Mechanical Properties of Ceramics and Composites

Earlier work by Goyette et al. [107] showed that the vertical forces in single point diamond machining of five dense sintered Al2O3 bodies decreased significantly, e.g. twofold, from the smallest to the largest G (2–40 m) for a fixed rpm over the > threefold rpm range used. Similarly, Marshall et al. [108] showed that normal grinding forces increased with depth of cut as expected and that for any fixed depth of cut was substantially higher for finer G ( 3 m) than coarser G (20 and 40 m) high purity alumina bodies. However, a 96% alumina with intermediate G ( 11 m) had higher forces, sapphire still higher, and a 90% alumina (G 4 m) still higher forces. Thus they noted that purity was also a factor: some less pure materials had higher forces. Normal fracture toughness values from conventional tests, i.e. with cracks large with respect to most microstructures, showed an inverse correlation with grinding forces (hence grinding resistance), but there was a better, though scattered, correlation with toughness values projected to finer crack sizes, some of these approaching single crystal values.

Xu et al. [89] showed similar effects of G on grinding results in the alumina bodies used in their earlier summarized studies. Normal and tangential grinding forces both increased with depth of cut in respectively a nearly linear and a linear fashion, with substantially higher rates of increase for G = 3 m, but no significant differences for G = 9–35 m. Average surface roughness progressively increased, but with diminishing increases as G increased; the number, and hence also the area, of microcracks (intergranular) was zero for G = 3m, but beginning at G = 9 m they increased at a substantial, linear, rate as a function of G-1/2.

VII. DISCUSSION AND SUMMARY

The properties considered in this chapter are commonly more varied and complex than those of Chapters 2 and 3, and less well documented, for their dependence on G and other material, body, and test parameters. All have several aspects in common, i.e. compressive stresses, as for hardness, and all have at least a general correlation with hardness and involve some degree of plastic deformation, which varies, often in incompletely known fashions, for the different properties. Grain parameters play some, commonly an important, role in all of them, but only grain size has been addressed to any, but still limited, extent (sometimes not explicitly), so other grain effects offer important opportunities not only for study and understanding of their roles in each of the properties but also for better and broader understanding of the properties themselves. For example, a number of materials and bodies studied most likely have measurable but varying degrees of grain elongation, e.g. Si3N4, α-SiC, Al2O3, and TiB2, and various bodies, e.g. hot pressed ones, commonly have some preferred orientation, so these unaddressed factors are probably factors in data scatter, and especially uncertainties in property correla-

tions. Thus better attention to grain and other microstructural effects will significantly increase understanding of each of the properties.

An important factor limiting correlation of properties of this chapter with those of earlier chapters, and hence with better known microstructural correlations, is the common correlation with multiple properties. Properties in previous chapters commonly have strong correlations with two properties, namely Young’s modulus and fracture energy (which are also related), though there are variations and uncertainties, especially in the latter (Chap. 2, Sec. III; Chap. 3, Sec. VII). These uncertainties and those of the specific roles of TEA and EA are compounded for the properties in this chapter due to the uncertainties, and often more complex dependence of their properties.

Three factors illustrate the added uncertainties in the dependence of properties of this chapter on other more basic properties and hence on their grain structure dependence. First, the correlation of H with properties in this chapter is more uncertain because the load, indenter geometry, surface condition, strain rate, and environment, hence the grain structure dependences probably vary in uncertain fashions, even for those properties where loading is localized to specific areas as in erosion and wear similar to indentation. However, even for these cases, there are differences and complexities, e.g. scratch hardness and wear inherently involve more interaction with the grain structure than in at least some ranges of load, geometry, and grain structures than for indentation hardness. Similarly, both erosion and especially ballistic performance involve effects of the hardness of both the impacting object and the target. The second factor is the high strain rates of some of these processes such as many erosion situations (e.g. for some missile domes and windows) and especially armor applications, particularly against kinetic energy penetrators.

The third factor is uncertainty in the local toughness to use and impacts of TEA and EA stresses on the local fracture process. The most pervasive issue is that of toughness associated with cracks on a scale <, equal to, or only somewhat > the local G, i.e. similar to situations discussed for tensile failure (Chap. 2, Sec. III; Chap. 3, Sec. VII). Note first that addressing this issue in the terms of short versus long crack behavior is misleading, since this implies that even a short crack, which can still have a length large in comparison to the grain size, would have behavior substantially closer to that of a long crack in comparison to a crack with both its length and depth similar to or < G. Further, the treatment in terms of long and short cracks has focused on the baseline toughness being that for easier single crystal fracture, instead of also including that for grain boundary fracture, which may be similar, or substantially lower, depending on boundary character and on how many boundary facets are involved. For erosion and wear, and possibly compression, effects of environment may also be factors, though for compression this may be more of a factor for failure involving more surface connected cracks due to nonuniform stressing. Also such possible

effects in compression may be more due to lubrication effects between cracks than to true slow crack growth, since compressive failure typically appears to involve varying friction between crack faces.

