Nonlinear spring model for frictional stick-slip motion

Frictional stick-slip dynamics is discussed using a model of one oscillator pulled by a nonlinear spring force. We focus our attention on the nonlinear spring parameter k₀. The dynamics of the model is carefully studied, both numerically and analytically. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasi-periodic and chaotic states. On the other hand, and for a good selection of parameters , the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of motion strongly depends on the nonlinear parameter k₀. The system also displays resonance at fractional frequencies of the oscillator.     

Very low friction for natural diamond in water of different pH values

Very high reductions in the friction coefficient are reported for natural diamond sliding upon natural diamond when water is introduced at the interface of contact. This reduction is found to depend on the pH value of the water, the load and the sliding velocity. The results are interpreted in terms of the reduction of adhesion due to adsorption of the liquid on the surface, and of graphitisation occurring during sliding, with graphite acting as a lubricant. Received 15 September 1999     

Generalization of a nonlinear friction relation for a dimer sliding on a periodic substrate

An atomic cluster moving along a solid surface can undergo dissipation of its translational energy through a direct mode, involving the coupling of the center-of-mass motion to thermal excitations of the substrate, and an indirect mode, due to damping of the internal motion of the cluster, to which the center-of-mass motion can be coupled as a result of surface potential. Focussing only on the less well understood indirect mode, on the basis of numerical solutions, we present, departures from a recently reported simple relationship between the force and velocity of nonlinear friction. A generalization of the analytic considerations that earlier led to that relationship is carried out and shown to explain the departures satisfactorily. Our generalization treats for the system considered (dimer sliding over a periodic substrate) the complete dependence on several of the key parameters, specifically internal dissipation, natural frequency, substrate corrugation, and length ratio. Further predictions from our generalizations are found to agree with new simulations. The system analyzed is relevant to nanostructures moving over crystal surfaces.     

Rolling friction of a hard cylinder on a viscous plane

The resistance against rolling of a rigid cylinder on a flat viscous surface is investigated. We found that the rolling-friction coefficient reveals strongly non-linear dependence on the cylinder's velocity. For low velocity the rolling-friction coefficient rises with velocity due to increasing deformation rate of the surface. For larger velocity, however, it decreases with velocity according to decreasing contact area and deformation of the surface. Received 24 December 1998 and Received in final form 14 January 1999     

Influence of surface roughness and contact load on friction coefficient and scratch behavior of thermoplastic olefins

To study the effects of surface roughness and contact load on the friction behavior and scratch resistance of polymers, a set of model thermoplastic olefins (TPO) systems with various surface roughness (R_a) levels were prepared and evaluated. It is found that a higher R_a corresponds to a lower surface friction coefficient (μ_s). At each level of R_a, μ_s gets larger as contact load increases, with a greater increase in μ_s as R_a level increases. It is also observed that with increasing contact load and increasing R_a, the μ_s tend to level off. In evaluating TPO scratch resistance, a lower μ_s would delay the onset of ductile drawing-induced fish-scale surface deformation feature, thereby raising the load required to cause scratch visibility. However, as the contact load is further increased, the μ_s evolves to become scratch coefficient of friction (SCOF) as significant sub-surface deformation and tip penetration occur and material displacement begins, i.e., ploughing. No dependence of R_a and μ_s on the critical load for the onset of ploughing is observed. In this work, the distinction between μ_s and SCOF will be illustrated. Approaches for improving scratch resistance of polymers via control of R_a are also discussed.     

Front roughening in three-dimensional imbibition

We investigate the structure and dynamics of the interface between two immiscible liquids in a three-dimensional disordered porous medium. We apply a phase-field model that includes explicitly disorder and discuss both spontaneous and forced imbibition. The structure of the interface is dominated by a length scale ξ_× which arises from liquid conservation. We further show that disorder in the capillary and permeability act on different length scales and give rise to different scalings and structures of the interface properties. We conclude with a range of applications.     

