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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.
A linear relationship between the ratio of elastic work to the total indentation work and hardness to reduced modulus, i.e., We/Wt = λ H/Er, has been derived analytically and numerically in a number of studies and has been widely accepted. However, the scaling relationship between We/Wt and H/Er has recently been questioned, and it was found that λ is actually not a constant but is related to material properties. In this study, a new relationship between We/Wt and H/Er has been derived, which shows excellent agreement with numerical simulation and experimental results. We also propose a method for obtaining the elastic modulus and hardness of a material without invoking the commonly used Oliver and Pharr method. Furthermore, it is demonstrated that this method is less sensitive to tip imperfections than the Oliver and Pharr approach is.
This study proposes a method developed to simultaneously solve contact hardness and reduced modulus by loading and unloading coefficients together with the inclined angle of an indenter. The ratios of the applied load to the squared slopes of load–depth curves during loading and unloading processes were used to determine loading and unloading coefficients. The values of the contact area estimated by the present method were found to be precise for a variety of materials. Compared to the reduced modulus, errors due to underestimated contact area were found more significant in the evaluation of contact hardness.
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 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.
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.
Although alterations in the gross mechanical properties of dynamic and compliant tissues have a major impact on human health and morbidity, there are no well-established techniques to characterize the micromechanical properties of tissues such as blood vessels and lungs. We have used nanoindentation to spatially map the micromechanical properties of 5-μm-thick sections of ferret aorta and vena cava and to relate these mechanical properties to the histological distribution of fluorescent elastic fibers. To decouple the effect of the glass substrate on our analysis of the nanoindentation data, we have used the extended Oliver and Pharr method. The elastic modulus of the aorta decreased progressively from 35 MPa in the adventitial (outermost) layer to 8 MPa at the intimal (innermost) layer. In contrast, the vena cava was relatively stiff, with an elastic modulus >30 MPa in both the extracellular matrix-rich adventitial and intimal regions of the vessel. The central, highly cellularized, medial layer of the vena cava, however, had an invariant elastic modulus of ∼20 MPa. In extracellular matrix-rich regions of the tissue, the elastic modulus, as determined by nanoindentation, was inversely correlated with elastic fiber density. Thus, we show it is possible to distinguish and spatially resolve differences in the micromechanical properties of large arteries and veins, which are related to the tissue microstructure.
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.
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.
Substrate influence is a common problem when using instrumented indentation (also known as nanoindentation) to evaluate the mechanical properties of thin films. In this work, finite element analysis was used to develop an ad hoc model that predicts the substrate influence when testing thin dielectric films on silicon. The model was evaluated experimentally using three sets of films that were nominally the same except for thickness. Using the model significantly reduced the measurement error for the thinnest films (<250 nm) by accurately accounting for the influence of the substrate. The model also significantly reduced the measurement uncertainty, because properties were evaluated using larger indents that would normally be unduly affected by the substrate. The process for developing this model may be useful in developing other ad hoc models for analyzing film-substrate systems.
Instrumented indentation (referred to as nanoindentation at low loads and low depths) has now become established for the single point characterization of hardness and elastic modulus of both bulk and coated materials. This makes it a good technique for measuring mechanical properties of homogeneous materials. However, many composite materials are composed of material phases that cannot be examined in bulk form ex situ (e.g., carbides in a ferrous matrix, calcium silicate hydrates in cements, etc.). The requirement for in situ analysis and characterization of chemically complex phases obviates conventional mechanical testing of large specimens representative of these material components. This paper will focus on new developments in the way that nanoindentation can be used as a two-dimensional mapping tool for examining the properties of constituent phases independently of each other. This approach relies on large arrays of nanoindentations (known as grid indentation) and statistical analysis of the resulting data.
The objective of the present study is to investigate the dynamic indentation behavior of steel plate material when impacted by ogive-shaped projectiles and in particular under indentation conditions involving large depths of penetration (i.e., depth of penetration greater than projectile radius). Toward the above purpose, dynamic indentation of steel plates of thickness 20, 40, and 80 mm have been carried out using projectiles of diameter 6.2 and 20 mm, and over a range of impact velocities so as to attain depths of penetration in the range 1.4 to 3.6 times the projectile radius. The results indicate that the dynamic hardness, the plastic zone size, specific energy consumed in plastic deformation within the plastic zone, and the average plastic strain within the plastic zone increases continuously with increasing values of depth of penetration normalized by projectile radius. Certain subtle differences regarding the nature of plastic deformation between indentation at large and shallow depths of penetration are presented. However, on a macroscopic scale, the indentation mechanisms and processes are broadly similar and show continuity in terms of behavior across the whole penetration depth range.
