Constant strain rate nanoindentation hardness measurements at high sustained strain rates cannot be made in conventional nanoindentation testing systems using the commonly employed continuous stiffness measurement technique (CSM) because of the “plasticity error” recently reported by Merle et al. [Acta Mater.134, 167 (2017)]. To circumvent this problem, here we explore an alternative testing and analysis procedure based on quasi-static loading and an independent knowledge of the Young's modulus, which is easily obtained by standard nanoindentation testing. In theory, the method applies to any indentation strain rate, but in practice, an upper limit on the rate arises from hardware limitations in the testing system. The new methodology is developed and applied to measurements made with an iMicro nanoindenter (KLA, Inc.), in which strain rates up to 100 s−1 were successfully achieved. The origins of the hardware limitations are documented and discussed.

Constant strain rate nanoindentation is a popular technique for probing the local mechanical properties of materials but is usually restricted to strain rates ≤0.1 s−1. Faster indentation potentially results in an overestimation of the hardness because of the plasticity error associated with the continuous stiffness measurement (CSM) method. This can have significant consequences in some applications, such as the measurement of strain rate sensitivity. The experimental strain rate range can be extended by increasing the harmonic frequency of the CSM oscillation. However, with commercial instruments, this is achievable only by identifying higher CSM frequencies at which the testing system is dynamically well behaved. Using these principles, a commercial system operated at the unusually high harmonic frequency of 1570 Hz was successfully used to characterize of the strain rate sensitivity of a Zn22Al superplastic alloy at strain rates up to 1 s−1, i.e., an order of magnitude higher than with standard methods.

A high-temperature nanoindentation system was used to examine the steady state indentation creep behavior of CsHSO4. This high proton conductivity solid-acid material is a candidate for use as a solid-state electrolyte in intermediate temperature fuel cells. Constant strain rate indentation creep tests yielded a stress exponent and a creep activation energy in close agreement with results obtained from previous uniaxial compression testing. The large penetration depths reached during creep testing necessitated validating an indenter area function well beyond depths measurable in fused silica. The developed methodology is material agnostic meaning it can be used for indentation creep measurements in other high creep rate materials. In addition, it is shown how an analysis developed by Bower et al. (Proc. Royal Soc. 441, 97–124, 1993) can be successfully used to convert the indentation creep parameters into the more common material parameters measured in uniaxial creep tests.

From recent nanoindentation experiments, two types of pop-in modes have been identified: a single pop-in with a large displacement excursion and a number of pop-ins with comparable and small displacement excursions. Theoretical analyses are developed here to study the roles played by indenter tip radius, pre-existing defect density, heterogeneous nucleation source type, and lattice resistance on the pop-in modes. The evolution of dislocation structures in earlier pop-ins provides input to modeling a stochastic, heterogeneous mechanism that may be responsible for the subsequent pop-ins. It is found that when the first pop-in occurs near theoretical shear stress, the pop-in mode is determined by the lattice resistance and tip radius. When the first pop-in occurs at low shear stress, whether the successive pop-in mode occurs depends on how the heterogeneous dislocation nucleation source density increases as compared to the increase of the total dislocation density. The above transitions are found to correlate well with the ratio of indenter tip radius to the mean spacing of dislocation nucleation sources.

New experimental methods have been developed to optimize the accuracy and precision of the measured phase angle in nanoindentation experiments on viscoelastic materials performed with a Berkovich indenter. Measurements conducted in fused silica and sapphire form the basis of a new instrument calibration. Experimental verification of the new calibration and an enhanced test method is demonstrated in polycarbonate (PC) and polymethyl methacrylate (PMMA). In comparison to the standard continuous stiffness measurement (CSM) technique, the new calibration and test method reduces the measurement error in the phase angle of PC from 1900% to 10% and from 135% to 10% in PMMA. Scatter in phase angle measured by the new test method is nearly 10 times less than the level observed using the standard CSM technique. The effect of time dependent deformation on the measured phase angle is also documented. The experimental observations and results are applicable to a variety of dynamic nanoindentation test methods.

