Molecular dynamics simulations were performed to gain fundamental insight into crystal plasticity, and its size effects in nanowires deformed by spherical indentation. This work focused on <111>-oriented single-crystal, defect-free Ni nanowires of cylindrical shape with diameters of 12 and 30 nm. The indentation of thin films was also comparatively studied to characterize the influence of free surfaces in the emission and absorption of lattice dislocations in single-crystal Ni. All of the simulations were conducted at 300 K by using a virtual spherical indenter of 18 nm in diameter with a displacement rate of 1 m·s−1. No significant effect of sample size was observed on the elastic response and mean contact pressure at yield point in both thin films and nanowires. In the plastic regime, a constant hardness of 21 GPa was found in thin films for penetration depths larger than 0.8 nm, irrespective of variations in film thickness. The major finding of this work is that the hardness of the nanowires decreases as the sample diameter decreases, causing important softening effects in the smaller nanowire during indentation. The interactions of prismatic loops and dislocations, which are emitted beneath the contact tip, with free boundaries are shown to be the main factor for the size dependence of hardness in single-crystal Ni nanowires during indentation.

A spherical indentation method was developed to characterize the phase transition behaviors of shape memory alloys (SMAs). Based on deformation analysis, the measured indentation force-depth curves of SMAs can be converted to their nominal stress-strain curves. The predicted elastic modulus and phase transition stress of SMAs from spherical indentation agree well with those directly measured from tensile tests. This approach should be especially useful for characterizing the phase transition properties of SMA materials of small size or thin films.

An attempt was made to predict the macroscopic plastic flow of a high-performance pipeline steel, consisting of dual constituent phases (soft ferrite and hard bainite), by performing nanoindentation experiments on each microphase with two spherical indenters that have different radii (550 nm and 3.3 μm). The procedure is based on the well known concepts of indentation stress-strain and constraint factor, which make it possible to relate indentation hardness to the plastic flow of the phases. Additional consideration of the indentation size effect for sphere and application of a simple “rule-of-mixture” led us to a reasonably successful estimation of the macroscopic plastic flow of the steel from the microphases properties, which was verified by comparing the predicted stress-strain curve with that directly measured from the conventional tensile test of a bulky sample.

The aim of the investigation was to study the influence of indenter tip geometry on the conventionally obtained indentation modulus of enamel by nanoindentation. Indentation tests on bovine enamel using three different diamond pyramidal indenters with half face angles 65.27°, 45°, and 35.26° were conducted to evaluate the indentation modulus using the Oliver–Pharr method [W.C. Oliver and G.M. Pharr, J. Mater. Res.7, 1564 (1992)]. In addition, three different dehydration conditions were studied: wet under Hank's balanced salt solution, laboratory dried, and vacuum dehydrated. For the Berkovich indenter (65.27°) and 45° pyramidal indenters, there was only a small difference between indentation modulus values, whereas for the cube-corner indenter (35.26°) a ratio of 2.4 between laboratory dry and wet samples was found. A detailed evaluation, including indentation creep and recovery as well as pileup, resulted in a reduction of this latter ratio to 1.7. This still large difference was rationalized on the basis of the different deformation mechanisms generated by indenters of different face angles.

Measurement of the mechanical behavior of hydrated gels is challenging due to a relatively small elastic modulus and dominant time-dependence compared with traditional engineering materials. Here polyacrylamide gel materials are examined using different techniques (indentation, unconfined compression, dynamic mechanical analysis) at different length-scales and considering both viscoelastic and poroelastic mechanical frameworks. Elastic modulus values were similar for nanoindentation and microindentation, but both indentation techniques overestimated elastic modulus values compared to homogeneous loading techniques. Hydraulic and intrinsic permeability values from microindentation tests, deconvoluted using a poroelastic finite element model, were consistent with literature values for gels of the same composition. Although elastic modulus values were comparable for viscoelastic and poroelastic analyses, time-dependent behavior was length-scale dependent, supporting the use of a poroelastic, instead of a viscoelastic, framework for future studies of gel mechanical behavior under indentation.

