Recent extensive nanomechanical experiments have revealed that the instantaneous strength and plasticity of a material can be significantly affected by the size (of sample, microstructure, or stressed zone). One more important property to be added into the list of size-dependent properties is time-dependent plastic deformation referred to as creep; it has been reported that the creep becomes more active at the small scale. Analyzing the creep in the small scale can be valuable not only for solving scientific curiosity but also for obtaining practical engineering information about the lifetime or durability of advanced small-scale structures. For the purpose, nanoindentation creep experiments have been widely performed by far. Here we critically review the existing nanoindentation creep methods and the related issues and finally suggest possible novel ways to better estimate the small-scale creep properties.

Creep during loading and recovery phases after load removal are studied using a homemade experimental device that allows us to record in situ the evolution of the true contact area and of the residual imprint versus the time. Indentation tests are performed using a spherical indenter with a tip radius R = 400 μm onto amorphous polymeric surface poly(methylmethacrylate) (PMMA) at different contact durations (10–105 s) and controlled temperatures varying between −20 and 100 °C. Original experimental results are presented about the true evolution of the contact area during creep and recovery phases. An interesting experimental parameter, defined by the ratio a(t)/a0, (with a(t), evolution of the contact radius with creep or relaxation time, and a0, the initial value of the contact radius at the end of the loading phase or at the end of the creep phase) has been introduced to describe the evolution of imposed strain during indentation. As a function of the temperature and of the initial average strain imposed at the end of the loading phase, some nonlinear phenomena can be observed. Using two-dimensional axisymmetric finite element modeling, assuming only viscoelastic behavior, creep and recovering phases during indentation have been reproduced. The simulation results indicate that (i) the test is mainly controlled by the imposed strain and not by the contact pressure, and (ii) some plasticity could appear in the contact zone and as a function of the location and the size of the volume where the strain is maximal, the recovery is more or less limited.

This study investigates spherical indentation of plastically graded materials (PGMs). The hardness of these materials decreases with depth due to microstructural or compositional changes. To predict the behavior of PGM, the knowledge of the plastic properties of the surface and the substrate is necessary. In this work, the spherical indentation technique is applied on carbonitrided steels to obtain their mechanical properties. First, spherical indentation was applied to characterize homogenous materials using inverse analysis. The comparison with tensile test’s results shows that the inverse analysis using spherical indentation data is a reliable method to determine the plastic properties of homogeneous materials. In the second part spherical indentation was used to characterize carbonitrided steels using inverse analysis to obtain plastic properties of the surface. The results show that spherical indentation using inverse analysis has a real potential for evaluating mechanical properties of PGM.

Indentations tests have been performed on two standard materials SiO2 and Si (100) using two Berkovich indenters presenting different tip defects. Estimations of the tip radii deduced from analyses of maximal applied load versus contact depth and stiffness versus contact depth curves have been compared for experimental observation of each indenter tip obtained with atomic force microscopy (AFM). Results indicate that the determination of the tip defect from data extracted form load–displacement curves is partly dependent on the mechanical properties of the tested material. Then, an original study is proposed to evidence the influence of the tip defect on mechanical response during indentation. Experimental AFM observations of the tip indenter geometries have been introduced in finite element software MSC MARC to reproduce indentation tests on bulk material surfaces. We demonstrated at very shallow penetration depth (less than 50 nm) that the real indenter tip defects have to be considered in the simulation runs, especially to identify accurately the rheological parameters of the tested surface.

Pop-ins on nanoindentation load–displacement curves of a ferritic steel were correlated with yield drops on its tensile stress–strain curves. To investigate the relationship between these two phenomena, nanoindentation and tensile tests were performed on annealed specimens, prestrained specimens, and specimens aged for various times after prestraining. Clear nanoindentation pop-ins were observed on annealed specimens, which disappeared when specimens were indented right after the prestrain, but reappeared to varying degrees after strain aging. Yield drops in tensile tests showed similar disappearance and appearance, indicating that the two phenomena, at the nano- and macro-scale, respectively, are closely related and influenced by dislocation locking by solutes (Cottrell atmospheres).

The elastic anisotropy of cementite (Fe3C) is still under discussion. Recent theoretical (ab initio) calculations predict a very high elastic anisotropy for this iron carbide, and a few published experiments suggest that prediction could be true. This work presents a first attempt of using nanoindentation for assessing the elastic anisotropy of such an important component of steels. Our nanoindentation results show that the elastic anisotropy of Fe3C is high but smaller than predicted by ab initio calculations. The elastic modulus is obtained from the load–penetration curves before the first pop-in indicative of plasticity nucleation is detected. The tests thus provide information on the plastic anisotropy of cementite. Surprisingly, the mean indentation pressure or the maximum shear stress under the indenter at the onset of plasticity has been observed to be nearly independent of the crystalline orientation of the indented surface.

