Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

In this paper we extend the theory of contact mechanics and rubber friction developed by one of us (B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)) to the case of surfaces with anisotropic surface roughness. As an application we calculate the viscoelastic contribution to the rubber friction. We show that the friction coefficient may depend significantly on the sliding direction, while the area of contact depends weakly on the sliding direction. We have carried out experiments for rubber blocks sliding on unidirectionally polished steel surfaces. The experimental data are in a good qualitative agreement with the theory.     

Heat transfer between elastic solids with randomly rough surfaces

We study the heat transfer between elastic solids with randomly rough surfaces. We include both the heat transfer from the area of real contact, and the heat transfer between the surfaces in the non-contact regions. We apply a recently developed contact mechanics theory, which accounts for the hierarchical nature of the contact between solids with roughness on many different length scales. For elastic contact, at the highest (atomic) resolution the area of real contact typically consists of atomic (nanometer) sized regions, and we discuss the implications of this for the heat transfer. For solids with very smooth surfaces, as is typical in many modern engineering applications, the interfacial separation in the non-contact regions will be very small, and for this case we show the importance of the radiative heat transfer associated with the evanescent electromagnetic waves which exist outside of all bodies.     

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

The authors have employed a numerical procedure to analyse the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution to the problem, which belongs to the class of the free boundary problems, is obtained by calculating Green’s function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel. The boundaries of the contact area are calculated by requiring the energy of the system to be stationary. This methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in the presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the predictions of an extended version of Persson’s contact mechanics theory, which is able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson’s theory underestimates the contact area by about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than for 2D rough surfaces in the case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson’s theory is a mean-field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe that the predicted value of separation is in agreement with our numerical results as well as the exponents of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson’s theory captures almost exactly the main qualitative behaviour of the rough contact phenomena.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

Dentinal tubules driven wetting of dentin: Cassie-Baxter modelling

We investigate the wetting properties of dentin surfaces submitted to a phosphoric acid etching followed by an air drying procedure, as in clinical situations of adhesive dentistry. The surface topography of the etched surfaces was characterized by AFM, and the wetting properties of water on these rough and heterogeneous surfaces were studied, by contact angle measurements. We showed that the contact angle increases with the acid exposure time and consequently with both surface roughness and the organic-mineral ratio of the dentin components. From the whole results, obtained on dentin and also on synthesized hydroxyapatites samples, we inferred a water contact angle of ∼ 133^° on the dentinal tubule. These experimental results may be described by the Cassie-Baxter approach, and it is suggested that small air pockets could be formed inside the dentinal tubules.     

表面黏附导致的接触行为转变

应用大规模分子动力学方法, 模拟了具有不同原子级粗糙形貌的两种刚性球形探头与弹性平面基体的黏附接触行为. 研究了载荷与真实接触面积、接触界面排斥力与真实接触面积, 以及黏附力与真实接触面积之间的关系. 分子模拟得到的载荷与真实接触面积的关系, 与连续力学接触理论预测很好地定性一致. 无论是原子级光滑探头还是粗糙探头, 黏附接触下的排斥力与真实接触面积的关系, 都与无黏附接触时的规律相一致, 即黏附力对接触行为的影响作用, 可以等效为附加在真实外载荷基础上的虚拟载荷, 将对黏附接触行为的分析转变为无黏附接触分析. 两种探头的黏附力随真实接触面积都呈幂函数形式的增长, 但是, 原子级光滑探头的幂指数大于1, 而原子级粗糙探头的幂指数小于1. 关键词： 接触行为 表面黏附 分子动力学模拟     

Stiffness of contacts between rough surfaces

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal stiffness rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughness, system size, and Poisson ratio can be collapsed using Persson's contact theory for continuous elastic media. The compliance due to atomic-scale motion at the interface between solids has little effect on the area and normal stiffness, but can reduce the total transverse stiffness by orders of magnitude. The scaling of this effect with system size is discussed.     

