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We review current practice for describing force–displacement curves from pointed indenters, highlighting the consequences of the simplifications normally adopted. We derive two corrections, the ‘variable epsilon factor’ and the ‘radial displacement correction.’ These are especially important for highly elastic materials such as fused silica where the combined corrections can amount to 13% in the contact area, significantly increasing the accuracy of hardness and modulus results. In contrast, the so-called beta factor has minor importance. We compare our analytical results with finite element (FE) calculations and experimental results. Indenter area functions, obtained using the corrections, agree well with independent direct measurements by a traceably calibrated metrological atomic force microscope (AFM). Further formulae are derived to calculate the complete force–displacement curve of conical indenters and the indentation elastic and total energy. These formulae immediately identify a physical material limit above which a cone cannot generate plastic deformation; for a Berkovich indenter this is a hardness-to-modulus ratio of 0.18.

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The determination of the mechanical properties of ultra-thin coatings has become more and more important because of the increasing number of applications using such films. However, an accurate mechanical testing of coatings with a thickness down to some nanometers is still a challenge, despite the improvements of existing measurement techniques. Nanoindentation is an often used mechanical nanoprobe. Using the conventional test method with a sharp Berkovich indenter, the problem of the influence of the substrate on the results arises with decreasing film thickness. Therefore, it is nearly impossible to measure the modulus of films with a thickness less than 100-200 nm. The problem can be overcome by using spheri cal indenters in combination with an analytical solution for the Hertzian contact of coated systems. It allows a separation of film and substrate properties from the load-displacement curve of the compound. Indentation measurements were done at a 44 nm TiN film and at diamondlike carbon coatings in the thickness range between 4.3 nm and 125 nm on Si substrates. Several corrections were applied to obtain wholly elastic force-displacement curves with high accuracy. It is shown in more detail how zero point and thermal drift corrections are used to obtain statistical depth errors below 0.2 nm. Laser-acoustic measurements based on ultra sonic surface waves were chosen as second method, which also measures the Youngs modulus in this thickness range. Although the indentation technique is a local probe and the laser-acoustic technique gives an integrated value for a surface range of some millimetres, the results agree well for the investigated samples. In contrast, it was impossible to get the correct Youngs modulus results by co nventional indentation measurements with Berkovich indenter, even for ultra-low loads

There is increasing interest in using sharp cube-corner indenters in nanoindentation experiments to study plastic properties. In combination with finite element methods, it is, for example, possible to extract stress-strain curves from load-displacement curves measured with differently shaped pyramidal indenters. Another example is the fracture toughness of coatings, which can be studied using cracks produced during indentation with cube-corner tips. We have carried out indentation experiments with Berkovich and cube-corner indenters on eight different materials with different mechanical properties. To gain information about the formation of pile-up and cracks, indentation experiments with cube-corner indenter were performed inside a scanning electron microscope (SEM) using a custom-built SEM-microindenter. The results show that reliable hardness and modulus values can be measured using cube-corner indenters. However, the fit range of the unloading curve has a much bigger influence on the results for the cube-corner than for the Berkovich tip. The unloading curves of a cube-corner measurement should, therefore, be carefully inspected to determine the region of smooth curvature, and the unloading fit range chosen warily.Comparison of the modulus results shows that there is no significant difference between cube-corner and Berkovich measurements. Also for hardness, no fundamental difference is observed for most of the investigated materials. Exceptions are materials, such as silicon nitride, cemented carbide or glassy carbon, where a clear difference to the hardness reference value has been observed although the modulus difference is not pronounced.