Figure 2. Schematic of indentation showing the displacements observed during an indentation experiment
Instrumented indentation is therefore able to determine the stiffness of the contact and thus the indentation modulus EIT as well as the indentation hardness HIT (equivalent to Meyer Hardness and similar to HV for a Vickers indenter) and the Martens hardness HM (previously known as Universal hardness, HU) of a material. In addition, this technique enables time-dependent material properties, such as the ratio of elastic to plastic work done during an indentation, to be defined.
Table 1 reproduces from the draft standard the three scale ranges covered.
Table 1. Instrumented indentation hardness scale ranges and test forces
|Macro range||2 N < F < 30 000 N|
|Micro range||2 N > F and h > 0,000 2 mm|
|Nano range||0,000 2 mm ³ h|
HM is defined only for Vickers and Berkovich indenters, as shown below. However, in the standard , a wide range of other materials properties calculable from instrumented indentation data is defined for a wide range of indenter geometries: cube corner, Knoop or ball indenters (including "hardmetal" ball indenters with diameters ranging from 0,5 mm to 10 mm), and diamond sphero-conical indenters with the range of flank angles I of 30º, 45º, and 90º, and radius of curvature varying from 0,500 mm > R > 0,050 mm.
|a) Vickers indenter||b) Berkovich indenter|
The indentation hardness HIT is calculated from the test force, F, divided by the projected area of the indenter in contact with the test piece at maximum load:
The projected contact area A(hc) is calculated from knowledge of the geometry of the indenter and the stiffness of the contact . In many materials, the area of contact under moderate forces is a good approximation to that which remains when the indenter is fully unloaded and removed from the surface. In such cases, the indentation hardness is very similar to Vickers hardness, the exceptions being that the indentation area is calculated from measured displacement data instead of optical measurement and that the Vickers scale assumes a perfect geometry whereas instrumented indentation uses a measured shape of the indenter which makes allowance for tip rounding and other common deviations. In practice, tip rounding means that the two scales diverge as the indentation contact becomes more elastic until, at the elastic limit, HV becomes infinite and HIT ceases to be a measure of plasticity.Indentation modulus
The indentation modulus EIT is calculated from the slope of the unloading curve through the formula:
|where:||vIT = the Poisson's ratio of the test piece|
vindenter = the Poisson's ratio of the indenter
S = the slope of the tangent of the force/indentation curve during the unloading cycle (Figure 1)
hc = the contact depth value, which is dependent on the shape of the indenter (Figure 2)
The full procedure for this is described in the standard . For homogeneous and isotropic materials, EIT approaches the Young's modulus of the material. For an isotropic material, the value is a 3D average of the crystallographic moduli.