Nanomechanical Probes of Single Corneal Epithelial Cells: Shear Stress and Elastic Modulus

Living human corneal epithelial cells have been probed in vitro via atomic force microscopy, revealing the frictional characteristics of single cells. Under cell media, measured shear stresses of 0.40 kPa demonstrate the high lubricity of epithelial cell surfaces in contact with a microsphere probe. The mechanical properties of individual epithelial cells have been further probed through nanometer scale indentation measurements. A simple elastic foundation model, based on experimentally verifiable parameters, is used to fit the indentation data, producing an effective elastic modulus of 16.5 kPa and highlighting the highly compliant nature of the cell surface. The elastic foundation model is found to more accurately fit the experimental data, to avoid unverifiable assumptions, and to produce a modulus significantly higher than that of the widely used Hertz–Sneddon model.     

In Situ Studies of Cartilage Microtribology: Roles of Speed and Contact Area

The progression of local cartilage surface damage toward early stage osteoarthritis (OA) likely depends on the severity of the damage and its impact on the local lubrication and stress distribution in the surrounding tissue. It is difficult to study the local responses using traditional methods; in situ microtribological methods are being pursued here as a means to elucidate the mechanical aspects of OA progression. While decades of research have been dedicated to the macrotribological properties of articular cartilage, the microscale response is unclear. An experimental study of healthy cartilage microtribology was undertaken to assess the physiological relevance of a microscale friction probe. Normal forces were on the order of 50 mN. Sliding speed varied from 0 to 5 mm/s, and two probes radii, 0.8 and 3.2 mm, were used in the study. In situ measurements of the indentation depth into the cartilage enabled calculations of contact area, effective elastic modulus, elastic and fluid normal force contributions, and the interfacial friction coefficient. This work resulted in the following findings: (1) at high sliding speed (V = 1–5 mm/s), the friction coefficient was low (μ = 0.025) and insensitive to probe radius (0.8–3.2 mm) despite the fourfold difference in the resulting contact areas; (2) the contact area was a strong function of the probe radius and sliding speed; (3) the friction coefficient was proportional to contact area when sliding speed varied from 0.05 to 5 mm/s; (4) the fluid load support was greater than 85% for all sliding conditions (0% fluid support when V = 0) and was insensitive to both probe radius and sliding speed. The findings were consistent with the adhesive theory of friction; as speed increased, increased effective hardness reduced the area of solid–solid contact which subsequently reduced the friction force. Where the severity of the sliding conditions dominates the wear and degradation of typical engineering tribomaterials, the results suggest that joint motion is actually beneficial for maintaining low matrix stresses, low contact areas, and effective lubrication for the fluid-saturated porous cartilage tissue. Further, the results demonstrated effective pressurization and lubrication beneath single asperity microscale contacts. With carefully designed experimental conditions, local friction probes can facilitate more fundamental studies of cartilage lubrication, friction and wear, and potentially add important insights into the mechanical mechanisms of OA.     

Lubricity of Surface Hydrogel Layers

Many biological interfaces provide low friction aqueous lubrication through the generation and maintenance of a high water content polymeric surface gel. The lubricity of such gels is often attributed to their high water content, high water permeability, low elastic modulus, and their ability to promote a water film at the sliding interface. Such biological systems are frequently characterized as “soft,” where the elastic moduli are on the order of megapascals or even kilopascals. In an effort to explore the efficacy of such systems to provide lubricity, a thin and soft hydrogel surface layer (~5 μm in thickness) with a water content of over >80 % was constructed on a silicone hydrogel contact lens, which has a water content of approximately 33 %. Nanoindentation measurements with colloidal probes on atomic force microscopy (AFM) cantilevers revealed an exceedingly soft elastic modulus of ~25 kPa. Microtribological experiments at low contact pressures (6–30 kPa) and at slow sliding speeds (5–200 μm/s) gave average friction coefficients below μ = 0.02. However, at higher contact pressures, the gel collapsed and friction loops showed a pronounced stick–slip behavior with breakloose or static friction coefficient above μ = 0.5. Thus, the ability of the soft surface hydrogel layers to provide lubricity is dependent on their ability to support the applied pressure without dehydrating. These transitions were found to be reversible and experiments with different radii probes revealed that the transition pressures to be on the order of 10–20 kPa.     

