The dynamic indentation response of polycrystalline copper under cyclic fatigue loading is studied with a flat cylindrical indenter. First, a simple analytical model shows that in a purely elastic solid, the indentation depth responds with the same wavelength and frequency as the applied sinusoidal fatigue load. Next, a numerical simulation of an indentation fatigue test on an elastic-plastic solid (polycrystalline copper) is performed. Finite element analyses reveal that the mean indentation depth is controlled by both the mean of the indentation fatigue load and the load amplitude, while the amplitude of the indentation depth is independent of the mean load. Further investigations indicate that with an increased number of cycles, the increment of indentation depth reaches a constant rate. The steady state indentation depth rate is dependent not only on the amplitude of indentation fatigue load but also on the fatigue mean load, which is similar to strain accumulation during a conventional fatigue test. A parallel indentation experiment on annealed polycrystalline copper also confirms the effect of the fatigue mean load, indicating consistency with numerical results.

Whenever a nanoindent is placed near an edge, such as the free edge of the specimen or heterophase interface intersecting the surface, the elastic discontinuity associated with the edge produces artifacts in the load–depth data. Unless properly handled in the data analysis, the artifacts can produce spurious results that obscure any real trends in properties as functions of position. Previously, we showed that the artifacts can be understood in terms of a structural compliance, Cs, which is independent of the size of the indent. In the present work, the utility of the SYS (Stone, Yoder, Sproul) correlation is demonstrated in its ability to remove the artifacts caused by Cs. We investigate properties: (i) near the surface of an extruded polymethyl methacrylate rod tested in cross section, (ii) of compound corner middle lamellae of loblolly pine (Pinus taeda) surrounded by relatively stiff wood cell walls, (iii) of wood cell walls embedded in a polypropylene matrix with some poorly bonded wood–matrix interfaces, (iv) of AlB2 particles embedded in an aluminum matrix, and (v) of silicon-on-insulator thin film on substrate near the free edge of the specimen.

In the present paper the formulas for the stiffnesses of a new and more general surface tester concept are given and discussed. The concept is based on the idea that the next generation of surface testers will provide the means to use all degrees of freedom of movement a probe on a sample surface could perform. Thus, in addition to the ordinary normal stiffness, lateral and tilting stiffness are measured, as well as twisting stiffness, and then used in the subsequent parameter determination of the investigated materials. It is shown in the paper that such a concept would not only solve classical problems such as “pileup” and “sink-in” completely, but it would also supersede the need of area-function calibration for the indenter tips and allow direct measurement of local intrinsic and residual stresses, anisotropy, and many other things, too.

In this work, the effects of indenter tip roundness on the load–depth indentation curves were analyzed using finite element modeling. The tip roundness level was studied based on the ratio between tip radius and maximum penetration depth (R/hmax), which varied from 0.02 to 1. The proportional curvature constant (C), the exponent of depth during loading (α), the initial unloading slope (S), the correction factor (β), the level of piling-up or sinking-in (hc/hmax), and the ratio hmax/hf are shown to be strongly influenced by the ratio R/hmax. The hardness (H) was found to be independent of R/hmax in the range studied. The Oliver and Pharr method was successful in following the variation of hc/hmax with the ratio R/hmax through the variation of S with the ratio R/hmax. However, this work confirmed the differences between the hardness values calculated using the Oliver–Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (Wp/Wt) was found to be independent of the ratio R/hmax, which demonstrates that the methods for the calculation of mechanical properties based on the indentation energy are potentially not susceptible to errors caused by tip roundness.

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed on three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

In recent studies, nanoindentation experiments combined with the Oliver and Pharr method (OP method) are frequently used to measure the mechanical properties of “one-dimensional” structural materials (micro/nanowires and nanobelts) regardless of the corresponding assumptions of the OP method. This article reports the numerical simulation studies of the nanoindentations of wire structural materials on elastic-plastic substrates using dimensional analysis and the finite element method. We find that the measured hardness and Young’s modulus of wire structural materials are significantly influenced by their geometries and indenters as well as the mechanical properties of substrates and wires.

