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This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

A generic model has been developed to simulate the effect of phonon interactions during nanoscale sliding with an incommensurate interface. A rigid slider or array of sliders is translated across a 3D elastic slab whose mass elements are harmonically coupled, either in a simple cubic structure (for vast majority of cases) or in a face-centered cubic structure. Each slider interacts with the slab via the Lennard-Jones 6–12 intermolecular potential. Elastic waves are allowed to propagate without any damping and no energy is removed from the system. Boundary conditions are set sufficiently remotely that no significant wave energy returns to the interface from boundary reflection. Simulation results demonstrate that for such nanoscale contacts, (1) the presence of one slider can affect the friction felt by another slider through phonon generation; (2) friction force scales with contact width rather than with contact area; and (3) the friction force may be sensitive to the number of contact regions that comprise a given total area.

In this work, a three-dimensional model for liquid-mediated adhesion between two rough surfaces is presented. The approach is based on a spectral (multi-scale) representation of compressive rough surface deformation along with the capillary equations governing the tensile deformation. An iterative numerical algorithm is designed to solve the equations of elasticity and capillarity simultaneously. It is shown that, under certain conditions, a contact instability occurs leading to unbounded rates of change of tensile force, average gap and wetted radius. The effects of liquid volume, liquid surface tension, surface topography, nominal contact area, and external load on the stability of contact interface are studied. Key dimensionless ratios are identified that govern the equilibrium state and onset of instability.

The frictional interactions of two bodies sliding pass each other is modeled using a modification of the Olami, Feder, Christensen (OFC) spring-block model. The major modification is based on relaxing the assumption of global driving, whereby one can simulate cases of partial contact. The effect of real contact area on several statistical measures of the sliding process is investigated. Scale-independent behavior is observed in the slip sequence size distribution, similar to OFC results, but with a different functional form. Additionally, it is found that the mean and standard deviation of the friction force may be used to determine the number of contact regions as well as a local (asperity-level) friction coefficient.

A liquid film can flow between two solid surfaces in close proximity due to capillary effects. Such flow occurs in natural processes such as the wetting of soils, drainage through rocks, water rise in plants and trees, as well as in engineering applications such as liquid flow in nanofluidic systems and the development of liquid bridges within small-scale devices. In this work, a numerical model is formulated to describe the radial capillary-driven flow between two contacting, elastic, annular rough surfaces. A mixed lubrication equation with capillary-pressure boundary conditions is solved for the pressure within the liquid film and both macro- and micro-contact models are employed to account for solid–solid contact pressures and interfacial deformation. Measurements of interfacial spreading rate are performed for liquids of varying viscosity flowing between an optical flat and a metallic counter surface. Good agreement is found between modeling and experiment. A semi-analytical relation is developed for the capillary flow between the two contacting surfaces.

Aluminum is widely used in electrical contacts due to its electrical properties and inexpensiveness when compared to copper. In this study, we investigate the influence of operating conditions like contact load (pressure), sliding speed, current, and surface roughness on the electrical and tribological behavior of the interface. The tests are conducted on a linear, pin-on-flat tribo-simulator specially designed to investigate electrical contacts under high contact pressures and high current densities. Control parameters include sliding speed, load, current, and surface roughness. The response of the interface is evaluated in the light of coefficient of friction, contact resistance, contact voltage, mass loss of pins, and interfacial temperature rise. As compared to sliding speed, load, and roughness, current is found to have the greatest influence on the various measured parameters. Under certain test conditions, the interface operates in a “voltage saturation” regime, wherein increase in current do not result in any increase in contact voltage. Within the voltage saturation regime the coefficient of friction tends to be lower, a result that is attributed to the higher temperatures associated with the higher voltage (and resulting material softening). Higher interfacial temperatures also appear to be responsible for the higher wear rates observed at higher current levels as well as lower coefficients of friction for smoother surfaces in the presence of current.

The issue of thermal management of two components sliding against each other plays an important role in the proper functioning of the machine components. Jaeger, using his and Blok's hypotheses, presented the curves to compute the average and the maximum temperature rise in square and band shaped interfaces. It is often observed that designers refer to those curves even in scenarios when the contact geometry is different. In many cases, a more accurate temperature distribution is needed and using a constant heat partition to evaluate the temperature rise at the interface can lead to over-design or under-design of the components. In this study the authors apply a recently developed methodology of obtaining the temperature distribution at the interface of two sliding semi-infinite bodies by partitioning the heat between them in such a way that the temperature at every point in the interface is same for both the bodies. Elliptical contacts with a semi-ellipsoidal heat distribution are considered. In order to aid designers, curve fit equations are presented to calculate maximum temperature and average temperature rise in non-dimensional form over a wide range of Peclet numbers, thermal conductivity ratios and ellipticity ratios.

A computational analysis is conducted on a solid–liquid–solid interface: a rough, elastic surface is brought into contact with rigid flat while being influenced by an intervening liquid film of fixed volume. The problem is solved (iteratively) by satisfying the equations of elasticity and capillarity, while conserving liquid volume and honoring the constraints of no surface interpenetration and no negative pressures at dry contact points. As the liquid volume is increased from low values, a critical condition is reached whereby there are sudden increases in the values of certain output parameters, such as tensile force and wetted length. For the smaller values of surface roughness, the critical point is associated with a near complete collapse of the surface topography.

