Mechanical Properties of Ceramics and Composites

FIGURE 5.6 Compressive strength versus H/3 for various ceramics from better conducted tests with and without superimposed hydrostatic stress levels (shown in GPa) at 22°C. (Data from Refs. 5,14,15,22,28,50.)

being 80% of the shear moduli for [111] loading of crystals of Ge, Si, and diamond [44]. Further, the substantially increased data, especially for the G dependence of H, also raises some questions, and the load and indenter shape dependence of H raises the issue of what H values are appropriate. While higher load H values appear more appropriate, as noted earlier, there are uncertainties regarding which indenter shape is more pertinent, e.g. possibly Vickers over Knoop, but with the merits of spherical indenters relative to these unknown. Further, the use of any indenter geometry at a fixed load means that the resultant indents are changing in the number of grains involved as G (or the G range) of a given sample changes, raising the issue of to what extent such changing grain- to-microplastic-zone size ratios in measuring H correspond to such ratios of possible microplasticity in compressive failure. There are also issues raised by the σC–G data that do not appear to correlate well in detail with H–G data, e.g. though limited, the σC–G data shows no evidence of σC minima at any intermediate G, as H often does. Most likely the H minimum found in more compre-

hensive H testing of a number of ceramics is not directly pertinent to compressive failure, since this entails free surface cracking versus bulk, i.e. much more constrained, cracking in compressive failure (though the possible mechanisms of generating the surface cracking–spalling in H testing may be pertinent, as is discussed below). However, neglecting the H minimum exacerbates another possible problem in detailed correlation of H–G and σC–G data, namely that σC–G data often shows more change over the same G range than does H. Thus while there is a very useful general correlation between H and σC, the specifics of the mechanisms and their impact on the correlation through factors such as the G dependences of H and σC are uncertain.

Consider now the evidence for microcrack formation and coalescence as the basic mechanism of compressive failure. Though again the data is generally limited, there is considerable support for such cracking, mainly from four sources, but very limited information on most details, which are generally important. The first source is extensive modeling showing that compressive loading results in cracks parallel with the applied uniaxial stress initiating from pores (see Adams and Sines [52] and Sammis and Ashby [53]). The second source is direct observation of such cracks from both large artificial pores in glass [53] and fine natural pores in relatively dense polycrystalline ceramics such as Al2O3 [9] and SiC [11]. Further and very important is direct observation of individual cracks or reduced transparency of single crystals of MgO and Al2O3 [29,38,39]. The third source is acoustic emission data, e.g. as for the previous Al2O3 [9] and SiC [11]. While some emission may be from other sources, much of it, e.g. of Nash [47], is highly likely to reflect cracking. The fourth source is interrupted compressive loading followed by subsequent tensile loading normal to the original compressive loading axis by Sines and Taira [54]. They did such testing on a commercial Al2O3, reaction bonded SiC, and HIPed Si3N4 and showed that such compressive loading prior to tensile testing in the normal direction resulted in the onset of tensile strength degradation with prior compressive loading above 40% of the compressive strength and further degradation approaching zero tensile strength at double the level of compressive loading relative to the ultimate compressive strength in Al2O3 and SiC, which had porosity and coarser microstructures. However, no degradation from such prior compressive loading was found in the nominally pore free, finer G Si3N4 tested. Thus there is considerable data showing microcracking from compressive loading, but much remains to be determined about the specifics of the onset, growth, and coalescence of such cracking. It is also important to recognize that the extent and cause(s) of such crack processes may change with material, microstructure, loading, and temperature. Another indication of crack generation during compressive stressing is the results of Stucke and Wronski [55] showing progressive reductions in tensile (flexure) strength as superimposed hydrostatic pressure on three MgO, two Al2O3, and one UO2 bodies was increased.

Turning to the mechanism of microcrack generation, growth, and coalescence, it is highly probable that there are multiple mechanisms with varying contributions as a function of which stage of compressive failure is being addressed and what the material, microstructure, and loading conditions are. While microcracking from pores is clearly an important source, there must be other sources of microcracks for two reasons. First, similar compressive strength behavior is seen for ceramics with little or no porosity and those with more substantial porosity, e.g. between sintered and hot pressed Al2O3, but corrected to P = 0. The second is the extrapolation of polycrystalline compressive strengths with little or no porosity, or corrected to zero porosity, to the range of single crystal compressive strengths, e.g. for UO2 and Al2O3 (Fig. 5.2). For other mechanisms of generating microcracks than from pores it is logical to consider the same candidate mechanisms as for indent-related cracking and resultant H minima due to cracking from deformation, especially slip anisotropy, and TEA and EA stresses. Clearly there are important differences between the two microcracking situations, i.e. indent cracking is mostly or exclusively surface connected and occurs at or near the edge of the zone of hydrostatic compression, while compressive microcracking occurs in conjunction with local tensile stresses in an overall compressive stress field. The latter is the logical cause of compressive microcracking presumably occurring at much higher stresses. TEA and EA are clearly possible sources of microcracks, since they can result in significantly increased local stress that could exceed the local stress for nucleation of microcracks. Some or all of the G dependence of compressive strengths would thus be due to the probable G dependence of such microcracking from TEA and EA [56,57]. Note that the stress concentrations due to EA can be substantial, e.g. commonly to 1.5–3 [58]. However, it varies substantially not only with the degree of EA but also interactively and significantly with grain shape, i.e. aspect ratio, and with the orientation of the grain elongation relative to both the stress axis and the relation of the grains or regions of them with higher versus lower local elastic moduli from the EA per modeling by Hasselman [58].