纳米接触过程中黏着规律的变化

本文应用大规模分子动力学方法, 模拟了两种具有不同粗糙形貌的、刚性球形探头与弹性平面基体之间的纳米尺度接触, 计算了探头与基体之间的拉离力和黏着功, 研究了接触过程中界面黏着力随载荷的变化规律, 分析了接触界面原子的法向应力分布. 研究发现, 原子级光滑接触的黏着力随着载荷的增大而线性增大, 而原子级粗糙接触的黏着力-载荷曲线分为以不同斜率增长的两个阶段. 相比于原子级光滑探头, 原子级粗糙探头与基体之间具有较小的拉离力和黏着功, 却在接触过程中形成了较大的黏着力. 因此, 拉离力和黏着功不能表征出纳米接触过程中原子吸引作用对界面法向力的贡献大小.     

Electrostatic forces in micromanipulation: Experimental characterization and simulation including roughness

Manipulation by contact of objects between 1 m and 1 mm are often disturbed by adhesion between the manipulated object and the gripper. Electrostatic forces are among the phenomena responsible for this adhesive effect. Analytical models have been developed in the literature to predict electrostatic forces. Most models have been developed within the framework of scanning probe microscopy, i.e. for a contact between a conducting tip and a metallic surface. In our study, we developed a simulation tool based on finite elements modeling. The strength of this model lies in the fact that it integrates roughness parameters. Measurements of electrostatic forces in function of roughness were conducted by atomic force microscopy. The experimental results were compared with the simulation results showing very good correlation. This demonstrates the influence of surface topography on electrostatic forces, especially for very small separation distances and proves the utility of the simulation tool in designing surfaces with controlled adhesion. Some application fields to which these results can be applied are drug delivery devices and micromanipulation tools.     

Surface characterization of plasma deposited nano-structured fluorocarbon coatings for promoting in vitro cell growth

Nano-structured “teflon-like” coatings characterized by highly-fluorinated, random, ribbon-shaped, micrometers-long structures were deposited on polyethylenetherephtalate (PET) substrates by plasma enhanced-chemical vapour deposition (PE-CVD) using modulated radiofrequency (RF, 13.56 MHz) glow discharges fed with C₂F₄ in modulated discharge (MD) and continuous wave (CW) regimes. Surfaces obtained in this way featured identical chemical composition and different roughness in the nanometric scale. Water contact angle (WCA) measurements, scanning electron microscopy (SEM) and atomic force microscopy (AFM) were utilized to characterize the surfaces. A positive relationship was shown to exist between the WCA value and the mean nano-structure height and the area root-mean-square (RMS) roughness of coatings. The possibility of obtaining coatings of varying nano-structure height, i.e., roughness, in a nanometric scale represents a promising result for further use of these surfaces as substrates for experiments on cell adhesion, proliferation and growth.     

Study on effect of dimples on friction of parallel surfaces under different sliding conditions

The influence of rectangle dimples with flat bottom on the friction of parallel surfaces at different sliding conditions is investigated based on lubrication equations. The elastic deformation of rough surfaces is evaluated using continuous convolution fast Fourier transform (CC-FFT). The friction coefficients for dimpled and non-dimpled parallel surfaces by simulation are compared with experimental results. Results show that this kind of dimples can reduce the friction coefficient for cases with the smaller ratio of film thickness to roughness (h/R_q), small roughness or large applied load. The friction force for the parallel surfaces can decrease due to the dimple effect over the range of the larger sliding speed, larger load or smoother surfaces.     

Multipoint contact modeling of nanoparticle manipulation on rough surface

In this paper, the atomic force microscopy (AFM)-based 2-D pushing of nano/microparticles investigated on rough substrate by assuming a multipoint contact model. First, a new contact model was extracted and presented based on the geometrical profiles of Rumpf, Rabinovich and George models and the contact mechanics theories of JKR and Schwartz, to model the adhesion forces and the deformations in the multipoint contact of rough surfaces. The geometry of a rough surface was defined by two main parameters of asperity height (size of roughness) and asperity wavelength (compactness of asperities distribution). Then, the dynamic behaviors of nano/microparticles with radiuses in range of 50–500 nm studied during their pushing on rough substrate with a hexagonal or square arrangement of asperities. Dynamic behavior of particles were simulated and compared by assuming multipoint and single-point contact schemes. The simulation results show that the assumption of multipoint contact has a considerable influence on determining the critical manipulation force. Additionally, the assumption of smooth surfaces or single-point contact leads to large error in the obtained results. According to the results of previous research, it anticipated that a particles with the radius less than about 550 nm start to slide on smooth substrate; but by using multipoint contact model, the predicted behavior changed, and particles with radii of smaller than 400 nm begin to slide on rough substrate for different height of asperities, at first.     

