In small-scale testing at elevated temperatures, impurities in inert gases can pose problems so that testing in vacuum would be desirable. However, previous experiments have indicated difficulties with thermal stability and instrument noise. To investigate this, measurements of the temperature changes in a modified nanoindenter have been made and their influence on the displacement and load measurements is discussed. It is shown that controlling the temperatures of the indenter tip and the sample enabled flat punch indentations of gold, a good thermal conductor, to be carried out over several minutes at 665 °C in vacuum, as well as permitting thermal stability to be quickly re-established in site-specific microcompression experiments. This allowed compression of nickel superalloy micropillars up to sample temperatures of 630 °C with very low levels of oxidation after 48 h. Furthermore, the measured Young moduli, yield and flow stresses were consistent with literature data.

The (001) GaAs surfaces have been modified by thin elastically stressed InGaAs-buried layers and tested under Berkovich contact. The elastic–plastic transition determined from the pop-in event observed in the force control mode of the indentation machine appears at slightly lower loads (0.44–0.46 mN) when compared to bare GaAs surface (0.50 mN). Estimations indicate that for both studied sublayers, the stored elastic energy is about 20% of the elastic indentation energy reached at elastic–plastic transition when the sublayer is observed not to relax plastically.

When an elastic half-space is subjected to both normal and tangential contact, the ratio of normal and tangential contact stiffnesses can be measured by various scanning force microscopy techniques. For elastically isotropic solids, this stiffness ratio depends on Poisson’s ratio as given by the Mindlin solution. An anisotropic elastic contact analysis here shows the difference between the effective Poisson’s ratio as defined from the stiffness ratio and its uniaxial counterpart with respect to various crystal structures and various normal/tangential contact directions. Closed-form analytical solutions of effective indentation moduli are derived for materials with at least one plane of transverse isotropy. Since the Sneddon (normal contact) and Mindlin (lateral contact) solutions are derived under different frictional conditions, finite element simulations were performed which show that the effects of elastic dissimilarity and contact shape are generally small but not negligible. The predicted dependence on crystallographic orientation and elastic anisotropy has been compared favorably with previously reported multiaxial contact experiments for a number of cubic single crystals. Implications for atomic force microscopy based experiments are also discussed.

Instrumented nanoindentation technique is a powerful approach for accurately measuring mechanical properties of materials in micron or even nanoscale. In this article, the effect of tin (Sn) content upon mechanical properties of the α-phase in Cu–Sn alloys was studied by using an instrumented nanoindentation. The experimental results revealed that: (i) the hardness of the α-phase exhibited a linear relationship with Sn content (C) increasing, i.e., H = 0.0757C + 0.8916, when it was less than the maximum solid solubility (15.8 wt.%), which is in good agreement with the Friedel–Mott–Suzuki theory; (ii) the variation of Young’s modulus in a narrow range of 120–130 GPa is attributed to orientation variation of the α-phase in casting Cu–Sn dendrites.

An instrumented indentation method is established to accurately measure the local elastic-plastic material properties of a single fiber by accounting for the additional sources of compliance associated with fiber indentation. The Oliver-Pharr instrumented indentation data analysis method is compared for indentation of a standard, planar fused silica sample and in the radial direction of homogeneous, isotropic E-glass fibers of two different diameters. Compliance contributions from substrate deflection and other nonindentation-related fiber deflections are quantified and shown to be negligible. The added compliance observed is attributed to the lack of constraint due to the finite geometry of a curved fiber surface. This compliance contribution is accounted for by using a proposed area correction to capture the geometry of the curved fiber-probe contact combined with a structural compliance correction. Implementation of these corrections to experimental indentation curves results in accurate measurements of the fiber elastic modulus and hardness.

The Oliver and Pharr method for evaluating nanoindentation load–displacement data is based on the measurement of the contact stiffness, which is usually determined at the very beginning of the unloading sequence, or, using dynamic nanoindentation, continuously during the whole loading segment. A new experimental method has been developed to continuously monitor the contact stiffness throughout the unloading sequence. It provides supplementary information about the shape and area of the residual impression, as well as a direct measurement of the shape of the effective indenter previously introduced by Pharr and Bolshakov. The new method was applied to indentations on fused silica, sapphire, nanocrystalline nickel, and ultrafine-grained aluminum. Lastly, the new procedure was adapted to directly measure the epsilon factor used in the Oliver and Pharr method. A value of 0.76 was found from indentation into fused silica, in close agreement with literature values.

