Finite-element analysis of contact between elastic self-affine surfaces

Surface Depassivation via B-O Dative Bonds Affects the Friction Performance of B-Doped Carbon Coatings

Boron doping of diamond-like carbon coatings has multiple effects on their tribological properties. While boron typically reduces wear in cutting applications, some B-doped coatings show poor tribological performance compared with undoped films. This is the case of the tribological tests presented in this work in which an alumina ball is placed in frictional contact with different undoped and B-doped amorphous carbon coatings in humid air. With B-doped coatings, a higher friction coefficient at a steady state with respect to their undoped counterparts was observed. Estimates of the average contact shear stress based on experimental friction coefficients, surface topographies, and Persson's contact theory suggest that the increased friction is compatible with the formation of a sparse network of interfacial ether bonds leading to a mild cold-welding friction regime, as documented in the literature. Tight binding and density functional theory simulations were performed to investigate the chemical effect of B-doping on the interfacial properties of the carbon coatings. The results reveal that OH groups that normally passivate carbon surfaces in humid environments can be activated by boron and form B-O dative bonds across the tribological interfaces, leading to a mild cold-welding friction regime. Simulations performed on different tribological pairs suggest that this mechanism could be valid for B-doped carbon surfaces in contact with a variety of materials. In general, this study highlights the impact that subtle modifications in surface and interface chemistry caused by the presence of impurities can have on macroscopic properties, such as friction and wear.

Molecular simulations of sliding on SDS surfactant films

We use molecular dynamics simulations to study the frictional response of monolayers of the anionic surfactant sodium dodecyl sulfate and hemicylindrical aggregates physisorbed on gold. Our simulations of a sliding spherical asperity reveal the following two friction regimes: at low loads, the films show Amonton's friction with a friction force that rises linearly with normal load, and at high loads, the friction force is independent of the load as long as no direct solid-solid contact occurs. The transition between these two regimes happens when a single molecular layer is confined in the gap between the sliding bodies. The friction force at high loads on a monolayer rises monotonically with film density and drops slightly with the transition to hemicylindrical aggregates. This monotonous increase of friction force is compatible with a traditional plowing model of sliding friction. At low loads, the friction coefficient reaches a minimum at the intermediate surface concentrations. We attribute this behavior to a competition between adhesive forces, repulsion of the compressed film, and the onset of plowing.

Predicting frictional aging from bulk relaxation measurements

The coefficient of static friction between solids normally increases with the time they have remained in static contact before the measurement. This phenomenon, known as frictional aging, is at the origin of the difference between static and dynamic friction coefficients but has remained difficult to understand. It is usually attributed to a slow expansion of the area of atomic contact as the interface changes under pressure. This is however challenging to quantify as surfaces have roughness at all length scales. In addition, friction is not always proportional to the contact area. Here we show that the normalized stress relaxation of the surface asperities during frictional contact with a hard substrate is the same as that of the bulk material, regardless of the asperities' size or degree of compression. This result enables us to predict the frictional aging of rough interfaces based on the bulk material properties of two typical polymers: polypropylene and polytetrafluoroethylene.

Acceleration of Diels-Alder reactions by mechanical distortion

Challenges in quantifying how force affects bond formation have hindered the widespread adoption of mechanochemistry. We used parallel tip-based methods to determine reaction rates, activation energies, and activation volumes of force-accelerated [4+2] Diels-Alder cycloadditions between surface-immobilized anthracene and four dienophiles that differ in electronic and steric demand. The rate dependences on pressure were unexpectedly strong, and substantial differences were observed between the dienophiles. Multiscale modeling demonstrated that in proximity to a surface, mechanochemical trajectories ensued that were distinct from those observed solvothermally or under hydrostatic pressure. These results provide a framework for anticipating how experimental geometry, molecular confinement, and directed force contribute to mechanochemical kinetics.

Robust microscale structural superlubricity between graphite and nanostructured surface

Structural superlubricity is a state of nearly zero friction and no wear between two contacted solid surfaces. However, such state has a certain probability of failure due to the edge defects of graphite flake. Here, we achieve robust structural superlubricity state between microscale graphite flakes and nanostructured silicon surfaces under ambient condition. We find that the friction is always less than 1 μN, the differential friction coefficient is on the order of 10^-4, without observable wear. This is attributed to the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminate the edge interaction between the graphite flake and the substrate. This study not only challenges the traditional understanding in tribology and structural superlubricity that rougher surfaces lead to higher friction and lead to wear, thereby reducing roughness requirements, but also demonstrates that a graphite flake with a single crystal surface that does not come into edge contact with the substrate can consistently achieve robust structural superlubricity state with any non-van der Waals material in atmospheric conditions. Additionally, the study provides a general surface modification method that enables the widespread application of structural superlubricity technology in atmospheric environments.

