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.     

Effects of non-flat contact and interference on self-assembled monolayers under sliding friction

The nanotribology mechanism of alkanethiol self-assembled monolayers (SAM) chemisorbed on a gold surface under a non-flat contact by a tilt plane was studied using molecular dynamics (MD) simulations. The molecular trajectories, tilt angles, normal forces, shear forces, and frictional coefficient of the SAM were evaluated during the friction and relaxation processes for various parameters, including the tilt angle of the slider, interference magnitude, and SAM length. At the nanoscale, the magnitude of interface interactional forces is strongly dependent on the magnitude of the contact area, not on the surface geometry. The contact area and the exerted normal force of the SAM increase with decreasing the tilt angle of the slider at the same contact interference. In contrast, the periods in both normal force and shear force are gradually delayed as the tilt angle of the slider increases. Once the contact interference increases, the normal force and shear force increase together. During the sliding friction process with a smaller tilt slider angle, SAM molecules can maintain a better collective ordered structure. Short SAM molecules are more sensitive to a compressive loading and react to a larger normal force under the same contact interference due to the deformation of a larger tilt angle and decrease in chain length. The friction coefficient of SAM is significantly more dependent on the tilt angle of the slider than the contact interference.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Study of the shear-rate dependence of granular friction based on community detection

In this study, computer simulations are performed on three-dimensional granular systems under shear conditions. The system comprises granular particles that are confined between two rigid plates. The top plate is subjected to a normal force and driven by a shearing velocity. A positive shear-rate dependence of granular friction, known as velocity-strengthening, exists between the granular and shearing plate. To understand the origin of the dependence of frictional sliding, we treat the granular system as a complex network, where granular particles are nodes and normal contact forces are weighted edges used to obtain insight into the interiors of granular matter. Community structures within granular property networks are detected under different shearing velocities in the steady state. Community parameters, such as the size of the largest cluster and average size of clusters, show significant monotonous trends in shearing velocity associated with the shear-rate dependence of granular friction. Then, we apply an instantaneous change in shearing velocity. A dramatic increase in friction is observed with a change in shearing velocity in the non-steady state. The community structures in the non-steady state are different from those in the steady state. Results indicate that the largest cluster is a key factor affecting the friction between the granular and shearing plate.     

基于非连续能量耗散的滑动摩擦系数计算模型

分析了界面摩擦状态下能量非连续耗散过程,建立了简化条件下晶体材料界面摩擦滑动摩擦系数计算模型.结果表明:在弹性接触状态下,滑动摩擦系数与载荷及实际接触面积无关,当实际接触面积接近名义接触面积时,滑动摩擦系数随载荷增加而减小.在缓慢滑动时,滑动摩擦系数随滑动速度的增高而缓慢增大,相对滑动速度愈高,滑动摩擦系数增大趋势愈显著.滑动摩擦系数随晶格常数的增加而降低,而当晶格常数较大时,其变化对滑动摩擦系数影响较小.同时,滑动摩擦系数随原子的可能温升增加而增大.研究结论对工程应用及相关的理论研究具有一定的参考意义. 关键词： 滑动摩擦系数 非连续能量耗散 界面摩擦     

Molecular dynamics investigation on the atomic-scale friction behaviors between copper(0 0 1) and diamond(1 1 1) surfaces

Classical molecular dynamics (MD) simulations are conducted to examine the atomic-scale friction behavior of an infinite flat-flat contact between copper(0 0 1) and diamond(1 1 1) surfaces. Two types of diamond surface, namely H-free and hydrogenated, are constructed and on each of them the copper counterface is brought to slide along the [1 1 −2] and [1 −1 0] crystallographic directions with a variety of loads. The simulation results demonstrate that the hydrogen atoms chemisorbed to the diamond surface can to large extent eliminate the directional dependency of its friction behavior with copper. Under pressures less than 30 GPa, the sliding between copper and hydrogenated is wearless. In this period, the shear stress of them just slightly increases to 0.6 GPa. Between 30 GPa and 32 GPa, copper atoms near the interface begin to be worn and incorporate into the diamond substrate and this causes a sharp shift from 0.6 GPa to 2.7 GPa in their shear stress. In contrast, the sliding process between copper and H-free diamond is always wearless even under pressure beyond 40 GPa. The H-free [1 −1 0] model exhibits much higher shear stress than H-free [1 1 −2] under pressures less than 35 GPa. Beyond 35 GPa, they present nearly consistent shear stress evolution. Moreover, the simulations for hydrogenated diamond models suggest that their friction behavior is independent on sliding velocity only under wearless sliding regime.     