Next consider the related issues of self-consistency of the results and their completeness, since the two are closely related, i.e. fewer results mean less opportunity to evaluate self-consistency. An important aspect of self-consistency is consideration of data scatter, and its consistency with both the property and the mechanisms involved as well as the microstructural variations and their impact and correlation with property variations. Thus, for example, though widely neglected, the coefficients of variation, hence also the Weibull moduli, of well conducted compression tests are higher, commonly substantially so, in comparison to such values on the same materials in tension (Table 5.2). This is consistent with compressive failure being a process of cumulative failure from the nucleation and growth of many small cracks in the body versus tensile failure reflecting failure due to the most severe flaw developed or existing in the region of high stress. Similarly, with more data it may be feasible to correlate variations in erosion and wear with factors such as the distribution of asperities and surface grain sizes, shapes, and orientations.

Despite the limitations and uncertainties outlined above, consider the grain size trends demonstrated beyond the general decrease with increasing G. Compressive strengths, which extrapolate to the range of differing single crystal values (indicating probable effects of grain shape and elongation), generally decrease more with increasing G and show less variation (for well conducted tests), than tensile strengths; but many issues remain. These include specifics and variations of plastic deformation; crack nucleation and growth; strain rate, environment, and size effects. Though not addressed very extensively, grain size probably plays a role in ballistic stopping abilities of ceramics, e.g. as indicated by limited data with smaller, slower, softer bullets; but much more study is needed to address the complexities due to the high strain rates, differing projectiles, and apparent accentuation of other microstructural variables such as grain boundary phases and bonding. Differentiation between microstructural and property effects as a threshold requirement versus a continuous factor seems important. Erosion shows higher material removal as G increases and indicates some possible correlation with the G dependence of H, e.g. possibly via reduction of the resistance to erosive material removal at intermediate G. There are also uncertainties in the G dependence of strengths remaining after some erosion, with an important question being what fracture toughness values to use as a function of cracks approaching, or becoming <, G. Again the terminology of long versus short cracks does not adequately reflect this issue of crack size relative to G, and toughness values for fracture along a few or one grain boundary facet need to be considered; these K values may be substantially < single crystal values.

Scratch hardness, which can simulate aspects of a single wear asperity,

clearly has similarities with indentation hardness, e.g. Fig. 5.11 with values over a significant G range below single crystal values indicating possible effects of TEA and EA and of grain shape and orientation. This data also indicates the bias of results toward better correlation with the sizes of larger grains where there is a substantial G distribution. This is similar to the role of larger grains in tensile failure, probably partly reflecting fracture as part of the scratch track generation mechanisms. However, there must also be differences between scratch and hardness, and especially tensile strength, tests. Thus, for example, the motion of the scratch indenter increases interaction with the grain structure over that for hardness indentation only, as indicated by materials such as Si3N4 and AlN deviating significantly from the correlation of the two tests and these deviations apparently being associated with greater plastic flow (which presumably also has significant G dependence). An important factor in repeated scratching is the interaction of adjacent scratches by enhanced fracture between the scratches, initiating and reaching maxima respectively at 3 and 2 times G, showing another important impact of G (and suggesting similar studies of in- dent-related cracking) (Fig. 5.16). The preeminent difference of tensile failure and scratch fracture is that the former is usually dominated by a single weak link, and thus is impacted by the statistical aspects of flaw location, e.g. from machining, and a single large grain or cluster of them. On the other hand, scratches cross many grains and can interact with each other, both of which can be impacted by the character of many individual larger grains or grain clusters. Thus the role of grain size distribution on wear is a potentially important but generally unaddressed topic.

Wear, despite many variations in conditions, usually correlates with hardness and thus commonly increases with G, i.e. wear rate decreases as G decreases, as do machining rates (Figs. 5.18 and 5.19). However, opposite wear trends with G were noted, e.g. with effects of residual porosity changing from primarily intergranular to some intragranular locations as grains grow, being suggested in one of the cases of opposite G dependence. In the other case, the greater difficulty of forming or removing wear debris was suggested as a possible cause of the opposite G dependence from that commonly found. These clearly highlight the need for further study, especially with more comprehensive testing and characterization, and evaluation of possible contributions of a broader range of material properties such as TEA and EA, as is true for all properties in this chapter. Impacts of TEA and EA in wear are indicated by the frequent increase in intergranular fracture as G increases (i.e. opposite of most fracture trends, Fig. 2.5 in both noncubic materials (with TEA and EA) and cubic materials (with EA only), e.g. Figs., 5.13, 5.14.

Finally, four key factors, especially about erosion and wear, deserve added emphasis. First, they clearly depend on G via its impacts on both plastic deformation and fracture, with various probable environmental, reaction, and interac-

tive effects. Second, there is a probable role of EA and TEA in these behaviors, which probably underlie material-dependent G levels for onset or changes in mechanisms and results, e.g. to intergranular fracture. Third, a major issue out of several that need much more study, but deserves particular note, is the transition from individual impacting particle or asperity indentations or scratches to many interactive ones, and the probable enhancement of effects of such impacts or tracks when their dimensions are in a range similar to that of the grains. Fourth, both the importance and the diversity of wear make it an important area for further study.

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