Hydrophobic recovery of UV/ozone treated poly(dimethylsiloxane): adhesion studies by contact mechanics and mechanism of surface modification

Silicone elastomers (Sylgard 184 and 170), based on poly(dimethylsiloxane) (PDMS), were surface treated by a combined exposure to UV and ozone. The effects of the treatments were analyzed as a function of time elapsed after stopping the treatments using different standard surface characterization techniques, such as water contact angle measurements, XPS and atomic force microscopy (AFM). However, the primary focus of this study was to apply the Johnson–Kendall–Roberts (JKR) contact mechanics approach to investigate PDMS samples prior to and following UV/ozone surface treatment. A gradual formation of a hydrophilic, silica-like surface layer with increasing modulus was observed with increasing UV/ozone exposure. A subsequent hydrophobic recovery after UV/ozone exposure was observed, as indicated by increasing contact angles. This supports the hypothesis that the hydrophobic recovery is mainly caused by the gradual coverage of a permanent silica-like structure with free siloxanes and/or reorientation of polar groups. PDMS containing a homogenously dispersed filler (Sylgard 184), exhibited a decreasing surface roughness (by AFM) when the oxidized surface region “collapsed” into a smooth SiO_x layer (final surface roughness <2 nm). PDMS containing heterogeneously distributed, aggregated filler particles (Sylgard 170), exhibited an increasing surface roughness with treatment dose, which was attributed to the “collapse” of the oxidized surface region thus exposing the contours of the underlying filler aggregates (final surface roughness ∼140 nm). A dedicated device was designed and built to study the contact mechanics behavior of PDMS prior to, and following surface treatment. The value of the combined elastic modulus obtained for PDMS lens and semi-infinite flat surface system showed an increase in full agreement with the formation of a silica-like layer exhibiting a high elastic modulus (compared with untreated PDMS). The work of adhesion observed in JKR experiments exhibited an increasing trend as a function of treatment done in agreement with contact angle data. JKR experiments showed hydrophobic recovery behavior as anticipated from contact angle measurements. Single pull-off force measurements by JKR and numerical analysis of full-approach JKR curves were in quantitative agreement regarding practical work of adhesion values.     

Effects of symmetric and asymmetric contact angles and division of menisci during separation

Meniscus and viscous forces are sources of adhesive force when two surfaces are separated with a micro-meniscus present at the interface. The adhesive force can be one of the main reliability issues when the contacting surfaces are ultra-smooth and the normal load is small, as is common for micro/nano devices. In this paper, both meniscus and viscous forces of menisci with symmetric and asymmetric contact angles are modelled. Equations for both meniscus and viscous forces in division of menisci are analytically formulated. The role of these two forces is evaluated during the separation process. The effects of the contact angles, division of menisci, as well as liquid thicknesses, surface tension and viscosity of the liquid, and separation distance and time during separation are presented. It is found that contact angles significantly affect the break point and meniscus force, and the magnitude of meniscus force can be largely reduced by choosing proper asymmetric contact angles. ‘Force scaling’ effects are found to be true for both meniscus and viscous forces when one larger meniscus is divided into large numbers of identical micro-menisci. Meniscus force increases with the number of divisions whereas viscous force decreases by an order of inverse the number of division (1/N). Optimal configurations for low adhesion are identified. This study presents a comprehensive analysis of meniscus and viscous forces during separation of menisci under different physical configurations. It provides a fundamental understanding of the physics of the process and knowledge for control of adhesion due to liquid menisci.     

