Mechanical Properties of Ceramics and Composites

a Polycrystalline and single crystal values per Table 2.1, the latter in ().

b Values in () are the slopes multiplied by 0.71 to convert them to comparable toughness values, since grain size (G) is measured as a diameter and flaw size(c) as a radius.

c Values shown are calculated for a surface half penny crack per Eq. (3.3) using either polycrystalline or (where known) single crystal fracture toughnesses, the latter results shown in ( ).

FIGURE 3.22 Strengths of various machined beta aluminas versus G-1/2 of Virkar and Gordon [195] (hot pressed or sintered, plotted vs. Gm) and various other studies [196–200] of hot pressed, HIPed, and sintered bodies plotted versus average G, Ga (horizontal bars for some bodies with a wider G range). (From Ref. 2, published with the permission of the Journal of Materials Science.)

fundamental difference between the G dependences of strength and toughness (Figure 2.18), i.e. the strength continuously decreasing as G increases, while toughness goes through a, commonly significant, maximum at certain G, e.g. 1–3 µm. Thus there is a need to integrate the σ – G-1/2 behavior with evaluation of mechanisms for transformation toughening. Some of this may involve increased G increasing the martinsitic start temperature, which reduces KIC [189–194] and hence generally σ, thus also impacting σ – G-1/2 trends, but such effects are not pertinent to fully stabilized ZrO2 and are of uncertain applicability to precipitate toughened PSZ. Thus the toughness maximum must reflect testing effects not pertinent to normal strength behavior, though the general increase in toughness from transformation does increase strength in two ways, as is discussed later.

given G between the different investigators, data of Lin et al. [205] being higher than the others. This probably reflects typical flaw differences due to differences in machining, residual processing defects, and specimen size and other testing effects, which are particularly pertinent to this probably being the finer G branch. This data is consistent with an intersection with the larger G branch being at ≥ G = 10 µm, which in turn is consistent with typical polishing flaws in dense (transparent) MgF2 being of the order of 10–20 µm [18]. Note that polycrystalline strengths are below single crystal strengths. Also note the clear decreases in strength as G decreased below 1 µm, attributed to retention of (primarily anion, e.g. OH) impurities [204] from higher pressure hot pressing at lower temperatures, e.g. 210 MPa at 650°C [205] and 240 MPa at 568–713°C [207], both for powders of 0.1 µm particles.

Earlier TiB2 [11, 208–210] agrees with more recent data of Baumgartner and Steiger [211] as well as that of Becher et al. [212], and Telle and Petzow’s [213] evaluation of Watanabe and Kouno’s [214] data indicate a clear larger G branch and possible finer G branches at various strength levels (Fig. 3.25). Other limited data is generally consistent with these trends [215–218].

B4C data from mostly hot pressed bodies in a previous survey [13] showed two branches, with finer G branches showing more effect of grinding parallel or perpendicular to the tensile axis than the larger G branch (i.e. each forming a finer G branch [17]. A further survey [2] (Fig. 3.26) of substantially more data [219–234] corroborated these trends, i.e. generally showing positive finer G slopes, but greater G dependence of the larger G branch, which may or may not extrapolate to σ = 0 at G = ∞. These data cover a considerable composition range, showing no clear, substantial effect of this on σ, other than via G, except for the hot pressed B4C data of Rybalchenko et al. [225] ( 2–5% porosity), which generally falls well below the other data. This may be in part due to lower quality (unspecified) surface finish but appears to reflect processing effects. Thus σ increased at a given G with both hot-pressing temperature and pressure, and for a given pressing pressure σ often even increased with increasing G for G ≤ 5 µm (for all but one of their bodies). The trend for limited effects of composition in most cases is consistent with evaluations of B4C hardness data showing that most of the composition effects were via G [231], in contrast to claims of Niihara and colleagues [232, 233].

Fractography has played an important role in better defining the G dependence of B4C strength, for example some failure from substantially isolated or clustered larger (exaggerated) grains [2, 13]. While this is similar to Al2O3, it is also different, since the large grains in B4C are typically equiaxed, occur less frequently than in Al2O3, and have almost, if not universal transgranular fracture. Frequent twins in B4C, at least in larger grains, may be a factor in these differences, but correction for observed and expected failure from isolated or clustered larger grains (e.g. Figs. 1.20, 1.30) shifts some data points to the larger G branch,

FIGURE 3.25 TiB2 σ–G-1/2 data of Mandorf and Hartwig [208], Alliegro [209], and Holiday et al. [210] from an earlier survey [11] along with more recent data for similar materials by Baumgartner and Steiger [211] as well as data of Becher et al. [212] (for specimens with 0–1.5% Ni additions) and from Telle and Petzow’s [213] evaluation of data for nearly dense bodies of TiB2 with three different additives from Watanabe and Kouno [214]. (From Ref. Rice [2], published with the permission of the British Ceramic Society.)

increasing its slope a limited amount, and removing some more extreme lower strengths from the finer G branch. However, again fractography has also shown that some data points are (incorrectly) moved further to the left than most of the data, and some not far enough by using Gm, indicating respectively that they (1) are not pertinent to σ–G behavior, i.e. reflect a more serious defect and (2) are not large enough to be the flaws by themselves. Further, fractography clearly showed cases of failure initiation not occurring from large grains (Fig. 3.27), again showing that the arbitrary use of Gm even in the vicinity of the fracture origin can lead to serious errors. Both the σ – G-1/2 data and fractography again show intersection of the finer and larger G branches when c G. Fractography also showed (via extensive transgranular fracture) mist and hackle, arguing

FIGURE 3.26 B4C σ–G-1/2 data (mostly hot pressed) from an earlier survey [13] as well as subsequent studies of Rice [17] of two different bodies ground parallel or perpendicular to the tensile axis are shown along with data of Osipov et al. [219], de With [220] (all hot pressed), Champagne and Angers [221] (with varying excess B) Beauvy [222], Seaton and Dutta [223], Vasilos and Dutta [224], Rybal’chenko et al. [225], Bougoin et al. [226] (sintered), Schwetz and Grellner [227], and Schwetz et al. [228] (sintered-HIPed with varying excess C). Numbers next to points are % porosity where > 1%. Vertical lines are standard deviation, and associated numbers are the number of tests. (From Ref. 2 published with the permission of the Journal of Materials Science.)

FIGURE 3.27 Fractographic demonstration of failure not occurring from much larger grains in dense B4C. (A) Lower magnification SEM showing a nearly half penny origin (arrow) from a machining flaw in the fine grain structure and a higher magnification of it in (B). Note in (A) the two large grains to the left of the origin, the largest one touching the tensile surface, are clearly not the origin (From Ref. [2], published with the permission of the Journal of Materials Science.)

against significant subcritical crack growth and bridging, which typically is via mostly intergranular fracture. Finally, note (1) that Rice [234] showed evidence of TEA stresses contributing to tensile failure (Fig. 3.35), and (2) that σ trends with G are clearly inconsistnt with toughness results, typically having significant maxima at G 10 µm [2] (Chap. 2, Sec. III.F).

As is shown in Fig. 3.13, the limited α-SiC data is generally consistent