Surface topography as a material parameter

ABSTRACT

Materials science is about understanding the relationship between a material's structure and its properties-in the sphere of mechanical behavior, this includes elastic modulus, yield strength, and other bulk properties. We show in this issue that, analogously, a material's surface structure governs its surface properties-such as adhesion, friction, and surface stiffness. For bulk materials, microstructure is a critical component of structure; for surfaces, the structure is governed largely by surface topography. The articles in this issue cover the latest understanding of these structure-property connections for surfaces. This includes both the theoretical basis for how properties depend on topography, as well as the latest understanding of how surface topography emerges, how to measure and understand topography-dependent properties, and how to engineer surfaces to improve performance. The present article frames the importance of surface topography and its effect on properties; it also outlines some of the critical knowledge gaps that impede progress toward optimally performing surfaces.

Elastic contact of random surfaces with fractal and Hurst effects

Most of the recent research on random surface contact mechanics has been on self-affine surfaces. In such models, the fractal dimension (which represents the ‘roughness’) and the Hurst parameter (which represents the ‘spatial memory’) are linearly dependent. In this study, we investigate the non-adhesive, frictionless contact between elastic solids with non-self-affine manifolds. In particular, we use Cauchy and Dagum covariance functions, which can decouple the fractal and Hurst effects, to describe the height distribution of the random surfaces. A numerical model based on the Boussinesq point load fundamental solutions is employed along with the discrete convolution FFT method to perform the contact analysis. We investigate the true contact area evolution under increasing load for surfaces with a wide range of fractal and Hurst parameters. It is observed that the contact area evolution at light loads is almost independent of the Hurst parameter and non-monotonically dependent on the fractal dimension. By contrast, previous studies predicted the contact evolution to be weakly dependent on the Hurst parameter and the fractal dimension. The curvature of the plots of the slope of the contact area evolution is found to depend on the fractal dimension, contrary to previous studies, which predicted either convexity or concavity.

Structural Analysis and Experimental Study on the Spherical Seal of a Subsea Connector Based on a Non-Standard O-Ring Seal

Underwater oil and gas pipelines are prone to alignment differences and angle offsets during docking, and the spherical flange connector can address this problem. Its main function is to enable compensation of the different angles of the pipeline during docking and to apply a non-standard spherical sealing structure using O-rings to the connection. In this paper, the study of a spherical sealing structure using O-rings was based on a spherical structural model of the connector. The Mooney–Rivlin constitutive equation and material parameters of the O-ring were determined according to nonlinear theory. The structure of the non-standard spherical sealing groove was designed and analysed with reference to the standard sealing groove, the calculation expression of the spherical groove specific size was deduced, and the width and depth of the groove were determined. A finite element analysis of the non-standard O-ring sealing structure was carried out using ANSYS Workbench software; the effects of different pressures and compression ratios on the O-ring sealing performance were analysed and studied in terms of von Mises stress, contact pressure and contact width of different contact surfaces so as to determine a more reasonable compression ratio in the sealing structure. Finally, the theoretical analysis of the non-standard spherical sealing structure using O-rings was validated by testing, and it was proven that it could maintain a good seal under high pressure.

An experimental study on the relation between friction force and real contact area

Classical laws of friction suggest that friction force is proportional to the normal load and independent of the nominal contact area. As a great improvement in this subject, it is now widely accepted that friction force is proportional to the real contact area, and much work has been conducted based on this hypothesis. In present study, this hypothesis will be carefully revisited by measuring the friction force and real contact area in-site and real-time at both normal loading and unloading stages. Our experiments reveal that the linear relation always holds between friction force and normal load. However, for the relation between friction force and real contact area, the linearity holds only at the loading stage while fails at the unloading stage. This study may improve our understanding of the origin of friction.

Dynamic Analysis of the Rod-Fastened Rotor Considering the Characteristics of Circumferential Tie Rods

The research on the dynamic performance of the rod-fastened rotor (RFR) has always been a hotspot. However, the structural complexity of RFR has brought significant challenges to the dynamic study of the RFR. The tie rods provide preload for the rotor shaft segment, while the coordinate deformation of the tie rods will occur during the process of vibration. In addition, the tie rods and the rotor shaft segments are structurally connected in parallel. These factors all will influence the dynamic performance of the RFR. In this paper, for a RFR system, the vibration equation of the RFR considering all factors of the tie rods is deduced in detail. The influence of various factors on the dynamic performance of the rotor is investigated. Results show that the preload directly affects the dynamic performance of the RFR system. When the preload is small, the tie rod has a larger influence on the natural frequencies of the rotor. However, when the preload force reaches a certain value, the influence of the tie rod on the natural frequencies of the rotor is almost negligible. The research results provide a theoretical reference for the understanding of and further research on RFR.

