies in which larger cracks, effected by R-curve and related effects, are formed, but are more difficult to propagate.

most cases it reaches a minimum value below lower single crystal values and then increases to extrapolate to lower single crystal values (Figs. 4.1-4.4,4.7- 4.13, 4.15). The minimum is associated with grain cracking and spalling around indents (Figs.4.16-4.20), which reaches a maximum when the indent and grain sizes are similar, apparently due to extrinsic factors such as grain boundary phases and residual porosity and intrinsic factors of grain mismatch stresses due to TEA and EA. As indent load increases, so does the associated cracking, while the G location of the minimum and its hardness value decrease, with these trends more pronounced for Vickers versus Knoop indents. However, such cracking is superimposed on the underlying mechanism of indentation, which is now recognized to be plastic flow, e.g. as shown by the crystal orientation dependence of hardness (Figs. 4.21, 7.1).

Compressive strength shows a strong G-1/2 dependence, with strengths at larger G extrapolating to lower single crystal values. Compressive strengths from well-conducted tests generally approach H/3 ( E/10) as an upper limit, but this is not exact, since the G dependence of compressive strength is typically > that of H. This correlation of compressive strength and H indicates that compressive failure typically involves some microplastic processes, e.g. microcrack nucleation and growth. However, compressive failure typically results from cumulative growth and coalescence of many finer cracks under local tensile stresses, but with growth limited by the macro compressive stress. This is clearly supported by the similar G dependence of compressive strength with superimposed hydrostatic pressures, but with somewhat increased strength levels and increased evidence of plastic deformation. The cumulative compressive failure from many sources in a body is also supported by higher Weibull moduli for compressive versus tensile failure. Such failure also implies less extreme dependence on larger grains than tensile failure, but no study has been made of this.

The one reasonably comprehensive study of grain size effects on the ballistic performance of Al2O3 bodies against lower velocity, smaller (.22) caliber projectiles shows a limited but definite decrease in stopping power as G-1/2 decreases (i.e. G increases, Fig. 5.7), including sapphire data (i.e. G = ∞). Similarly, .30 caliber armor piercing (AP) tests of AlN show a similar G dependence of ballistic stopping power, but much less for .50 caliber AP tests (Fig. 5.8). Less comprehensive studies of the G dependence of ceramics against higher velocity and caliber projectiles do not indicate any clear dependence of ballistic performance on G. It may be a factor, but it is probably in competition with other body factors. Thus limited data indicates a G dependence of ballistic performance of ceramics at lower threat levels, but with this decreasing as the threat level increases.

Turning to wear, erosion, and related behavior, there is less data on their grain size dependences, and greater complexity is expected because of variations in the mechanisms resulting from the diversity of conditions for varying aspects

of such behavior. However, there are broad trends for increased resistance to wear, etc., as G decreases, commonly as a function of G-1/2, i.e consistent with H dependence on G, especially at finer G. Further, there are some results that show marked decreases in wear resistance above certain (apparently) material-depen- dent grain sizes, e.g. consistent with probable contributions of grain mismatch stresses, wear asperity or eroding particle indentation or both, to local cracking. Limited direct observations show that at least some wear rates are significantly increased by larger grains within the body, but in view of limited overall G effect studies, there has been little study of the effects of grain size distribution on wear.

The effects of grain shape and orientation are much less documented than the effects of grain size. Elongated grain shape can clearly increase crack bridging in the wake region and thus increase large crack toughness values. However this occurs primarily when crack propagation remains intergranular around the elongated grains, i.e. being limited when transgranular fracture of the elongated grains occurs. Grain boundary phases that enhance intergranular fracture can extend the toughening benefits of elongated grains with large cracks, but often at the expense of strength. Elongated grains are larger than equiaxed grains of the same diameter and thus should lower compressive and especially tensile strengths based on size differences, which may be exacerbated by enhanced microcracking from elongated grains. Similarly, it is expected that elongated grains will commonly reduce wear, erosion, etc., resistance due to enhanced fracture and grain pullout. Limited grain orientation data supports the expectation that mechanical properties of polycrystalline bodies will vary with preferred grain orientation in proportion to the orientation dependence of properties in the corresponding single crystals.

D.Particle and Grain Size Dependence of Crack Propagation, Toughness, and Tensile Strength of Ceramic Composites

Elastic moduli of composites do not depend on particle size, D, unless D is large enough to trigger the onset of microcracking, e.g. as estimated by Eq. (2.4). However, elastic moduli clearly depend on the volume fraction added phase and its elastic properties (and the onset, extent, or both of microcracking can be aided by increasing volume fraction second phase). Generally a rule of mixtures estimate of elastic moduli is used, i.e. per Eq. (8.1), since it often gives reasonable results and characterization for selecting and accurately using more sophisticated models, and their parameters are almost universally lacking. However, there can be significant deviations, for which suitable models may or may not be available, e.g. again spontaneous microcracking clearly occurs at finer particle sizes, more extensively, or both as volume fraction of second phase increases, which is not predicted by present models. Further, the extent to which this reflects extrinsic

effects due to second phase agglomerates or intrinsic effects due to interaction of mismatch stresses between nearby particles is unknown.

