Stick-slip melting of a boundary lubricant between two rigid surfaces with nanoscale asperities

With a simple mechanical analog of the elastic tribological system, the friction of two rough surfaces is studied using the model of first-order phase transitions. The surfaces rub under boundary friction conditions in the presence of a lubricant layer in between. Stick-slip motion is considered, which is due to periodic phase transitions arising between kinetic friction conditions. It is shown that when rubbing surfaces are rough, a time-varying domain structure with a spatially distributed order parameter occurs in the plane of friction during motion.     

Tribological system in the boundary friction mode under a periodic external action

A mechanical analog of a tribological system in the boundary friction mode is studied. A thermodynamic model is used to analyze the first-order phase transition between liquidlike and solidlike structures of a lubricant. The time dependences of the friction force, the relative velocity of the interacting surfaces, and the elastic component of the shear stresses appearing in the lubricant are obtained. It is shown that, in the liquidlike state, the shear modulus of the lubricant and the elastic stresses become zero. The intermittent (stick-slip) friction mode detected experimentally is described. It is shown that, as the lubricant temperature increases, the frequency of phase transitions between the lubricant structural states decreases and the total friction force and elastic stress amplitudes lower. When the temperature or the elastic strain exceeds the corresponding critical value, the lubricant melts and a kinetic slip mode in which the elastic component of the friction force is zero takes place.     

Bubbles under stress

We present an experimental and theoretical investigation of a system composed of two soap bubbles strained between two parallel solid surfaces. The two-bubble cluster can be found in several configurations. The existence and stability of each of these states is studied as a function of the distance between the two facing surfaces. The change of this distance can induce a transition from one configuration to another; we observe that most transitions are subcritical, showing that the system is often trapped in states where the minimum of free energy is only local. The hysteretic transitions are responsible for the dissipation of elastic energy. The existence of more than one stable states for given boundaries conditions combined with the absence of thermalization means that the history of the system has to be taken into account and that there is no unique stress-strain relation. In the present system, because of its simplicity, a complete quantitative analysis of these general processes is obtained. The presented results may contribute to a better understanding of the dynamics of more complex systems such as foams or granular materials where similar processes are at work.     

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.     

Structure and topography modifications of austenitic steel surfaces after friction in sliding contact

Friction experiments between two austenitic stainless steel (AISI 304L) surfaces in sliding contact were carried out under very low loads in two liquid environments, namely demineralized water and methanol, in order to study the correlation between surface damage (wear and surface topography) and structural modifications (phase formation and microstructure). The particularity of our approach was to perform the tests under Hertzian pressures, which were several orders of magnitude lower than the elastic limit of stainless steel. The structural modifications produced during friction were analysed by X-ray diffraction and transmission electron microscopy and the surface topography was studied by scanning electron microscopy and three-dimensional (3D) profiling. Whatever the experimental conditions investigated, the morphology of the damage observed on both surfaces consisted of very fine, smooth and parallel grooves typical of an abrasive wear process of a ductile material caused by the ploughing action of hard particles. From the beginning of the tests, the transformation of austenite into martensite was observed in the superficial layers and the dominant presence of martensite was identified in the wear debris. These results suggest that, under our experimental conditions, abrasion is the dominant mechanism of material removal. Received: 12 March 2002 / Accepted: 3 May 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +33-5/4949-6692, E-mail: jean.paul.riviere@univ-poitiers.fr     

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.     

First-order phase transition between the liquidlike and solidlike structures of a boundary lubricant

A thermodynamic model for characterization of the first-order phase transition between the structural states of a boundary lubricant is suggested. It is shown that melting of the lubricant is due both to a rise in its temperature and to shear experienced by friction surfaces when elastic strains (stresses) exceed a critical value. A phase diagram with regions of dry and sliding friction is constructed. Using a mechanical analogue of the tribological system, the dependence of the friction force on the lubricant temperature and relative shear rate of the friction surfaces is analyzed. The observed conditions of stick-slip friction, which is the main reason for friction parts wear, are described. Reasons for stick-slip friction are revealed.     

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.     

On the dependence of the static friction force between a rigid,randomly rough fractal surface and a viscoelastic body on the normal force

The present investigation is based on the assumption that the static coefficient of friction can be characterized roughly by the rms value of the surface gradient in the contact region. We numerically investigate the contact between a rigid, randomly rough surface and an elastic half-space and determine the dependence of the rms slope in the contact region on the normal force. For fractal surfaces with a Hurst exponent of H ≈ 1, the rms slope can be approximated very well by a logarithmic function of the normal force. Parameters of the approximation have been determined as functions of the Hurst exponent. The rms value of the slope always increases with the normal force, which indicates that the coefficient of friction should be an increasing function of the normal force.     

High friction from a stiff polymer using microfiber arrays

High dry friction requires intimate contact between two surfaces and is generally obtained using soft materials with an elastic modulus less than 10 MPa. We demonstrate that high-friction properties similar to rubberlike materials can also be obtained using microfiber arrays constructed from a stiff thermoplastic (polypropylene, 1 GPa). The fiber arrays have a smaller true area of contact than a rubberlike material, but polypropylene's higher interfacial shear strength provides an effective friction coefficient of greater than 5 at normal loads of 8 kPa. At the pressures tested, the fiber arrays showed more than an order of magnitude increase in shear resistance compared to the bulk material. Unlike softer materials, vertical fiber arrays of stiff polymer demonstrate no measurable adhesion on smooth surfaces due to high tensile stiffness.     

