Indentation size effect

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 friction coefficient is expected to depend on the normal pressure which is quite high (of order hundreds of kilobars) surface roughness surface homogeneity and humidity (or other environmental factors). As a result, a is not known, so a quantitative model is not possible, but the expected qualitative behavior is clear. 

Neglecting the elastic forces, lumping the geometric factors into a constant, b, and assuming the plastic shear deformation is x/r, yields the plastic resistive force  

Similarly, for the frictional resistive force, Ff, lumping the geometry factors into a constant, c, and letting a = friction coefficient  

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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. 

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

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). 

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-... 

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. 

Comparing the Grain Size Effect and the Indentation Size Effect... 

Figure 8. Grain size effects in the hardness of alumina ceramics (HV-10, triangies), and indentation size effect (load influence) in the hardness of sapphire (squares). For HVIO vaiues, the lower x-axis gives the average grain size (data for sapphire indicated at 1000 pm). For the curves describing the size effect in sapphire, the upper x-axis represents the length of the Vickers diagonal (n = 1) or the plastic zone size ( = 4) [6,16]. See Fig. 2 (p. 166) for theoretical background.

Vickers hardness as a principal parameter for the mechanical characterization of materials has been commonly used as a technique to measure the mechanical properties of materials, but the microhardness commonly decreases with applied load, which is known as the indentation size effect (ISE). 

There is no preferential orientation and the grain sizes are 0.43 mm for (a), 1.4 mm for (b) and 2.5 mm for (c). Furthermore, as expected, an indentation size effect with hardness values should be observed for all carbides tested, because the size of the impressions are related to the load applied, being smaller for smaller loads or for harder materials. This, indeed, is the case, as shown in Rg. 1.58. The shapes of the cmves in the illustrated materials are similar to those given by Li [34] and associates as ... 

Fig. 4.73 Indentation size effect fOT fine- and coarsegrained spinel [11]. With kind permission of Elsevier...

In Chapter 1 applied load and sample grain size were highlighted as two variables affecting the determination of absolute hardness values for ceramic materials Figures 1.2 and 1.3 emphasize the point. The load variation of hardness is better called the indentation size effect, ISE, because this emphasizes the volume dependence of hardness when this property is determined by a pyramidal indenter. 

INDENTATION SIZE EFFECT ON THE HARDNESS OF ZIRCONIA POLYCRYSTALS... 

Indentation Size Effect on the Hardness of Zirconia Polycrystals... 

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