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.     

Stick-slip regime of melting of boundary lubrication taking into account spatial inhomogeneity

The processes of boundary friction between two atomically smooth solid surfaces with an ultrathin layer of lubricant between them are studied in the context of the model of the first-order phase transitions, taking into account the spatial inhomogeneity. The stick-slip regime of motion, which is often observed experimentally for such systems, is considered. Such a regime is represented as the periodic first-order phase transitions between the structural states of the lubricant. It is shown that during motion, the lubricant tends to assume a homogeneous structure over the sliding plane, which results in the periodicity of time dependences of the basic parameters in the stick-slip regime. The dependence of the order parameter on the shear rate is analyzed and it is shown that this dependence has the same shape for all the regions on the contact plane.     

Effect of correlated temperature fluctuations on the phase dynamics in an ultrathin lubricant film

The melting of an ultrathin lubricant film at friction between atomically smooth surfaces is studied with allowance for fluctuations of its temperature, which are described by the Ornstein-Uhlenbeck process. The behavior of the most probable types of shear stresses arising in the lubricant is considered, and phase diagrams for second-and first-order phase transformations (the melting of an amorphous lubricant and that of a crystalline lubricant, respectively) are constructed. It is shown that, in the former case, lubricant temperature fluctuations lead to the formation of a stick-slip friction domain separating the domains of dry and sliding friction, which is typical of first-order transitions. In the latter case, three domains of stick-slip friction arise, which mark the transitions between dry friction and metastable and stable sliding friction. As the time of correlation of lubricant temperature fluctuations gets longer, the temperature of rubbing surfaces rises to the point where sliding friction sets in.     

Melting of ultrathin lubricant film due to dissipative heating of friction surfaces

Melting of an ultrathin lubricant film during friction between atomically smooth surfaces is studied. Additive noise of shear stress and strain as well as of film temperature is introduced and the phase diagram is constructed. On the diagram, the noise intensity for this temperature and the temperature of friction surfaces determine the regions of sliding, dry, and stick-slip friction. As a result of numerical analysis of the Langevin equation for various regions of the diagram, time series of stresses are constructed, which make it possible to explain the experiment on friction, in which intermittent motion is observed. Lubricant melting due to dissipative heating of friction surface is considered and the experimental time dependences of friction force are interpreted.     

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.     

Stochastic theory of ultrathin lubricant film melting in the stick-slip regime

Melting of an ultrathin lubricant film under friction between atomically smooth surfaces is studied in terms of the Lorentz model. Additive noise associated with shear stresses and strains, as well as with film temperature, is introduced, and a phase diagram is constructed where the noise intensity of the film temperature and the temperature of rubbing surfaces define the domains of sliding, dry, and stick-slip friction. Conditions are found under which stick-slip friction proceeds in the intermittent regime, which is characteristic of selforganized criticality. The stress self-similar distribution, which is provided by temperature fluctuations, is represented with allowance for nonlinear relaxation of stresses and fractional feedbacks in the Lorentz system. Such a fractional scheme is used to construct a phase diagram separating out different types of friction. Based on the study of the fractional Fokker-Planck equation, the conclusion is drawn that stick-slip friction corresponds to the subdiffusion process.     

Periodic intermittent regime of a boundary flow

Melting of an ultrathin lubricant film during friction between two atomically smooth surfaces is investigated using the Lorentz model for approximating the viscoelastic medium. Second-order differential equations describing damped harmonic oscillations are derived for three boundary relations between the shear stresses, strain, and temperature relaxation times. In all cases, phase portraits and time dependences of stresses are constructed. It is found that under the action of a random force (additive uncorrelated noise), an undamped oscillation mode corresponding to a periodic intermittent regime sets in, which conforms to a periodic stick-slip regime of friction that is mainly responsible for fracture of rubbing parts. The conditions in which the periodic intermittent regime is manifested most clearly are determined, as well as parameters for which this regime does not set in the entire range of the friction surface temperature.     