In ductile metals, sliding contact induces plastic deformation resulting in subsurfaces, the mechanical properties of which are different from those of the bulk. This article describes a novel combination of nanomechanical test methods and analysis techniques to evaluate the mechanical behavior of the subsurfaces generated underneath a wear surface. In this methodology, nanoscratch techniques were first used to generate wear patterns as a function of load and number of cycles using a Hysitron TriboIndenter. Measurements were made on a (001) single crystal plane along two crystallographic directions, <001> and <011>. Nanoindentation was then used to measure mechanical properties in each wear pattern. The results on the (001) single crystal nickel plane showed that there was a strong increase in hardness with increasing applied load that was accompanied by a change in surface deformation. The amount of deformation underneath the wear patterns was examined from focused ion beam cross-sections of the wear patterns.

Nanoindentation measurements using the Berkovich diamond tip with a load up to 700 and 210 mN were performed on 1-μm hydrogenated diamond-like carbon (DLCH) films and 6-μm polyimide (PI) films under different thermal treatment. The average nanohardness and elastic modulus from nanoindentation measurements are 25.13 and 192.18 GPa for as-deposited DLCH film and 22.93 and 174.22 GPa for as-annealed DLCH film, respectively. The ID/IG ratio of Raman spectra is 1.72 for as-deposited DLCH film and 2.04 for as-annealed DLCH film. The average nanohardness and elastic modulus from nanoindentation measurements are 0.37 and 5.58 GPa for 300 as-cured PI film and 0.42 and 5.19 GPa for 400 as-cured PI film, respectively. The relative cured rate is 92.1% for 300 as-cured PI film and 100% for 400 as-cured PI film. Both the nanohardness and elastic modulus derived from nanoindentation test results can correlate well with the trend of Raman spectra and FTIR spectra for hard DLCH film and soft PI film under different thermal treatment effects.

Nanoindentation is a widely accepted test method for materials characterization. On account of the complexity of contact deformation behavior, design of parametric constitutive models and determination of the unknown parameters is challenging. To address the need for identification of mechanical properties of viscoelastic/plastic materials from nanoindentation data, a combined numerical finite element/optimization-based indentation modeling tool was developed, fully self-contained, and capable of running on a PC as a stand-alone executable program. The approach uses inverse engineering and formulates the material characterization task as an optimization problem. The model development consists of finite element formulation, viscoelastic/plastic material models, heuristic estimation to obtain initial solution boundaries, and a gradient-based optimization algorithm for fast convergence to extract mechanical properties from the test data. A four-parameter viscoelastic/plastic model is presented, then a simplified three-parameter model with more rapid convergence. The end result is a versatile tool for indentation simulation and mechanical property analysis.

Nonlinear viscoelastic problems are in general not analytically solvable. However, it is shown here that, for any viscoelastic materials describable by a constitutive law with linear elastic and (in general) nonlinear viscous elements arranged in any network fashion, such as the Maxwell or standard linear solid arrangements, it is always possible to eliminate the viscous terms by replacing the displacement, strain, and stress fields of the problem by the jumps in rates of these fields. After the viscous terms are eliminated, the problem is reduced to a linear elastic problem defined on the same spatial domain and with the same elastic constant as in the original viscoelastic problem. Such a reduced elastic problem is analytically solvable in many practical cases, and the solution yields a relation between jumps in the load rate and the displacement rate, pertinent to the boundary conditions in the original problem. Such a relation can often be used as the basis for an experimental scheme to measure the elastic constants of materials. The material can be time- or strain-dependent, and the value of the elastic constant measured corresponds to the time instant or the strain value when the jump in load or displacement rate is implemented.