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modified distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

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.     

Crystalline misfit-angle implications for solid sliding

For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the pinning energy barrier dependency on the misfit angle and contact area. This simple model allows us to investigate a broad contact-size and angular range, thus obtaining the statistical properties of the energy barriers opposing sliding for a single asperity. These data are used to generate the distribution of static frictional thresholds for the contact of polycrystals, as in dry or even lubricated friction. This distribution is used as the input of a master equation to predict the sliding properties of macroscopic contacts.     

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.     

Friction and normal forces of model friction modifier additives in simulations of boundary lubrication

ABSTRACT

Interaction forces between solid surfaces are often mitigated by adsorbed molecules that control normal and friction forces at nanoscale separations. Molecular dynamics simulations were conducted of opposing semi-ordered monolayers of united-atom chains on sliding surfaces to relate friction and normal forces to imposed sliding velocity and inter-surface separation. Practical examples include adsorbed friction-modifier molecules in automatic transmission fluids. Friction scenarios in the simulations had zero, one, or two fluid layers trapped between adsorbed monolayers. Sliding friction forces increased with sliding velocity at each stable separation. Lower normal forces were obtained than in most previous nanotribology molecular simulations and were relatively independent of sliding speed. Distinguishing average frictional force from its fluctuations showed the importance of system size. Uniform velocities were obtained in the sliding direction across each adsorbed film, with a gradient across the gap containing trapped fluid. The calculated friction stress was consistent with measurements reported using a surface forces apparatus, indicating that drag between an adsorbed layer and trapped fluid can account sufficiently for sliding friction in friction modifier systems. An example is shown in which changes in molecular organisation parallel to the surface led to a large change in normal force but no change in friction force.     

A model for the characterization of friction contacts in turbine blades

Stresses produced by the forced vibrations can lead to a significant reduction of the life of turbo engine blades. To predict the vibration amplitudes of this components an accurate dynamic analysis is necessary. The forced response calculation of these dynamic systems is strongly affected by the presence of the contact interfaces (i.e., underplatform dampers, shrouds, root joints). Different contact models are available in literature. These models make use of contact parameters, contact stiffness and friction coefficient to evaluate the damping and stiffness related to the contact interfaces. In this paper a model is proposed to characterize friction contact of non-spherical contact geometries obeying the Coulomb friction law with constant friction coefficient and constant normal load. The hysteresis curves of the oscillating tangential contact forces vs. relative tangential displacements and the dissipated energy at the contact are obtained for different contact geometries. The developed model is suitable to be implemented in numerical solvers for the calculation of the forced response of turbine blades with embedded friction contacts.     

Interaction potential and hopping dynamics governing sliding friction

The friction force on a nanometer-sized tip sliding on a surface is related to the thermally activated hopping of the contact atoms on an effective atomic interaction potential. A general analytical expression relates the height of this potential and the hopping attempt frequency to measurements of the velocity dependence of the friction force performed with an atomic force microscope. While the height of the potential is roughly proportional to the normal load, the attempt frequency falls in the range of mechanical eigenfrequencies of the probing tip in contact with the surface.     

Tribological properties of silicate materials on nano and microscale

We studied the friction properties of four model silicate materials at the nanoscale and microscale. From nanotribology, we characterized the tribological properties at single asperity contact scale and from microtribology, we characterized the tribological properties at multi asperity contact scale. First, for each material we measured chemical composition by XPS, Young's modulus by acoustical microscopy and roughness σ by atomic force microscopy (AFM). Second, we measured the nanofriction coefficients with an AFM and the microfriction coefficients with a ball probe tribometer, for three hardnesses of the ball probe. We identified one friction mechanism at the nanoscale (sliding friction) and two friction mechanisms at the microscale (sliding friction and yielding friction). Comparison of the nano and microfriction coefficients at the same sliding friction regime shown, that the tribological properties of these materials didn’t depend on roughness.     

Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction

A transition from stick-slip to continuous sliding is observed for atomically modulated friction by means of a friction force microscope. When the stick-slip instabilities cease to exist, a new regime of ultralow friction is encountered. The transition is described in the framework of the Tomlinson model using a parameter eta which relates the strength of the lateral atomic surface potential and the stiffness of the contact under study. Experimentally, this parameter can be tuned by varying the normal load on the contact. We compare our results to a recently discussed concept called superlubricity.     

Experimental study of different modes of block sliding along interface. Part 1. Laboratory experiments

This paper is the first part of an experimental work on studying the formation of different deformation modes of rock discontinuities under laboratory and field conditions. The formation conditions of different sliding modes were studied under laboratory conditions for several types of discontinuities, such as rigid surface contact and cracks filled with quartz sand, talc, and clay. A wide range of shear deformation modes were experimentally reproduced—from dynamic slip with a maximum velocity of tens of mm/s to stable sliding with a velocity of 1 µm/s. The behavior of a crack with a clay-containing gouge drastically changes after its wetting. The larger is the content of clay, the longer is the slip duration. The motion of a block consists of a long phase (~100 s) in which displacement velocity smoothly increases, and a retardation phase of almost the same duration in which displacement velocity decreases down to a few tens of µm/s. The used sensors detected no acoustic emission prior to the beginning of block sliding as well as on all stages of block motion until its full stop. It is shown that slow slip events have all stages typical for stick-slip motion: acceleration, long sliding, retardation, arrest, and quiescence. The conducted laboratory experiments substantiate the earlier statement that all types of deformation processes in the Earth’s crust produce a common range of phenomena.     

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.     

Ultrasonic excitation affects friction interactions between food materials and cutting tools

In the food industry, ultrasonic cutting is used to improve separation by a reduction of the cutting force. This reduction can be attributed to the modification of tool–workpiece interactions at the cutting edge and along the tool flanks because of the superposition of the cutting movement with ultrasonic vibration of the cutting tool. In this study, model experiments were used to analyze friction between the flanks of a cutting tool and the material to be cut. Friction force at a commercial cutting sonotrode was quantified using combined cutting–friction experiments, and sliding friction tests were carried out by adapting a standard draw-off assembly and using an ultrasonic welding sonotrode as sliding surface. The impact of material parameters, ultrasonic amplitude, and the texture of the contacting food surface on friction force was investigated. The results show that ultrasonic vibration significantly reduces the sliding friction force. While the amplitude showed no influence within the tested range, the texture of the contact surface of the food affects the intensity of ultrasonic transportation effects. These effects are a result of mechanical interactions and of changes in material properties of the contact layer, which are induced by the deformation of contact points, friction heating and absorption heating because of the dissipation of mechanical vibration energy.     

Dilatancy and friction in sheared granular media

We introduce a simple model to describe the frictional properties of granular media under shear. We model the friction force in terms of the horizontal velocity and the vertical position z of the slider, interpreting z as a constitutive variable characterizing the contact. Dilatancy is shown to play an essential role in the dynamics, inducing a stick-slip instability at low velocity. We compute the phase diagram, analyze numerically the model for a wide range of parameters and compare our results with experiments on dry and wet granular media, obtaining a good agreement. In particular, we reproduce the hysteretic velocity dependence of the frictional force. Received 16 November 1999     

Diffusion model of internal friction in nanocrystalline materials

The stress normal and tangenital components arise in grain-boundary segments differently oriented with respect to an external periodic load, causing the fluxes of vacancies and impurity atoms between neighboring segments. By solving the diffusion problem, one can find the velocity of mutual displacement of grains, the stress distribution in the segments with allowance for stress adjustment, and the amount of internal friction. The frequency dependence of the internal friction shows peaks associated with the redistribution of impurity atoms over the segments, grain sliding, and a high-temperature background.