SCG occurs in composites with oxide matrices susceptible to SCG, and also in at least some nonoxide composites with oxide containing grain boundary phases. However, the dispersed phase often inhibits SCG, raises toughness, or both to reduce effects of SCG, but again the issue of crack size effects, i.e. the extent to which this also occurs with normal strength controlling cracks, is generally unknown.

Though not documented as extensively or in detail, it is clear that the microstructural dependence of mechanical properties of ceramic composites closely parallels that of monolithic ceramics, especially for synthetic ceramic particulate composites, with major deviations primarily with ceramic fiber composites. Thus fracture toughness of ceramic composites at and near room temperature also varies substantially with different tests and exhibits substantial R-curve effects, especially as the volume fraction of dispersed phase and the coarseness of it and the matrix grain size increase. Again the primary correlation with significant increases of toughness is crack wake bridging by larger dispersed particles. However, this in part reflects general neglect of other possible mechanisms such as those discussed in Chap. 8, Sec. II.B, since the discovery of, and subsequent focus on, crack wake bridging (with the exception of enhanced effects from clustered microcracks, Fig. 8.2, for thermal shock resistance, as is discussed below).

The same issues arise regarding the meaning and applicability of large crack toughness and related wake effects, especially crack bridging, for composites as for monolithic ceramics. Thus observations being based on large cracks intersecting machined surfaces after propagation at generally low, unspecified velocities, followed by arrest, versus typically much smaller strength controlling cracks propagating more into the bulk of the body at accelerating velocity to failure, are again key issues. These concerns are heightened by the two cases where higher crack velocity effects on toughness have been considered in composites; these indicate reduced effectiveness of the composites on fracture toughness of metal particles in a glass matrix [36,37] and WC-Co [38]. Similarly, fracture mode argues against extensive effects of crack wake bridging effects on strength, since the latter is favored by intergranular and interparticle fracture, while most composites tend to enhance transgranular and transparticle fractures. Also, while not quantitatively studied, qualitative observations of fracture mirror, mist, hackle, and crack branching patterns around fracture origins in strength testing of composites question significant increases in toughness during crack propagation to failure. Fracture mirror and related data should show, but also do not support, effects of bridging on strength. Thus while effects of mismatch stresses can decrease mirror sizes in the smaller mirror size range (and in fact control

spontaneous failure in a crystallized glass under high energy pulse loading [34,39]), no effects of increased mirror sizes due to R-curve effects have been shown. However, as with monolithic ceramics, the basic differences between strength and large crack toughness behavior as a function of microstructure are the most detailed and compelling arguments that crack wake bridging generally has little or no effect on strength.

While many studies have not documented effects of particle or grain size on properties, the considerable number that have all show strengths decreasing as particle or matrix grain size, or both individually, increase, i.e. opposite to toughness dependence (e.g. Figs. 9.13-9.15). Further, limited (and apparently not previously considered) available data covering a sufficient particle size range shows a D-1/2 strength dependence for machined samples (Figs. 9.2, 9.15,9.16) the same as for G dependence of monolithic ceramics. Again the mechanisms and specifics of the particle size dependence are also the same as for the G dependence of strength, i.e. as a first approximation flaw sizes do not vary widely with the microstructure of a given composite composition. At finer particle sizes, machining flaws are > the particle (and matrix grain) size, so there is limited effect of particle (or grain) size on strength, resulting in a finer particle size strength branch directly analogous to the finer G branch for monolithic ceramics. As particle size further increases, a size will be reached where machining flaws causing failure are contained in or around individual particles, so at and beyond this particle size the particles become the flaws causing failure (again recalling that flaw sizes are measured by a radius and particle and grain sizes by a diameter). Thus strength decreases more rapidly as D-1/2, forming the larger particle branch of the strength–D-1/2 behavior.

Similar to the strength–G-1/2 behavior of monolithic ceramics, the strength–D-1/2 dependence of composites is not necessarily zero along the finer particle strength branch for at least two reasons. First, limited effects of increasing particle (and matrix grain) size can reduce local properties, e.g. hardness and toughness, impacting machining flaw initiation and growth, thus modestly increasing flaw sizes, yielding modest decreases in strength. Second, mismatch stresses from expansion and elastic differences between the particles and matrix could increasingly contribute to failures as flaw sizes increase, approaching larger D sizes, resulting in some strength decreases, which might often be greater than for monolithic ceramics. Besides the direct data showing these trends, their direct correlation with strength–G-1/2 effects and mechanisms, this mechanism is also supported by lower strengths generally found for platelet composites, since platelets have larger, flat interfaces along which machining flaws can form. This is further supported by the limited fractography of platelet composites showing failure frequently occurring from such platelet surfaces. However, it is also important to note that other mech-

anisms can be operative in composites in addition to or instead of machining flaw–particle size interactions. Thus microcracking can clearly occur, as is shown by data with larger or more particles or platelets, or both, as differences in elastic, and especially expansion, properties increase.

