Indentation size

The Vickers hardness test is commonly made on a flat specimen on which the indenter is hydrauhcaHy loaded. When the desired number of indentations have been made, the specimen is removed and both diagonals of the indentations, measured using a caUbrated microscope, are then averaged. The Vickers hardness number may be calculated, or for standard loads taken from a precalculated table of indentation size vs VHN. The preferred procedures are described in ASTM E92 (2). 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

It is observed that indentations made with low loads on an indenter are smaller than expected from the sizes made with high loads. Thus the apparent hardness of a specimen increases as the indentation size decreases. This is known as the indentation size effect (ISE). It has been given a variety of interpretations, but the most simple is that it is associated with friction at the interface between the indenter and the specimen (Li et al., 1993). 

The indentation process is driven by the applied load, and resisted by two principal factors the resistance of the specimen to plastic deformation (and elastic deformation) plus the frictional resistance at the indenter/specimen interface. The ratio of these resistances changes with the size of the indentation because the plastic resistance is proportional to the volume of the indentation, while the frictional resistance is proportional to the surface area of the indentation. Therefore, the ratio varies as the reciprocal indentation size. This interpretation has been tested and found to be valid by Bystrzycki and Varin (1993). 

The susceptibility of hardness measurements of silica and silicate glasses to environmental factors is consistent with the effects of water on the deformation of quartz. The load effect and indentation size effect appear to be a result of the frictional forces at the indenter-specimen interfaces. 

There is disagreement in the literature about the role of friction. Compare, for example, Cai (1993) with Ishikawa et al. (2000) This has arisen in various ways. In the case of metals, where the Chin-Gilman parameter is small, friction is not important for relatively large indents. However, as the C-G parameter becomes much larger for covalent crystals, and as the indent size decreases friction becomes more important. Also, environmental factors, such as humidity, affect friction coefficients. In the regime of superhardness with dry specimens and small indents friction becomes very important. 

W.W. Gerberich et al Interpretations of indentation size effects. J. Appl. Mech. 69,443 152... 

Polymers showing a viscoelastic behaviour occupy the intermediate range. Out of all the existing hardness tests, the pyramid indenters are best suited for research on small specimens and microstructurally inhomogeneous samples (Tabor, 1951). Pyramid indenters provide, in addition, a contact pressure which is nearly independent of indent size and are less affected by elastic release than other indenters. 

Elmustafa, A.A. Stone, D.S. Indentation size 35. effect in polycrystalline fee metals. Acta Mater. 

In addition, tests of this type also reveal some of the key effects that emerge once the characteristic dimensions of the problem (i.e. the grain size, the indenter size, etc.) begin to reach into the nanometer range. Indeed, one compelling example of such size effects has been argued for in the context of nanoindentation as seen in fig. 12.32. 

Nix W. D. and Gao H., Indentation Size Effects in Crystalline Materials A Faw for Strain Gradient Plasticity, J. Mech. Phys. Solids 46, 411 (1998). 

To measure hardness more precisely a known load is applied slowly to a hard indenter that is placed onto the smooth surface to be tested. The surface is deformed plastically, and the indent size or depth after the indenter is removed is taken as the measure of the indentation hardness of the material. The hardness is often recorded as an empirical hardness number, related to the size of the indentation. 

Flardness tests are widely used as a non-destructive method of estimating the yield stress of metal products, to check whether heat or surface treatments have been carried out correctly. The test is less common for plastics, partly because such treatments are not used, and partly because viscoelasticity makes the indentation size decrease with time. Recently, nano-indentation has been used to examine microstructural variation in polymers. This section considers the case where the indentation depth is much smaller than the product thickness, whereas Section 8.2.6 considers the case of the indenter penetrating the product. 

It may be argued [3] that the goal hardly attainable in the experiments using high-pressure diamond anvil cells could be more easily achieved in as simple an experiment as a conventional hardness test. The well-documented indentation size effect (ISE) [189] reveals itself in the following relation between the Meyer hardness HM (equivalent to the mean contact pressure) and the applied load P [190] ... 