Phenomenological theory for the melting of a thin lubricant film between two atomically smooth solid surfaces

A thermodynamic model is developed for the melting of an ultrathin lubricant film squeezed between two atomically smooth solid surfaces. To describe the state of lubricant, an excess volume parameter is introduced; it appears due to the chaos in the structure of a solid body induced by melting. This parameter increases with the total internal energy upon melting. Thermodynamic melting and shear melting are described. The dependences of the friction force on the lubricant temperature and the shear rate of friction surfaces are analyzed. The calculated results are compared to the experimental data.     

Tribological properties of dry,fluid, and boundary friction

A friction pair is studied under lubricant-free dry friction, hydrodynamic, and boundary lubricant conditions. It is shown that, in dry friction, the number of harmonics in the time dependence of the coordinate of the lower rubbing block decreases with increasing frequency of an applied periodic action until the interacting surfaces stick when a critical frequency is exceeded. The surfaces then move together. The behavior of a friction pair with a lubricant made of a Newtonian fluid, pseudoplastic fluid, or dilatant non-Newtonian fluid is analyzed in the hydrodynamic case. It is found that a pseudoplastic fluid or a boundary lubricant leads a intermittent (stick-slip) friction mode, which is one of the main causes of fracture of rubbing parts, over a wide parametric range.     

Influence of Stress Dependence of Lubricant Shear Modulus on Self-Similar Behavior of Stress Time Series

Here we consider melting of an ultrathin lubricant layer between two atomically smooth solid surfaces taking into account the stress dependence of the lubricant shear modulus and its decrease with increasing stress (strain). In the adiabatic approximation with the stress relaxation time far longer than strain and temperature relaxation times, a Langevin equation is written and its respective Fokker-Planck equation is derived using the Stratonovich calculus. Phase diagrams for the steady case are presented illustrating the effect of the system parameters on the lubricant behavior. A joint numerical and analytical analysis demonstrates a very close match between probability distributions at different parameters. It is shown that in a limited stress range, a self-similar mode of dry friction is established showing up in self-similar behavior of stress time series.     

Nanopolishing by colloidal nanodiamond in elastohydrodynamic lubrication

In this paper, the feasibility of using explosion synthesized diamond nanoparticles with an average particle size (APS) of 3–5 nm with a concentration of 1 % by weight for improving lubrication and friction in elastohydrodynamic lubrication (EHL) was investigated. Owing to the orders of magnitude increase in the viscosity of the lubricant in the EHL contact zone, diamond nanoparticles in the lubricant polish the surfaces at the nanoscale which decreases the composite roughness of contacting surfaces. The reduced composite roughness results in an increased film thickness ratio which yields lower friction. In the numerical analysis, governing equations of lubricant flow in the full elastohydrodynamic lubrication were solved, and the shear stress distribution over the fluid film was calculated. Using an abrasion model and the shear stress distribution profile, the material removal by the nanofluid containing nanoparticles and the resultant surface roughness were determined. The numerical analysis showed that in full EHL regime, the nanolubricant can reduce the composite roughness of moving surfaces. Experimental results from prior studies which exhibited surface polishing by such nanolubricants in boundary, mixed, and full elastohydrodynamic lubrication were used for comparison to the numerical model.     

Boundary lubrication properties of materials with expansive freezing

We have performed molecular dynamics simulations of solid-solid contacts lubricated by a model fluid displaying many of the properties of water, particularly its expansive freezing. Near the region where expansive freezing occurs, the lubricating film remains fluid, and the friction force decreases linearly as the shear velocity is reduced. No sign of stick-slip motion is observed, even at the lowest velocities. We give a simple interpretation of these results, and suggest that, in general, good boundary lubrication properties will be found in the family of materials with expansive freezing.     

Correlation between charge transfer and stick-slip friction at a metal-insulator interface

Techniques have been developed that facilitate the measurement and imaging of the charge exchanged between metal-insulator surfaces in relative motion. In the regime where the forces of friction lead to stick-slip motion, we find that the charge transfer accompanying the slip events is proportional to the force jumps and is bunched at the stick locations. The constant of proportionality is measured in electron volts per angstrom and has a small variance over a large range of slip sizes, suggesting that in these experiments macroscopic friction originates from and scales to the intrinsic electronic interactions that form between metal and insulator surfaces.     