While EA and TEA are highly probable factors in compressive microcracking, it is likely that microplastic deformation due to slip, twinning, or both is also a factor for several reasons. These include the clear occurrence of slip at similar stress levels under indenters, the implications of yielding at H/3, and the correlation of this with σC. Another indicator of plasticity is the G dependence of σC following a Petch relation and thus correlating with single crystal behavior where there is no TEA or EA. While some might argue that the Petch relation is misleading, as it was for the finer G branch for tensile strengths (Fig. 3.1), it should be noted that there is no clear evidence for a larger G branch for σC as for tensile strength, and stresses for σC are much more consistent with those for plastic deformation than those of the finer G branch for tensile strength. Two other important, but widely neglected, factors are the transitions from fail-

ure with no to substantial supporting hydrostatic pressure and the changes in H and especially σC with modest differences in temperature (Chap. 6).

Additional support for plasticity as an important factor in compressive failure is provided by specific observations. While Nash’s transgranular fracture mode of what is probably rhombohedrahl cleavage in Al2O3 may be evidence of twinning, his TEM observations of twins, along with some of the substantial acoustic emission he observed probably being from twinning, are reasonable indicators of twinning in Al2O3 [47]. An important observation is the demonstration of deformation accompanying compressive testing of Al2O3, MgO, and UO2 crystals, as well as considerable evidence of this in polycrystalline MgO. Another is Lankford’s observation of crack initiation by blockage of slip or twin bands or both in compressive, as well as tensile, stressing of dense sintered Al2O3 [9,10], and both microscopic and macroscopic evidence of plastic deformation in compressive testing of PSZ bodies, including a clear yield point and substantial subsequent plastic strain [12,13]. While it is legitimately argued that each of these is to some extent a special case, they clearly show that plasticity can occur in compressive failure. More importantly, they show that there are different options for plasticity in ceramics at these stress levels, which is a reminder that thinking of a single mechanism is probably an inappropriate and simplistic approach. Further, the extent of compressive plasticity in the MgO and especially PSZ cases clearly implies that other cases of progressively less plasticity are likely to occur and be a factor.

It should also be noted that some of the arguments raised against microplasticity by some are at best uncertain. Thus the argument that common intergranular fracture in compressive failure or crack propagation is contrary to microplasticity is on shaky grounds, since slip and twinning, while sometimes leading to transgranular fracture, result in intergranular fracture e.g. in Al2O3 [9,10] and MgO (Chap. 3, Sec. III). Wiederhorn et al.’s [59] observation via transmission electron microscopy (TEM) that there are no dislocations associated with tips of cracks introduced into Al2O3 by indents or thermal shock is of uncertain applicability. These observations are most likely of the tips of arrested cracks rather than of their initiation, thus showing only that crack growth and arrest was not associated with slip at or near the arrested crack tips. Further, the argument that such TEM is necessary to confirm the role of plasticity in compressive failure is potentially misleading, since it neglects the issue of the number and scale of microcrack nuclei that may be needed, especially for earlier stages of ultimate compressive failure, and the feasibility of finding these by TEM. Thus, for example, crack nucleation due to blockage of one slip or twin band at the boundary with an adjacent grain occurring at one in a thousand grains may well be a substantial number of crack nuclei in a body, but they clearly provide a very low probability of suitable detection by TEM. It is much more logical to recognize that there is probably a substantial range of plastic contributions, many on a very modest scale, so

a variety of self-consistent tests and evaluations are needed to address this issue. Such more comprehensive evaluations should preferably entail testing of a variety of materials, with a variety of microstructures, loading conditions, test temperatures, and associated evaluations, e.g. acoustic emission, microscopies, and radiography.