Friction and energy dissipation mechanisms in adsorbed molecules and molecularly thin films

This review provides an overview of recent advances that have been achieved in understanding the basic physics of friction and energy dissipation in molecularly thin adsorbed films and the associated impact on friction at microscopic and macroscopic length scales. Topics covered include a historical overview of the fundamental understanding of macroscopic friction, theoretical treatments of phononic and electronic energy dissipation mechanisms in thin films, and current experimental methods capable of probing such phenomena. Measurements performed on adsorbates sliding in unconfined geometries with the quartz crystal microbalance technique receive particular attention. The final sections review the experimental literature of how measurements of sliding friction in thin films reveal energy dissipation mechanisms and how the results can be linked to film-spreading behavior, lubrication, film phase transitions, superconductivity-dependent friction, and microelectromechanical systems applications. Materials systems reported on include adsorbed films comprised of helium, neon, argon, krypton, xenon, water, oxygen, nitrogen, carbon monoxide, ethane, ethanol, trifluoroethanol, methanol, cyclohexane, ethylene, pentanol, toluene, tricresylphosphate, t-butylphenyl phosphate, benzene, and iodobenzene. Substrates reported on include silver, gold, aluminum, copper, nickel, lead, silicon, graphite, graphene, fullerenes, C60, diamond, carbon, diamond-like carbon, and YBa₂Cu₃O₇, and self-assembled monolayers consisting of tethered polymeric molecules.     

Development of a new molecular dynamics method for tribochemical reaction and its application to formation dynamics of MoS2 tribofilm

Recently we have developed a novel molecular dynamics program NEW-RYUDO-CR, which can deal with chemical reactions. The developed method has been applied to the study of tribochemical reaction dynamics of MoS₂ tribofilm on iron surface. The initially amorphous MoS₂ layer self-organized its structure as result of the tribochemical reactions and formed layered MoS₂ tribofilm. The friction coefficient significantly decreased as the MoS₂ tribofilm was formed. Besides, sliding was observed between sulfur layers of MoS₂ tribofilms which occurred due to repulsive Coulombic interaction forces between sulfur atoms. This indicates that the formation of the layered MoS₂ tribofilm is important to achieve better lubrication properties.     

Laser-generated surface acoustic waves in a ring-shaped waveguide resonator

Surface acoustic wave (SAW) waveguide resonator is formed by a ring-shaped strip of copper 10 μm wide and ∼130 μm in diameter embedded into a 0.8 μm thick layer of silica on a silicon wafer. SAWs are excited at one side of the copper ring by a short laser pulse focused into a spatially periodic pattern and detected via diffraction of the probe laser beam overlapped with the excitation spot. SAW wavepackets with central frequency 460 MHz travel around the ring and are detected each time they make a full circle and pass trough the probe spot. Potential applications of ring resonators for SAWs are discussed.     

Hysteresis and elastic interactions of microasperities in dry friction

Velocity independent dry friction of a slider upon a base is due to an hysteretic response of relative displacement to a tangential driving force F. We show that the purely elastic model for multistability considered in a previous publication is in no way essential: multistability arises just as well from adhesion. We emphasize the physical consequences of multistability for dynamic/static, a.c./d.c. friction. When the slider is moved from rest by an amount the transition from the zero force static configuration to dynamic behaviour is progressive, spreading on a range equal to the width of the hysteresis cycle. When is small, an elastic restoring force ensues, in agreement with observations. The competition of that elastic pinning with bulk elasticity generates a screening length which we believe is the natural size of Burridge Knopoff blocks. We then study the effect of elastic interactions between asperities: it is weak for dilute asperities, but its long range makes it important. In lowest order the interaction mediated displacement of a given asperity has logarithmically divergent fluctuations: they become comparable to the asperity radius when the slider size reaches another characteristic “Larkin length”, which for dilute micronic asperities is exponentially large. We give arguments suggesting that individually monostable asperities display collective multistability on scales larger than . For individually multistable sites we show that elastic interactions give rise to cascade processes in which the spinodal jump of a given asperity triggers the jump of others. We estimate the size of these cascades that should show up in the noise spectrum. Received: 3 February 1998 / Accepted: 19 March 1998     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

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.     