Sudden displacement excursions during load-controlled nanoindentation of relatively dislocation-free surfaces of metals are frequently associated with dislocation nucleation, multiplication, and propagation. Insight into the nanomechanical origins of plasticity in metallic crystals may be gained through estimation of the stresses that nucleate dislocations. An assessment of the potential errors in the experimental measurement of nucleation stresses, especially in materials that exhibit the elastic–plastic transition at small indentation depths, is critical. In this work, the near-apex shape of a Berkovich probe was measured by scanning probe microscopy. This shape was then used as a “virtual” indentation probe in a 3-dimensional finite element analysis (FEA) of indentation on 〈100〉-oriented single-crystal tungsten. Simultaneously, experiments were carried out with the real indenter, also on 〈100〉-oriented single-crystal tungsten. There is good agreement between the FEA and experimental load–displacement curves. The Hertzian estimate of the radius of curvature was significantly larger than that directly measured from the scanning probe experiments. This effect was replicated in FEA simulation of indentation by a sphere. These results suggest that Hertzian estimates of the maximum shear stresses in the target material at the point of dislocation nucleation are a conservative lower bound. Stress estimates obtained from the experimental data using the Hertzian approximation were over 30% smaller than those determined from FEA.

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.

Damage response of brittle curved structures subject to cyclic Hertzian indentation was investigated. Specimens were fabricated by bisecting cylindrical quartz glass hollow tubes. The resulting hemicylindrical glass shells were bonded internally and at the edges to polymeric supporting structures and loaded axially in water on the outer circumference with a spherical tungsten carbide indenter. Critical loads and number of cycles to initiate and propagate near-contact cone cracks and far-field flexure radial cracks to failure were recorded. Flat quartz glass plates on polymer substrates were tested as a control group. Our findings showed that cone cracks form at lower loads, and can propagate through the quartz layer to the quartz/polymer interface at lower number of cycles, in the curved specimens relative to their flat counterparts. Flexural radial cracks require a higher load to initiate in the curved specimens relative to flat structures. These radial cracks can propagate rapidly to the margins, the flat edges of the bisecting plane, under cyclic loading at relatively low loads, owing to mechanical fatigue and a greater spatial range of tensile stresses in curved structures.

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.

A unique atomic force microscope-based local thermal-mechanical analysis (LTA) technique was used to study the influence of room temperature aging on viscoelastic properties of ethylene-methacrylic (E/MAA) acid ionomers. This approach permits easy access to structural relaxation effects on viscoelasticity at a short aging time, for instance, before the occurrence of secondary crystallization differential scanning calorimetry (DSC) melting peak. A Burger model along with finite element method yields quantitative analysis of viscoelastic properties versus the aging time. Creep curves were obtained with LTA after various times of aging at room temperature upon cooling from the melt. Measurements were carried out at both 30 and 70 °C. The results reveal the effects of structural relaxation upon aging in the ion-rich amorphous region, the influence of secondary crystallites on the viscoelastic properties, and shed light on the processes associated with aging in E/MAA ionomers.

A finite-element (FE) microstructurally based dislocation density multiple-slip crystalline formulation that is coupled to molecular dynamic (MD) simulations has been used to predict how nanoindentation affects behavior in crystalline gold polycrystals at scales that span the molecular to the continuum level. Displacement profiles from MD simulations of nanoindentation were used to obtain scaling relations, which are based on indented depths, grain sizes, and grain aggregate distributions. These scaling relations are then used in a microstructurally based FE formulation that accounts for dislocation density evolution, crystalline structures, and grain sizes. This hierarchical methodology can be used to ascertain inelastic effects, such as shear-slip distribution, pressure accumulation, and dislocation density and slip-rate evolution at physical scales that are commensurate with ductile behavior at the microstructural scale.

The hydrogen effect on dislocation nucleation in FeAl single crystal with (100) surface orientation has been examined with the aid of a specifically designed nanoindentation setup for in situ electrochemical experiments. The effect of the electrochemical potential on the indent load–displacement curve, especially the unstable elastic-plastic transition (pop-in), was studied in detail. The observations showed a reduction in the pop-in load for both samples due to in situ hydrogen charging, which is reproducibly observed within sequential hydrogen charging and discharging. Clear evidence is provided that hydrogen atoms facilitate homogeneous dislocation nucleation.

A data analysis procedure has been developed to estimate the contact area in an elasto-plastic indentation of a thin film bonded to a substrate. The procedure can be used to derive the elastic modulus and hardness of the film from the indentation load, displacement, and contact stiffness data at indentation depths that are a significant fraction of the film thickness. The analysis is based on Yu's elastic solution for the contact of a rigid conical punch on a layered half-space and uses an approach similar to the Oliver-Pharr method for bulk materials. The methodology is demonstrated for both compliant films on stiff substrates and the reverse combination and shows improved accuracy over previous methods.