The effects of contact atom distribution at the interface on the phonon transport

At the nanometer scale, heat (phonon) transport is sensitive to the contact details at the interface due to the phonon wave property. However, the effects of contact atom distribution are ignored. In this work, the atomic Green's function (AGF) method and molecular dynamics (MD) simulation are applied to explore those effects. A parameter named as the average distance d[combining macron] is raised here to measure the distribution of contacted atoms at the interface. Based on the AGF method, phonon transmission profiles at different d[combining macron] (distribution) with the same number of contacted atoms have a coincident point, the reverse frequency fr. If the phonon frequency f is smaller (larger) than fr, smaller d[combining macron] has smaller (larger) phonon transmission. The overlap of the vibrational density of states from the MD simulation and the local density of states from the AGF method indicate that the reverse frequency is caused by the match degree of vibration modes across the interface. The existence of reverse frequency leads to the reverse temperature Tr. Increasing the contact area or the interfacial coupling strength can cause the blue shift of fr and the increase of Tr. The MD simulations observe a larger temperature jump at the interface for larger d[combining macron], similar to that from the AGF method at temperatures higher than Tr due to the high-temperature limit property in MD. The results are independent of the choice of cutoff distance in potential and interfacial coupling strength, indicating that the conclusion here is applicable for the general interface.

Two-dimensional finite element analysis of elastic adhesive contact of a rough surface

Adhesive contact of a rigid flat surface with an elastic substrate having Weierstrass surface profile is numerically analyzed using the finite element method. In this work, we investigate the relationship between load and contact area spanning the limits of non-adhesive normal contact to adhesive contact for various substrate material properties, surface energy and roughness parameters. In the limit of non-adhesive normal contact, our results are consistent with published work. For the adhesive contact problem, we employ Lennard-Jones type local contact interaction model with numerical regularization to study the transition from partial to full contact including jump-to-contact instabilities as well as load-depth hysteresis. We have investigated evolution of bonded contact area and pull-off force for various surface roughness parameters, substrate material properties and surface energy. We have identified two non-dimensional parameters to adequately explain experimentally observed adhesion weakening and strengthening phenomena. A design chart of the relative pull-off force as function of non-dimensional parameters is also presented.

Linking energy loss in soft adhesion to surface roughness

A mechanistic understanding of adhesion in soft materials is critical in the fields of transportation (tires, gaskets, and seals), biomaterials, microcontact printing, and soft robotics. Measurements have long demonstrated that the apparent work of adhesion coming into contact is consistently lower than the intrinsic work of adhesion for the materials, and that there is adhesion hysteresis during separation, commonly explained by viscoelastic dissipation. Still lacking is a quantitative experimentally validated link between adhesion and measured topography. Here, we used in situ measurements of contact size to investigate the adhesion behavior of soft elastic polydimethylsiloxane hemispheres (modulus ranging from 0.7 to 10 MPa) on 4 different polycrystalline diamond substrates with topography characterized across 8 orders of magnitude, including down to the angstrom scale. The results show that the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. Further, the energy loss during contact and removal is equal to the product of the intrinsic work of adhesion and the true contact area. These findings provide a simple mechanism to quantitatively link the widely observed adhesion hysteresis to roughness rather than viscoelastic dissipation.

Effect of Roughness and Elasticity on Interactions between Charged Colloidal Spheres

The effects of realistic roughness and elasticity on the interactions between charged silica spheres are studied as a function of surface potential, screening length, interfacial energy, and roughness. The repulsive force F_rep that must be overcome to bring charged spheres into contact is relatively insensitive to elasticity unless spheres are hundreds of times softer than silica. F_rep is also insensitive to roughness and interfacial energy. In contrast, roughness has a large effect on the binding energy of spheres and the force F_sep to separate them. Both are lowered by 1 to 2 orders of magnitude by the measured surface roughness of less than 1 nm on 1 μm silica spheres. The reason is that interactions between rigid spheres are dominated by the highest surface peaks rather than the entire spherical surface. Elasticity can increase the pull-off force of rough spheres by a factor of 2 or more because additional surface area can be brought into contact. The implications of these results for shear-thickening transitions are discussed.

