Indentation hardness grain-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.

Figure 1.2. Grain size effects in microhardness testing, (a) Results from tungsten carbide cutting-tool compositions, (b) Apparent hardness changing as grain size to indent size decreases.

More serious errors may result when the grain-size of a specimen is small compared with the size of an indentation. Then, since all crystals are elastically anisotropic a rigid indenter will produce differing amounts of elastic strain in the grains depending on their orientations. This will create an effective roughening of the surface and increase the friction coefficient. This may result in overestimates of hardnesses. For example, this may underlie reports of nanocrystalline materials being harder than diamond. 

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. 4.65 a Effect of grain size on Vickers hardness as a function of applied load. For both microstructures, the asymptotic hardness value is 4 GPa. b Four-point flexural strength versus indentation load. Inclined dashed line has a slope of —1/3, which is the expected behavior for a perfectly brittle material. Hatched area on the left represents the strength of the samples as a result of natural flaws [17]. With kind permission of John Wiley and Sons... 

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. 

The hardness of a material is usually defined as the resistance to deformation and is usually measured as the permanent deformation of a surface by a specifically shaped indenter under a given load. This does not give an indication of the plastic deformation associated with loading. The hardness of a material may be influenced by grain size, dispersed phases, defect structure, microstructure, density, temperature, deformation rate, etc. For films and coatings there may be substrate influences on the deformation that affect the measurements. As a rule, the coating should be ten times the indentation depth to obtain meaningful results. Surface effects may also influence the measurements for thin films, particularly those with oxide layers. 

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