Intermolecular Forces, Adhesion, and the Elastic Foundation

A model for the elastic contact between a rigid sphere and an ideal elastic foundation with adhesion has been developed. The model was derived by integrating the full Lennard-Jones potential to arrive at a closed-form equilibrium condition that balances surface energy with strain energy. It was found that the separation height is not a function of the penetration. Using this energy criterion for separation of contact in an elastic foundation, a model for the force displacement relationship was then developed. In this derivation there exists a tensile zone of deformation along the perimeter of the contact. The model also reveals a number of unique aspects of the adhesive contact, including: the maximum adhesion occurs when the apex of the sphere is tangent to the plane of the undeformed surface, the maximum adhesion force $ F_{\text{adh}} = - 2\pi R\Updelta \gamma $ , and the contact area is linearly dependent on penetration. The ability to fit high fidelity indentation data from finite-element analysis and molecular dynamics simulation for thin films was demonstrated. Additionally, experiments were performed on thin films (~40 μm) of PDMS using a custom-built microtribometer with in situ optical interferometry that enabled simultaneous measurements of contact area, penetration depths, externally applied force, and the detailed measurements of the free-surface deformations, which include the predicted tensile zone along the perimeter of contact.     

Friction coefficient of soft contact lenses: measurements and modeling

Tribological conditions for contact lenses have very low contact pressures in the range 3–5 kPa and sliding speeds around 12 cm/s. Using a microtribometer a series of experiments was run on commercially available contact lenses made from Etafilcon-A. These tests were run using 10–50 mN of normal load at speeds from 63 to 6280 m/s using a 1-mm radius glass sphere as a pin. The resulting contact pressures are believed to be nearly an order of magnitude larger than the targeted 3–5 kPa. It is hypothesized that the viscoelastic nature of the hydrogel, viscous shearing of the packaging solution, and interfacial shear between the glass sphere and the contact lens all contribute to the friction forces. A model that includes all three of these contributors is developed and compared to the experimental data. The experimental friction coefficients vary from = 0.025 to 0.075. The calculated fluid filmthicknesses were between 1 and 30 nm. The average surface roughness of the lens and the glass sphere are R_a=15 nm and R_a=8 nm, respectively, suggesting that the contact is not in full elastohydrodynamic lubrication. Finally, the largest contributors to the friction force in these experiments were found to be viscous dissipation within the hydrogel and interfacial shear within the contact zone.     

Biomechanical characteristics of the normal medial and lateral porcine knee menisci

The purpose of this investigation was to examine the compressive properties of the porcine meniscus at a variety of topographical locations using a creep indentation experiment. Three different solution techniques were used to analyse the creep response of the tissue. Specifically, the indentation stiffness, aggregate modulus, permeability, Poisson's ratio, and shear modulus were determined at six different testing locations (anterior, central, and posterior regions; femoral and tibial sides) of both the medial and lateral porcine menisci. Results indicate topographical variations among the testing locations, with the femoral-anterior portion of the medial meniscus having the highest indentation stiffness (350+/-110 kPa), aggregate modulus (270+/-90 kPa), and shear modulus (140+/-40 kPa). The tibial-posterior region of the medial meniscus exhibited the lowest indentation stiffness (170+/-40 kPa), aggregate modulus (130+/-30 kPa), and shear modulus (60+/-20 kPa). No statistical differences were found at the six tested locations of the lateral meniscus.     

Effect of elastic modulus mismatch on the contact crack initiation in hard ceramic coating layer

Effect of elastic modulus mismatch on the contact crack initiation is investigated to find major parameters in designing desirable surface-coated system. Silicon nitride coated soft materials with various elastic modulus mismatch,E _c /E _s = 1.06 — 356 are prepared for the analysis. Hertzian contact test is conducted for producing contact cracks and the acoustic emission detecting technique for measuring the critical load of crack initiation. The implication is that coating thickness and material strength are controllable parameters to prevent the initiation of contact cracks resulted from the elastic modulus mismatch in the hard ceramic coating layer on the soft materials.     

