Indentation with spherical tips

Fig. 34. ACP vs indenter displacement curve for GaAs obtained in indentation with spherical tip. The catastrophic plastic deformation starting at 200 nm leads to the drop in hardness value from 15 to 8 GPa. Data from Reference [122].

ELASTO-PLASTIC BEHAVIOR OF GLASSY CARBON AND SILICA GLASS BY NANO-INDENTATION WITH SPHERICAL TIPPED INDENTER... 

Figure 11. (a) Illustration of polymer indentation by spherical tip with radius of curvature R and contact diameter 2a. (b) Illustration of trench-shaped deformation region swept out by sliding spherical indentor. 

In this study, we tried to use spherical diamond indenters with different tip radius on the instrumented indentation tests. We tried to find the test force dependence of the surface fracture with these indenters, and the grain size dependence of the instrumented indentation results on ceramic materials. 

There are four major indentation hardness tests, which differ from each other in the shape of the indenter (Figure 10.23). The first of these, described in 1900, was the Brinell test, using a 10 mm steel ball indenter (Figure 10.23a), giving the Brinell hardness number, BHN. This was suitable only for metals softer than steel. In 1920 Rockwell developed a number of tests, including the B, E, F and G scales, in which the indenter is steel, and the A, C and D scales, using a conical diamond indenter with a spherical tip (Figures 10.23b and 10.23c). In the Rockwell test the difference in size between the... 

The elastic moduli of the as-sintered porous LSCF cathode film samples were measured using a NanoTest nanoindentation platform (Micromaterials, UK) with a spherical diamond indenter tip of 50pm diameter. Compared with sharp indenters like Berkovich tips, benefits of using spherical tips include less sensitivity to surface condition. At least 20 measurements were conducted in different locations for each sample in order to measure the variability of the mechanical response of the sample. Prior to nanoindentation tests, the NanoTest platform was precisely calibrated using a standard sihca sample to establish the system frame compliance. 

As mentioned earlier, nanoindentation measurements of porous films deposited on substrates are much more complicated than that of bulk samples due to more factors affecting the indentation behaviour. Surface roughness was inherent to the processing method of our films and could be less problematic due to the use of spherical tips and diluted ink. Crack-free films with macroscopically flat surface were fabricated as shown in Figure 2. 

Special attention is required when selecting the correct indenter tip. Sharp indenters such as the Berkovich tip indenter have been used by most researchers to measure the hardness and Young s modulus. However, the assumption of the transition from elastic to plastic behavior of the material is not permissible with a sharp-tipped indenter because these indenters create a nominally constant plastic strain impression. With a spherical tip, on the other hand, the depth of penetration increases as the contact stress increases therefore, the response of the elastic to plastic transition and the contact stress—strain property of a material can be determined (He and Swain, 2007). 

Rockwell Hardness Number. A value derived from the increase in depth of an impression as the load on an indenter is increased from a fixed minimum value to a higher value and then returned to the minimum value. Indenters for the Rockwell test include steel balls of several specific diameters and a diamond cone penetrator having an included angle of 120 deg with a spherical tip having a radius of 0.2 mm. Rockwell hardness numbers are always quoted with a prefix representing the Rockwell scale corresponding to a given combination of load and indenter. 

Field and Swain have studied elasto-plastic response on a number of brittle materials, including silicate glass, silicon single crystal and single crystalline sapphire, by the indentation with small micron sized spherical tipped indenters. The analysis of indentation stress-strain curve was performed from the indentation on... 

Field and Swain found that the indentation force-displacement behavior for GC exhibited almost complete recovery with a significant hysteresis between loading and unloading when indented with 3 and 10 pm radius spherical tipped indenters. And also we have studied on elasto-plastic deformation of silica glass and glassy carbons with different type of indenters ... 

Figure 1. Load penetration curve of fused silica glass with 3 pm radius spherical tipped indenter.

