We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work-hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.

Indentation studies of polycrystalline heavily work-hardened and annealed oxygen-free copper have been made using spherical indenters of radii 7, 35, 60, 200 and 500 μm. In the case of the 200 and 500 μm radii indenters an instron mechanical testing machine was used for applying the load, whereas for the smaller indenters a UMIS 2000 machine was used. It is shown that the relationship between the mean indentation pressure, Pm and a/R (i.e. indentation stress-strain), where a and R are the radii of the circle of contact and indenter, respectively, is independent of indenter radius, provided the indentation radius, a, is correctly measured. It is also shown that in the case of the work-hardened copper, the departure from the elastic behaviour occurs at Pm ≈ 1.1 Y, where Y is the uni-axial yield stress of the copper. In the case of the annealed copper, although the Pm vs a/R curve for the smallest indenter has the same form as for the 200 and 500 7mu;m radii indenters, the values of Pm, are higher by 50% over the enitre range of a/R. It is discussed that the spherical indentation hardness measurements, using micron-sized spherical indenters, provide a suitable method for estimating the yield stress of thin coatings and surfaces.

Results of nanoindentation experiments on glasses and polymers, carried out at different loading rates and regimes (loading, hold segment and unloading), were compared with simulated models based on rheological principles. The best fit was obtained by combining the rheological elements for elasticity, plasticity and viscosity in series with squares of the indentation depth.

Conventional analysis of load displacement curves in nanoindentation experiments determine modulus by using the elastic portion of the unloading slope or power law fitting the unloading slope. For polymeric materials, however, this analysis is not adequate because they behave viscoelastically. In companion research, L. Cheng has developed analytical models for flat tip and spherical tip indentation using a three element Kelvin-Voigt model, with a spring in series with a parallel dashpot and a spring for compressible and incompressible materials.

Incompressible (v=0.5) polydimethylsiloxane coatings with thicknesses of 2 and 78 microns, a compressible (v=0.33) bulk polystyrene (PS) and a 16 Jim styrene-acrylate block copolymer coating (v=0.33) have been used to verify the models. The polymers were indented using flat tip and spherical tip indenters with a nanoindentation apparatus in creep (constant load) and relaxation modes (constant depth). The data was fit to the analytical models using a non-linear least squares fit algorithm varying three parameters. In general the fitted elastic and shear moduli compared favorably with conventional rheological and mechanical measurements on the same bulk polymers. However, it appears that the agreement for the thin film analysis can be improved by taking the hydrostatic pressure dependence of the modulus and substrate effects into consideration.

Molecular Dynamics simulations have been used to investigate the rheological properties and dynamics of nanoscopically confined lubricating films. Comparative experimental studies of 10 to 20Å thin polymer films confined between mica-type layers explore the dynamics of similar systems, and confirm the computer simulation predictions. The use of model systems of polymers intercalated in layered mica-type silicates facilitates the study of SFA-like geometries with a variety of common analytical techniques, thus dramatically expanding the horizons of studying nanometer wide confined polymer films.

Although self-assembled monolayers (SAMs) are promising candidates for interfacial lubricants in micro-electromechanical systems, the relationship between the monolayer structure and its viscoelastic properties is not understood. Using Acoustic Wave Damping (AWD), we have measured the complex shear modulus of linear alkane thiol monolayers, HS(CH2)n-1 CH3 denoted as Cn, on Au(111)-textured substrates. The AWD technique measures the elastic energy storage and dissipative loss within a SAM adsorbed onto the electrodes of a quartz crystal microbalance. For C12, C14, and C18, SAMs, the storage modulus increases with alkane chain length, but the loss modulus exhibits no systematic correlation. To investigate the origins of energy dissipation, we used a new, high-sensitivity oscillator circuit to simultaneously monitor the adsorption kinetics and acoustic damping during monolayer growth from the gas phase. For both C9 and C12 thiols, the dissipation in the growing monolayer can be correlated with distinct two-dimensional fluid phases and the nucleation and growth of condensed-phase islands.

The surface vibrational spectrum of atactic polypropylene was measured using IR+Visible Sum Frequency Generation (SFG) vibrational spectroscopy, in the temperature range 23 to -50 °C. A sharp rise in the intensity of the C-H symmetric stretch of CH2 groups is observed in the temperature range 0 to -20 °C . The elastic modulus and friction of the same polymer were measured with Atomic Force Microscopy (AFM) in the same temperature range i.e. 23 to -50 °C. There is a sharp rise in the modulus and a sharp decrease in the friction coefficient, at temperatures between 23 and 0 °C. These changes are attributed to the glass transition in atactic polypropylene which is expected to occur in the temperature range 10 to -10 °C. The temperature at which the glass transition is observed, from changes detected in AFM experiments, is higher than that observed by SFG experiments and that expected from bulk measurements. This elevation in the glass transition temperature has been attributed to the high pressure applied to the polymer under the AFM tip.

