The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques as well as from advances in our understanding of the mechanics of elastic–plastic contact. Here, we review our current understanding of the mechanics governing elastic–plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how we now implement the method to make the most accurate mechanical property measurements. The limitations of the method are also discussed.

A perspective on the issue of scale in the fracture and deformation properties of ordinarily brittle covalent–ionic solids (ceramics) is presented. Characteristic scaling dimensions for nanomechanical properties of this class of solids are identified—specimen size or layer thickness, microstructural scale, and contact dimension. Transitions in mechanical damage processes occur as the characteristic dimensions diminish from the macroscale to the submicroscale. Such transitions generally preclude unconditional extrapolations of macroscopic-scale fracture and deformation laws into the nanomechanics region. Strength of brittle solids tends to increase while toughness tends to decrease as the scaling dimensions diminish. The nature of flaws that control strength in the submicroscale region also undergoes fundamental changes—even flaws without well-developed microcracks can be deleterious to strength.

This review surveys the phenomenon of plastic instabilities occurring in depth-sensing indentation measurements. Investigations presented focus on the characterization of Portevin–Le Châtelier type instabilities observed in different metal alloys during indentation. The effect of some important factors such as solute concentration, the formation of Guinier–Preston zones, and grain size and orientation are described and discussed. The phenomenon of plastic instabilities as serrated flow recently observed in bulk metallic glasses is also briefly reviewed.

The development of instrumented nanoindentation equipment has occurred concurrently with the discovery of many new families of bulk metallic glass during the past decade. While indentation testing has long been used to assess the mechanical properties of metallic glasses, depth-sensing capabilities offer a new approach to study the fundamental physics behind glass deformation. This article is a succinct review of the research to date on the indentation of metallic glasses. In addition to standard hardness measurements, the onset of plasticity in metallic glasses is reviewed as well as the role of shear banding in indentation, structural changes beneath the indenter, and rate-dependent effects measured by nanoindentation. The article concludes with perspectives about the future directions for nanocontact studies on metallic glasses.

Using a new multidimensional contact mechanics system, the normal and tangential elastic contact stiffnesses of six bulk materials with Poisson’s ratios ranging from 0.17 to 0.42 were measured. It is shown that the experimentally measured tangential to normal stiffness ratio can be described as a function of the bulk Poisson’s ratio of the material as predicted by Mindlin. The technique shows a high sensitivity to variations in Poisson’s ratio, suggesting that the technique is a viable means for measuring the Poisson’s ratio of new novel materials. The technique was subsequently applied to two metal film–glass substrate systems. Experimental observations indicate that even when Poisson’s ratio mismatch between the film and the substrate is large, the technique yields appropriate bulk values for the Poisson’s ratio of the film. The experimental details and apparatus are introduced and described.

The use of three-dimensional x-ray structural microscopy for nondestructive investigations of the deformation microstructure under microindents was demonstrated. Point to point, micrometer-resolution x-ray microbeam measurements of local lattice rotations were made for selected positions under 100-mN Berkovich and conical indents in single-crystal copper. Local lattice orientation measurements were used to extract micrometer by micrometer lattice misorientations and rotation axes along x-ray microbeams. Measurements of the deformation microstructure in symmetry and off-symmetry geometries are reported and discussed in terms of their potential for fundamental deformation investigations.

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic–plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load–displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3° in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

Mechanical characterizations using nanoindentation technique were performed for the martensitic steel used as practical dies steel containing carbide-former elements of Cr, Mo, W, and V, which are responsible for secondary hardening by tempering. The nanohardness Hn corresponding to the matrix strength shows obvious secondary hardening, and the hardening-peak temperature coincides with that of the macroscale hardness Hv. By comparing the temper-softening behavior of the high-purity Fe–C binary martensite, the ratio of the nanohardness Hn of the dies steel to that of the Fe–C binary steel is approximately a factor of two, whereas the same ratio of the macroscopic hardness Hv is three at the secondary-hardening peak. These results suggest that the secondary hardening of the dies steel during tempering is attributed not only to the nanoscale strengthening factors such as precipitation hardening by the alloy carbides, but also to some other factors in larger scale. One of the strengthening factors in larger scale is a decomposition of 9% retained austenite to much harder phases, such as martensite and/or ferrite–cementite constituent.

Finite element simulations of conical indentations in two-phase elastic–plastic materials were used to investigate the influence of the shape and the aspect ratio of particles embedded in a matrix material on the deformation behavior and hardness during depth-sensing indentation. Starting with single-phase materials, pile-up behavior and its influence on the contact area was studied. Particle–matrix systems were simulated for elastic–perfectly plastic particles embedded in a matrix, with a yield-strength ratio of 2 or 0.5, respectively. The simulations were motivated by indentation experiments in precipitation hardened nickel-base superalloy with a nanoindenting atomic force microscope. In the studied alloys, the matrix formed channels with a thickness of about 100 nm around the precipitates with diameters of about 500 nm. The simulations explained an experimentally observed transition from particle to matrix deformation behavior during indentation. Depth limits in hardness testing in particle–matrix systems were evaluated. Depending on the aspect ratio, soft and hard particles were tested reliably up to a normalized contact radius of about 70% particle diameter.