Surface and chemomechanical effects are very important in tribology, wear and friction, but are difficult to quantify due to being confined in the near-surface region. Nanoindentation techniques have been successfully used to investigate environmental effects on mechanical response. In this work, nanoindentation tests have been performed on various materials (silicon, fused silica, and gold nanofilms on a glass substrate) immersed in long-chain alcohols (i.e., 1-hexanol, 1-heptanol, 1-octanol, and 1-nonanol). The results consistently show an increase in mechanical properties for silicon and gold nanofilms immersed in the alcohols at shallow nanoindentation depths. The results for fused silica show little effect of immersion. The changes in the observed mechanical properties are attributed to the ability of the long-chain organic molecules to sustain elastic strains when they are in confined geometry. These long organic chains also distribute the normal stress of the indenter over a larger area on the sample surface thereby causing a decrease in the perceived contact area (Ac). As a result the long-chain alcohols modify both the Ac and the elastic compliance of the contact.

Nanoindentation is a popular experimental technique for characterization of the mechanical properties of soft and biological materials. With its force resolution of tens of pico-Newtons, the atomic force microscope (AFM) is well-suited for performing indentation experiments on soft materials. However, nonlinear contact and adhesion complicate such experiments. This paper critically examines the application of the Johnson-Kendall-Roberts (JKR) adhesion model to nanoindentation data collected with an AFM. The use of a nonlinear least-square error-fitting algorithm to calculate reduced modulus from the nanoindentation data using the JKR model is discussed. It is found that the JKR model fits the data during loading but does not fit the data during unloading. A fracture stability analysis shows that the JKR model does not fit the data collected during unloading because of the increased stability provided by the AFM cantilever.

Spherical indentation, particularly at low loads, can ensure fully reversible deformations, suitable for the study of viscoelastic properties. However, there are growing concerns about the effective indenter radius in contact at small penetrations and the effect of thermal drift. The aim of this study was to characterize spherical indentation on polymethylmethacrylate (PMMA) and fused silica (FS). Several types of indentation experiments were performed on PMMA to determine its viscoelastic behavior, and a corresponding model was applied to calculate the main mechanical properties. A series of measurements on FS were performed to determine the effective indenter radius and thermal drift of the indentation system. It was shown that at low depths the effective radius of the spherical indenter can substantially differ from the nominal one and calibration of the indenter might be necessary for certain experiments. The effect of thermal drift and its consequences on creep measurements were discussed.

Fluid flow in biological tissues is important in both mechanical and biological contexts. Given the hierarchical nature of tissues, there are varying length scales at which time-dependent mechanical behavior due to fluid flow may be exhibited. Here, spherical nanoindentation and microindentation testings are used for the characterization of length scale effects in the mechanical response of hydrated tissues. Although elastic properties were consistent across length scales, there was a substantial difference between the time-dependent mechanical responses for large and small contact radii in the same tissue specimens. This difference was far more obvious when poroelastic analysis was used instead of viscoelastic analysis. Overall, indentation testing is a fast and robust technique for characterizing the hierarchical structure of biological materials from nanometer to micrometer length scales and is capable of making quantitative material property measurements to do with fluid flow.

The authors discuss the contact-area-based indentation contact mechanics instead of the conventional penetration-depth-based analysis. In time-independent elastoplastic regime, the indentation load P versus contact area A relationship for a cone indentation is linear both for the loading and the unloading paths. The slope of the loading path directly yields the Meyer hardness HM, and the slope of the unloading path, i.e., the unloading modulus M, is related to the elastic modulus E′ through the relation of M = E′tan β/2. The relation of the total contact area A to the purely elastic and the purely plastic contact areas of Ae and Ap are theoretically as well as numerically examined. The normalized relationship between Ap/A versus Ap/Ae is equivalent to the Johnson’s hardness plot of HM/Y versus E′tan β/Y. By extending the concept of Ae and Ap to time-dependent viscoelastic-plastic regime, a detailed discussion is made how to eliminate the plastic deformation/flow from the total contact area A(t) to yield the viscoelastic contact area Ave(t) prior to determining the linear-viscoelastic parameters and functions.