Fluorescence microscopy visualization of the roughness-induced transition between lubrication regimes

We investigate the transition between different regimes of lubrication and directly observe the thickness of nanometric lubrication films with a sensitivity of a single molecular layer at a multi-asperity interface through fluorescence microscopy. We redefine specific film thickness as the ratio of the lubricant film thickness and the surface roughness measured only at those regions of the interface where the gap is "minimal." This novel definition of specific film thickness successfully captures the transition from full elastohydrodynamic lubrication to mixed and boundary lubrication. The transition can be triggered by increasing the surface roughness and is accurately predicted by using the new film thickness definition. We find that when the liquid carries part of the load, its apparent viscosity is greatly increased by confinement, and show how the transition between different lubrication regimes is well described by the viscosity increase and subsequent glass transition in the film.

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius [Formula: see text] governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding [Formula: see text] presents a pseudogap [Formula: see text], where θ is a nonuniversal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudogap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite-size effect, while the slip nucleation radius [Formula: see text] diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

Finite Element Method-Based Skid Resistance Simulation Using In-Situ 3D Pavement Surface Texture and Friction Data

Skid resistance is an important surface characteristic that influences roadway safety. Various studies have been performed to understand the interaction between pavement and tires through numerical simulation for skid resistance prediction. However, the friction parameters required for simulation inputs are generally determined by objective assumptions. This paper develops a finite element method (FEM)-based skid resistance simulation framework using in-situ 3D pavement surface texture and skid resistance data. A 3D areal pavement model is reconstructed from high resolution asphalt pavement surface texture data. The exponential decay friction model is implemented in the simulation and the interface friction parameters required for the simulation are determined using the binary search back-calculation approach based on a trial process with the desired level of differences between simulated and observed skid numbers. To understand the influence of texture characteristics on interface friction parameters, the high-resolution 3D texture data is separated into macro- and micro-scales through Butterworth filtering and various areal texture indicators are calculated at both levels. Principal component analysis (PCA) regression analysis is conducted to quantify the relationship between various texture characteristics and the interface friction parameters. The results from this study can be used to better prepare the inputs of friction parameters for FEM simulation.

Contact-Patch-Size Distribution and Limits of Self-Affinity in Contacts between Randomly Rough Surfaces

True contact between solids with randomly rough surfaces tends to occur at a large number of microscopic contact patches. Thus far, two scaling regimes have been identified for the number density n ( A ) of contact-patch sizes A in elastic, non-adhesive, self-affine contacts. At small A, n ( A ) is approximately constant, while n ( A ) decreases as a power law at large A. Using Green’s function molecular dynamics, we identify a characteristic (maximum) contact area A c above which a superexponential decay of n ( A ) becomes apparent if the contact pressure is below the pressure p cp at which contact percolates. We also find that A c increases with load relatively slowly far away from contact percolation. Results for A c can be estimated from the stress autocorrelation function G σ σ ( r ) with the following argument: the radius of characteristic contact patches, r c , cannot be so large that G σ σ ( r c ) is much less than p cp 2 . Our findings provide a possible mechanism for the breakdown of the proportionality between friction and wear with load at large contact pressures and/or for surfaces with a large roll-off wavelength.

On the Proportionality Between Area and Load in Line Contacts

The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor κ . In its common definition, the reduced pressure contains the root-mean-square gradient (RMSG) of the surface. Although easy to measure, the RMSG of the entire surface does not coincide, at small loads, with the RMSG over the actual contact area g ¯ r , which gives a better description of the contact between rough surfaces. It was recently shown that, for Hertzian contacts, linearity between area and load is indeed obtained only if the RMSG is determined over the actual contact area. Similar to surface contacts, in line contacts, numerical data are often studied using theories that predict linearity by design. In this work, we revisit line contact problems and examine whether or not the assumption of linearity for line contacts holds true. We demonstrate, using Green's function molecular dynamics simulations, that κ for line contacts is not a constant: It depends on both the reduced pressure and the Hurst exponent. However, linearity holds when the RMSG is measured over the actual contact area. In that case, we could compare κ for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using g ¯ r in the original model of Greenwood and Williamson, a value is obtained that is surprisingly in good agreement with our numerical results for rough surface contacts.

Chemical aging of large-scale randomly rough frictional contacts

It has been shown that contact aging due to chemical reactions in single asperity contacts can have a significant effect on friction. However, it is currently unknown how chemically induced contact aging of friction depends on roughness that is typically encountered in macroscopic rough contacts. Here we develop an approach that brings together a kinetic Monte Carlo model of chemical aging with a contact mechanics model of rough surfaces based on the boundary element method to determine the magnitude of chemical aging in silica-silica contacts with random roughness. Our multiscale model predicts that chemical aging for randomly rough contacts has a logarithmic dependence on time. It also shows that friction aging switches from a linear to a nonlinear dependence on the applied load as the load increase. We discover that surface roughness affects the aging behavior primarily by modifying the real contact area and the local contact pressure, whereas the effect of contact morphology is relatively small. Our results demonstrate how understanding of chemical aging can be translated from studies of single asperity contacts to macroscopic rough contacts.

