What Does Indentation Hardness Measure

If slip-line fields do not control plastic indentation, what does The answer is not the beginning of the plastic deformation, but the end of it. The end means after deformation hardening has occurred. That is, it is not the initial yield stress, Y0, that controls indentation, but the limiting yield stress, Y. This is 

The flow toward the surface is caused by the pressure under the indenter. It is analogous to the upward flow around a sphere dropped into a liquid. It is also analogous to inverse extrusion. A model of the flow has been proposed by Brown (2007) in terms of rotational slip. This model reproduces some of the observed behavior, but it is a continuum model and does not define the mechanism of rotational slip. 

This model is not precise, but does identify some of the factors that are important to indentation. Like the model, the hardness measurement process is not precise. At the micro-hardness level, the projected areas of indentations are measured, but this can only be done with about 10% accuracy. At the nano-indentation level, relative values can determined accurately, but absolute values are probably only about 10% accurate. 

This analysis is consistent with the conclusion of Gerk (1977) that the behavior that determines hardness is deformation-hardening not the yield stress. He was one of the first authors to point this out. For other types of materials, it is the maximum stress that the material can bear after deformation (plastic, or that associated with phase transitions in eluding twinning). Hardness is not directly related to the elastic limit, although there is an indirect connection with the offset plastic deformation of metals as demonstrated by Tabor (1951). 

Deformation-hardening in the 5-50% deformation range is known to be proportional to either the Young s modulus, Y, or the shear modulus, G, in metals. The Young s modulus depends strongly on the shear modulus since Y = 2(1+v) G where v = Poisson s ratio. For both fee and bcc pure metals data 

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