An analytical model was developed to derive an approximate closed-form solution for indenter displacement when a rigid spherical indenter is pressed onto a coating/substrate system. Finite element analyses were also performed to verify the analytical solution. The results showed that the solution could be obtained from the analytical expression for Hertzian indentation on a homogeneous semi-infinite elastic medium multiplied by a modification term. This modification term is a function of two ratios: (i) Young’s modulus ratio between the coating and the substrate and (ii) the ratio between the coating thickness and the contact radius. Based on this modification term, master curves for Hertzian indentation on coating/substrate systems were plotted.

In this paper a new loading history for extracting the stress–strain curve as well as the viscosity and creep behavior from indentation experiments is developed. It is based on a simple model describing the viscoplastic spherical indentation with a power-law hardening rule and a velocity-dependent overstress. Using this model, patterns were generated consisting of load-depth data and corresponding material parameters. The loading history for the simulation of the patterns was considered as a variable combination of loading and creep processes. To compare the identification potential of different loading histories, the inverse problem of determining the viscoplastic material parameters was solved by using neural networks. The emerging loading history uses a multiple-creep process with equidistant load steps and allows an identification of material parameters with much higher accuracy than with single creep. It will be used for further work, where the identification method is generalized using more realistic finite element simulations for a finite deformation elastic–viscoplastic material behavior.

A three-dimensional finite element analysis (FEA) model with elastic–plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver–Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver–Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

Depth-sensing indentation at ultramicroscopic and macroscopic contacts (“nanoindentation” and “macroindentation,” respectively) was performed on four brittle materials (soda-lime glass, alumina titanium carbide, sapphire, and silicon) and the resulting load–displacement traces examined to provide insight to the elastic and plastic deformation scaling with contact size. The load–displacement traces are examined in terms of the unloading stiffness, the energies deposited during loading and recovered on unloading, and the effect of the indenter tip radius on the loading curve. The results of the analyses show that the elastic and plastic deformation during loading and unloading is invariant with the scale of the contact, and the unloading curve is best described by neither a conical tip nor a paraboloid of revolution, but of some compromise.

We studied the polarity-induced changes in the nanoindentation response of GaAs{111}. The nanoindentations were made under a large range of loads (Fmax between 0.2 mN and 50 mN) at room temperature on {111} faces of A (Ga) or B (As) character. The loading–unloading curves were compared first, with special attention addressed to pop-in events and hardness values (reported previously for microindentation). Transmission electron microscopy was used to observe the nanoindentation structures generated at the two polar surfaces. The size of the dense plastic zone generated around the indent site was found to increase linearly with √Fmax and similarly for both polar surfaces. The indentation rosettes possess a threefold symmetry with arms developed along the <110> directions parallel to the surface. Sizes were found to be very close for both polar surfaces and the entire load range. For an A-polar face, the rosette arms are constituted by two arms: a long arm (LA, α dislocations) and a short arm (β dislocations). At the B surface, only the LA (β dislocations) are formed. Furthermore, microtwinning was observed only for an A-polar face, similar to previous observations of anisotropic microtwinning at GaAs(001) surfaces.

In conventional continuum mechanics, the yield behavior of a material is size independent. However, in nanoindentation, plasticity size effects have been observed for many years, where a higher hardness is measured for smaller indentation size. In this paper we show that there was a size effect in the initiation of plasticity, by using spherical indenters with different radii, and that the length scale at which the size effect became significant depended on the mechanism of plastic deformation. For yield by densification (fused silica), there was no size effect in the nanoindentation regime. For phase transition (silicon), the length scale was of the order tens of nanometers. For materials that deform by dislocations (InGaAs/InP), the length scale was of the order a micrometer, to provide the space required for a dislocation to operate. We show that these size effects are the result of yield initiating over a finite volume and predict the length scale over which each mechanism should become significant.

Nanoindentation is one of the very few techniques that can measure both the elastic and plastic properties of very small volumes of materials. Recently it has been shown that the properties of thin coatings can be determined by nanoindentation, even when the normal indentation response includes a significant component due to the substrate. This paper takes the method a step further and shows how by combining acoustical test methods with nanoindentation, a validated set of values for the thickness, Young's modulus, and Poisson ratio for a coating can be obtained.

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic–plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

Instrumented indentation testing was used to evaluate the changes in mechanical properties of single-walled carbon nanotube composite specimens with varying weight percentage (0, 0.1, 0.5, and 1.0 wt%) of nanotubes using a low-viscosity liquid epoxy resin. The nanotubes were prepared using laser ablation technique. Reference tensile tests were also performed on the same samples, and relevant comparisons with indentation results were made. The variations in modulus and hardness obtained using nanoindentation (considering time effects) showed quantifiable differences between the various composite specimens, but differed from tensile test data. The small changes in the observed stiffness and breaking strength of carbon nanotube composites was due to the formation of bundles, their curvy morphology, and microporosity in the specimens. Interesting fluctuations obtained from the interpreted values of modulus with depth of indentation is attributed to varying degrees of the local confining effect of nanotube bundles. Creep exponents for these nanocomposites were also evaluated and indicate considerable improvements.

The fracture and instrumented indentation behavior of a range of materials subjected to indentation by four sharp probes varying in acuity from the Berkovich to the cube-corner was studied. Quantities derived from load, displacement, and continuous stiffness measurements were evaluated for their ability to detect “pop-in”—sudden displacement excursions associated with fracture. It was found that gross unloading character was sensitive to the presence of fracture, even when no pop-in was detected. This may be useful in the development of fracture toughness estimation models that do not rely on the imaging of cracks.