Adhesion between elastic bodies with randomly rough surfaces

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account the fact that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macroasperity contact areas. For a fractal dimension larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased.     

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.     

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.     

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     

Local friction at a sliding interface between an elastomer and a rigid spherical probe

This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.     

Elastoplastic contact between randomly rough surfaces

I have developed a theory of contact mechanics between randomly rough surfaces. The solids are assumed to deform elastically when the stress sigma is below the yield stress sigma(Y), and plastically when sigma reaches sigma(Y). I study the dependence of the (apparent) area of contact on the magnification. I show that in most cases the area of real contact A is proportional to the load. If the rough surface is self-affine fractal (Hurst exponent H) the whole way up to the lateral size L of the nominal contact area, then (assuming no plastic deformation) A approximately L(H).     

Nonlinear dynamics of a rub-impact micro-rotor system with scale-dependent friction model

Scale effects in dry friction at microscale and the coefficients of friction due to adhesion force and two- and three-body deformations are considered. A rub-impact micro-rotor model with scaling nonlinear rub-impact force is presented and the nonlinear dynamic characteristics of the system in micro-electro-mechanical systems (MEMS) are investigated when the rotating speed, imbalance, damping coefficient, scale length and fractal dimension are regarded as the control parameters. Effects of scale length, fractal dimension, velocity-dependent impact factor and contact form on the coefficients of dry friction are investigated and discussed, and used to study the nonlinear behavior of rub-related vibrations with a large number of numerical simulations. The effects of rotating speed, imbalance, damping coefficient, and friction coefficient on the micro-rotor system responses are studied. It is indicated that the rub-impact micro-rotor system with the scale effects in friction alternates among the periodic, quasi-periodic and chaotic motions as the system parameters change. The results can be effectively used to diagnose the rub-impact fault, reduce the failure and improve the characteristics of a micro-rotor system, and optimize the design of micro-rotating machinery in MEMS.     

Capillary Adhesion of Microbeams： Finite Deformation Analysis

Capillary force may cause adhesion of devices at micro- and nano-scales. Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using finite deformation elasticity theory. The critical adhesion condition can be obtained from the present method as a function of the bending stiffness, Young＇s contact angle, the spacing of the two beams as well as the surface tensions of the solid and liquid phases. The solution for the capillary adhesion of a beam with a rigid substrate is also given. The results from the finite deformation analysis are compared with that of infinitesimal deformation method in order to show the necessity of accounting for the nonlinear effect associated with large deflection. The method adopted in this study can also be used to solve other adhesion problems associated with van der Waals force or electrostatic force.     

Friction Properties of Bio-mimetic Nano-fibrillar Arrays

Nano-fibrillar arrays are fabricated using polystyrene materials. The average diameter of each fiber is about 300 nm. Experiments show that such a fibrillar surface possesses a relatively hydrophobie feature with a water contact angle of 142°. Nanoscale friction properties are mainly focused on. It is found that the friction force of polystyrene nano-fibrillar surfaces is obviously enhanced in contrast to polystyrene smooth surfaces. The apparent coefficient of friction increases with the applied load, but is independent of the scanning speed. An interesting observation is that the friction force increases almost linearly with the real contact area, which abides by the fundamental Bowden-Tabor law of nano-seale friction.     

Effect of micro-dimple patterns on capillary pull-off force and friction force of silicon surface

A microtribometer is used to measure and compare pull-off forces and friction forces exerted on (a) micro-dimpled silicon surfaces, (b) bare silicon surfaces, and (c) octadecyltrichlorosilane (OTS) treated silicon surfaces at different relative humidity (RH) levels separately. It is found that above a critical RH level, the capillary pull-off force increases abruptly and that the micro-dimple textured surface has a lower critical RH value as well as a higher pull-off force value than the other two surfaces. A micro topography parameter, namely sidewall area ratio, is found to play a major role in controlling the capillary pull-off force. Furthermore, micro-dimpled silicon surface is also proved to be not sensitive to variation in RH level, and can realize a stable and decreased friction coefficient compared with un-textured silicon surfaces. The reservoir-like function of micro dimples is considered to weaken or avoid the breakage effect of liquid bridges at different RH levels, thereby maintaining a stable frictional behaviour.     

