National Physical Laboratory

Instrumented Indentation

Hardness has conventionally been defined as the resistance of a material to permanent penetration by another harder material with measurement being made after the test force has been removed, such that elastic deformation is ignored. Instrumented indentation hardness [9] provides the ability to measure the indenter penetration h under the applied force F throughout the testing cycle and is therefore capable of measuring both the plastic and elastic deformation of the material under test. Figure 1 is a typical load displacement hysteresis curve obtained from an elastic / plastic material and Figure 2 shows the schematic representation of the indent under load and in the unloaded condition. Apart from the measurement of the indenter penetration under the applied force, the unloading contact compliance C (= 1/S) and the contact depth hc can be calculated. The value of hc is dependent on the exact shape of the indenter and material response to the indentation; 'sinking-in' and 'piling-up' around the indenter also affect the value.

Figure 1. Typical force displacement curve showing measured and derived parameters

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

Scale Force/indentation depth
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 [9], 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.

Martens hardness scale

The Martens hardness value is calculated by dividing the test force F by the surface area of the indenter penetrating beyond the original surface of the test piece As(h):

a) Vickers indenter   b) Berkovich indenter

Indentation hardness scale

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 [9]. 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 [9]. 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.

Last Updated: 25 Mar 2010
Created: 18 Jun 2007