Micro-indentation with precision displacement rate changes was used to determine the activation volume of polymeric polished cross-sections and coatings. In the un-pigmented clear ABS, the hardness changes with depth were much smaller than those with the activation volume. It was then hypothesized that the thermally activated portion of the flow stress can be separated from the athermal part and a self-consistent model was developed. In the case of silica modified polyester paint, the hardness increase with depth was correlated to the effective increase in the fraction of the particles with increasing deformation volume. The ageing of the polyester could be clearly demonstrated with large reductions in the activation volume with time.

Due to huge uncertainties in the geometric dimensions of atomic force microscopy (AFM) probes, samples' rheological properties and lateral forces are difficult to measure and compare quantitatively. Hence, mathematical calibration methods fail to calibrate AFM probes accurately. To solve this problem, we will introduce in this paper “blind calibration methods” to determine quantitatively lateral forces, elastic constants and viscosity. For lateral force, a geometry factor is used to calibrate any cantilever using this “blind method”. The essential part of this method is a calibration standard sample that is commercially available. We have chosen silicon for our calibration standard sample and will discuss a cleaning procedure for reproducible lateral force measurements. We will provide an absolute friction value, which will serve as one of three parameters necessary to obtain the geometry factor. The other two components being the normal spring constant and the relative friction signal measured with the cantilever of interest. Further, we will discuss force modulation measurements and the problems that occur around resonances. We will provide a procedure to determine elastic constants also based on the silicon calibration standard. Finally, the “blind calibration method” will also be used to achieve kinematic viscosity values.

The responses of viscoelastic solids indented by flat-ended cylindrical and spherical tip indenters are analyzed in this paper. The viscoelastic solid is a semi-infinite medium described by a standard three-element model. The theoretical relaxation and creep solutions are derived for a viscoelastic half-space using the method of functional equations. These solutions can apply to the responses of compressible as well as incompressible coatings to flat-ended cylindrical punch and spherical tip indentation. They establish a fundamental basis for probing mechanical properties of polymeric coatings with micro- and nanoindentation tests. To obtain the strain and stress distributions, an explicit finite difference method is employed to solve a viscoelastic indentation problem. The experimental creep and relaxation tests are conducted on both bulk polystyrene and polyurethane coatings. The viscoelastic properties are derived by fitting the theoretical solutions with the experimental data measured.

Yield stress and modulus of polymeric coatings on polyethylene terephthalate (PET) film have been measured by nanomechanical methods. Yield stresses were found with a simplified version of Johnson's cavity model of elastic-plastic indentation and Tabor's approximation. Moduli were obtained by the tangent method. From creep and relaxation measurements, viscoelastic moduli were extracted with the aid of the standard three-parameter model.

The mechanical properties of four polymer coatings on aluminum foil substrates are examined using nanoindentation with a Hysitron Triboscope, an add-on to an AFM. In addition to static hardness and modulus measurements, the viscoelastic properties of the films, which differ in Tg and extent of crosslinking, are investigated by employing two techniques: using nanoindentation parameters to fit the creep response of the material to a one-dimensional equation based on a three-element Zener model of the viscoelastic behavior of the polymer; and fitting the creep response of the material to a previously developed, three-dimensional model of the response of a viscoelastic material to indentation by a spherical indenter. It is found that the measured static moduli are about 1.5 times greater than results of fitting creep data to the 1-D model, and are a factor of 3–6 times greater than those obtained by fits of the 3-D model.

AFM techniques were used to interrogate the mechanical properties of weathered polyester copolymer sheets near the exposed surface. Tapping mode tips, as well as a diamond tip mounted on a high spring constant cantilever, were used to scratch overlapping quadrilateral patterns into the polymer. The marred sites were micrographed and the RMS roughness was used as an index of brittleness. Propagation speed and normal force of the test cycle were optimized.

The extremely high measurement sensitivity and accuracy has made scanning probe microscopy (SPM) a valuable tool for detecting various kinds of tip surface interactions such as Van der Waals force for AFM, electron tunneling for STM, electric / magnetic forces for EFM/MFM, frictional force for LFM, etc. This paper presents a new technique, SPM nanoindentation technique, for monitoring the repulsive force between the sharp probe and material surface as a means to detect the mechanical properties of materials. The key advantages of SPM nano-indentation are its imaging capability which allows accurate measurement of indentation geometry and precise location of indentation probe for micro-mechanical measurement. This particular study explores the areas of applicability of SPM for measuring mechanical properties such as Young's modulus of materials. Limit studies have been done in understanding the reproducibility of force curves, the effect of surface roughness on force curve, substrate on Young's modulus measurement, etc.. Examples of Young's modulus extraction for organic films will be presented.