Effect of chain length on the adhesion behaviour of n-alkanethiol self-assembled monolayers on Au(111): An atomic force microscopy study

The effect of chain length on the adhesion behaviour of n-alkanethiols CH₃(CH₂)_nSH, wheren = 5, 6, 7, 9, 10, 11, 14 and 15 has been followed by carrying out pull-off force measurement using atomic force microscopy (AFM). The self-assembled monolayers on Au(111) surface has been characterized by reflection absorption infra-red spectroscopy (RAIRS) and contact mode AFM. It is observed that the work of adhesion is independent of thiol chain length though the standard deviation is high for short chain length thiol-based monolayers. This may be attributed to the relatively more deformable nature of the short chain thiol films due to their heterogeneity in the monolayer structure than the long chain ones. This, in turn, increases the contact area/volume between the AFM tip and the monolayer, and hence the force of adhesion. However, in the presence of water, the force of adhesion is lower than that observed in air reflecting the effects of capillary forces/polar components associated with the surface energy.     

Adhesion of fluid vesicles at chemically structured substrates

The adhesion of fluid vesicles at chemically structured substrates is studied theoretically via Monte Carlo simulations. The substrate surface is planar and repels the vesicle membrane apart from a single surface domain γ , which strongly attracts this membrane. If the vesicle is larger than the attractive γ domain, the spreading of the vesicle onto the substrate is restricted by the size of this surface domain. Once the contact line of the adhering vesicle has reached the boundaries of the γ domain, further deflation of the vesicle leads to a regime of low membrane tension with pronounced shape fluctuations, which are now governed by the bending rigidity. For a circular γ domain and a small bending rigidity, the membrane oscillates strongly around an average spherical cap shape. If such a vesicle is deflated, the contact area increases or decreases with increasing osmotic pressure, depending on the relative size of the vesicle and the circular γ domain. The lateral localization of the vesicle's center of mass by such a domain is optimal for a certain domain radius, which is found to be rather independent of adhesion strength and bending rigidity. For vesicles adhering to stripe-shaped surface domains, the width of the contact area perpendicular to the stripe varies nonmonotonically with the adhesion strength.     

Experimental investigation of the adhesive contact of an elastomer

The present work is an experimental study of adhesion between an elastomer and a rigid cylindrical indented The experimental characterization was carried out using a specially developed apparatus. Adhesive force was measured as function of contact geometry, pull-off velocity, normal force, temperature, waiting time, and material properties. Experimental results are compared with existing theoretical models for adhesion of elastic and viscoelastic bodies. Our study shows that the adhesive force between the studied elastomer and a steel cylinder is determined by completely different mechanisms than assumed in the Kendall’s theory. In particular, it does not depend on the surface energy and is almost entirely dominated by the viscosity of the elastomer.     

The effect of substrate roughness on the static friction of CuO nanowires

The dependence of static friction on surface roughness was measured for copper oxide nanowires on silicon wafers coated with amorphous silicon. The surface roughness of the substrate was varied to different extent by the chemical etching of the substrates. For friction measurements, the nanowires (NWs) were pushed by an atomic-force microscope (AFM) tip at one end of the NW until complete displacement of the NW was achieved. The elastic bending profile of a NW during this manipulation process was used to calculate the ultimate static friction force. A strong dependence of static friction on surface roughness was demonstrated. The real contact area and interfacial shear strength were estimated using a multiple elastic asperity model, which is based on the Derjaguin–Muller–Toporov (DMT) contact mechanics. The model included vertical elastic flexure of NW rested on high asperities due to van der Waals force.     

Evolution of real contact area during stick-slip movement observed by total reflection method

We build an experiment system based on total reflection(TR) method to observe the evolution of real contact area of polymethyl methacrylate(PMMA) in the continual stick-slip movement. The bilateral friction is adopted to overcome the bending moment in the lateral friction movement. Besides some classical phenomena of stick-slip movement such as periodical slow increase of frictional force in sticking phase and a sudden drop when slipping, a special phenomenon that the contact area increases with the tangential force is observed, which was called junction growth by Tabor in 1959.Image processing methods are developed to observe the variation of the junction area. The results show that the center of the strongest contact region will keep sticking under the tangential force until the whole slipping, the strongest point undergoes three stages in one cycle, which are named as sticking stage, fretting stage, and cracking stage, respectively. The combined analysis reveals a physical process of stick-slip movement: the tangential force causes the increase of the real contact area, which reduces the pressure between the contact spots and finally leads to the slipping. Once slipping occurs,the real contact area drops to the original level resulting in the pressure increase to the original level, which makes the sticking happen again.     

