Nanoindentation, also called instrumented indentation testing, is a variety of indentation hardness tests applied to small volumes. Indentation is perhaps the most commonly applied means of testing the mechanical properties of materials. The nanoindentation technique was developed in the mid-1970s to measure the hardness of small volumes of material.
Background In a traditional indentation test (macro or micro indentation), a hard tip whose mechanical properties are known (frequently made of a very hard material like diamond) is pressed into a sample whose properties are unknown. The load placed on the indenter tip is increased as the tip penetrates further into the specimen and soon reaches a user-defined value. At this point, the load may be held constant for a period or removed. The area of the residual indentation in the sample is measured and the hardness, H {\displaystyle H} , is defined as the maximum load, P max {\displaystyle P_{\text{max}}} , divided by the residual indentation area, A r {\displaystyle A_{\text{r}}} :
H = P max A r . {\displaystyle H={\frac {P_{\text{max}}}{A_{\text{r}}}}.}
For most techniques, the projected area may be measured directly using light microscopy. As can be seen from this equation, a given load will make a smaller indent in a "hard" material than a "soft" one. This technique is limited due to large and varied tip shapes, with indenter rigs which do not have very good spatial resolution (the location of the area to be indented is very hard to specify accurately). Comparison across experiments, typically done in different laboratories, is difficult and often meaningless. Nanoindentation improves on these macro- and micro-indentation tests by indenting on the nanoscale with a very precise tip shape, high spatial resolutions to place the indents, and by providing real-time load-displacement (into the surface) data while the indentation is in progress.
In nanoindentation small loads and tip sizes are used, so the indentation area may only be a few square micrometres or even nanometres. This presents problems in determining the hardness, as the contact area is not easily found. Atomic force microscopy or scanning electron microscopy techniques may be utilized to image the indentation, but can be quite cumbersome. Instead, an indenter with a geometry known to high precision (usually a Berkovich tip, which has a three-sided pyramid geometry) is employed. During the course of the instrumented indentation process, a record of the depth of penetration is made, and then the area of the indent is determined using the known geometry of the indentation tip. While indenting, various parameters such as load and depth of penetration can be measured. A record of these values can be plotted on a graph to create a load-displacement curve (such as the one shown in Figure 1). These curves can be used to extract mechanical properties of the material.
Young's modulus The slope of the curve, d P / d h {\displaystyle dP/dh} , upon unloading is indicative of the stiffness S {\displaystyle S} of the contact. This value generally includes a contribution from both the material being tested and the response of the test device itself. The stiffness of the contact can be used to calculate the reduced Young's modulus E r {\displaystyle E_{\text{r}}} :
E r = 1 β π 2 S A p ( h c ) , {\displaystyle E_{\text{r}}={\frac {1}{\beta }}{\frac {\sqrt {\pi }}{2}}{\frac {S}{\sqrt {A_{p}(h_{\text{c}})}}},}
where A p ( h c ) {\displaystyle A_{p}(h_{\text{c}})} is the projected area of the indentation at the contact depth h c {\displaystyle h_{c}} , and β {\displaystyle \beta } is a geometrical constant on the order of unity. A p ( h c ) {\displaystyle A_{\text{p}}(h_{\text{c}})} is often approximated by a fitting polynomial as shown below for a Berkovich tip:
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