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.

The ultra-low load indentation response of ceramic single crystal surfaces (Al2O3, SiC, Si) has been studied with a software-controlled hardness tester (Nanoindenter) operating in the load range 2–60 mN. In all cases, scanning and transmission electron microscopy have been used to characterize the deformation structures associated with these very small-scale hardness impressions. Emphasis has been placed on correlating the deformation behavior observed for particular indentations with irregularities in recorded load-displacement curves. For carefully annealed sapphire, a threshold load (for a given indenter) was observed below which the only surface response was elastic flexure and beyond which dislocation loop nucleation occurred at, or near, the theoretical shear strength to create the indentation. This onset of plasticity was seen as a sudden displacement discontinuity in the load-displacement response. At higher loads, indentations appeared to be accommodated predominantly by dislocation activity, though microcracks were observed to form ät contact loads of only tens of milliNewtons. Possibly such cracks are the incipient slip-induced nuclei for the much larger, indentation-induced cracks usually apparent only on the surface at much higher loads and often used for estimating indentation toughness. By contrast, silicon did not show this behavior but exhibited unusually large amounts of depth recovery within indentations, resulting in a characteristic reverse thrust on the indenter during unloading. TEM studies of indentations in silicon revealed less evidence of obvious dislocation activity than in sapphire (particularly at the lowest loads used) but did show residual highly imperfect–and often amorphous–structures within the indentations, consistent with a densification transformation occurring at the very high hydrostatic stresses produced under the indenter. The reverse thrust is caused by the relaxation of densified material during unloading. Thus, it appears that the low-load hardness response of silicon is controlled by a pressure-sensitive phase transformation. Though SiC has been predicted to undergo a densification transformation similar to silicon, its load-displacement behavior was found to be similar to Al2O3 suggesting that, for these contact experiments at least, the critical resolved shear stress for dislocation nucleation is exceeded before the critical hydrostatic pressure for densification is reached. In all cases, residual, plastically formed indentations were measured to be smaller than the fully loaded indentation depths would suggest, confirming that a significant portion of the deformation is elastic surface flexure. However, there is some doubt as to whether silicon displays elastic-only deformation even at very small penetration depths. The use of microstructural studies to complement nanoindentation experiments is shown to be a key route not only to interpreting the recorded load-displacement responses, but also to examining the deformation mechanisms controlling the mechanical behavior of ceramics to surface contacts at these small spatial scales.

The finite element method has been used to study the behavior of aluminum alloy 8009 during elastic-plastic indentation to establish how the indentation process is influenced by applied or residual stress. The study was motivated by the experiments of the preceding paper which show that nanoindentation data analysis procedures underestimate indentation contact areas and therefore overestimate hardness and elastic modulus in stressed specimens. The NIKE2D finite element code was used to simulate indentation contact by a rigid, conical indenter in a cylindrical specimen to which biaxial stresses were applied as boundary conditions. Indentation load-displacement curves were generated and analyzed according to standard methods for determining hardness and elastic modulus. The simulations show that the properties measured in this way are inaccurate because pileup is not accounted for in the contact area determination. When the proper contact area is used, the hardness and elastic modulus are not significantly affected by the applied stress.

Using a high-damping thermoplastic as a standard reference material, the purpose of this work is to compare measured values of the complex modulus as determined by dynamic nanoindentation and dynamic mechanical analysis (DMA). Experiments were performed at approximately 22 • C and seven frequencies over the range 1-50 Hz. The indentation measurements were performed using a 103 µm diameter flat punch and a newly developed test method that optimizes the accuracy and precision of the measured stiffness and damping. As determined by dynamic nanoindentation, values of the storage modulus and loss factor (tangent delta) ranged from 4.2 to 10.2 MPa, and 0.28 to 1.05, respectively. Over the range 1-25 Hz, DMA confirmed the nanoindentation results to within 15% or better. Collectively, these data and the testing methods used to generate them should help future investigators make more accurate and precise measurements of the dynamic properties of viscoelastic solids using nanoindentation.