In this work, a numerical method is developed to study the liquid-mediated adhesion between 3D rough surfaces. The presence of a wetting liquid between two rough surfaces generates a negative pressure inside the liquid film, which in turn induces tensile stresses in the contact region. Opposing these tensile stresses are the compressive stresses generated at solid–solid contact spots. An iterative deterministic contact model based on influence coefficients is employed to solve the equations of elasticity and capillarity simultaneously. Results for tensile (adhesive) force, wetted radius, average gap, and contact area between the rough surfaces are obtained. The results show that sudden changes in tensile force, average gap, and contact area occur with an increase in certain parameters, suggesting an elasto-capillary instability and surface collapse.

The interaction between two elastic spheres with an intervening liquid film of given volume is studied theoretically. Using an energy minimization approach, equilibrium contact configurations are determined through numerical computation. Several dimensionless groups are identified that govern the character of the solution. Curve fits are performed to reveal analytical relationships among the dimensionless groups. At extreme values of particular parameters, the curve fits are found to recover the analytical results of the well-known Hertzian and Johnson–Kendall–Roberts elastic (dry contact) models, as well as the force of a liquid bridge between rigid spheres. Qualitative agreement is found between the current model and some published experiments.

An approximate analytical model is proposed to describe the process of separating a sphere from a flat in the presence of a Newtonian liquid, under conditions of constant force. The model is based on consideration of the effects of sphere inertia in characterizing the critical point of separation—namely, that there is a sudden onset of significant sphere acceleration. Good agreement is found between the predictions of the analytical model with those of a full numerical simulation.

The interaction between two elastic half-spaces coupled by a small liquid bridge is investigated theoretically. A non-dimensional number, Nc, is found to govern the interface stability. When Nc is greater than or equal to 1, the two surfaces jump into solid–solid contact. Once this occurs, the contact area will continue to expand until the two surfaces are in full contact.

A recent study showed that for a liquid bridge of volume Vo interposed between two half-spaces and originally separated by uniform gap H, the interface stability was determined by a single dimensionless parameter. When the parameter exceeds a certain value, the interface loses stability and the solid surfaces come into contact. Further, once contact is made, the contact zone will continue to spread without bound. In the present work, the interaction between two curved elastic bodies coupled via a small liquid bridge is investigated. The equilibrium configurations are determined by minimizing the total free energy stored in the interface among all provisional equilibrium configurations; i.e., those configurations consistent with the equations of elasticity and capillarity. In the case of curved bodies, the stability of the interface is governed by the above parameter as well as by a dimensionless ratio involving the liquid volume (Vo), the composite radius (R) and the original (undeformed) minimum sphere–sphere separation (H). When the interface becomes unstable, solid–solid separation cannot be sustained and contact ensues. The resulting solid–solid contact radius is found to depend on the above parameters as well as on the ratio of solid–liquid and liquid–air surface energies. Based on the numerical calculations, simple relations are found between the contact radius and the other relevant parameters.

This paper reports on a feasibility study in the detection of nanometer thick lubricated regions on a hard disk by a novel use of a Kelvin probe. A nonvibrating Kelvin probe was constructed and used to measure the voltages between the copper surface of the probe and a hard disk partially-lubricated with a perfluoropolyether. The probe, constructed of a shielded 1.6 mm diameter gold-coated copper wire, was fixed above the hard disk and the probe voltage was obtained as a function of the speed of the disk and lubricant thickness. The probe generates an electrical signal as the interface between the lubricated and unlubricated regions is crossed. Results show that the probe can distinguish between regions on the hard disk that contain 3 and 10 nm thick lubricant films.

Previous friction measurements in the magnetic head-disk interface (HDI) indicated some anomalous friction force behavior with low sliding speeds (.25 mm/s to 0.25 m/s) and lubricant film thicknesses in the range of 20–80 nm, showing decreasing friction force with increasing apparent shear rate. The physical explanation for such behavior has not yet been established. Possible explanations for such behavior have included dramatic shear thinning, interfacial slip and partial loss of contact with the lubricant film due to slider tipping. In the present study, we investigate the possibility of slider tipping as an explanation for the decreasing friction force with increasing sliding speed. Measurements with an optical probe indicate that slider tipping does not occur for the conditions tested. Numerical analysis of slider equilibrium also supports this conclusion.

Further increase in magnetic recording density requires a reduction in slider flying height. The current study employs the short-bearing approximation to determine analytically the static equilibrium configuration of a slider supported by a starved liquid bearing that operates between ideally smooth surfaces. The solution incorporates rheological behavior based on previously acquired data. The accuracy of the short-bearing approximation is assessed by determining how well the resulting solution satisfies the Reynolds equation. The analysis suggests a means of designing a slider to achieve head/medium spacings in the neighborhood of 20 nm.

