Bending of thin sheets or ribbons is a ubiquitous phenomenon that impacts our daily lives, from the household thermostat to sensors in airbags. At nanometer-scale thicknesses, the mechanics responsible for bending and other distortions in sheets can be employed to create a nanofabrication approach leading to novel nanostructures. The process and resulting structures have been aptly referred to as “nanomechanical architecture.” In this article, we review recent progress in atomistic simulations that not only have helped to reveal the physical mechanisms underlying this nanofabrication approach, but also have made predictions of new nanostructures that can be created. The simulations demonstrate the importance of the atomic structure of the crystalline membrane and of the intrinsic surface stress in governing membrane bending behavior at the nanoscale and making the behavior fundamentally distinct from that at the macroscale. Molecular dynamics simulations of the bending of patterned graphene (a single-atomic layer film) suggest a new method for synthesizing carbon nanotubes with unprecedented control over their size and chirality.

Experiments were performed on a (100) copper single crystal to examine the influences that small displacement oscillations used in continuous stiffness measurement techniques have on hardness and elastic-modulus measurements in nanoindentation experiments. For the commonly used 2-nm oscillation, significant errors were observed in the measured properties, especially the hardness, at penetration depths as large as 100 nm. The errors originate from the large amount of dynamic unloading that occurs in materials like copper that have high contact stiffness resulting from their high modulus-to-hardness ratios. A simple model for the loading and unloading behavior of an elastic–plastic material is presented that quantitatively describes the errors and can be used to partially correct for them. By correcting the data in accordance with model and performing measurements at smaller displacement oscillation amplitudes, the errors can be reduced. The observations have important implications for the interpretation of the indentation size effect.

Knowledge of mechanics in atelectasis (alveolar collapse) and reinflation would be useful during anesthesia and critical care. Here an investigation is presented in which atelectasis is induced in a controlled manner on excised inflated lungs using spherical indentation, and noninvasive imaging of the deformed subsurface region is performed using optical coherence tomography (OCT). Indentation loads are physiologic, and spatial dimensions are far larger than alveolar size to allow continuum discussions. Experimental observations of atelectasis are compared with finite element model calculations of maximum stresses. Finally, atelectasis is compared during inflation of lungs with different gases (e.g., air, oxygen/anesthesia mixture).

The storage and loss stiffnesses for the composite response of the sample, indenter, and load frame during dynamic nanoindentation are derived. In the first part of the analysis, no physical model is assigned to the composite system. It is shown that this case is equivalent to the conventional nanoindentation analysis. In the second part of the analysis, the sample is modeled as a standard linear solid in series with the indenter and load frame. The results for the storage and loss stiffnesses as computed by the two methods differ by at most ∼3% for the elastomeric system under consideration. Results for the storage and loss moduli are also similar. The relative merits and weaknesses of each analysis are discussed.

The development of nanoindentation test systems with high data collection speeds has made possible a novel type of indentation creep test: broadband nanoindentation creep (BNC). Using the high density of data points generated and analysis techniques that can model the instantaneous projected indent area at all times during a constant-load indentation experiment, BNC can reveal materials properties across a range of strain rates spanning up to five decades (10−4–10 s−1). BNC experiments aimed at measuring activation parameters for plasticity were conducted on three systems: two Zr-based bulk metallic glasses and poly-(methyl methacrylate) (PMMA). The results give insight into the operation of the deformation mechanisms present in the test materials, including the dependence of the deformation rate on the hydrostatic component of the stress for PMMA and the form of the activation energy function for the metallic glasses.

In this work, we investigated experimentally the various factors influencing the extraction of indentation stress-strain curves from spherical nanoindentation on metal samples using two different tip radii. In particular, we focused on the effects of (i) the surface preparation techniques used, (ii) the presence of a surface oxide layer, and (iii) the occurrence of pop-ins at the elastic-plastic transition on our newly developed data analysis methods for extracting reliable indentation stress-strain curves. Rough mechanical polishing was shown to introduce a large scatter in the measured indentation yield strengths, whereas electropolishing or vibropolishing produced consistent results reflective of the pristine sample. The data analysis techniques used were able to discard the portions of the raw data affected by a thin oxide layer, present on most metal surfaces, and yield reasonable indentation stress-strain curves. Experiments with different indenter tip radii on annealed and cold-worked samples indicated that pop-ins are caused by delayed nucleation of dislocations in the sample under the indenter.