Over the past two decades, nanoindentation has been the most versatile method for mechanical testing at small length scales. Because of large strain gradients, it does not allow for a straightforward identification of material parameters such as yield and tensile strength, though. This represents a major drawback and has led to the development of alternative microscale testing techniques with microcompression as one of the most popular ones today. In this research, the influence of the realistic sample configuration and unavoidable variations in the experimental conditions is studied systematically by combing in-situ microcompression experiments on ultrafine-grained nickel and finite element simulations. It will be demonstrated that neither qualitative let alone quantitative analyses are as straightforward as they may appear, which diminishes the apparent advantages of microcompression testing.

Al/SiC nanolaminates have been shown to possess excellent combination of mechanical strength and flexibility. While metal–ceramic multilayers present a tremendous opportunity for hard coatings, the strength evaluation is usually carried out under static loading conditions such as nanoindentation and microcompression testing. In this study, we have studied the scratch resistance behavior of Al/SiC nanolaminates. These properties are then compared to monolithic films of Al and SiC. Finally, the deformation behavior under such loading was quantified by critical load, work of deformation, and postexperimental microstructural analysis by scanning electron microscopy and focused ion beam cross sections. It is shown that the combination of hard SiC and plastic Al layers provides enhanced resistance to scratch loading and makes these materials as very good candidates for wear-resistant coatings.

A study is made of the rotation field in wedge indentation of metals using copper as the model material system. Wedges with apical angles of 60° and 120° are used to indent annealed copper, and the deformation is mapped using image correlation. The indentation of annealed and strain-hardened copper is simulated using finite element analysis. The rotation field, derived from the deformation measurements, provides a clear way of distinguishing between cutting and compressive modes of deformation. Largely unidirectional rotation on one side of the symmetry line with small spatial rotation gradients is characteristic of compression. Bidirectional rotation with neighboring regions of opposing rotations and locally high rotation gradients characterizes cutting. In addition, the rotation demarcates such characteristic regions as the pile-up zone in indentation of a strain-hardened metal. The residual rotation field obtained after unloading is essentially the same as that at full load, indicating that it is a scalar proxy for plastic deformation as a whole.

Availability of atomic force microscope (AFM) is discussed in the point of view of the measurement standard. For indenter geometry verification in the pyramidal part, the fully mathematical method, Regression Polyhedral Model, is used to avoid the effects of human factors and the misalignment of the indenter axis. As an example, facet angles, angles between opposite faces, and the interior angles of the square base of pyramid of a Vickers indenter are analyzed to demonstrate the efficiency of this method. The area function of the indenter is also calculated as an analytical result of AFM image. The procedure of uncertainty of measurement of those geometrical parameters is developed. For geometrical parameters of pyramid, the uncertainty can be estimated by combining the resolution and linearity of the AFM, the effect of the scanning tip, the uncertainty of the reference standard used to calibrate the AFM, and the regression error which includes flatness and roughness of the pyramid faces; and for the uncertainty of the area function, the uncertainty of AFM coordinates are taken into account. The results show that the uncertainty of facet angles and angles between opposite faces is small; but on the other hand, the uncertainty of the interior angles of square base of pyramid is not negligible. The uncertainty of the area function is almost proportional to the contact depth, but the relative uncertainty is exponentially increased where the contact depth is small. In addition, the observations of indents are shown to verify the indentation hardness HIT of the certified reference materials (CRMs) by comparing with Vickers hardness determined with AFM observations. Through those examples, the possibility to improve certified values of CRMs is suggested.

Here we quantify the time-dependent mechanical properties of a linear viscoelastoplastic material under contact loading. For contact load relaxation, we showed that the relaxation modulus can be measured independently of concurrent plasticity exhibited during the loading phase. For indentation creep, we showed that the rate of change of the contact creep compliance can be measured independently of any plastic deformation exhibited during loading through , where a(t) is the contact radius, h(t) is the displacement of the contact probe, and Pmax is the constant applied load during the creep phase. These analytical relations were compared with numerical simulations of conical indentation creep for a viscoelastoplastic material and validated against sharp indentation creep experiments conducted on polystyrene. The derived relations enable extraction of viscoelastic material characteristics, even if sharp probes confer concurrent plasticity, applicable for a general axisymmetric contact probe geometry and a general time-independent plasticity.