The SEM images of the Berkovich indentations in the (111) surface of B4.3C reveal the presence of discrete deformation bands within the indentation contact area, which apparently follow the sample crystallography (Fig. 44). Similar features have been observed previously in TiB2 and AI2O3 [213] and discussed in detail in connection with the indentation size effect by Bull et al. [214]. It was proposed [214] that the yielding beneath the indenter occurs nonuniformly in some hard materials and the discrete dislocation slip-steps are generated to re-... 

The repeated measurement of the size of indents, and the interpretation of indent geometry for the purposes of calculation, may be tedious, and operator bias is almost unavoidable. The edge of the impression is not always well defined, and misleading edge effects may be associated with anisotropic plasticity or plastic recovery. Faceted and elongated grains, or other microstructural features, together with the limitations of contrast and resolution in the optical microscope, complicate the interpretation, while the shape of the indent may differ in different materials so-called pin-cushion or barreled indents, associated with different constitutive relations and frictional shear on the faces of the indentor in contact with the plastic zone [3]. Mismeasurement of indent size is a major source of scatter in the experimental data and the relative errors in the results of different operators. 

The median crack is a single, penny-shaped crack nucleated beneath the apex of the plastic zone created by the indentor. The diameter of the median crack is comparable with the indent size, and a median crack is not visible in a polycrystalline, opaque material. The driving force for nucleation of the median crack is the elastic tensile stress developed normal to the indentation direction at the elastic-plastic boundary when the external load is relaxed. Nucleation of a median crack depends on the presence of a suitable flaw. Once nucleated, the median crack will propagate spontaneously to a stable flaw size. The critical flaw size for growth is ... 

After nucleation, the median crack propagates away from the elastic-plastic zone boundary. Stable propagation occurs on increasing the external load, and the ratio of the diameter of the median crack, D, to the indent size is given by ... 

The indent size, the surface crack morphology, and the extent of subsurface damage are all influenced by the crystal structure, chemical composition, and micro-structural morphology of the material. 

Interrelations Between the Influences of Indentation Size, Surface State, Grain Size, Grain-Boundary Deformation, and Temperature on the Hardness of Ceramics... 

To be able to compare grain size and indentation size influences, the size of the plastically deformed zone must be known. This information comes from TEM investigations where an approximately constant ratio 2R /2a 4-5 between the plastic zone size 2/ pi and the length of the Vickers diagonals 2a can be derived for single as well as po/ycrystalline ceramics and for hard materials with fundamentally different bonding like (ionic) alumina [2] and (covalent) SiC [8]. 

For example, people are often upset when sometimes a strong size (load) effect is observed - which disappears in other microstructures of the same material (or simply on measuring on surfaces prepared in another way). Therefore, it seems interesting to ask whether dislocation activity (or an associated deformability that changes with increasing load) can introduce an indentation size effect that possibly depends on the microstructure. 

The expressions (3) and (3a) give a load influence that compares well with measurements in single crystalline AI2O3 (Fig. 3). However, it should be emphasized again that with the phenomenological character of the model this agreement is not an evidence for some specific micromechanism, it just means that there is no general discrepancy between the dislocation idea and the observed indentation size effect. 

With Eq. (3/3a), this deereasing influence of the load in more fine-grained microstructures is expressed by smaller values of the ratio (5e/5i)o- Table 2 displays fitting parameters for the experimental data of Fig. 4 for smaller grain sizes, increasing asymptotic hardness values H o are associated with decreasing parameters ( e/ i)o- la submicrometer alumina microstructures, the increase of the microplastic deformability (the decrease of the hardness) becomes smaller and smaller and approaches zero already at small indent sizes of 10-20 pm (see Fig. 4), and which characterizes the extension of the plastic zone approaches the initial deformability at rather small loads of about 1N. 

A difference appears only when, on increasing the load, the indentation size becomes much larger than the grains whereas in sapphire the deformability increases with the growing plastic zone, in the polycrystals this size effect is partly offset by the hindrance of dislocation activity due to the close spacing of the grain boundaries. 

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