The hardness of PVD thin films is of great interests regarding to their applications. It is well known that the hardness is influenced by different deposition energies. For the present work, two different coating processes were used to deposit a CrN layer on high speed steels type HS 6-5-2 (M2). The deposition processes were carried out by the Cathodic Arc Ion Plating Process (AIP) and the Magnetron Sputter Ion Plating Process (MSIP) by varying the deposition energy. The AIP process was used to deposit coatings under a strong ion bombardment. Magnetron Sputtering was used for comparison with the AIP process. The MSIP process is distinguished by a lower emission of ions in contrast to the AIP process.

To evaluate the film hardness of CrN PVD coatings the NanoindenterTM XP was used taking into account the different deposition energies and ionization levels as characteristics of the used deposition processes. A strong chromium ion bombardment leads to a homogenous and uniform coatings structure. As shown in this paper, the film hardness is mainly influenced by the coatings microstructure generated by different deposition energies.

Results from a series of molecular dynamics simulations are reported in which a nanoscale tip was used to indent gold lattices subjected to external strains. The changes in the slope of the loading curves reflect the stress state of the sample. This was true even in the absence of material pile-up, suggesting that the change in loading reflects changes in elastic properties of materials and not a change in contact area due to pile-up. Shallow nanoindentation was also evaluated as a method to map residual surface stresses by simulating indentation at a series of points near a dislocation intersecting a surface. Correlations between the maximum force on the tip and the initial local stresses at the point of indentation were observed. Thus, preliminary atomistic simulations indicate that atomic-force microscopy can be used as a nondestructive, nanoscale probe of the surface stress distributions

The sensitivity of modulus measured by traceably calibrated Depth Sensing Indentation (DSI) is investigated as a function of the indentation parameters: maximum load; loading rate; hold time at maximum load; and single vs. repeated loading. Other issues, including instrument compliance, indenter area function and in-plane anisotropy are also discussed.

To provide comparative assessment for bulge test and indentation mechanical properties, titanium nitride (TiNx) thin films deposited in a r.f. magnetron sputtering system were subjected to both measurements. For this purpose thin layers of titanium nitride (t = 400–700 nm) were grown on the Si(100) wafers containing a layer of free standing low stress (LPCVD) silicon nitride. The composite membranes made of silicon nitride and TiNx were bulged and by means of the rule of mixture formula the mechanical properties of TiNx thin films were extracted. These measurements allowed to investigate the variation of Young's modulus, hardness, and residual stresses of TiNx films versus deposition parameters such as the nitrogen partial pressure and substrate bias voltage. It was found that, at low negative bias (≤ -15 V) stoichiometric thin films of low density and in tensile stress are deposited. Increasing the negative bias increases the initially tensile residual stress to a maximum, then drops to zero and converts to the compressive stress which grows again with further negative bias. At the same time, both modulus and hardness rise monotonously with the substrate bias without any abrupt changes. The nanoindentation modulus extracted from dynamically loading-unloading curves was found to be comparable to the bulge test measurements for denser coatings, but noticeably higher than the bulge test data for porous coatings. The morphology of TiNx films were observed using scanning electron microscopy and the relationships between microstructural evolution of columns and the mechanical properties of coatings are discussed in terms of deposition parameters.

Load controlled nanoindentation in conjunction with a potential step method were utilized for the investigation of precipitated iron sulfate film stresses and growth. Two types of experiments have been undertaken on thin sheet samples of Fe 3% Si single crystal in IM H2SO4. Samples were either allowed to deflect in the indentation direction or constrained. A distinctive difference between the indentation curves for the above two types of tests allowed separation of the effects of film stresses and local electrochemical processes. A proposed theoretical model accounting for both electrochemical and mechanical effects allowed modeling of the indenter tip motion following a potential step. Within the scope of the model, the time dependent film thickness (3.5 μm at maximum), electrostrictive film stress (330 MPa at maximum) have been determined.

A model for the elastic contact between an indenter and a layered half-space allows the projected contact area to be estimated based on measured contact stiffness. In this way, the model allows the hardness to be determined indirectly based solely on load and contact stiffness rather than load and contact area. We apply the approach to Cu, Nb, and Cu/Nb multilayer thin films on Si.