Adhesion between rubber and glass in dry and lubricated condition

We study the adhesion between differently processed glass and filled bromobutyl rubber in dry conditions, in water, and in silicone oil. The boundary line between contact and non-contact in adhesion experiments can be considered as a mode I crack, and we show that viscoelastic energy dissipation, close to the opening (or closing) crack tip and surface roughness, strongly affects the work of adhesion. We observe strong adhesion hysteresis and, in contrast to the Johnson-Kendall-Roberts theory prediction for elastic solids, this results in a pull-off force (and work of adhesion) which depends on the loading force and contact time. In particular, for the system immersed in water and silicone oil, we register very weak adhesive bonding. For glass ball with baked-on silicone oil, the pull-off force is nearly independent of the contact time, but this is not observed for the unprocessed glass surface.

Numerical simulation of high-temperature thermal contact resistance and its reduction mechanism

High-temperature thermal contact resistance (TCR) plays an important role in heat-pipe-cooled thermal protection structures due to the existence of contact interface between the embedded heat pipe and the heat resistive structure, and the reduction mechanism of thermal contact resistance is of special interests in the design of such structures. The present paper proposed a finite element model of the high-temperature thermal contact resistance based on the multi-point contact model with the consideration of temperature-dependent material properties, heat radiation through the cavities at the interface and the effect of thermal interface material (TIM), and the geometry parameters of the finite element model are determined by simple surface roughness test and experimental data fitting. The experimental results of high-temperature thermal contact resistance between superalloy GH600 and C/C composite material are employed to validate the present finite element model. The effect of the crucial parameters on the thermal contact resistance with and without TIM are also investigated with the proposed finite element model.

Molecular probes reveal deviations from Amontons' law in multi-asperity frictional contacts

Amontons’ law defines the friction coefficient as the ratio between friction force and normal force, and assumes that both these forces depend linearly on the real contact area between the two sliding surfaces. However, experimental testing of frictional contact models has proven difficult, because few in situ experiments are able to resolve this real contact area. Here, we present a contact detection method with molecular-level sensitivity. We find that while the friction force is proportional to the real contact area, the real contact area does not increase linearly with normal force. Contact simulations show that this is due to both elastic interactions between asperities on the surface and contact plasticity of the asperities. We reproduce the contact area and fine details of the measured contact geometry by including plastic hardening into the simulations. These new insights will pave the way for a quantitative microscopic understanding of contact mechanics and tribology.

Amontons’ law assumes that friction and normal forces depend linearly on the contact area. Here, the authors use a new contact detection method to show that the law is broken because asperities interact and deform in the contact area to change it, thereby also changing the friction force.

An Investigation of the Influence of Initial Roughness on the Friction and Wear Behavior of Ground Surfaces

Friction and wear tests were performed on AISI 1045 steel specimens with different initial roughness parameters, machined by a creep-feed dry grinding process, to study the friction and wear behavior on a pin-on-disc tester in dry sliding conditions. Average surface roughness (Ra), root mean square (Rq), skewness (Rsk) and kurtosis (Rku) were involved in order to analyse the influence of the friction and wear behavior. The observations reveal that a surface with initial roughness parameters of higher Ra, Rq and Rku will lead to a longer initial-steady transition period in the sliding tests. The plastic deformation mainly concentrates in the depth of 20–50 μm under the worn surface and the critical plastic deformation is generated on the rough surface. For surfaces with large Ra, Rq, low Rsk and high Rku values, it is easy to lose the C element in, the reciprocating extrusion.

