Vickers indenter

Fig. 8. (a) Schematic of a Vickers indentation-induced Hertzian cone crack, (b) View from the bottom of an aluminosihcate glass block of a Vickers... 

Fig. 7. Strain boundaries for the crystal destruction zone (assuming a spherical shape) round the Vickers indent for two PE samples with a = 0.95 and a = 0.21 respectively...

The question whether hardness is a property related to modulus (E) or yield stress (Y) is a problem which has been commented before by Bowman and Bevis 13). These authors found an experimental relationship between microhardness and modu-lus/yield-stress for injection-moulded semicrystalline plastics. According to the clasical theory of plasticity the expected indentation hardness value for a Vickers indenter is approximaterly equal to three times the yield stress (Tabor s relation). This assump-... 

Fig. 20. Vickers indentations of oriented CEPE along the fiber axis for various loads showing the typical anisotropic impressions...

Figure 1.3 Correlation between the Moh scratch hardness and Vickers indentation hardness scales.

Vickers indentation method will be pursued here (in both its micro- and nanomanifestations). 

Figure 1.3 compares the Moh scratch scale with the more quantitative Vickers scale (Gilman, 1973). Clearly the two scales are not linearly related. Each has its own realm of application. For brittle minerals, and similar materials, the Moh scale is most useful. For ductile materials like metals the Vickers indentation scale can detect small differences more readily. Note that the range on the Vickers scale is large about 1000, while range of the Mohs scale is about 10. 

Figure 2.11 Correlation of Mohs (M) and Vickers indentation hardnesses (VHN). Data from Mott (1957). The dependence is roughly exponential. That is VHN exp (M). Similar to Figure 1.3, but coordinates are linear.

The dimensional ratios of indentations obtained with the first three, most common, indenters, taking indentation depth to be 1, are for the measured parameters 7—with the Vickers indenter 30.5—with the Knoop indenter 7.4—with the Berkovich indenter. 

Proceeding from equation (4.3.19), we obtain, as for the Vickers indenter (4.3.22) and (4.3.23), the following hardness formulae for commonly used indenters ... 

Fig. 4.3.14. Plexiglass, differential interference contrast, grey of 1st order, Vickers indenter, load 122.5 mN, filter 546 mm, measurement magnification 260 x, photograph enlargement 400 x. (After OPTON Feintechnik, Oberkochen)...

Fig. 4.5.3. Smith-Sandland of included-angle design in Vickers indenter.

Gragert and Meyer (Fig. 6.2.1) and Boyarskaya (Fig. 6.2.2) by observation of surface deformations induced by indentation with a tungsten carbide ball and by scratch. The observations were carried out using secondary electron beam and in cathodoluminescence. They demonstrated on MgO and LiF crystals the occurrence of cracks around the impression of the ball similar to those induced by a Vickers indenter, and also the occurrence of a concentration of screw and edge dislocations in the area of the cracks. 

A general model for sharp indenters (Fig. 6.2.8) with the geometry of a Vickers indenter and with critical state considered, is proposed by Marshall... 

A comparison of this number with the test results of Boyarskaya (1972), listed in Table 7.7, shows that practical measurements of anisotropy, both with Vickers indenter and by scratch, depart widely from the theoretical result which is too low. Similarly, results which are too low, are given by Boyarskaya for disthene, 1.8 instead of 3.13 (Lebedeva, 1963), also diverging from the results reported by Winchell (1946), who determined the ratio 1120/420 = 2.68. 

Fig. 6.1.3. Shape of Vickers indenter impressions and character of cracks on sulphur crystal face.

Similar tests of sections deformed under the action of a Vickers indenter were conducted by Lawn et al. (1980) who used transmission and interference microscopy for this purpose. Tests with Si, Ge, SiC and A1203 crystals revealed a similar, spherical pattern of stress curves for sharp cracking and sharp indenter. Chandhri -et al. (1980) confirmed the test results of... 

Fig. 6.2.9. Indentation /strength model system, (a) Vickers indenter, peak load P, generates median/radial crack, characteristic dimensions (value c0 at completion of contact cycle, with further post-indentation, supercritical extension to c0, if exposed to moisture), (b) Tensile field a in combination with residual ( ghost ) contact field, drives crack system to failure. (After Marshall and Lawn, 1980)...