A simple stochastic model is developed to determine the pop-in load and maximum shear stress at pop-in in nanoindentation experiments conducted with spherical indenters that accounts for recent experimental observations of a dependence of these parameters on the indenter radius. The model incorporates two separate mechanisms: pop-in due to nucleation of dislocations in dislocation-free regions and pop-in by activation of preexisting dislocations. Two different types of randomness are used to model the stochastic behavior, which include randomness in the spatial location of the dislocations beneath the indenter and randomness in the orientation of the dislocations, i.e., randomness in the stress needed to activate them. In addition to correctly predicting the experimentally observed average maximum shear stress at pop-in, the model also correctly describes the scatter in pop-in loads and how it varies with indenter radius. Monte Carlo simulations are used to validate the model and visualize the scatter expected for a limited number of tests.

In-situ tensile tests have been performed in a dual beam focused ion beam and scanning electron microscope on as-grown and prestrained single-crystal molybdenum-alloy (Mo-alloy) fibers. The fibers had approximately square cross sections with submicron edge lengths and gauge lengths in the range of 9–41 μm. In contrast to previously observed yield strengths near the theoretical strength of 10 GPa in compression tests of ∼1–3-μm long pillars made from similar Mo-alloy single crystals, a wide scatter of yield strengths between 1 and 10 GPa was observed in the as-grown fibers tested in tension. Deformation was dominated by inhomogeneous plastic events, sometimes including the formation of Lüders bands. In contrast, highly prestrained fibers exhibited stable plastic flow, significantly lower yield strengths of ∼1 GPa, and stress–strain behavior very similar to that in compression. A simple, statistical model incorporating the measured dislocation densities is developed to explain why the tension and compression results for the as-grown fibers are different.

Extended abstract of a paper presented at Microscopy and Microanalysis 2011 in Nashville, Tennessee, USA, August 7–August 11, 2011.

The method we introduced in 1992 for measuring hardness and elastic modulus by nanoindentation testing has been widely adopted and used in the characterization of mechanical behavior at small scales. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques, as well as advances in our understanding of the mechanics of elastic-plastic contact. In this article, we briefly review the history of the method, comment on its capabilities and limitations, and discuss some of the emerging areas in materials research where it has played, or promises to play, an important role.

The deformation behavior of amorphous selenium near its glass transition temperature (31 °C) has been investigated by uniaxial compression and nanoindentation creep tests. Cylindrical specimens compressed at high temperatures and low strain rates deform stably into barrel-like shapes, while tests at low temperatures and high strain rates lead to fragmentation. These results agree well with stress exponent and kinetic activation parameters extracted from nanoindentation creep tests using a similarity analysis. The dependence of the deformation modes on temperature and strain rate can be understood as a consequence of material instability and strain localization in rate-dependent solids.

A new method is proposed to determine the elastic modulus and residual stress of freestanding thin films based on nanoindentation techniques. The experimentally measured stiffness-displacement response is applied to a simple membrane model that assumes the film deformation is dominated by stretching as opposed to bending. Dimensional analysis is used to identify appropriate limitations of the proposed model. Experimental verification of the method is demonstrated for Al/0.5 wt% Cu films nominally 22 µm wide, 0.55 µm thick, and 150, 300, and 500 µm long. The estimated modulus for the four freestanding films match the value measured by electrostatic techniques to within 2%, and the residual stress to within 19.1%. The difference in residual stress can be completely accounted for by thermal expansion and a modest change in temperature of 3 °C. Numerous experimental pitfalls are identified and discussed. Collectively, these data and the technique used to generate them should help future investigators make more accurate and precise measurements of the mechanical properties of freestanding thin films using nanoindentation.

Extended abstract of a paper presented at Microscopy and Microanalysis 2004 in Savannah, Georgia, USA, August 1–5, 2004.

The frictional behavior of rocks in the laboratory is reasonably well described by rate- and state-variable friction laws, which reproduce a rich variety of natural phenomena when used in models of earthquakes. Despite the widespread adoption of the rate and state formalism in earthquake mechanics, the physical mechanisms that occur at microscopic contacting asperities on the sliding surface, which give rise to the observed rate and state effects, are still poorly understood. In an attempt to identify these underlying mechanisms, a series of nanoindentation experiments on quartz, an abundant mineral in the earth’s crust, was conducted. These experiments demonstrate the utility of using continuous stiffness measurements as a means of obtaining reliable indentation creep data on hard materials like quartz at room temperature. The projected area of indentation in quartz increases linearly with the logarithm of the time of indentation, in agreement with the increase in real area of contact with log time inferred from slide-hold-slide friction experiments on quartz rocks. However, the increase in fractional area with time in the indentation tests was larger than that inferred from friction experiments by a factor of 1.7. Differences between the rates of fractional area increase in the two tests may indicate that the increase in contact area during the hold portion of slide-hold-slide tests was modulated by slip that occurs during reloading after the hold, as was observed for other materials. The nanoindentation results suggest that the increase in frictional strength (i.e., the increase of state in the rate- and state-variable friction laws) during slide-hold-slide friction experiments was caused by creep of the highly stressed asperity contacts.