Rubber contact mechanics: adhesion, friction and leakage of seals

We study the adhesion, friction and leak rate of seals for four different elastomers: Acrylonitrile Butadiene Rubber (NBR), Ethylene Propylene Diene (EPDM), Polyepichlorohydrin (GECO) and Polydimethylsiloxane (PDMS). Adhesion between smooth clean glass balls and all the elastomers is studied both in the dry state and in water. In water, adhesion is observed for the NBR and PDMS elastomers, but not for the EPDM and GECO elastomers, which we attribute to the differences in surface energy and dewetting. The leakage of water is studied with rubber square-ring seals squeezed against sandblasted glass surfaces. Here we observe a strongly non-linear dependence of the leak rate on the water pressure ΔP for the elastomers exhibiting adhesion in water, while the leak rate depends nearly linearly on ΔP for the other elastomers. We attribute the non-linearity to some adhesion-related phenomena, such as dewetting or the (time-dependent) formation of gas bubbles, which blocks fluid flow channels. Finally, rubber friction is studied at low sliding speeds using smooth glass and sandblasted glass as substrates, both in the dry state and in water. The measured friction coefficients are compared to theory, and the origin of the frictional shear stress acting in the area of real contact is discussed. The NBR rubber, which exhibits the strongest adhesion both in the dry state and in water, also shows the highest friction both in the dry state and in water.

Evolution of the Contact Area with Normal Load for Rough Surfaces: from Atomic to Macroscopic Scales

The evolution of the contact area with normal load for rough surfaces has great fundamental and practical importance, ranging from earthquake dynamics to machine wear. This work bridges the gap between the atomic scale and the macroscopic scale for normal contact behavior. The real contact area, which is formed by a large ensemble of discrete contacts (clusters), is proven to be much smaller than the apparent surface area. The distribution of the discrete contact clusters and the interaction between them are key to revealing the mechanism of the contacting solids. To this end, Green's function molecular dynamics (GFMD) is used to study both how the contact cluster evolves from the atomic scale to the macroscopic scale and the interaction between clusters. It is found that the interaction between clusters has a strong effect on their formation. The formation and distribution of the contact clusters is far more complicated than that predicted by the asperity model. Ignorance of the interaction between them leads to overestimating the contacting force. In real contact, contacting clusters are smaller and more discrete due to the interaction between the asperities. Understanding the exact nature of the contact area with the normal load is essential to the following research on friction.

The effect of surface roughness and viscoelasticity on rubber adhesion

Adhesion between silica glass or acrylic balls and silicone elastomers and various industrial rubbers is investigated. The work of adhesion during pull-off is found to strongly vary depending on the system, which we attribute to the two opposite effects: (1) viscoelastic energy dissipation close to an opening crack tip and (2) surface roughness. Introducing surface roughness on the glass ball is found to increase the work of adhesion for soft elastomers, while for the stiffer elastomers it results in a strong reduction in the work of adhesion. For the soft silicone elastomers a strong increase in the work of adhesion with increasing pull-off velocity is observed, which may result from the non-adiabatic processes associated with molecular chain pull-out. In general, the work of adhesion is decreased after repeated contacts due to the transfer of molecules from the elastomers to the glass ball. Thus, extracting the free chains (oligomers) from the silicone elastomers is shown to make the work of adhesion independent of the number of contacts. The viscoelastic properties (linear and nonlinear) of all of the rubber compounds are measured, and the velocity dependent crack opening propagation energy at the interface is calculated. Silicone elastomers show a good agreement between the measured work of adhesion and the predicted results, but carbon black filled hydrogenated nitrile butadiene rubber compounds reveal that strain softening at the crack tip may play an important role in determining the work of adhesion. Additionally, adhesion measurement under submerged conditions in distilled water and water + soap solutions are also performed: a strong reduction in the work of adhesion is measured for the silicone elastomers submerged in water, and a complete elimination of adhesion is found for the water + soap solution attributed to an osmotic repulsion between the negatively charged surface of the glass and the elastomer.

Effects of surface roughness on shear viscosity

This paper investigates the effect of surface roughness on fluid viscosity using molecular dynamics simulations. The three-dimensional model consists of liquid argon flowing between two solid walls whose surface roughness was modeled using fractal theory. In tandem with previously published experimental work, our results show that, while the viscosity in smooth channels remains constant across the channel width, in the presence of surface roughness it increases close to the walls. The increase of the boundary viscosity is further accentuated by an increase in the depth of surface roughness. We attribute this behavior to the increased momentum transfer at the boundary, a result of the irregular distribution of fluid particles near rough surfaces. Furthermore, although the viscosity in smooth channels has previously been shown to be independent of the strength of the solid-liquid interaction, here we show that in the presence of surface roughness, the boundary viscosity increases with the solid's wettability. The paper concludes with an analytical description of the viscosity as a function of the distance from the channel walls, the walls' surface roughness, and the solid's wetting properties. The relation can potentially be used to adjust the fluid dynamics equations for a more accurate description of microfluidic systems.