Palmquist S., 1962, Occurrence of crack formation during Vickers indentation as a measure of the toughness of hard metals, Arch. Eisenhuettenwes., 33 (9) 629-633. 

There are two main techniques used to measure the fracture toughness of ceramics fracture stress and hardness indentation. The former measures the load to fracture of a pre-cracked specimen using a single edge notched beam (SENB) or a chevron notched beam (CNB) sample. The main drawback of this technique is ensuring that the crack tip is atomically sharp. The second method uses the crack formed at the corners of the indentation produced during a Vickers indentation hardness test. This technique is rapid and relatively inexpensive. However, the toughness values measured are those of the surface, unlike the values obtained by fracture of the pre-cracked beams which are a measure of the bulk material properties. 

LGMs of the AT/alumina and AT/ZTA displayed some very interesting properties which include excellent machinability, low thermal expansion coefficient, improved thermal shock resistance, low hardness (about 5 GPa), low Young s modulus (E) (250 GPa) and excellent flaw tolerance [Pratapa, 1997 Pratapa Low, 1998 Skala, 2000 Manurung, 2001], These materials appeared to display a large degree of near-surface quasi-plasticity under the Hertzian or the Vickers indenter which effectively inhibits the formation and propagation of cracks. The ductile behaviour of these materials was... 

The phase composition from the surface to the interior of the samples was determined by X-ray diffractometry (XRD) through successive grinding of the surface at 100 pm intervals. The microstructural characterization of the sintered specimens was achieved by scanning electron microscopy (SEM) in backscattered mode. The hardness change from the surface to the interior of the sample was measured by the Vickers indentation method at 19.6 N load. 

Cottom, B.A., Mayo, M.J., Fracture toughness of nanocrystalline Zr02-3 mol% Y203 determined by Vickers indentation, Scripts Mater., 1996, 34(5) 809. 

Tancret, E, Osterstock, E (1997), The Vickers indentation technique used to evaluate thermal shock resistance of brittle materials , Scripta. Mater., 37(4), 443 447. 

The bulk densities of all the materials were determined using Archimedes method (AS 1774.5, 1979). The Vickers indentation technique was used to measure the hardness in each case. The applied load in the Vickers hardness tests was 10 kg for silicon nitrides and sialons. However, using the same load produced severe lateral cracking in silicon carbides around indents, which prevented the accurate measurement of the diagonals of indents. Therefore the load was reduced to 0.3 kg for silicon carbide samples. 

SEM micrographs of Vickers indentation-induced damage in material SiC-S (peak load 10 kg) (a) SE image, (b) and (c) BSE images. 

Figure 2.35. Examples of indentation processes to determine surface hardness. Shown are (a) Vickers indentation on a SiC-BN composite, (b) atomic force microscope images of the nanoindentation of a silver nanowire, and (c) height profile and load-displacement curve for an indent on the nanowire. Reproduced with permission fromNanoLett. 2003, 3(11), 1495. Copyright 2003 American Chemical Society.

The effects of very high stresses and strain-rates have been investigated in microhardness experiments. In these experiments, loads of 50-500 g (corresponding to stresses as high as 2 GPa) are exerted by a diamond or sapphire Vickers indenter for about 20 seconds at temperatures up to 1,(X)0°C. Clearly, steady-state flow is never achieved but such experiments have provided important information about the dislocations involved in the deformation of olivine, for example. 

Figure 2.1 illustrates the stress distribution on an amorphous PET sample at an indentation depth, h = 2 mi (Rikards et al, 1998). It can be seen that the depth of the plastic zone shown is here about five times the penetration distance of the Vickers indenter. 

Figure 2.4 schematically depicts the indentation geometry for a Vickers indenter penetrating a cylindrical surface with a radius r. In the case of an ideal plastic deformation (i.e. when elastic stresses are absent) after load removal, the square pyramidal indenter leaves a rhombic indentation with one of its diagonals parallel to the filament axis. Let 2BC be the measured indentation length, f x, normal to the filament axis and 2DE the indentation length, which would arise on a flat surface for the same penetration depth. For an isotropic material, = C. However, as a result of the existing curvature, i > (anisometric indentation). From Fig. 2.4, DE = BC + BD tan a/2) and since tan(a/2) —1/2 one has = li + IBD.

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