基于粗糙度曲线统计特征的接触热阻模型

本文在对粗糙度曲线统计特征分析的基础上,提出了一种接触热阻的计算模型。分别采用四种接触峰的评定标准,对实际机械加工表面的接触热阻进行了计算。研究结果表明,评定标准的选取直接影响接触热阻的计算结果;在同一接触峰评定标准下,两块平均粗糙度值相差较大的表面,其接触热阻计算值的离散区域也有可能重叠。所以,在计算接触热阻时,仅仅使用一两个平均化的粗糙度统计参数来表征整个表面的形貌特征是不够的。     

Some mechanisms of excitation of a railway wheel

Railway wheel vibrations are caused by a number of mechanisms. Two of these are considered: (a) gravitational load reaction acting on different points of the wheel rim, as the wheel rolls on, and (b) random fluctuating forces generated at the contact patch by roughness on the mating surfaces of the wheel and rail. The wheel is idealized as a thin ring, and the analysis is limited to a single wheel rolling on a rail. It is shown that the first mechanism results in a stationary pattern of vibration, which would not radiate any sound. The acceleration caused by roughness-excited forces is much higher at higher frequencies, but is of the same order as that caused by load reaction at lower frequencies. The computed acceleration level (and hence the radiated SPL) caused by roughness is comparable with the observed values, and is seen to increase by about 10 dB for a doubling of the wagon speed. The driving point impedance of the periodic rail-sleeper system at the contact patch, which is used in the analysis, is derived in a companion paper.     

Elastic contact mechanics: Percolation of the contact area and fluid squeeze-out

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.     

A review on the effects of different parameters on contact heat transfer

In this paper, a complete literature review for thermal contact between fixed and periodic contacting surfaces and also thermal contact between exhaust valve and its seat in internal combustion engines is presented. Furthermore, the effects of some parameters such as contact pressure, contact frequency, the contacting surfaces topography and roughness, curvature radius of surfaces, loading–unloading cycles, gas gap conductance and properties, interface interstitial material properties, surfaces coatings and surfaces temperature on thermal contact conductance are investigated according to the papers presented in this field. The reviewed papers and studies included theoretical/ analytical/experimental and numerical studies on thermal contact conductance. In studying the thermal contact between exhaust valve and its seat, most of the experimental studies include two axial rods as the exhaust valve, and seat and the one ends of both rods are considered at constant and different temperatures. In the experimental methods, the temperatures of multi-points on rods are measured in different conditions, and thermal contact conductance is estimated using them.     

Effects of surface roughness on surface acoustic wave propagation in semiconductor materials

The effect of surface roughness on adhesion and tribological properties of films and interfaces is of key importance. Therefore, it is of utmost importance to be able to measure this quantity and to predict the effects that different roughness levels may cause. Roughness affects the propagation of surface acoustic waves on a material but there is little useful quantitative data on the topic. This work investigates the dispersive effect of roughness on surface acoustic wavepackets (30-200 MHz frequency range) for different degrees of nanometer roughness on silicon (0 0 1) and (1 1 1) surfaces, we show that the roughness-induced frequency dispersion effect is significant, and that although available theories agree qualitatively with the results, the theory is not adequate to predict the real SAW dispersion. These experimental results have considerable implications for design of SAW devices, for accuracy of Brillouin spectroscopy measurements, and for possible applications to non-destructive testing of materials. Previously unknown dispersive effects on anisotropic crystal surfaces are also demonstrated.     

Effective boundary slip and wetting characteristics of water on substrates with effects of surface morphology

ABSTRACT

In the present study, molecular dynamics (MD) simulation was used to investigate the relationship between wetting behaviour and slip length on patterned substrates. We adopted two solid surfaces of Si(100) and graphite due to similarities in their intrinsic contact angle. Contact angle and apparent slip length were obtained using discrete simulations with the same thermodynamic states. In the present study, a number of questions regarding surface roughness and the problem of contact angle (θ) and slip length (L_s) are discussed. These questions include the relationship between θ and surface roughness, the characteristics used to describe the difference between static and dynamic fluid fields and the reason for a lack of multilayer sticking observed in the current cases. Our results indicate that the quasi-universal θ ? L_s equation proposed by Hung et al. (2008) is applicable to cases involving a Cassie-like nanoscale roughened surface. In contrast, in cases with a Wenzel-like nanostructure, the no-slip boundary conditions are independent of variations in the contact angle. The adoption of a Wenzel–Cassie hybrid model helped to verify that the fluid density inside the cavity is a critical indicator of wettability of the wall–fluid interface. Our results also demonstrate that ρ_{f, cav} is a critical property in the measurement of hydrodynamic effects and thus its importance as an indicator of the validity of the equation θ ? L_s. The average time that water molecules are trapped and the number of averaged hydrogen bonds within cavities in a dynamic fluid field were also investigated.