III.BALLISTIC STOPPING CAPABILITIES OF CERAMIC ARMOR, GRAIN AND OTHER DEPENDENCE

Ceramics are often used as armor against bullets and other, often heavier, projectiles, since they typically have the best stopping power, especially as a function of weight. As noted earlier, much of the physics of failure in such impact regimes is different from that of conventional failure due to the much high loading rates of such impact. This commonly occurs at rates that exceed the speed of sound in both the impacting and the impacted bodies, so stresses propagate in both as shock waves, since the normal elastic distribution of stress is exceeded, which means that any portion of the target does not experience stress until the shock wave reaches it. Again, the initial shock wave is compressive and then becomes tensile on reflection from the ceramic surfaces, with the latter causing much of the fracturing, e.g. the typical “spider web” crack pattern with normal bullets and granulation from special armor piercing (i.e. long rod, kinetic energy) projectiles after the projectile has been destroyed.

At the low end of projectiles in terms of size, hardness, and velocities there are limited tests indicating some improved stopping power as G decreases and purity increases in alumina bodies. Thus tests by Ferguson and Rice [60] on alumina bodies of varying G and purity, with limited or no porosity (including sapphire, showed some G dependence, especially in less pure bodies (Fig. 5.7). While these tests were with smaller, softer projectiles (nonarmor piercing, that were used to simulate energetic metal fragments), they have some value as a starting point.

Rafaniello’s [43] .30 caliber AP data for dense sintered AlN, though scattered, clearly also shows that ballistic stopping ability, i.e. ballistic limit velocity, decreases as G increases (Fig. 5.8). However, his data for .50 caliber AP stopping ability (using depth of penetration into the Al backing material as the measure of this) is more widely scattered and is at best only somewhat suggestive of decreasing stopping ability as G decreases. The apparent progressive decrease in the clarity, extent, or both of stopping ability increasing as G decreases for the above .22, .30, and .50 caliber tests is consistent with even less indication of G effects against heavier projectile threats. Thus as one proceeds progressively to more serious projectiles ranging from .30 and .50 caliber to various types of armor piercing projectiles that differ greatly in density, hardness (e.g. of W or WC), size, and velocity (e.g. ≤ 1000 versus to 2000 m/s) [14,15], correlation

FIGURE 5.7 Ballistic limit velocity (i.e. the velocity at which half the projectiles penetrate the target and half fail to do so) normalized by the areal density of the target (i.e. the weight per unit area) versus the inverse square root of grain size

(G) for tests of various alumina bodies at 22°C with high power .22-caliber ductile bullets used to simulate fragment stopping capabilities of armor. Note the two lines, the upper one for pure alumina bodies (including sapphire) and the lower one for less pure aluminas (i.e. with less stopping ability). (From Ref. 60, published with the permission of Plenum Press.)

with G reduces significantly. This changes material rankings; B4C is commonly the most weight efficient ceramic armor against .30 and .50 caliber bullets, but it is less effective against more severe armor piercing projectiles.

While the specifics of the material properties and hence microstructures that determine the range of behavior, especially stopping different armor piercing projectiles, are not fully understood, there are some guidelines [14,15]. The first and most fundamental one is that ballistic projectile stopping power is probably dependent on more than one property and changes with the nature of the projectile, so microstructural needs probably change. Second, properties controlling normal tensile fracture, i.e. fracture toughness and tensile strength, have no positive correlation, and some have negative correlations, with armor performance. For example, grain boundary phases that often increase fracture toughness by enhancing intergranular fracture and crack bridging and branching (at

FIGURE 5.8 Ballistic stopping ability of dense ( 3 to 0.3% porosity) sintered AlN (the same bodies as in Figs. 3.28 and 5.4) versus average G for .30 and .50 caliber AP (armor piercing) projectiles, using respectively ballistic stopping velocity and depth of penetration into the Al backing for the ceramic target as the measures of stopping ability.

least as measured with large scale cracks, Chap. 2, Sec III) typically give poorer armor performance. Thus many ceramic composites are less desired, and larger G bodies that may give more concentration of boundary phases are typically less desired materials.

There are some rough indicators of armor performance, since successful ceramics typically have high Young’s moduli and indentation hardnesses, moderate to low densities (at low to zero porosity), low Poisson’s ratios, and moderate to fine G. However, the specific dependences on these properties and the above noted microstructures are not established, due not only to the complexity and possible multiplicity of processes but also to the probability that in many cases there is a threshold requirement, beyond which the property or related microstructural dependence decreases. Thus armor must have a hardness greater than that of the projectile to stop the latter effectively, but beyond that there is only a rough correlation with hardness. It is also known that the presence of preexisting flaws in ceramic armor reduces its performance, but the mechanism of flaw generation during impact, e.g. due to EA and TEA and associated grain size,