Molecular Dynamic Simulation of Collision-Induced Third-Body Formation in Hydrogen-Free Diamond-Like Carbon Asperities

The collision of two cylindrical hydrogen-free diamond-like carbon (DLC) asperities with approximately 60 % sp³ hybridization has been studied using classical molecular dynamics. The severity of the collision can be controlled by the impact parameter b that measures the width of the projected overlap of the two cylinders. For a cylinder radius of R = 23 nm, three collisions with b = 0.5 nm, b = 1 nm and b = 2.0 nm are compared. While for the two small b a single shear band between the collision partners and a strongly localized sp²/sp¹ hybridised third-body zone between the asperities is observed, the b = 2 nm collision is accompanied by pronounced plastic deformation in both asperities that destabilize the metastable sp³-rich phase leading to a drastic increase in the amount of rehybridized tribomaterial. In addition, pronounced roughening of the cylinder surfaces, asymmetric material transfer and the generation of wear debris are found in this case. For the b = 0.5 and 1 nm collision, the evolution of third-body volume can be quantitatively described by a simple geometric overlap model that assumes a sliding-induced phase transformation localized between both asperities. For b = 2 nm, this model underestimates the third-body volume by more than 150 % indicating that plasticity has to be taken into account in simple geometric models of severe DLC/DLC asperity collisions.

Loading-unloading hysteresis loop of randomly rough adhesive contacts

We investigate the loading and unloading behavior of soft solids in adhesive contact with randomly rough profiles. The roughness is assumed to be described by a self-affine fractal on a limited range of wave vectors. A spectral method is exploited to generate such randomly rough surfaces. The results are statistically averaged, and the calculated contact area and applied load are shown as a function of the penetration, for loading and unloading conditions. We found that the combination of adhesion forces and roughness leads to a hysteresis loading-unloading loop. This shows that energy can be lost simply as a consequence of roughness and van der Waals forces, as in this case a large number of local energy minima exist and the system may be trapped in metastable states. We numerically quantify the hysteretic loss and assess the influence of the surface statistical properties and the energy of adhesion on the hysteresis process.

Insights into the Mechanical Behaviour of a Layered Flexible Tactile Sensor

This paper shows realizations of a piezoresistive tactile sensor with a low cost screen-printing technology. A few samples were fabricated for different materials used as insulator between the conductive layers and as top layer or cover. Both can be used to tune the sensitivity of the sensor. However, a large influence is also observed of the roughness at the contact interface on the sensitivity and linearity of the output, as well as on mismatching between the outputs from different taxels. The roughness at the contact interface is behind the transduction principle of the sensor, but it also limits its performance if the wavelength of the roughness is comparable or even longer than the size of the contacts. The paper shows experimental results that confirm this relationship and discusses its consequences in sensor response related to the materials chosen for the insulator and the cover. Moreover, simulations with FEA tools and with simple models are used to support the discussions and conclusions obtained from the experimental data. This provides insights into the sensor behaviour that are shared by other sensors based on the same principle.

Static friction between rigid fractal surfaces

Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

Friction and universal contact area law for randomly rough viscoelastic contacts

We present accurate numerical results for the friction force and the contact area for a viscoelastic solid (rubber) in sliding contact with hard, randomly rough substrates. The rough surfaces are self-affine fractal with roughness over several decades in length scales. We calculate the contribution to the friction from the pulsating deformations induced by the substrate asperities. We also calculate how the area of real contact, A(v, p), depends on the sliding speed v and on the nominal contact pressure p, and we show how the contact area for any sliding speed can be obtained from a universal master curve A(p). The numerical results are found to be in good agreement with the predictions of an analytical contact mechanics theory.

Normal contact and friction of rubber with model randomly rough surfaces

We report on normal contact and friction measurements of model multicontact interfaces formed between smooth surfaces and substrates textured with a statistical distribution of spherical micro-asperities. Contacts are either formed between a rigid textured lens and a smooth rubber, or a flat textured rubber and a smooth rigid lens. Measurements of the real area of contact A versus normal load P are performed by imaging the light transmitted at the microcontacts. For both interfaces, A(P) is found to be sub-linear with a power law behavior. Comparison with two multi-asperity contact models, which extend the Greenwood-Williamson (J. Greenwood and J. Williamson, Proc. Royal Soc. London Ser. A, 295, 300 (1966)) model by taking into account the elastic interaction between asperities at different length scales, is performed, and allows their validation for the first time. We find that long range elastic interactions arising from the curvature of the nominal surfaces are the main source of the non-linearity of A(P). At a shorter range, and except for very low pressures, the pressure dependence of both density and area of microcontacts remains well described by Greenwood-Williamson's model, which neglects any interaction between asperities. In addition, in steady sliding, friction measurements reveal that the mean shear stress at the scale of the asperities is systematically larger than that found for a macroscopic contact between a smooth lens and a rubber. This suggests that frictional stresses measured at macroscopic length scales may not be simply transposed to microscopic multicontact interfaces.