Sudden displacement excursions during load-controlled nanoindentation of relatively dislocation-free surfaces of metals are frequently associated with dislocation nucleation, multiplication, and propagation. Insight into the nanomechanical origins of plasticity in metallic crystals may be gained through estimation of the stresses that nucleate dislocations. An assessment of the potential errors in the experimental measurement of nucleation stresses, especially in materials that exhibit the elastic–plastic transition at small indentation depths, is critical. In this work, the near-apex shape of a Berkovich probe was measured by scanning probe microscopy. This shape was then used as a “virtual” indentation probe in a 3-dimensional finite element analysis (FEA) of indentation on 〈100〉-oriented single-crystal tungsten. Simultaneously, experiments were carried out with the real indenter, also on 〈100〉-oriented single-crystal tungsten. There is good agreement between the FEA and experimental load–displacement curves. The Hertzian estimate of the radius of curvature was significantly larger than that directly measured from the scanning probe experiments. This effect was replicated in FEA simulation of indentation by a sphere. These results suggest that Hertzian estimates of the maximum shear stresses in the target material at the point of dislocation nucleation are a conservative lower bound. Stress estimates obtained from the experimental data using the Hertzian approximation were over 30% smaller than those determined from FEA.

Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) analyses of small indentations in copper single crystals exhibit only slight changes of the crystal orientation in the surroundings of the imprints. Far-reaching dislocations might be the reason for these small misorientation changes. Using EBSD and TEM technique, this work makes an attempt to visualize the far-propagating dislocations by introducing a twin boundary in the vicinity of small indentations. Because dislocations piled up at the twin boundary produce a misorientation gradient, the otherwise far-propagating dislocations can be detected.

In a statistical nanoindentation study using a spherical probe, the effect of crystallographic orientation on the phase transformation of silicon (Si) was investigated. The occurrence and the contact pressures at which events associated with phase transformation occur, for an indentation force range from 20 to 200 mN, were analyzed and compared for the orientations Si(001), Si(110), and Si(111). It was found that plastic deformation combined with phase transformation during loading was initiated at lower forces (contact pressures) for Si(110) and Si(111) than for Si(001). Also, the contact pressure at which the phase transformation occurred during unloading was strongly influenced by the crystallographic orientation, with up to 38% greater values for Si(110) and Si(111) compared to Si(001). Mapping the residual stress field around indentations by confocal Raman microscopy revealed significant differences in the stress pattern for the three orientations.

In coating/substrate bilayer systems, the indentation contact behavior transitionally varies from coatinglike to substratelike behaviors. Spatial confinement effects of the substrate induce very complicated plastic flows in the coating beneath the indenter, leading to a crucial difficulty that is not accounted for by any of the present quantitative analytical/theoretical predictions for the substrate-affected contact hardness. In this work, the author presents finite-element-based studies on the elastoplastic indentation contact mechanics of coating/substrate systems. The effect of the substrate is taken into account by introducing the spatially variable elastic modulus and the yield stress; this approach quantitatively describes the substrate-affected stress/strain field in the spatially localized area beneath the indenter. The elastoplastic constitutive relationship of the contact hardness for semi-infinite homogeneous bulks combined with these spatially variable material characteristics are successfully applied to analytically as well as quantitatively predict the substrate-affected contact hardness of bilayer composite systems having wide ranges of elastoplastic coating/substrate characteristics. The experimental procedures for determining the elastic/plastic parameters both of the coating and the substrate are also discussed, in which the importance of the experimental determination of substrate-affected indentation contact radius/area is emphasized.