The effective strain associated with a spherical tipped indenter may be written as the ratio of radius of contact circle to the radius of indenter, ajR ... 

Table 2. Elastic modulus, yield stress, yield strain, constants of power law fitting and indentation elasticity index obtained from stress strain curves with 3 xm radius spherical tipped indenter on GCs and silica glass.

As shown in the present work, elastic and elasto-plastic deformations derived by spherical tipped indentation on glassy carbons depended strongly on their crystal structure. The elastic modulus and the yield stress of glassy carbons decreased with the elevation of HTT of glassy carbons. 

For all samples the penetration depth is determined at 27 C and 67 C at a given load of 20 nN. PS2 and PS6 at 27 °C exhibited similar values of about 2.5 nm. For the PSIOO sample, the tip indentation is 3.5 nm. Assuming a spherical tip with a radius of 20 nm, the difference in penetration depth is equal to a difference in contact area of about 30 %. Comparable penetration depths of 3 to 3.5 nm have been found for all samples upon heating to 67 °C. The change in contact radius can influence the measured adhesive force and must be taken into account for the following discussion. 

Force-Curves Measurements In force curve measurements, a vertical displacement of the sample, z, is imposed and the subsequent tip displacement, d, is measured. The tip-sample interaction force, F, is deduced by means of the Hooke s relation, F = -kcd, where is the cantilever stiffness. Force curves arc generally divided into different regions (7). If the part where the electrostatic repulsion forces are dominant is only considered, with silicon tips much stiffer than polymers, tips penetrate the sample surface and an indentation depth, 5, equal to Z d, can be measured. The lower the sample elastic modulus, the greater will be the indentation depth. By using the Hertz mechanical model adapted to the geometry of the tip-sample system (8,9) surface elastic modulus could be deduced from the following equations corresponding respectively to a spherical, a paraboloid and a conical tip ... 

Johnson (1985) assumed that the tip of an indenter (hemispherical or conical) is encased in a hemispherical core region (Fig. 8.10a) of radius a, in which the material has a hydrostatic pressure p. The upper surface of this region is in contact with the indenter. Outside the core, he used the solution for the expansion of a spherical cavity, in an elastic-plastic solid with a tensile yield stress Y. The stresses and displacements have radial symmetry. In the core, the mean pressure is... 

Indentation Depth Reading Rockwell Test, in this test, the depth of the indentation is read from a dial indicator no microscope is required (34). In the Rockwell hardness tests, a load of 98 N is first applied to the surface and the depth of penetration is thereafter reckoned as the zero of measurement. A further load of 588, 980, or 1470 N is applied and removed leaving the additional depth of indentation recorded on a dial. The hardness is then expressed in terms of the dial reading on an arbitrarily numbered scale. The indenter used may be a steel spherical penetrator or a diamond cone with a hemispherical tip. The scales, indenter, and loads employed are chosen to adapt to the material properties. Results given by different testers are not readily interconverted. 

The characterisation of the mechanical behaviour profile requires a local measurement that can not be obtained by a global compressive test. Nano indentaticHi test has thoi been used to stress locally the mata-ial. Expo-iments have been conducted on Nano-instruments model II nano-indento, that has been fitted with a spherical diamond tip of 105 pm radius. This apparatus, (schematically described in figure 2) allows the simultaneous record of the applied load W (ranging form 0 to 700 mN) and of the displacement of the indentation head. El Ghazal... 

The micro- and nanoindentation methods have been widely used to determine the hardness of ZnO over a wide range of size scales and temperatures. Hardness measurements are usually carried out on the (0001) surface of the crystal using the conventional pyramidal or spherical diamond tip, or alternatively, with a sharp triangular indentei The depth-sensing indentation measurements provide the complete information on the hardness and pressure-induced phase transformation of semiconductor materials. Table 1.6 shows the measured and calculated mechanical parameters for ZnO crystallized in the form of wurtzite, zinc blende, and rocksalt phases. 

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