Estimations of work hardening exponents of engineering metals using residual indentation profiles of nano-indentation

This study was designed to predict work hardening exponent n of materials from AFM (atomic force microscope) observations of residual indentation impression in sharp indentations. FE simulations of nano-indentation were performed to 140 combinations to each parameter (elastic modulus E, yield stress σ _y , work hardening exponent n, and Poisson’s ratio gv) expressing elastic-plastic behaviors of universal engineering metals. Using the results from FE simulations and dimensional analysis, dimensionless functions were established to correlate residual indentation profiles with the work hardening exponent. This function was examined with nano-indentation, tensile test, and AFM observations after indentation for two materials (Al6061-T6 and copper).     

Temperature-Dependent Atomic Scale Friction and Wear on PbS(100)

Friction and wear on PbS(100) surfaces have been investigated on the atomic scale as a function of temperature with atomic force microscopy. At room temperature and above, the PbS(100) surface exhibited low friction (μ < 0.05) in contact with a silicon nitride probe tip, provided that interfacial wear was not encountered. In the absence of wear, friction increased exponentially with decreasing temperature, transitioning to an athermal behavior near 200 K. An Arrhenius analysis of the temperature dependence of friction yielded an activation energy ∆E = 0.32 ± 0.02 eV for the sliding contact of a silicon nitride tip on PbS(100).     

Energy, Adhesion, and the Elastic Foundation

A theory for elastic contact adhesion between a rigid sphere and an elastic foundation is developed. The theory derives relationships between the contact deformation and the externally applied force. The derivation is based on elastic contact between a sphere and a thin linear-elastic foundation in which the strain energies are balanced by the work of indentation and the change in surface energy. Contacting regimes where there is either compressive strain energy or only tensile strain energy (pull-off regime) are both treated. The model is non-dimensionalized and an order of magnitude analysis is performed in order to develop simplified closed form solutions; the simplified model is then evaluated and compared to the full solution. This theory finds that the adhesion force is significantly larger for an elastic foundation in which the surface elements act independently as compared to more traditional solutions for elastic solids. The theory gives an adhesion force of $ F_{\text{adh}} \cong 7\pi R\Updelta \gamma . $      

Evaluation of friction coefficient using indentation model of Brinell hardness test for sheet metal forming

This work presents an indentation model of the Brinell hardness test, which is a rigid ball-deformable plane contact model (RB-DP model), to elucidate the sliding friction mechanism of sheet metal forming. In the proposed model, the friction force can be defined as a combination of shear (shearing effect) and plough (ploughing effect) forces. The real contact area ratio α is determined from the RBDP model under sliding condition. Moreover, the lateral contact area ratio A _c /A _r can be specified as a function of the real contact area ratio α. Based on Meyer’s law and Hertz contact problem, the maximum contact area ratio α _u , a limiting condition of the real contact area ratio α, can be described as a function of the strain hardening exponent n. Additionally, a limiting condition applies: the strain hardening exponent n must be less than 0.64 in the present model. The present friction model reveals that the friction coefficient μ _d is a function of strain hardening exponent n, the real contact area ratio α and the maximum contact area ratio α _u . The calculated friction coefficient μ _d agrees with the published experimental results.     

On the Pressure Dependence of Shear Strengths in Sliding, Boundary-Layer Friction

Density functional theory, as implemented in a full-potential linearized augmented plane wave method, flair, is used to calculated the pressure-dependent shear strength S of KCl on a Fe(100) substrate and the results are compared to the experimental dependence given by S = S₀ + aP S = S_{0} + \alpha P , where P is the contact pressure and S ₀ = 65 ± 5 MPa and α = 0.14 ± 0.02. Calculations were performed for a KCl bilayer enclosed between two Fe(100) slabs, where the energy was found to vary harmonically as a function of the separation between the outermost layers. Thus, a simple analytical model was developed for the pressure-dependent shear strength of the film, which includes both linear and quadratic pressure dependence. However, the coefficient of the quadratic term was found to be much smaller than the linear term, leading to the linear shear-strength pressure dependence found experimentally. The calculated values of S ₀ 〈10〉 = 64 ± 9 and S ₀ 〈11〉 = 69 ± 8 MPa are in excellent agreement with experiment, while α 〈10〉 and α 〈11〉 equal 0.05 ± 0.01, somewhat lower than, but within the same range as the experimental values.     