Decreasing scales effectively increase nearly all important mechanical properties of at least some “brittle” materials below 100 nm. With an emphasis on silicon nanopillars, nanowires, and nanospheres, it is shown that strength, ductility, and toughness all increase roughly with the inverse radius of the appropriate dimension. This is shown experimentally as well as on a mechanistic basis using a proposed dislocation shielding model. Theoretically, this collects a reasonable array of semiconductors and ceramics onto the same field using fundamental physical parameters. This gives proportionality between fracture toughness and the other mechanical properties. Additionally, this leads to a fundamental concept of work per unit fracture area, which predicts the critical event for brittle fracture. In semibrittle materials such as silicon, this can occur at room temperature when the scale is sufficiently small. When the local stress associated with dislocation nucleation increases to that sufficient to break bonds, an instability occurs resulting in fracture.

Recent computational parametric studies have developed reverse algorithms to extract material properties of elastoplastic materials using experimental sharp nanoindentation. These methods used reduced modulus in their parameters to include the effect of indenter compliance. To investigate the validity of using reduced modulus, we conducted experimental indentation of a couple of representative cases for elastoplastic metals with a diamond and a sapphire Berkovich tip. Then, we performed a finite element study for sharp indentation of the same material systems. Both computational and experimental results indicate that the use of reduced modulus is invalid to describe indentation loading response for elastoplastic materials in a certain material regime. Our results show that indenter compliance is overestimated by the previous predictions using reduced modulus. This overestimation leads to underestimation of indenter curvature and causes error in extracting material properties by reverse algorithms.

The mechanical behavior of Ti-based metallic glass has been investigated by means of indentation experiments at different loading rates. Contrary to many crystalline materials, an increase of the loading rate causes a reduction of hardness, i.e., a mechanical softening. This effect is ascribed to deformation-induced creation of excess free volume, which is more pronounced for higher strain rates. The decrease of hardness is accompanied with an increase of the contact stiffness and a reduction of the reduced elastic modulus. Finite element simulations reveal that the mechanical response of this material can be described using the Mohr-Coulomb yield criterion. The changes in the nanoindentation curves with the increase of loading rate are well reproduced by decreasing the value of the Mohr-Coulomb cohesive stress. This result is consistent with the presumed enhancement of free volume.

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed on three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

This article presents an experimental procedure to perform highly localized compression tests on nanoscale structures/features, such as nanospheres and nanopillars, via standard nanoindentation equipment. Current manufacturing capabilities, such as focused ion beam (FIB), lend themselves well to the creation of micron-spaced nanostructures, but it is fundamental to target an individual instance with little or no damage to the surrounding ones. The procedure successfully addresses the problem of locating and testing purposely designed nanostructures of order of 50 nm or less. The technique is illustrated for the case of closely spaced arrays of nanopillars, which were successfully manufactured, characterized, and tested through several pieces of equipment. For the purposes of compression, along with a traditional Berkovich tip, a new multifunctional (MF) tip was devised. This last tip is endowed with a complex contact geometry enabling both atomic force microscope (AFM) scanning and flat punch compression of the nanostructure. The levels of accuracy in tip positioning as well as robustness to alignment errors are unprecedented in comparison with previous in situ compression tests. As a consequence, the MF tip becomes a versatile tool that can be used beyond uniform compression. As an example, ancillary shear tests in controlled conditions are reported. Such results may lay the bases for metal-forming processes at the nanoscale, such as nanoforging or cutting operations, which are relevant to MEMS design and manufacturing.

In this work, the time-dependent plastic deformation behavior of Ti40Zr25Ni3Cu12Be20 bulk and ribbon metallic glass alloys was investigated using a nanoindentation technique at room temperature with the applied load ranging from 5 to 100 mN. The stress exponent n, defined as, has been derived as a measure of the creep resistance. It was found that the measured stress exponent increases rapidly with increasing indentation size, exhibiting a positive size effect. The size effect on the stress exponent n obtained from the bulk sample is more pronounced than that obtained from the ribbon sample. The deformation mechanism involved will be discussed.