The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

Pristine graphene is the strongest material ever measured. However, large-area graphene films produced by means of chemical vapor deposition (CVD) are polycrystalline and thus contain grain boundaries that can potentially weaken the material. We combined structural characterization by means of transmission electron microscopy with nanoindentation in order to study the mechanical properties of CVD-graphene films with different grain sizes. We show that the elastic stiffness of CVD-graphene is identical to that of pristine graphene if postprocessing steps avoid damage or rippling. Its strength is only slightly reduced despite the existence of grain boundaries. Indentation tests directly on grain boundaries confirm that they are almost as strong as pristine. Graphene films consisting entirely of well-stitched grain boundaries can retain ultrahigh strength, which is critical for a large variety of applications, such as flexible electronics and strengthening components.

Results of Sneddon's analysis for the elastic contact between a rigid, axisymmetric punch and an elastic half space are used to show that a simple relationship exists among the contact stiffness, the contact area, and the elastic modulus that is not dependent on the geometry of the punch. The generality of the relationship has important implications for the measurement of mechanical properties using load and depth sensing indentation techniques and in the measurement of small contact areas such as those encountered in atomic force microscopy.

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One of the simplest ways to measure the mechanical properties of a thin film is to deform it on a very small scale. Because indentation testing with a sharp indenter is one convenient means to accomplish this, nanoindentation, or indentation testing at the nanometer scale, has become one of the most widely used techniques for measuring the mechanical properties of thin films. Other reasons for the popularity of nanoindentation stem from the ease with which a wide variety of mechanical properties can be measured without removing the film from its substrate and the ability to probe a surface at numerous points and spatially map its mechanical properties. The utility of the mapping capability is illustrated in Figure 1, which shows several small indentations made at selected points in a microelectronic device. The hardness and modulus of the device were determined at each point. In addition to microelectronics, nanoindentation has also proved useful in the study of optical coatings, hard coatings, and materials with surfaces modified by ion implantation and laser treatment.