Nematic films and radially anisotropic Delaunay surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.     

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.     

Optimization of the surface texture for silicon carbide sliding in water

Surface texturing has been recognized as an effective means to improve the tribological performances of sliding surfaces. Usually, generation additional hydrodynamic pressure to increase the load carrying capacity is regarded as the most significant effect of surface texture. In the case of silicon carbide sliding against identical material in water, the experimental results indicate that surface texture is also helpful to improve the running-in progress to smooth the contact surfaces, showing another reason to result in low friction. Based on the consideration of enhancing the generation of hydrodynamic pressure and improving running-in progress, a surface texture pattern, which was combined with large (circle, 350 μm in diameter) and small (rectangular, 40 μm in length) dimples, was designed to maximize the texture effect on the load carrying capacity of SiC surfaces sliding in water. The friction coefficient of such textured surface was evaluated and compared with that of untextured and those only with large or small dimples only. The friction reduction mechanisms of the patterns with different dimples in size are discussed.     

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.     

Propagation of SH-wave in a corrugated viscous sandy layer sandwiched between two elastic half-spaces

The present paper attempts to investigate the effect of sandiness, corrugated boundary surfaces, heterogeneity, and gravity on phase velocity and attenuation of SH-wave propagating in a viscous sandy layer with corrugated upper and lower boundary surfaces sandwiched between an upper heterogeneous elastic half-space and lower viscoelastic half-space under gravity. Heterogeneity associated with the upper half-space is due to exponentially varying density which is a function of depth; but the rigidity is constant. The closed form of dispersion relation is established and found to be in complex form. Real part and imaginary part of the dispersion relation correspond to dispersion curve and attenuation curve, respectively. One of the salient points of present study is the use of DEBYE asymptotic expansion to establish that the obtained dispersion relation is in well-agreement with the classical Love wave equation in isotropic case. The effect of presence and absence of corrugated boundary surfaces, measured by initial flatness parameter, on dispersion and attenuation curves have been meticulously examined. Moreover, the substantial effect of heterogeneity, sandiness, internal friction, and Biot’s gravity parameter on phase velocity and attenuation coefficient of SH-wave has been studied and demonstrated by means of graphical illustration and numerical computations.     

Diagnostics of elastic properties of a planar interface between two rough media using surface acoustic waves

The results of experimental studies on the nonlinear elastic properties of a planar interface between two media are presented—an optically polished glass substrate and flat samples with different degrees of roughness. The nonlinear elastic properties of the interfaces between two media were investigated by the spectral method using surface acoustic waves (SAWs). The effect of external pressure applied to the interface on the efficiency of the generation of the second SAW harmonic was studied. Using the measured amplitudes of the first and second harmonics of the SAW that passes along the interface, the second-order nonlinear acoustic parameter was calculated as a function of the external pressure applied to the sample at a fixed amplitude of a probing wave. It was revealed that the nonlinear parameter of the SAW is a nonmonotonic function of the pressure at the boundary. The results were analyzed on the basis of an elastic contact nonlinearity, and it is concluded that these results can be used in nondestructive testing for roughness and waviness of surfaces of flat solids.     

一类谐波激励相对转动非线性动力系统的稳定性与近似解

建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性. 关键词： 相对转动 非线性动力系统 Lyapunov函数 稳定性     

Simple microscopic theory of Amontons's laws for static friction

A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons's laws. However, the friction coefficient between bare surfaces vanishes as the area of individual contacts grows, except in the rare case of commensurate surfaces. An area independent friction coefficient is obtained for any surface geometry when an adsorbed layer of mobile atoms is introduced between the surfaces. The predictions from our simple analytic model are confirmed by detailed molecular dynamics simulations.     

Practical aspects of using Hertzian ring crack initiation to measure surface flaw densities in glasses: influence of humidity,friction and searched areas

Ring crack initiation loads on glass, using spherical Tungsten carbide (WC) and glass (G) indenters, are measured and analysed. Our measurements demonstrate that environmental humidity plays a key role in determining the load to fracture; experiments conducted without controlling this variable cannot be used to obtain material properties. The role of friction is explicitly considered for dissimilar (WC–G) elastic contacts. For this material pair, the stresses at fracture are well described by a boundary lubrication value of friction coefficient. The fracture loads are used in a fracture-mechanics formulation to calculate crack sizes on glass surfaces. The ‘searched-area’ concept for dissimilar contacts is described, and used to provide crack density values for these surfaces.     

Wetting of phospholipid membranes on hydrophilic surfaces - Concepts towards self-healing membranes

We report on the wetting behavior of phospholipid membranes on solid surfaces immersed in aqueous solution. Using fluorescence microscopy, the spreading velocity of fluid bilayers advancing from a lipid source is investigated. The kinetic spreading coefficient was measured as a function of temperature for pure DMPC membranes and as a function of charge density and cholesterol content for binary membranes. A theoretical model for the membrane flow is presented, which takes into account the liquid crystalline bilayer architecture of the lipid membrane. The spreading power results from the membrane-solid VdW interaction and is dissipated in hydrodynamic shear flow as well as by inter-monolayer friction within the bilayer. The frictional drag causes a dynamic tension gradient in the spreading membrane, which is manifested by a single exponential decay of the fluorescence intensity profile along the spreading direction. Obstacles are shown to act as pinning centers deforming the advancing line interface. However, no depinning was observed, since the centers are circumflown without abrupt relaxation. Received 6 November 1998