shape, and orientation, is unknown. The negative effects of preexisting flaws suggest correlation with Weibull moduli, e.g. some possible rough correlation with such tensile moduli has been noted [14,15]. However, while there is no clear correlation with even well measured compressive strengths, it seems more likely that such moduli for compressive failure, which roughly correlate with tensile moduli (Table 5.1), may be better candidates to reflect flaw density. Thus there are likely to be useful correlations of properties and their microstructural dependences that can benefit ceramic armor selection and fabrication, but they must require balances between various factors, as was noted above, with the balances probably shifting with the nature of the ballistic threat. Further testing of microstructural factors, as addressed in Figs. 5.7 and 5.8, with progressively higher-velocity and harder threats, with the recognition that various and changing property correlations are involved, seems needed. While hardness and compressive strength correlations suggest a possible dependence on grain size, i.e. better ballistic performance, hence “stopping power,” at finer G, there are many uncertainties and very few tests (especially in the unclassified literature).

Finally it should be noted that while there has been little study of plastic flow in ballistic impact on ceramics, there is clear evidence of substantial plastic flow in the debris near the impact zone. Given the complexity of the ballistic impact, including its very short duration and multiple interactions, there is uncertainty as to the extent to which the post-failure tensile shock wave contributes to this. However, the observed yielding under shock wave conditions, i.e. the Hugoniot Elastic Limit [10], indicates that such yielding is an important factor in ballistic stopping power.

IV. GRAIN DEPENDENCE OF EROSION WEAR AND RESIDUAL CERAMIC STRENGTH

Consider now the grain dependence of both erosion due to impact of particles on the surfaces of ceramics and the resultant ceramic strength. There is substantial interest in the effects of solid particles because erosive wear by them is an important issue in many applications components, e.g. potentially in engines where particles are ingested or generated, or in equipment to use streams of abrasive particles, e.g. grit blast nozzles. However, high-velocity impacts of liquid, especially rain, drops are also important for some aircraft and especially missile components, particularly microwave and IR windows and domes. Effects of the impacts of solid particles or liquid drops is a complex subject, but considerable modeling and testing has taken place to give at least partial insight into the mechanisms and parameter dependences. While, as is unfortunately very common, issues of microstructural, e.g. grain size, effects on erosion and induced damage of impacted bodies have received limited attention, there is some information on grain effects.

Consider first more general information on particle erosion, especially the general correlation of increasing H with increasing erosion resistance, or conversely increasing rates of erosion with decreasing H. As part of their particle erosion studies of ceramics (which are among the most extensive), Wada and Watanabe [61] showed that the erosion rate was inversely proportional to the ratio of the hardness of the impacted surface to that of the impacting particle, i.e. a linear dependence on a log–log plot. Similarly, others have shown correlations of erosion with H, e.g. of the onset of serious rain erosion with the hardness of the impacted ceramic [16,62,63]. Both the correlation of erosion with H and the generally recognized increase of H as G decreases suggest reduced erosion as G decreases, as did qualitative observations of lower erosion at finer G, e.g. of Wada and Watanabe [61] in Si3N4.

Consider now the limited experimental data on G dependence of particle erosion of ceramic surfaces. A study of SiC erosion using Al2O3 particles (37–270 m dia.) at velocities of 108 m/s by Routbort and Scattergood [64] provided some direct indication of a grain size effect. They showed that the erosion rate of reaction bonded (RB) SiC (i.e. with large G, P 0, and excess Si) progressively increased substantially as the size of the impacting particle increased, as expected from theory. However, similar tests of hot pressed SiC (G 2–4 m), while being consistent with their RB SiC at small particle sizes, progressively deviated to less erosion as the size of the eroding alumina particles increased, with erosion rates for the largest alumina particles being < for the finer particles, i.e. contrary to all models. They noted however that the damage zone sizes for single particle impacts was 0.2–0.3 times the particle size for normal incidence, so the finer impacting particles created damage on the scale of individual grains, while larger impacting particles created damage zones covering more grains as the particle size increased. These observations were supported by their fractography showing that whole grains were often removed. The implication is that erosion is a function of grain size, with possible maxima of erosion when the damage zone and G are equal, i.e. similar to the conditions for H minima as a function of G.

More quantitative data on the G dependence, though not a focus of the substantial study of Wiederhorn and Hockey [16], can be extracted from it. They measured the erosion rate (mass loss of a variety of ceramics using 150 m SiC abrasive particles carried at controllable velocities by injection of a particle stream into an air stream normal to the specimen flat surface. While their data shows general correlations of erosion rates with inverse functions of hardness and fracture toughness per Eq. (5.1), they made measurements on two dense, pure polycrystalline bodies, a sintered one (G 30 m) and a hot pressed one (G 3-4 m), as well as on a {1011} surface of sapphire. Their data was used to obtain the erosion resistance (the reciprocal of the erosion rate), which has been here normalized by dividing all resistance values by that for sapphire under the