In this work the hardening effect of Ta and Mo in Ni-base alloys was investigated using a combinatorial approach with diffusion couples. Furthermore, the Ni-Fe system was used as a reference system taking advantage of the full miscibility at high temperatures. Ta was chosen, as aside from having a technical relevance in the Ni-base superalloys, it also has a high miscibility in Ni. The main focus of this paper will be solid solution hardening. It will be shown that even though the determination of hardness is subject to varying indentation size effects (ISE) [Durst et al., Acta Mater.55(20), 6825 (2007)], only a few modifications are necessary to describe solid solution strengthening measured by nanoindentations using the Labusch theory [Labusch, Acta Metall.20(7), 917 (1972)]. Moreover, after a careful evaluation of the results, the data can be used to investigate solid solution hardening effects quickly and efficiently with small amounts of material.

Atomistic simulations of nanoindentation of a 20-nm-thick Ni thin film oriented in the [111] direction were carried out to study the effects of indenter velocity and radii, interatomic potentials, and the boundary conditions used to represent the substrate. The simulation results were compared directly with experimental results of Ni thin film of the same thickness and orientation. It was found that the high indenter velocity does not affect the hardness value significantly. Different radii used for indentation also have negligible effects on the hardness value. Two different interatomic potentials were tested, giving significantly different hardness values but both within 20% of the experimental result. Different boundary conditions used to represent the substrate have a significant effect for relatively deep indentation simulations.

In this work, we investigated experimentally the various factors influencing the extraction of indentation stress-strain curves from spherical nanoindentation on metal samples using two different tip radii. In particular, we focused on the effects of (i) the surface preparation techniques used, (ii) the presence of a surface oxide layer, and (iii) the occurrence of pop-ins at the elastic-plastic transition on our newly developed data analysis methods for extracting reliable indentation stress-strain curves. Rough mechanical polishing was shown to introduce a large scatter in the measured indentation yield strengths, whereas electropolishing or vibropolishing produced consistent results reflective of the pristine sample. The data analysis techniques used were able to discard the portions of the raw data affected by a thin oxide layer, present on most metal surfaces, and yield reasonable indentation stress-strain curves. Experiments with different indenter tip radii on annealed and cold-worked samples indicated that pop-ins are caused by delayed nucleation of dislocations in the sample under the indenter.

Knowledge of mechanics in atelectasis (alveolar collapse) and reinflation would be useful during anesthesia and critical care. Here an investigation is presented in which atelectasis is induced in a controlled manner on excised inflated lungs using spherical indentation, and noninvasive imaging of the deformed subsurface region is performed using optical coherence tomography (OCT). Indentation loads are physiologic, and spatial dimensions are far larger than alveolar size to allow continuum discussions. Experimental observations of atelectasis are compared with finite element model calculations of maximum stresses. Finally, atelectasis is compared during inflation of lungs with different gases (e.g., air, oxygen/anesthesia mixture).

An analytical solution was derived for the indentation of a cell using atomic force microscopy. It was found that the contribution of the cell membrane to the overall indentation stiffness is dependent on the size of the indenter. When a small indenter [for example, an atomic force microscopy (AFM) tip] is used to probe the mechanical properties of cells, the cell membrane and its prestress were important in interpreting indentation data. The solution allows the partition of contributions from the membrane and the interior soft phase. The apparent elastic modulus of the cell and the prestress of the cell membrane can be extracted. In addition, the modulus of the cell membrane could be estimated from the extracted apparent modulus if the interior soft phase of the cell was known and vice versa. However, when a large indenter is used (for example, a microbead attached to the cantilever beam of the AFM), the contribution of the cell membrane is negligible.

In a statistical nanoindentation study using a spherical probe, the effect of crystallographic orientation on the phase transformation of silicon (Si) was investigated. The occurrence and the contact pressures at which events associated with phase transformation occur, for an indentation force range from 20 to 200 mN, were analyzed and compared for the orientations Si(001), Si(110), and Si(111). It was found that plastic deformation combined with phase transformation during loading was initiated at lower forces (contact pressures) for Si(110) and Si(111) than for Si(001). Also, the contact pressure at which the phase transformation occurred during unloading was strongly influenced by the crystallographic orientation, with up to 38% greater values for Si(110) and Si(111) compared to Si(001). Mapping the residual stress field around indentations by confocal Raman microscopy revealed significant differences in the stress pattern for the three orientations.