Pile-up or sink-in is always a concern in a nanoindentation test because it gives rise to errors in the estimation of the projected contact area when it is theoretically analyzed with the classic Oliver–Pharr method. In this study, a three-dimensional finite element model is developed to simulate nanoindentation with a perfect Berkovich tip. The variation of the contact profile with respect to the work-hardening rate n and the ratio of yield stress to elastic modulus σy/E has been studied for a wide range of elastoplastic materials. The numerical results show that a low σy/E not only facilitates the pile-up for materials with little or no work-hardening but also enhances the sink-in for materials with a high work-hardening rate. It is attributed to the lateral-flow dominated plastic deformation in low work-hardening materials and the normal-flow dominated plastic deformation in high work-hardening materials, respectively. Because of the large sink-in, for the materials with high n and low σy/E, significant errors in the calculation of the projected contact area can be generated by using the classic Oliver–Pharr method.

Nanoindentation and nanoscratching of an indium phosphide (InP) semiconductor surface was investigated via contact mechanics. Plastic deformation in InP is known to be caused by the nucleation, propagation, and multiplication of dislocations. Using selective electrochemical dissolution, which reveals dislocations at the semiconductor surface, the load needed to create the first dislocations in indentation and scratching can be determined. The experimental results showed that the load threshold to generate the first dislocations is twice lower in scratching compared to indentation. By modeling the elastic stress fields using contact mechanics based on Hertz’s theory, the results during scratching can be related to the friction between the surface and the tip. Moreover, Hertz’s model suggests that dislocations nucleate firstly at the surface and then propagate inside the bulk. The dislocation nucleation process explains the pop-in event which is characterized by a sudden extension of the indenter inside the surface during loading.

The hardness of the carbon nanotubes (CNTs)-doped diamond-like carbon (DLC) films is modeled by a nanoindentation finite element analysis. A three-dimensional (3D) formation where CNTs are modeled as transverse isotropy is compared with a two-dimensional (2D) analysis with isotropic CNTs. The results showed that for small CNTs volume fraction, the overall hardness of CNTs/DLC/Si composites is controlled by the elastic modulus along the indentation direction. For vertical CNTs-doped DLC films, the hardness in 3D analysis is close to that in 2D analysis if the isotropic elastic modulus is taken as the long-axis direction. However, for horizontal CNTs-doped DLC films, the hardness in 3D and in 2D is similar if the 2D isotropic elastic modulus is taken as the short-axis direction of the 3D elastic modulus. As a result, for small CNTs volume fraction, the hardness of CNTs/DLC/Si composites can be modeled by a 2D isotropic inclusion as long as the elastic modulus is chosen properly. The hardness in CNTs/DLC/Si composites depends on the orientation of CNTs and the volume fraction. The mechanisms in hardness enhancement for different CNT orientations are explained by shear stress and the effective projected area. The issues like interface strength and indentation size effect are also addressed in terms of CNT orientations.

This article presents a study on elastic anisotropy of Cu by indentations at different penetration depth ranges (sub-10 nm, several-10 nm, and several-100 nm), and the impact of elastic anisotropy on the stress in 3D stacked integrated circuits (3D ICs). The reduced modulus, ER, values determined at sub-10 nm indentations on Cu single crystals are very close to the unidirectional values. Similarly, cross-sectional sub-10 nm indentation tests on the Cu grains in a through-silicon via (TSV) show unidirectional ER values. In contrast, the Hill’s average values are observed at several-100 nm indentations. We propose that before lattice rotation happens within a volume beneath the indentation, elastic anisotropy can be strongly reflected in the ER value. When the experimentally measured Cu elastic anisotropy is used in a technology computer-aided design simulation of a Cu-filled TSV, significant impacts are observed on the stress field and the carrier mobility variation in an active Si region.