Lubricant rheology governs the friction in any lubricated contact. In hydrodynamic lubrication, the genesis of friction is well-understood. However, when asperity contacts occur, the situation becomes more complex. In this “mixed” lubrication regime, it is known that lubricants can deviate dramatically from Newtonian behavior, but the source of this effect has not been identified. In particular, the question arises as to whether the non-Newtonian behavior of the lubricant is due to the extreme thinness of the film or to the very large shear rates to which it is subjected. In the current work, we analyze friction force measurements in the magnetic slider/disk interface to help resolve this question. Because of its precision geometry, the slider/disk interface is ideal for such an investigation. Results of the analysis indicate (1) the lubricant retains its bulk viscosity in films as thin as 11–12 molecular diameters; (2) the rheological state of the lubricant is determined by a parameter we introduce here as the “Newtonian” shear stress, and (3) the rheology of the lubricant at high Newtonian shear stress may indicate a newly discovered property of liquids.

The well-known problem of stiction in a magnetic disk drive largely depends on the forces induced by the presence of a thin liquid film. It is commonly recognized that both adhesive and viscous effects contribute to the magnitude of the stiction force, but is is not known what relative roles the two effects have in a lubricated contact. In the present work, the nature of adhesive and viscous effects is investigated for the slider/disk interface under conditions of constant-speed sliding. Friction measurements are conducted over a range of sliding speeds, 0.25-250 mm/s, with eight perfluoropolyether (PFPE) lubricants applied in various thicknesses, 0-6.6 nm, to carbon-coated magnetic thin-film disks. The lubricants were selected to cover a broad range of viscosities. For several sliding speeds and lubricant film thicknesses, the friction force is found to decrease significantly with increasing sliding speed for all lubricants. In several instances, large friction forces are observed at the lowest sliding s...

One of the key obstacles precluding the maturation and commercialization of planar solid oxide fuel cells has been the absence of a robust sealant. A computational model has been developed in conjunction with leakage experiments at Oak Ridge National Laboratory. The aforementioned model consists of three components: a macroscopic model, a microscopic model, and a mixed lubrication model. The macroscopic model is a finite element representation of a preloaded metal-metal seal interface, which is used to ascertain macroscopic stresses and deformations. The microscale contact mechanics model accounts for the role of surface roughness in determining the mean interfacial gap at the sealing interface. In particular, a new multiscale fast Fourier transform-based model is used to determine the gap. An averaged Reynolds equation derived from mixed lubrication theory is then applied to approximate the leakage flow across the rough annular interface. The composite model is applied as a predictive tool for assessing how certain physical parameters (i.e., seal material composition, compressive applied stress, surface finish, and elastic thermophysical properties) affect seal leakage rates. The leakage results predicted by the aforementioned computational leakage model are then compared with experimental results.

In many tribological investigations, the measurement of friction is complicated by the vibrational characteristics of the transducer. In particular, when a mechanical force transducer is excited, the static calibration factor no longer provides the friction force in the interface. In a recent study (Streator and Bogy, 1992), the problem of determining the friction force from a measurement of the periodic bending strain in a cantilever-mass transducer was solved using the equations of Euler-Bernoulli beam theory. The method showed that modelling the transducer as a single degree-of-freedom (DOF) system could lead to inaccuracies depending on the frequency content of the friction force, and depending on whether a measurement of beam strain or mass displacement was available. Employing the Euler-Bernoulli analysis, however, requires substantially greater analytical and computational effort. In the present work a two DOF model is considered which represents a compromise between the simplicity of the single DOF model and the accuracy of the more thorough analysis. Force computations are made for a simulated slider/disk tribological contact at different frequencies of disk rotation. One set of computations is performed based on knowledge of the beam strain and the other based on knowledge of the mass displacement. It is found that the friction force computed from the two DOF model compares well with that of the Euler-Bernoulli analysis for an extended range of frequencies as against the single DOF model, but loses accuracy at high frequencies. Nevertheless, if used in a careful manner, the two DOF model offers an improved method of determining dynamic friction forces for certain applications.

A critical factor in the successful operation of an electromagnetic launcher (EML) is the maintenance of good electrical contact between the armature and rail. While there have been numerous experimental and theoretical investigations of armature-rail interfaces, a well-accepted model of the contact conditions has not yet been established. In the current study, we consider the interface between a stationary metallic flat and a translating pin with a hemispherical tip. Operating conditions of the experiments are designed to yield the contact pressures (∼500 MPa) and electrical current densities (∼5 GA/m2 ) existing in typical EMLs, albeit with much lower sliding speeds (∼3 m/s). Electrical current to the interface is supplied by a programmable 8V/350A power supply. The test apparatus is configured so that the pin can translate continuously along a 1.5 m rail, its carriage being powered by a direct drive linear motor. Loading of the pin against the flat is provided by means of a pneumatic actuator. Current, voltage, load, friction, surface temperature and position are monitored throughout the sliding event. Changes in surface topography and morphology are assessed via optical and stylus profilometry as well as optical microscopy. Arcing and phase change events are observed.Copyright © 2006 by ASME