Herein rutile (TiO2) single-crystal surfaces, with (001) and (100) orientations, were indented with hemispherical indenters with radii of 13.5, 5, and 1.4 μm. By converting the load–displacement data to nanoindentation (NI) stress–strain curves, together with microscopic post-indentation observations, we conclude that in the (001) orientation, plastic deformation occurs by the activation of all four {101}<10> slip systems. In the (100) orientation, only two of the four {101}<10 > slip systems, along with {100}<00> slip, are activated. Because the four {101}<10> slip systems in the (001) orientation intersect, the surface is harder and exhibits higher hardening rates after the nucleation of dislocations. The latter are manifested by pop-ins, some of which are large. The pop-in stresses are adequately described by Weibull statistics and were significantly higher for the (001) orientation. The elastic moduli, determined from spherical NI stiffness versus contact radii plots, were 349 ± 5 and 229 ± 4 GPa for (001) and (100) orientations, respectively. Fully spontaneous reversible, stress–strain hysteretic curves—only manifest in the (100) orientation—are attributed to the to-and-fro motion of dislocations comprising incipient kink bands in the {100}<00> slip system.

An analysis of indentation hardness data from three ceramic materials, zirconium diboride, silicon carbide, and titanium nitride, is presented to extract the fundamental deformation parameters at 295 to 623 K. The measured activation volume was of the order of 1 × b3 to 4 × b3 (b is the Burgers vector). The calculated activation energies were in the range of 0.75 to 1.61 eV and are typical of lattice-controlled dislocation glide mechanism. Using finite difference simulations, it was demonstrated that there is a significant difference between the plastic strain rate and the total strain rate for materials showing substantial elastic deformation (i.e., large hardness/elastic modulus ratio). Therefore, the measured total strain rates must be converted into plastic strain rates, which require a reduction during loading and an increase during the dwell at maximum load. Additionally, importance of quantification of instrumental thermal drift was discussed and use of either short duration indentation tests or high loads was emphasized.

Most instrumented indentation theoretical studies and models consider bulk sample geometry, which implies no influence on the indentation response. In the particular case of thin samples, our previous studies have shown that the thickness has an influence on the experimental device behavior as well as on the sample and material response. This work is a numerical and experimental illustration of this particularity. Spherical macroindentation tests are performed on AISI 1095 steel samples of thicknesses varying from 0.55 to 10 mm. Experimental and numerical results are compared. Experimental limitations are investigated, and solutions to obtain results that are independent of the sample thickness and curvature are proposed. We show that the proposed solution leads to a reliable identification of the material mechanical properties of thin and moderately bent samples.

The performance of materials exposed to high doses of neutron radiation is currently of great interest for the development of nuclear fusion energy production. An Fe12%Cr alloy was subjected to high-dose (6 dpa) radiation with 2MeV Fe+ ions to simulate the damage structures caused by neutron radiation, resulting in a damage layer ∼0.7 μm in depth from the surface. Spherical nanoindentation, using indenters with radii of 5, 10, and 20 μm, was used to determine reliable values for the initial yield pressure, the evolution of plastic deformation and the elastic modulus of this material, in the irradiated and unirradiated condition. The results showed that the initial yield pressure within the damage layer can be determined and was approximately a factor of two higher than that of the same material in the unirradiated condition. The irradiated material appeared to display strain softening following yield.

This article focuses on the use of spherical nanoindentation measurements to estimate the pressure of cavitation impacts and its statistical distribution. Indeed, nanoindentation techniques are supposed to represent an effective tool in this field due to the similarities between substrate deformation under liquid impact and indentation testing. First, nanoindentation experiments were used to extract the mechanical parameters of a Nickel–Aluminum–Bronze alloy; second, pitting tests were performed at different operating pressures, and the geometrical characteristics of the pits were measured; and finally, the spectra of impact pressure and loads responsible for material erosion were obtained by coupling the findings of indentation tests with the analysis of pitting tests. Results assessed the capability of the proposed methodology to quantify the hydrodynamic aggressiveness of the cavitating flow. This procedure, which assumes the material itself as a sensor that is able to detect the impact loads, could represent an alternative solution to pressure transducers in estimating the cavitation intensity.

Most biological materials are hierarchically structured composites that often possess exceptional mechanical properties. We show that nanoindentation can be a powerful tool for understanding the structure‑mechanical property relationship of biological materials and illustrate this for fish teeth and scales, not heretofore investigated at the nanoscale. Piranha and shark teeth consist of enameloid and dentin. Nanoindentation measurements show that the reduced modulus and hardness of enameloid are 4‑5 times higher than those of dentin. Arapaima scales are multilayered composites that consist of mineralized collagen fibers. The external layer is more highly mineralized, resulting in a higher modulus and hardness compared with the internal layer. Alligator gar scales are composed of a highly mineralized external ganoin layer and an internal bony layer. Similar design strategies, gradient structures, and a hard external layer backed by a more compliant inner layer are exhibited by fish teeth and scales and seem to fulfill their functional purposes.

