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.

Nanoindentation was used to examine the impact of impurities and grain boundaries on the mechanical properties of a “model” (110)/(100) grain boundary (GB) interface prepared using direct silicon bonding via the hybrid orientation technique of (110) and (100) p-type silicon wafers. Remarkable differences were found between the mechanical behavior of Fe- and Cu-contaminated samples. The direct silicon bonded wafers contaminated with either Fe or Cu showed opposite effects on mechanical properties, with Fe enhancing the silicon hardness, while Cu contamination induces a gradual weakening. High-resolution transmission electron microscopy was used to verify that the abrupt hardness changes observed during increasing nanoindentation loading is attributed to local deformation induced by the GB interface, Cu precipitate colony induced dislocations, and the abrupt crystallographic orientation change across the GB. The resulting dislocation loop generation facilitated the deformation process during nanoindentation and therefore softened the material.

This study reports on the anisotropic indentation response of α-titanium. Coarse-grained titanium was characterized by electron backscatter diffraction. Sphero-conical nanoindentation was performed for a number of different crystallographic orientations. The grain size was much larger than the size of the indents to ensure quasi-single-crystal indentation. The hexagonal c-axis was determined to be the hardest direction. Surface topographies of several indents were measured by atomic force microscopy. Analysis of the indent surfaces, following Zambaldi and Raabe (Acta Mater. 58(9), 3516–3530), revealed the orientation-dependent pileup behavior of α-titanium during axisymmetric indentation. Corresponding crystal plasticity finite element (CPFE) simulations predicted the pileup patterns with good accuracy. The constitutive parameters of the CPFE model were identified by a nonlinear optimization procedure, and reproducibly converged toward easy activation of prismatic glide systems. The calculated critical resolved shear stresses were 150 ± 4, 349 ± 10, and 1107 ± 39 MPa for prismatic and basal 〈a〉-glide and pyramidal〈c + a〉-glide, respectively.

Indentation methods have been widely used to study bone at the micro- and nanoscales. It has been shown that bone exhibits viscoelastic behavior with permanent deformation during indentation. At the same time, damage due to microcracks is induced due to the stresses beneath the indenter tip. In this work, a simplified viscoelastic-plastic damage model was developed to more closely simulate indentation creep data, and the effect of the model parameters on the indentation curve was investigated. Experimentally, baseline and 2-year postovariectomized (OVX-2) ovine (sheep) bone samples were prepared and indented. The damage model was then applied via finite element analysis to simulate the bone indentation data. The mechanical properties of yielding, viscosity, and damage parameter were obtained from the simulations. The results suggest that damage develops more quickly for OVX-2 samples under the same indentation load conditions as the baseline data.

Novel lightweight intermetallic titanium aluminides, so-called γTiAl, provide good strength and creep resistance up to 700 °C. Their stress–strain behavior at room temperature is however strongly confined in elongation due to their low ductility. For studying the stress–strain behavior of γTiAl, the viscoplastic mechanical properties are determined using spherical indentation testing. The identification problem is solved on the continuum level by neural network analysis, which is based on a unified viscoplasticity model. The identified material parameters are validated by comparing the predicted stress–strain behavior with conventional compression tests at different deformation velocities. It was found that the average response of the indentation tests is in good agreement with the compression tests of round bars. Using a spherical indenter tip of R = 0.2 mm, a small volume is tested, offering possibilities for investigation of local property variations due to processing. The experimental indentation curves exhibited wide hysteresis loops, revealing the existence of pure kinematic hardening. Since tensile fracture strength for γTiAl is very low, microcracking occurred during loading as well as during unloading, significantly contributing to the unloading compliance.