Speed and Atmosphere Influences on Nanotribological Properties of NbSe<Subscript>2</Subscript>

Nanotribological properties of NbSe₂ are studied using an atomic friction force microscope. The friction force is measured as a function of normal load and scan speeds ranging from 10 nm s⁻¹ to 40 μm s⁻¹ under two atmospheres (air and argon). At low speed, no effect of atmosphere is noticed and a linear relationship between the friction and normal forces is observed leading to a friction coefficient close to 0.02 for both atmospheres. At high speed, the tip/surface contact obeys the JKR theory and the tribological properties are atmosphere dependent: the shear stress measured in air environment is three times lower than the one measured under argon atmosphere. A special attention is paid to interpret these results through numerical data obtained from a simple athermal model based on Tomlinson approach.     

Friction and Wear Properties of Silicon Carbide in Water from Different Sources

Low friction and low wear of SiC sliding against itself in water at room temperature have been well reported in the past 20 years, and some practical applications have been developed. However, the properties of friction and wear in pure, deionized or distilled water have been mainly observed and not in water from sources in nature. In this article, the fundamental properties of friction and wear between SiC ball and disk are observed in water from ground, river, and sea, and the results are compared with those in deionized water in the viewpoints of modes of lubrication and wear and the resultant values of friction coefficient and wear rate. The smallest friction coefficient (μ_ℓ = 0.005) in steady state is observed in deionized water and the largest (μ_ℓ = 0.013) in sea water. The smallest wear rate (w _s = 2.2 × 10⁻⁷ mm³/Nm) is observed in sea water and the largest (w _s = 3.1 × 10⁻⁷ mm³/Nm) in deionized water. The intermediate values of μ_ℓ and w _s between the smallest and the largest ones are observed in ground and river water. The modes of lubrication and wear, which generated observed values of μ_ℓ and w _s, are considered as mixed lubrication and tribochemical wear. The chemical elements of Na, Cl, Mg, and K in sea water observed on wear particles and pits are thought effective to generate the largest value of μ_ℓ and the smallest value of w _s.     

Boundary element numerical analysis of elastic indentation of a sphere into a bi-layer material

The initial part of load/penetration plot in depth sensing spherical indentation (nano-indentation) is analysed. The results of a numerical study using a specifically developed simulation tool based on the boundary element method are presented.They reveal that the usual linear relationship between the indentation depth and the square of the contact radius for homogeneous materials is also valid in the case of a bi-layer material.It is also shown that the elastic response of the bi-layer material is specific of the coating alone only if the indentation depth, h, is less than 2% of the coating thickness, t.For higher indentation depths (10%>h/t>1%), the macro-elastic response of the composite is seen to saturate with an overall elastic response still containing a contribution of roughly 10% of the coating modulus.The hypothesis of indentation limit h/t<10% of bi-layer material insuring coating-specific response for penetration hardness (Bückle's rule) is roughly two orders of magnitude high when applied by default to the corresponding coating-specific elastic response.     

Atomic Force Microscope Investigation on Static Nanomechanical Properties Versus Dynamic Nanotribological Evaluation of Metal–ZrN and ZrN Thin Films

The present study offers for the first time a correlation between static nanomechanical properties (nanohardness (H), elastic modulus (E), H/E and H ³/E ² ratio) and dynamic properties (resulting from nanoscratch measurements) for Metal–ZrN thin films (Inconel–ZrN, Cr–ZrN and Nb–ZrN) as well as monolayer polycrystalline ZrN thin films. Metal–ZrN thin films have a great industrial potential, as they can combine high hardness with good elasticity and toughness making them effective for wear resistant application. Nanomechanical and nanotribological properties of Metal–ZrN and ZrN thin films deposited by DC unbalanced magnetron sputtering were investigated using an atomic force microscope interfaced with a Hysitron Triboscope. The elastic recovery of thin films under a normal load applied during nanoindentation was evaluated and correlated with elastic recovery of thin films under dynamic loading during nanoscratch measurements in order to asses which film compositions provide superior wear resistance. It is demonstrated that dynamic elastic recovery measurements correlated well with those derived from static nanoindentation tests. The nanoscratch test combines both normal and tangential loading, therefore, it is expected to be an even better predictor of wear-resistance. The AFM nanoindentation and nanoscratch measurements show superior nanomechanical and nanotribological properties for Metal–ZrN thin films when compared to polycrystalline ZrN thin films.     