The conventional JKR theory was extended to the adhesive contact of a rigid sphere onto an elastic film perfectly bonded to a rigid substrate. An elasticity problem of axisymmetric indentation on an elastic film was revisited, in which the force–depth relations for both flat and spherical indentations were obtained in a simple form. With the obtained force–depth relations, the energy release rate at the debonding of a spherical tip from an elastic film was expressed in terms of pull-off force, elastic constants, and geometric parameters. The adhesion energy between a spherical tip and an elastic film can be measured as the critical energy release rate at the instability of debonding. This study suggests that when the critical radius of contact is larger than the thickness of an elastic film, the extended JKR theory should be used in place of the conventional JKR theory to correctly evaluate the adhesion energy between the spherical tip and the elastic film.

The instrumented indentation test is an important alternative in quantifying residual stresses. Various indentation models have been developed to determine residual stresses, but no previous models can be applied to a nonequibiaxial residual stress state. To overcome this limitation, a Knoop indentation technique was developed to use the asymmetric characteristics of the Knoop indenter. With the ratio of conversion factors and equations for the relation between the load differences and the residual stress, a model of Knoop indentation was developed to determine the stress directionality p. This model was verified and compared through experiments on various biaxial tensile stress states. Imperfections in the Knoop tip change the conversion factor ratio. Using finite element simulations, this change in the conversion factor was expressed by a fitting equation.

The analysis of nanoindentation force data are based on Sneddon’s solution for a linear elastic half space with a rigid axisymmetric indenter. Berkovich indenters commonly used in indentation experiments are normally modeled as cones. The idea of effective tip shape was presented to better explain the behavior of the unloading curve and pressure distribution under the tip in real experiments. We examine the concept of effective tip in three dimensions by importing real indenter metrology by atomic force microscope directly into finite element analysis and simulate fused silica indentation experiments. We show that fitting the elastic reloading curves overestimates the elastic modulus of fused silica. This is explained by studying the pressure distribution at maximum depth under the effective tip. While the effective tip describes the problem geometrically, it is believed that neglecting the deformed zone in the indented material is responsible for over estimating the modulus value.

A new expanding cavity model (ECM) for describing conical indentation of elastic-ideally plastic material is developed. For the proposed ECM, it is assumed that the volume of material displaced by the indenter is equal to the volume loss, due to elastic deformation, in the material and depends on the pile-up or sink-in. It was shown that the proposed ECM matches very well numerical data in the final portion of the transition regime for which the contact pressure lies between approximately 2.5Y and 3Y. For material of large E/Y ratio, the new ECM also provides results which are very close to the numerical data in the plastic-similarity regime (regime in which Cf = 3). For material of smaller E/Y ratio, the proposed ECM gives better results than the Johnson’s ECM because pile-up or sink-in is taken into account.

This article describes cracking during microcompression of Si, InAs, MgO, and MgAl2O4 crystals and compares this with previous observations on Si and GaAs micropillars. The most common mode of cracking was through-thickness axial splitting, the crack growing downward from intersecting slip bands in pillars above a critical size. The splitting behavior observed in all of these materials was quantitatively consistent with a previous analysis, despite the differences in properties and slip geometry between the different materials. Cracking above the slip bands also occurred either in the side or in the top surface of some pillars. The driving forces for these modes of cracking are described and compared with observations. However, only through-thickness axial splitting was observed to give complete failure of the pillar; it is, therefore, considered to be the most important in determining the brittle-to-ductile transitions that have been observed.

We use instrumented indentation to characterize the mechanical and transport behavior of a pH-sensitive hydrogel in various aqueous buffer solutions. In the measurement, an indenter is pressed to a fixed depth into a hydrogel disk and the load on the indenter is recorded as a function of time. By analyzing the load–relaxation curve using the theory of poroelasticity, the elastic constants of the hydrogel and the diffusivity of water in the gel can be evaluated. We investigate how the pH and ionic strength of the buffer solution, the hydrogel cross-link density, and the density of functional groups on the polymer backbone affect the properties of the hydrogel. This work demonstrates the utility of indentation techniques in the characterization of pH-sensitive hydrogels.

We report here a finite element simulation of the compression of inorganic WS2 hollow nanoparticles. The particle was modeled as a multilayered polyhedron to investigate the effect of the unique onion-like and highly faceted structure in the mechanical response. The simulation revealed the central role of the faceted structure of the WS2 nanoparticles in the mode of failure. The stress magnitude and distribution was shown to be size dependent, as predicted from previously published experimental results. Moreover, the simulation points to the influence of the layered structure on the energy release during compression loading via interlayer shear.