Knoop hardness anisotropy

UO2 has a surprisingly low brittle-ductile transformation. The only observed slip system at low temperatures is lll (110), and this does not depend on stoichiometry. Sources of mobile dislocation are an issue, however, and in order to achieve deformation at temperatures below 600 °C the crystals must be pre-deformed at 600 °C. With such pre-deformed crystals, deformation to plastic strains >1% is possible with modest yield stresses, typically 80 MPa at 450°C, 110 MPa at 400 °C, and 120 M Pa at 250 °C. Attempts to deform these crystals at room temperature were not successful, although perhaps a more careful alignment of the load train might have allowed plastic deformation at temperatures below 250 °C. Microindentation at room temperature is always possible, however, and the Knoop hardness anisotropy at room temperature is also consistent with 111 slip [74]. The yield stress at 600 °C was variable, but surprisingly was not a function of the 0/ U ratio the plastic deformation... 

The graphs obtained in Knoop hardness anisotropy investigations are typically like those in Figure 3.5. They are usually obtained by taking the... 

Figure 3.7. Knoop hardness anisotropy observed on specific planes of InP and cubic BN crystals. Note that 45° from <110> is equivalent to [100]. Data are represented from Brazen and Brookes. " ...

Radiation damage can, in some samples, introduce a degree of plasticity for example, in diamond the overall hardness is reduced after irradiation but there are no data showing what this does to the Knoop hardness anisotropy. We can, however, note that radiation damage in MgO increases the overall hardness but does not affect the anisotropy, a fact that seems to be general for the rock-salt structure. ... 

Figare 3.15. Knoop hardness anisotropy on (a) (0001) and (b) 1010 planes of beryl, BejAljSiftOig, from reference (22). 

From Knoop hardness anisotropy measurements on single crystals of 6H-SiC, discussed in Chapter 3, the following slip systems have been identified in experiments from ambient to 600°C (0001K1210), (OOOlKOllO),... 

Figure 3.6. Knoop hardness anisotropy observed on the (001) pl ine of Nao WO, using a load of 1.96 N at room temperature. After McColm and Wilson. ...

Figure 3.11. Planes and directions of importance in Knoop hardness anisotropy studies of hexagonal crystals.

Figure 3.14. Knoop hardness anisotropy on three sets of planes of SiC as observed by Sawyer ei with 4.9 N load.

Table 3.6. Knoop Hardness Anisotropy of Some Tetragonal Special Ceramics...

A clear crystallochemical interpretation of hardness anisotropy measurement results, especially for monocrystals, makes it possible to estimate the structural homogeneity of crystal. Button et al. (1979) testing the hardness of cubic sodium tungsten bronzes Na W03 (where 0.4 < x < 0.75) with the Knoop indenter, found the hardness of W03 to rise from 450 to 844 within a highly differentiated hardness anisotropy for various values of the Na+ ion. This variation is the outcome of differences in atomic spacings in crystals. 

Fig. 4-5. The measured anisotropy in Knoop hardness of p-BN as compared with predictions of the resolved shear stress model [20].

Figare 3Jt. Knoop hardness versus inden-ter angle for n-type germanium at two temperatures. After Roberts et This anisotropy is like that in Figure 3.7. 

Figare 3.12. Anisotropy of Knoop hardness observed on (a) (0001) plane and (b) (1100) plane of AI2O3. Redrawn from reference (9). 

Because this is not a commonly encountered indenter and because of the restricted type of plane that it can usefully investigate, there are very few results from which to draw conclusions. However, for cubic crystals the difference between those having 001 (011) slip systems and the other types is evident in the symmetry of the hardness anisotropy curves as it was in the case of the Knoop indenter and the Vickers diamond. 

It has already been stated in Section 3.5 that, although it is known to exist, the anisotropy effect has not been fully investigated. Figure 3.12 shows the anisotropy of hardness on (0001) and (1100) in alumina and Table 4.3 in Section 4.1.2 has the different ISE effects on the different planes and directions. Clearly the effect of hardness anisotropy is more marked on the prism planes than on the basal planes, as is not unexpected in view of the distorted nature of the AlOe octahedra in the structure. Knoop hardness shows that the anisotropy effect decreases rapidly with test temperature increase as shown in Figure 6.15. 

Results from a more specific examination of hardness anisotropy using the Knoop indenter have been given in Section 3.5.1, which shows that the direction of maximum hardness in the basal, (00.1) plane depends on the cation in the mirror plane active slip systems are (00.1)(1120) for Na" -j8- AI2O3 and (00.1 ) 10l0> for Ag, K, and T1 AI2O3, which suggests... 

Barium titanate (BaTi03), strength after indentation, 185 Barrel indents, 44-126 BeBg Knoop hardness, 303 Beevers-Ross sites, 280 Berkovich hardness anisotropy, 94 diamond, 11, 39-40 equation, 11... 

B SiOg, 223 Bhat equation, 174 Bierbaum hardness, 1 Blunt punch, 12-13, 166-168 crack development, 166-168 equation for stress, 113-114 flow pattern, 12 indenter analysis, 12, 166 and plastic zone. 111 Bond breaking model. 132 rate equation, 132 Borazon, 231 Borides, 297-301 bonding in, 298-299 hardness anisotropy, 84, 93, 108-109 Knoop hardness, 87 slip systems, 108-109 structures, 299... 

Yield and absolute hardness, 72 Y-sialon glass density, 229 Knoop hardness, 229 Modulus, 229 Young s modulus of AljOj, 241, 259-261 anisotropy in /3-AI2O3, 281 of B4C, 228, 241 and bond type, 172 and crack depth, 155 and cracking, 147 of CrjCj, 302 of germanium, 252 of glass, 238 and hardness, 72 hardness ratio, 179 from Knoop indents, 180 mismatch stress, 273 of MgO, 241, 269 and penetration depth, 47, 240 and plasticity parameter, 241 and residual impression parameter, 240... 

Because these curves closely parallel the results obtained in real systems, as shown in Figures 3.5, 3.6, 3.7, 3.8, 3.12, 3.13, 3.14, and 3.15, the types of observed anisotropy in Knoop hardness have been used to study plastic... 

Examination of Figure 3.21 shows that one of the three slip systems can be easily identified from Knoop hardness measurements, namely, the 110 [Pg.225]

It is obvious by now that the mismatch of symmetry between the Knoop indenter and 111 planes is a weakness when exploring hardness anisotropy of such planes. However, since scratch hardness does not suffer from such a mismatch, the resolved shear stress curves for the (111) plane in cubic crystals with the three commonly found slip systems shown in Figure 3.29 may be useful in anisotropy and slip system investigations. Clearly more detailed anisotropy is predicted but the small anisotropy factors implied in the scale-of Figure 3.29 must be remembered. Generally speaking, only the main features of the predicted curves have ever been established and experimental uncertainty makes it unlikely that the fine detail will be found. 

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