Study of thin surfactant films under shear using the tribological surface force apparatus

Static and dynamic behaviour of thin surfactant films in aqueous solution of hexadecyltrimethylammonium salicylate (C16TASal) were investigated using the tribological surface force apparatus. Normal force measurements show that 0.15 mM C16TASal builds up an innermost film of approximately 8–11 Å thickness at each mica surface, indicating that the surfactant adsorbs in a flat conformation. Furthermore, the height of the force barrier at approximately 60Å is low (ca 2 mN/m) indicating that the second adsorbed layer is easily pushed out. Addition of salicylate salt to 0.15 mM C16TASal give rise to a more close packed structure, with a total thickness of 62–65 Å, indicative of a micellar or bilayer arrangement at the surfaces. Furthermore, the frequency dependence of the shear modulus was investigated both at close separation at the innermost force barrier and at larger separations (up to 300–400 Å). The visco-elastic measurements show that the elasticity modulus, G′, dominates over the loss modulus, G″, for all studied cases, indicative of a more solid-like than liquid-like film. Finally, it is shown that shear at high contact pressures induces new aggregate structures at the surface.     

The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading

The goal of this paper is to provide the foundation for an analysis of contact between elastic-plastic solids, whose surface roughness is idealized with a Weierstrass profile. To this end, we conduct a parametric study of the plastic deformation and residual stress developed by the two-dimensional contact between a flat, rigid platen and an elastic-perfectly plastic solid with a sinusoidal surface. Our analysis shows that the general characteristics of the deformation can be characterized approximately by two parameters: α = a/λ, where a is the half-width of the contact and λ is the period of the surface waviness; ψ = E^*g/σ_Yλ, where E^* and σ_Y are the effective modulus and yield stress of the substrate, respectively, and g is the amplitude of the surface roughness. Depending on the values of these parameters, we identify eight general types of behavior for the asperity contacts: (a) elastic, elastic-plastic or fully plastic isolated Hertz type contacts; (b) elastic, or elastic-plastic non-Hertzian isolated contacts; and (c) elastic, elastic-plastic or fully plastic, interacting contacts. Relationships between contact pressure, contact size, effective indentation depth and residual stress are explored in detail in each regime of behavior. Implications on rough surface contacts are discussed.     

Exploring the “friction modifier” phenomenon: nanorheology of n‐alkane chains with polar terminus dissolved in n‐alkane solvent

Dilute solutions of two polar end‐functionalized linear alkanes (1‐hexadecylamine and palmitic acid), each dissolved in tetradecane, were confined between two mica surfaces and investigated using a surface forces apparatus modified to study shear nanorheology. These two solutions showed similar nanorheological properties that differed from those observed for pure n‐alkanes. In static measurements, a “hard wall”, rather than an oscillatory force, was observed as a function of film thickness. The polar alkane component formed a weakly adsorbed single layer at each mica surface, disrupting the layered structures found in neat n‐tetradecane. In dynamic experiments at low shear amplitude, the storage modulus G' exceeded the loss modulus G" at low frequencies; above some characteristic frequencies G' increased such that g' ≈ G", indicating significantly more energy loss through viscous modes at higher frequency. When the amplitude was varied at fixed frequency, no stick–slip was observed and the limiting value of the shear stress at high effective shear rate was an order of magnitude less than for unfunctionalized n‐alkanes at similar loads. Together, these results show that the addition of a small amount of polar alkane component, by disrupting the layered structures that would have been formed in the neat n‐alkane, is effective in suppressing static friction and reducing kinetic friction in the boundary lubrication regime. This revised version was published online in July 2006 with corrections to the Cover Date.