Determination of Indenter-tip Geometry and Indentation Contact Area for Depth-Sensing Indentation Experiments

Abstract

Indentation experiments have led to well-established methods for determining the mechanical properties of materials in small volumes. The availability of depth sensing indentation instruments with capabilities for measuring displacements on the order of nanometers now makes it possible to study mechanical properties of thin films and other finely structured materials where small volumes need to be probed. Research on nanoindentation has shown that elastic moduli, hardness, and time-dependent deformation effects
can be measured, provided the area of contact between the indenter and the test material is known. Indeed, determining the contact area from the indentation forces and displacements is central to the study of mechanical properties of materials in small volumes by nanoindentation.

It is widely known that the contact area at a particular depth of indentation depends not only on the shape of the indenter (diamond) but also on the elastic plastic response of the material being indented. In some cases the volume of material displaced by the indentation
pushes out to the sides of the indenter and forms a pile-up of material, making the projected contact area larger than the cross-sectional area of the indenter at that depth. For other materials, the displaced volume is accommodated mainly by far-field elastic displacements, producing what is called a sink-in effect. In this case the contact area is less than the cross-sectional area of the indenter at that depth.

Although the pile-up and sink-in effects are widely known, they are not explicitly considered in any of the current methods for determining contact areas from indentation loads and displacements. Typically the variations of contact area with depth are treated as indicating the shape of the diamond indenter itself. This approach to calibrating the shape of the indenter is not generally valid as it mixes the actual shape of the diamond indenter with the elastic-plastic response of the material used for the tip shape calibration. Naturally such a “combined” tip shape calibration will return accurate contact areas only if the material being subsequently studied exhibits
the same pile-up or sink-in behavior as the material used for the calibration experiments.

In this paper we develop a new technique for determining the indenter tip shape using both indentation loads and displacements and direct scanning electron microscopy (SEM) images of the impressions left by large indentations. The indenter tip shape found by this method represents the actual cross-sectional area of the indenter as a function of the distance from the tip. This new tip shape calibration can then be used in nanoindentation studies of other materials, regardless of their pile-up or sink-in behaviors. For the determination
of contact area, the extent of pile-up or sink-in must be measured for each material by making direct observations of the impressions made by large indentations. In this way we separate the indenter tip shape calibration (which needs to be done only once) from the pile-up or sink-in response of the material (which must be done each time a new material is studied).