Influence of surface roughness on dispersion forces

Surface roughness occurs in a wide variety of processes where it is both difficult to avoid and control. When two bodies are separated by a small distance the roughness starts to play an important role in the interaction between the bodies, their adhesion, and friction. Control of this short-distance interaction is crucial for micro and nanoelectromechanical devices, microfluidics, and for micro and nanotechnology. An important short-distance interaction is the dispersion forces, which are omnipresent due to their quantum origin. These forces between flat bodies can be described by the Lifshitz theory that takes into account the actual optical properties of interacting materials. However, this theory cannot describe rough bodies. The problem is complicated by the nonadditivity of the dispersion forces. Evaluation of the roughness effect becomes extremely difficult when roughness is comparable with the distance between bodies. In this paper we review the current state of the problem. Introduction for non-experts to physical origin of the dispersion forces is given in the paper. Critical experiments demonstrating the nonadditivity of the forces and strong influence of roughness on the interaction between bodies are reviewed. We also describe existing theoretical approaches to the problem. Recent advances in understanding the role of high asperities on the forces at distances close to contact are emphasized. Finally, some opinions about currently unsolved problems are also presented.

Systematic analysis of Persson's contact mechanics theory of randomly rough elastic surfaces

We systematically check explicit and implicit assumptions of Persson's contact mechanics theory. It casts the evolution of the pressure distribution Pr(p) with increasing resolution of surface roughness as a diffusive process, in which resolution plays the role of time. The tested key assumptions of the theory are: (a) the diffusion coefficient is independent of pressure p, (b) the diffusion process is drift-free at any value of p, (c) the point p = 0 acts as an absorbing barrier, i.e., once a point falls out of contact, it never re-enters again, (d) the Fourier component of the elastic energy is only populated if the appropriate wave vector is resolved, and (e) it no longer changes when even smaller wavelengths are resolved. Using high-resolution numerical simulations, we quantify deviations from these approximations and find quite significant discrepancies in some cases. For example, the drift becomes substantial for small values of p, which typically represent points in real space close to a contact line. On the other hand, there is a significant flux of points re-entering contact. These and other identified deviations cancel each other to a large degree, resulting in an overall excellent description for contact area, contact geometry, and gap distribution functions. Similar fortuitous error cancellations cannot be guaranteed under different circumstances, for instance when investigating rubber friction. The results of the simulations may provide guidelines for a systematic improvement of the theory.

Contact between rough surfaces and a criterion for macroscopic adhesion

At the molecular scale, there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength, and roughness parameters are varied by orders of magnitude. In all cases, the area of atomic contact is initially proportional to the load. The prefactor rises linearly with adhesive strength for weak attractions. Above a threshold adhesive strength, the prefactor changes sign, the surfaces become sticky, and a finite force is required to separate them. A parameter-free analytic theory is presented that describes changes in these numerical results over up to five orders of magnitude in load. It relates the threshold adhesive strength to roughness and material properties, explaining why most macroscopic surfaces do not stick. The numerical results are qualitatively and quantitatively inconsistent with classical theories based on the Greenwood-Williamson approach that neglect the range of adhesion and do not include asperity interactions.

Finite-size scaling in the interfacial stiffness of rough elastic contacts

The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.

Rubber friction for tire tread compound on road surfaces

We have measured the surface topography and calculated the surface roughness power spectrum for an asphalt road surface. For the same surface we have measured the friction for a tire tread compound for velocities 10(-6) m s(-1) < v < 10(-3) m s(-1) at three different temperatures (at -8 °C, 20 °C and 48 °C). The friction data was shifted using the bulk viscoelasticity shift factor a(T) to form a master curve. We have measured the effective rubber viscoelastic modulus at large strain and calculated the rubber friction coefficient (and contact area) during stationary sliding and compared it to the measured friction coefficient. We find that for the low velocities and for the relatively smooth road surface we consider, the contribution to friction from the area of real contact is very important, and we interpret this contribution as being due to shearing of a very thin confined rubber smear film.

Contact between representative rough surfaces

A numerical analysis of mechanical frictionless contact between rough self-affine elastic manifolds was carried out. It is shown that the lower cutoff wave number in surface spectra is a key parameter controlling the representativity of the numerical model. Using this notion we demonstrate that for representative surfaces the evolution of the real contact area with load is universal and independent of the Hurst roughness exponent. By introducing a universal law containing three constants, we extend the study of this evolution beyond the limit of infinitesimal area fractions.