Nanoindentation was undertaken near grain boundaries to increase understanding of their individual contributions to the material’s macroscopic mechanical properties. Prior work with nanoindentation in body-centered cubic (bcc) materials has shown that some grain boundaries produce a “pop-in” event, an excursion in the load–displacement curve. In the current work, grain boundary associated pop-in events were observed in a Fe–0.01 wt% C polycrystal (bcc), and this is characteristic of high resistance to intergranular slip transfer. Grain boundaries with greater misalignment of slip systems tended to exhibit greater resistance to slip transfer. Grain boundary associated pop-ins were not observed in pure copper (face-centered cubic) or interstitial free steel ~0.002 wt% C (bcc). Additionally, it was found that cold work of the Fe–0.01 wt% C polycrystal immediately prior to indentation completely suppressed grain boundary associated pop-in events. It is concluded that the grain boundary associated pop-in events are directly linked to interstitials pinning dislocations on or near the boundary. This links well with macroscopic Hall–Petch effect observations.

The purpose of this work is to further develop experimental methodologies using flat punch nanoindentation to measure the constitutive behavior of viscoelastic solids in the frequency and time domain. The reference material used in this investigation is highly plasticized polyvinylchloride (PVC) with a glass transition temperature of −17 °C. The nanoindentation experiments were conducted using a 983-μm-diameter flat punch. For comparative purposes, the storage and loss modulus obtained by nanoindentation with a 103-μm-diameter flat punch and dynamic mechanical analysis are also presented. Over the frequency range of 0.01–50 Hz, the storage and loss modulus measured using nanoindentation and uniaxial compression is shown to be in excellent agreement. The creep compliance function measured using a constant stress test performed in uniaxial compression and flat punch nanoindentation is also shown to correlate well over nearly 4 decades in time. In addition, the creep compliance function predicted from nanoindentation data acquired in the frequency domain is shown to correlate strongly with the creep compliance function measured in the time domain. Time–temperature superposition of nanoindentation data taken at 5, 10, 15, and 22 °C shows the sample is not thermorheologically simple, and thus the technique cannot be used to expand the mechanical characterization of this material. Collectively, these results clearly demonstrate the ability of flat punch nanoindentation to accurately and precisely determine the constitutive behavior of viscoelastic solids in the time and frequency domain.

In our previous paper [Feng et al., Acta Mater.55, 2929 (2007)], an analytical model is proposed to estimate the stress field around an elastoplastic indentation/contact, matching nicely with the finite element analysis. The model is related to an embedded center of dilatation (ECD) in a half-space. In this paper, we focus on determining the ECD strength B* and the ECD depth ξ. By matching an expanding cavity model and the ECD model, we find that B* ≈ Yc3/6 and ξ ≈ 0.4c, where Y is the yield strength and c is the plastic zone radius. We provide a method to predict Y, c, and thereby B* as well as ξ through nanoindentation data, and we also demonstrate that pileup is the physical reason for the existence of the upper limit for the ratio of hardness to Y. Thus, our ECD model is completed by combining our previous paper (the analytical expression) and this paper (the essential parameters).

Tabor’s book The Hardness of Metals, published in 1951, has had a major influence on the subject of indentation hardness and is by far the most widely cited source in this area. Although hardness testing was widely used for practical purposes in the first half of the 20th century, its use was generally based on little scientific understanding. The history of indentation hardness testing up to that point is reviewed, and Tabor’s contribution is appraised in this context.

Indentation is widely used to extract material elastoplastic properties from measured force-displacement curves. Many previous studies argued or implied that such a measurement is unique and the whole material stress-strain curve can be measured. Here we show that first, for a given indenter geometry, the indentation test cannot effectively probe material plastic behavior beyond a critical strain, and thus the solution of the reverse analysis of the indentation force-displacement curve is nonunique beyond such a critical strain. Secondly, even within the critical strain, pairs of mystical materials can exist that have essentially identical indentation responses (with differences below the resolution of published indentation techniques) even when the indenter angle is varied over a large range. Thus, fundamental elastoplastic behaviors, such as the yield stress and work hardening properties (functions), cannot be uniquely determined from the force-displacement curves of indentation analyses (including both plural sharp indentation and deep spherical indentation). Explicit algorithms of deriving the mystical materials are established, and we qualitatively correlate the sharp and spherical indentation analyses through the use of critical strain. The theoretical study in this paper addresses important questions of the application range, limitations, and uniqueness of the indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material constitutive properties.