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).
This article presents a nanoindentation study of polycrystalline and single crystals of yttria-doped zirconia with both tetragonal and cubic phases. Analysis of the deformation mechanisms is performed by both atomic force microscopy (AFM) and micro-Raman spectroscopy. Phase transformation from tetragonal to monoclinic phase is clearly distinguished on tetragonal crystals, whereas in cubic crystals the plastic deformation seems to be controlled by dislocation nucleation and interactions. AFM observations in tetragonal zirconia grains have shown that both grain size and autocatalytic transformation strongly influence the size of the transformed zone. Furthermore, the martensitic phase transformation seems to be also strongly dependent of the indenter shape. Experimental results suggest that a critical contact pressure is necessary to induce the phase transformation.
The mechanical response to indentation (including nano- and microindentation) has been investigated in Cu/Au and Cu/Cr multilayers with respective layer thickness ratios of 1:1 and 2:1, and individual layer thickness ranging from nanometer to submicrometer scale. It was found that the Cu/Cr multilayer has higher strength than the Cu/Au multilayer, although both multilayers have close Hall–Petch slope. Examination of indentation-induced deformation behavior shows that the Cu/Cr multilayer exhibits higher resistance to plastic deformation instability than the Cu/Au multilayer. Theoretical analysis indicates that the significant difference in mechanical response originates from the constituent layer configuration and interface structures, which impose distinguishing confining effect on dislocation activity.
To evaluate mechanical properties by means of nanoindentation, information on the contact area is crucial. However, the contact area is not directly accessible in experiments and is usually calculated according to the Oliver and Pharr procedure, which turned out to be unsatisfying when applied to viscoelastic materials like polymers. In this study, complementary in situ indentation testing and finite element analysis (FEA) were performed on silicone elastomers. Through this combination of techniques, several individual error sources in the conventional contact area determination have been identified and quantified. For shallow penetrations, contact areas after Oliver and Pharr were up to 40% smaller than the in situ testing results; for larger penetrations, the contact size was overestimated by approximately 6%. The deviations of the resulting mechanical properties were approximately 10%. Viscoelastic effects could be captured if dynamic indentation testing was performed.
The hardness of a material is generally affected by the indentation size effect. The strain gradient plasticity (SGP) theory is largely used to study this load dependence because it links the hardness to the intrinsic properties of the material. However, the characteristic scale-length is linked to the macrohardness, impeding any sound discussion. To find a relevant parameter, we suggest introducing a hardness length-scale factor that only depends on the shear modulus and the Burgers vector of the material and is easily calculable from the relation of the SGP theory. The variation of the hardness length-scale factor is thereafter used to discuss the hardness behavior of a magnetite crystal, the objective being to study the effect of the cumulative plasticity resulting from cyclic indentation. As a main result, the hardness length-scale factor is found to be constant by applying repeated cycles at a constant peak load whereas the macrohardness and the characteristic scale-length are both cycle dependent. When using incremental loads, the hardness length-scale factor monotonically decreases between two limits corresponding to those obtained at high and low loading rates, while the dwell-load duration increases. The physical meaning of such behavior is based on the modification of the dislocation network during the indentation process depending on the deformation rate.
Deformation field parameters in plane-strain indentation of a perfectly plastic solid with a punch have been mapped using particle image velocimetry, a correlation-based image analysis technique. Measurements of velocity and strain rate over a large area have shown that the deformation resembles that of the slip line field of Prandtl. A zone of dead metal is found to exist underneath the indenter adjoining which is a transition region of material flow similar to the centered-fan region in the slip line field. Shear bands demarcate the boundaries of these deformation regions. The observations suggest that a representative strain rate may be assigned to the indentation. By integrating the strain rate field along particle trajectories, the strains in the indentation region have been estimated. The strain values are seen to be large, 0.5 to 4, over a region extending to about twice the indenter half-width. A pocket of large strain, ∼4, is found to exist close to the edge of the indenter–specimen contact. Prandtl’s slip line field is modified based on the observations and used to estimate the strain field. The measurements of the deformation parameters are found to compare mostly favorably with the predictions of the slip line field and prior observations of indentation. The implications of these findings for analysis and interpretation of indentation hardness are briefly discussed.
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.