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.     

Coefficient of friction between a rigid conical indenter and a model elastomer: Influence of local frictional heating

We investigate the coefficient of friction between a rigid cone and an elastomer with account of local heating due to frictional dissipation. The elastomer is modeled as a simple Kelvin body and an exponential dependency of viscosity on temperature is assumed. We show that the coefficient of friction is a function of only two dimensionless variables depending on the normal force, sliding velocity, the parameter characterizing the temperature dependence as well as shear modulus, viscosity at the ambient temperature and the indenter slope. One of the mentioned dimensionless variables does not depend on velocity and determines uniquely the form of the dependence of the coefficient of friction on velocity. Depending on the value of this controlling variable, the cases of weak and strong influence of temperature effects can be distinguished. In the case of strong dependence, a generalization of the classical “master curve” procedure introduced by Grosch is suggested by using both horizontal and vertical shift factors.     

Kinetics and dynamics of frictional stick-slip in mesoscopic boundary lubrication

The kinetics and dynamics of frictional stick-slip motion of a slider of size extending from mesoscopic upward is analyzed within the framework of a multi-contact, earthquake-like model. The microscopic contacts are characterized by a distribution of static thresholds for individual breaking. The condition for an overall elastic instability leading to stick-slip sliding are derived and details of the slip motion are studied theoretically. The crucial model parameters emerging from this analysis include the delay time for each micro-contact to reform after breaking, the strength of elastic interaction between the contacts, the elasticity of contacts and of the slider, and the distribution of static thresholds for their breaking. The dynamics is also studied with the help of a scaling procedure. As a prototype application, we adopt parameters appropriate to describe recent surface force apparatus (SFA) boundary lubrication experiments. Despite suggestions of extremely large lubricant viscosities, the experimental data are shown to be fully compatible with ordinary, bulk-like viscosity values once the multi-contact aspects are taken into account.     

Hysteresis from dynamically pinned sliding states

We report a surprising hysteretic behavior in the dynamics of a simple one-dimensional nonlinear model inspired by the tribological problem of two sliding surfaces with a thin solid lubricant layer in between. In particular, we consider the frictional dynamics of a harmonic chain confined between two rigid incommensurate substrates which slide with a fixed relative velocity. This system was previously found, by explicit solution of the equations of motion, to possess plateaus in parameter space exhibiting a remarkable quantization of the chain center-of-mass velocity (dynamic pinning) solely determined by the interface incommensurability. Starting now from this quantized sliding state, in the underdamped regime of motion and in analogy to what ordinarily happens for static friction, the dynamics exhibits a large hysteresis under the action of an additional external driving force F_ext. A critical threshold value F_c of the adiabatically applied force F_ext is required in order to alter the robust dynamics of the plateau attractor. When the applied force is decreased and removed, the system can jump to intermediate sliding regimes (a sort of “dynamic” stick-slip motion) and eventually returns to the quantized sliding state at a much lower value of F_ext. Hysteretic behavior is also observed as a function of the external driving velocity.     

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.     

Temperature dependence of the structure and shear response of a Σ11 asymmetric tilt grain boundary in copper from molecular-dynamics

We investigate the effect of temperature on the structure and shear response of a Σ11 asymmetric tilt grain boundary in a classical embedded-atom model of elemental copper using molecular dynamics simulations. As the temperature is increased the structure of the boundary disorders considerably, but with a boundary width that remains finite at the melting point. The disordering of the boundary structure becomes significant for homologous temperatures above 0.83 (1100?K). As temperature increases above this point the boundary width and roughness increases monotonically. Near the temperature where the boundary starts to disorder we observe a change in the temperature dependence of the ideal shear strength of the boundary, as well as the value of the coupling parameter β, defined as the ratio of the velocity of relative translation of the grains parallel to the boundary plane to that corresponding to the motion of the boundary normal to its plane.     

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.