UV Raman scattering is employed as a nondestructive structure sensitive probe to investigate the vibrational properties of the wide bandgap, machined and indented surfaces of 6H-SiC and β-Si3N4. In these materials, the short absorption depth of UV light allows for accurate probing of the surface, and the transparency to visible light allows for analysis of the bulk material. The study on 6H-SiC (0001) included measurements of indentations, and of machined circular (0001) wafer edges. The indentation analysis indicates the response of the material to localized pressures. Machined 6H-SiC wafer edges and machined β-Si3N4 surfaces indicate a ductile response and ductile material removal for machining at cutting depths on a nm and μm scale. Raman scattering measurements of the ductile surfaces and ductile material removed indicate residual structure changes. The residual surface structures could indicate that a high-pressure phase transformation is the origin of a ductile response on machined brittle materials.

Much of our understanding of the elastic-plastic contact mechanics needed to interpret nanoindentation data comes from two-dimensional, axisymmetric finite element simulations of conical indentation. In many instances, conical results adequately describe real experimental results obtained with the Berkovich triangular pyramidal indenter, particularly if the angle of the cone is chosen to give the same area-to-depth ratio as the pyramid. For example, conical finite element simulations with a cone angle of 70.3° have been found to accurately simulate experimental load-displacement curves obtained with the Berkovich indenter. There are instances, however, where conical simulations fail to capture important behavior. Here, 3D finite element simulations of Berkovich indentation of fused silica are compared to similar simulations with a 70.3° cone. It is shown that a potentially significant difference between the two indenters exists for the contact areas and contact stiffnesses. Implications for the interpretation of nanoindentation data are discussed.

Measurement of material creep parameters by means of nanoindentation using continuous stiffness techniques avoids the problems associated with thermal drift that often plague creep measurements based on the time dependence of the indentation depth alone [1, 2]. Problems with thermal drift are negligible from a practical point of view during continuous stiffness measurements because the contact stiffness can be measured over a short time period, typically less than one second, during which time the displacements due to thermal drift are minimal. Determination of the time dependence of the indentation depth from the stiffness data relies on the well-known relation between contact stiffness and the square root of the contact area. For pyramidal indenters, the true indentation contact depth must be proportional to the contact stiffness, leading to the assumption that indentation depth is also proportional to the contact stiffness. In this study, we critically examine this assumption using data obtained from experiments on a relatively soft material, epoxy, and a relatively hard material, fused quartz. The results show that just after initial load application, the change in contact area may be different than that expected from the change in indentation depth. One possible explanation for the observed behavior is examined by finite element modeling.

A technique based on synchrotron radiation was developed that allows for rapid structural and chemical characterization of ternary alloys over a wide range of composition. The technique was applied to isothermal sections of the Cr–Fe–Ni system grown on Al2O3(0001) sapphire substrates by sequential deposition of layers of graded.thickness followed by annealing to interdiffuse the elements. A film spanning the Cr–Fe–Ni ternary system was measured in 4 h at a resolution of 2 at.% by rastering the sample under a focused beam of synchrotron radiation while simultaneously measuring the diffraction pattern with a charge-coupled device detector to determine crystallographic phases, texture, and lattice parameters and also measuring the x-ray fluorescence with an energy-dispersive detector to determine elemental composition. Maps of phase composition and lattice parameter as a function of composition for several annealing treatments were found to be consistent with equilibrium values. The technique will be useful in combinatorial materials design.

A method of preparing ternary alloy libraries for combinatorial materials development based on thick film deposition and interdiffusion was studied, using the Ni-Fe-Cr ternary system. Specimens were prepared by depositing films onto sapphire substrates with an e-beam evaporation system followed by annealing in a vacuum for interdiffusion. The specimens were examined using cross sectional scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS), scanning Auger microanalysis (SAM), angular resolved x-ray fluorescence (AR-XRF), x-ray diffraction (XRD), and nanoindentation. The method proved an effective way to make the alloy libraries for screening mechanical properties by means of nanoindentation.