Mechanical fatigue under cyclic tensile loading, though examined very little, has been demonstrated in some particulate composites [40]. This is similar to effects shown in monolithic ceramics, again with microstructural mismatch stresses seen as a basic mechanism. Such studies have also shown different ratios of crack propagation at and near machined surfaces from those in the interiors of specimens.

Consider now thermal shock behavior of composites as a transition to higher temperature behavior. Ceramic composites may offer some increases in TC, but some offer more significant improvements in strength retained on quenching at ≥ΔTC, e.g. consistent with higher toughnesses at larger crack sizes. However, this typically entails more modest starting strengths, with microcracking being a particularly important mechanism, e.g. with composites based on dual microcrack populations, Figure 8.2C, being a good example. A further limitation is that composites showing improved thermal shock resistance often exhibit thermal fatigue effects, that is, a progressive decrease in thermal shock performance with repeated thermal shock cycling (Fig. 11.7). While composites can still result in some improvements in thermal shock resistance, it is important to note that the improvements may be substantially less than seen from a single

thermal shock.

Limited tests of crystallized glasses all show both fracture toughness and tensile strength initially decreasing as temperature increases above room temperature, reaching a minimum, e.g. at 400°C (Fig. 11.1, 11.9). Decreases to minima have been attributed to decreased microcracking as increased temperature reduces mismatch stresses between the grains themselves and the residual glass matrix, which is clearly a candidate mechanism. However, there is no corroboration of this, and the reason for similar trends of toughness and strength, which are often opposite for microcracking, are uncertain, though this may reflect differences in the microcracking in such systems, e.g. their probable finer scale. Beyond the toughness and strength minima, both increase as temperature further increases (Fig. 11.1, 11.9). Strengths must subsequently go through maxima, beyond which they decrease extensively due to increased plastic flow. Whether increasing toughnesses go through similar maxima is not documented, but must occur. Some maxima may be different, e.g. extended to higher temperatures due to plastic deformation, which though varying with strain rate, often is accompanied by decreasing strength.

One other set of intermediate temperature tests is on PSZ single crystals, which show initial decreases in both toughness and strength consistent with expected decreases in transformation toughening; but this decrease reaches a min-

imum at about twice the toughnesses and strength of CZ crystals. Such remaining higher toughness and strength of PSZ over CZ crystals continues to above the monoclinic–tetragonal transformation temperature, which is attributed to toughening from nontransformation mechanisms from the tetragonal precipitates, such as crack deflection and branching. Such toughening and strengthening arise from mismatches in tetragonal versus cubic ZrO2 expansion and elastic differences, which exist whether the tetragonal precipitates are metastable or fully stable. At higher temperatures, ceramic composites of all crystalline constituents often show increasing toughness, which is attributed to crack tip blunting due to SCG and creep processes, which are quite strain rate dependent and generally do not reflect higher strengths; in fact they usually correlate with decreasing strengths.

Polycrystalline composites of all refractory crystalline ceramic constituents show accelerating decreases in strength at higher temperatures, similar to refractory monolithic ceramics, but often with less relative decrease. The rates of strength decrease are lower to some extent as the refractoriness of the phases present and their volume fractions increase, and more so with differing particle shape, with whiskers typically giving less rapid decreases. However, some of the ceramic composites retaining strengths to higher temperatures are directionally solidified eutectic (Fig. 11.11,11.12).

E.Particle and Grain Size Dependence of Other Mechanical Properties and Effects of Particle Shape and Orientation on All Mechanical Properties of Composite Ceramics

Hardness data for composites is most extensive for effects of volume fraction of dispersed second phase particles, with much more limited data on effects of particle (or matrix grain) size, and even less on particle (and grain) shape and orientation. Though there are variations, most hardness data is fairly consistent with a rule of mixtures effect of the volume fraction second phase [Eq. (10.1)]. An alternate model proposed for crystallized glasses does not deviate significantly from this, but modeling and data evaluation for WC-Co bodies shows modification of the rule of mixtures via weightings for the contiguity of each phase. Though limited evaluation of grain and particle size effects has been made in only part of the studies, collectively they clearly show hardness increases as either or both sizes decrease, as is expected from the finer G dependence of monolithic ceramics. This reflects a common advantage of composites via their common mutual inhibition of grain and particle growth limiting particle and grain sizes. These trends are consistent with measurements of directionally solidified ceramic composites showing hardness varying as λ-1/2, where λ is the mean separation between the single crystal rods and is thus also analogous to the G-1/2 dependence for monolithic ceramics (Chap. 10, Sec. III.A).