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.     

Influence of nanometer scale film structure of ZDDP tribofilm on Its mechanical properties: A computational chemistry study

We investigated the influence of a nanometer scale film structure of a tribofilm generated from zinc dialkyldithiophosphate (ZDDP) anti-wear additive on its mechanical properties using a combined molecular dynamics (MD) and finite element (FE) method. The frictional behavior of an interface between a native iron oxide layer on steel surface and zinc metaphosphate - regarded as a model material of ZDDP tribofilm - was firstly studied using the MD method. The results showed that the iron atoms in the oxide layer diffused into the phosphate layer during the friction process. The zinc atoms in the phosphate layer also diffused into the oxide layer. Significant interdiffusion of iron and zinc atoms was observed with increasing simulation time. Thus, metallic phosphate with a gradient composition of iron and zinc atoms was formed on the phosphate/oxide interface. We then constructed an axisymmetric nanoindentation simulation model from the MD-derived structures at a certain simulation time and carried out a FE calculation. As a result, we found that the rubbed ZDDP tribofilm, including the phosphate with the gradient composition of metallic atoms, showed larger contact stiffness and hardness. The combined MD/FE simulation indicates that the tribofilm becomes stiffer and harder due to the interdiffusion of iron and zinc atoms on the tribofilm/oxide interface. We have found that the gradient composition formation in ZDDP tribofilm during friction process influences on its mechanical properties.     

Adhesion between an elastic body and a randomly rough hard surface

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account 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 macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. Received 3 April 2002     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

A phenomenology of boundary lubrication: the lumped junction model

We propose a phenomenological model of boundary lubricated junctions consisting of a few layers of small molecules which describes the rheological properties of these sytems both in the static, frozen, and sliding, molten, states as well as the dynamical transition between them. Two dynamical regimes can be distinguished, according to the level of internal damping of the junction, which depends on its thickness and on the normal load. In the overdamped regime, under driving at constant velocity v through an external spring, the motion evolves continuously from “atomic stick-slip” to modulated sliding. Underdamped systems exhibit, under given external stress, a range of dynamic bistability where the sheared static state coexists with a steadily sliding one. The frictional dynamics under shear driving is analyzed in detail, it provides a complete account of the qualitative dynamical scenarios observed by Israelashvili et al., and yields semiquantitative agreement with experimental data. A few complementary experimental tests of the model are suggested. Received: 18 December 1997 / Received in final form and accepted: 26 March 1998     

Impact of gel balls beyond the Hertzian regime

We study experimentally the impact of spherical gel balls on a rigid substrate, where the balls largely deform like a pancake at high impact velocities. In our previous study (Y. Tanaka, Y. Yamazaki, K. Okumura, Europhys. Lett. 63, 149 (2003)), we measured the contact time τ_f and maximally deformed size versus impact velocity and explained the behaviors at the scaling level. In this study, we further measure τ_m, the time required to reach the maximum deformation (from the initial contact), and the restitution coefficient e. We also make a static experiment where we obtain the force-deformation curve of the gel balls up to fairly large deformations to explain the data on the impact. We propose two phenomenological treatments going beyond the scaling argument, one for intermediate impact velocities and the other for large velocities; the former is based on the static experiment while the latter on a Lagrangian constructed from appropriate constraints. Results from these treatments reproduce the experimental behavior of τ_m.     

Non-Amontons behavior of friction in single contacts

We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to a widely spread belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plasticity of a glass-like interfacial layer in the former case, and by pinning of polymer chains on the substrate in the latter one.     

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V = V _c. For V > V _c, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than V _c, hence with the existence of the healing instability. Received: 7 March 2003 / Accepted: 2 May 2003 / Published online: 11 June 2003 RID="b" ID="b"e-mail: ronsin@gps.jussieu.fr