Surface characterization and microstructure of ITO thin films at different annealing temperatures

In this study, the electron beam evaporation method is used to generate an indium tin oxide (ITO) thin film on a glass substrate at room temperature. The surface characteristics of this ITO thin film are then investigated by means of an AFM (atomic force microscopy) method. The influence of postgrowth thermal annealing on the microstructure and surface morphology of ITO thin films are also examined. The results demonstrate that the film annealed at higher annealing temperature (300 °C) has higher surface roughness, which is due to the aggregation of the native grains into larger clusters upon annealing. The fractal analysis reveals that the value of fractal dimension D_f falls within the range 2.16-2.20 depending upon the annealing temperatures and is calculated by the height-height correlation function.     

Adhesion elastic contact and hysteresis effect

In this paper, we study the relationship between the pull-off force and the transition parameter (or Tabor number) as well as the variation of the pull-off radius with the transition parameter in the adhesion elastic contact. Hysteresis models are presented to describe the contact radius as a function of external loads in loading and unloading processes. Among these models, we verified the hysteresis model from Johnson－Kendall－Roberts theory, based on which the calculated results are in good agreement with experimental ones.     

Relationship between the real contact area and contact force in pre-sliding regime

The pre-sliding regime is typically neglected in the dynamic modelling of mechanical systems. However, the change in contact state caused by static friction may decrease positional accuracy and control precision. To investigate the relationship between contact status and contact force in pre-sliding friction, an optical experimental method is presented in this paper.With this method, the real contact state at the interface of a transparent material can be observed based on the total reflection principle of light by using an image processing technique. A novel setup, which includes a pair of rectangular trapezoidal blocks, is proposed to solve the challenging issue of accurately applying different tangential and normal forces to the contact interface. The improved Otsu's method is used for measurement. Through an experimental study performed on polymethyl methacrylate(PMMA), the quantity of contact asperities is proven to be the dominant factor that affects the real contact area. The relationship between the real contact area and the contact force in the pre-sliding regime is studied, and the distribution of static friction at the contact interface is qualitatively discussed. New phenomena in which the real contact area expands along with increasing static friction are identified. The aforementioned relationship is approximately linear at the contact interface under a constant normal pressure, and the distribution of friction stress decreases from the leading edge to the trailing edge.     

A Generalized Johnson Parameter for Pull-Off Decay in the Adhesion of Rough Surfaces

There is no simple theory at present to predict accurately the decay of pull-off in the adhesion of randomly rough surfaces. The asperity model of Fuller and Tabor has shown significant error in recent numerical investigations by Pastewka and Robbins of self-affine random roughness from micrometer to atomic scale which corresponds to low values of Tabor parameter. For sinusoidal contact, the Johnson parameter, originally introduced for the JKR regime (from Johnson-Kendall-Roberts) is the dominant parameter ruling the pull-off at intermediate Tabor values. Hence, we define a generalized Johnson parameter as the ratio between the adhesive energy to the elastic strain energy to flatten the surface in the case of multiscale roughness and find that it correlates very well with the data of Pastewka and Robbins spanning almost five orders of magnitude of reduction from theoretical strength, improving significantly with respect to other possible single parameter criteria. For the most important case in practice, that of low fractal dimensions, this suggests the product of amplitude and slope of the largest wavelength components of roughness dominate pull-off decay, and not small scales features like slopes and curvatures, as suggested by Pastewka and Robbins.     

Rubber friction: Comparison of theory with experiment

We have measured the friction force acting on a rubber block slid on a concrete surface. We used both unfilled and filled (with carbon black) styrene butadiene (SB) rubber and have varied the temperature from −10 °C to 100 °C and the sliding velocity from 1 μm/s to 1000 μm/s. We find that the experimental data at different temperatures can be shifted into a smooth master-curve, using the temperature-frequency shifting factors obtained from measurements of the bulk viscoelastic modulus. The experimental data has been analyzed using a theory which takes into account the contributions to the friction from both the substrate asperity-induced viscoelastic deformations of the rubber, and from shearing the area of real contact. For filled SB rubber the frictional shear stress σ_f in the area of real contact results mainly from the energy dissipation at the opening crack on the exit side of the rubber-asperity contact regions. For unfilled rubber we instead attribute σ_f to shearing of a thin rubber smear film, which is deposited on the concrete surface during run in. We observe very different rubber wear processes for filled and unfilled SB rubber, which is consistent with the different frictional processes. Thus, the wear of filled SB rubber results in micrometer-sized rubber particles which accumulate as dry dust, which is easily removed by blowing air on the concrete surface. This wear process seams to occur at a steady rate. For unfilled rubber a smear film forms on the concrete surface, which cannot be removed even using a high-pressure air stream. In this case the wear rate appears to slow down after some run in time period.