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.     

Dynamics of the coefficient of friction between a rigid conical indenter and a viscoelastic foundation under step-wise change of sliding velocity

We numerically calculated the coefficient of friction between a rigid cone and a viscoelastic Kelvin body under step-wise change of the velocity of sliding. The time dependence of the coefficient of friction has been empirically approximated. We show that the transition process has different character for the cases of increasing and decreasing of the sliding velocity.     

Critical Velocity of Controllability of Sliding Friction by Normal Oscillations for an Arbitrary Linear Rheology

The application of ultrasonic vibrations is an established procedure in industry in order to significantly reduce and control sliding friction. One of the main characteristics of this phenomenon is that, beyond a certain critical sliding velocity, the friction is no longer controllable—although oscillations are still being externally applied. an a previous series of related studies, closed-form solutions of the critical velocity have been derived with respect to pure elastic and specific viscoelastic models. In the present paper we present a universal formula of the critical velocity which is valid for arbitrary linear rheology. The derivation relies on the same theoretical basis of the previous studies, where the reduction of friction is ascribed to a stick-slip motion of the contact. Therefore, all previous results represent limiting and special cases of this universal equation. In the second part of this paper we pursue the numerical analysis of the previous studies by investigating the reduction of friction for a viscoelastic Kelvin material for the first time.     

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.     

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     

Slow cracklike dynamics at the onset of frictional sliding

We propose a friction model which incorporates interfacial elasticity and whose steady state sliding relation is characterized by a generic nonmonotonic behavior, including both velocity weakening and strengthening branches. In 1D and upon the application of sideway loading, we demonstrate the existence of transient cracklike fronts whose velocity is independent of sound speed, which we propose to be analogous to the recently discovered slow interfacial rupture fronts. Most importantly, the properties of these transient inhomogeneously loaded fronts are determined by steady state front solutions at the minimum of the sliding friction law, implying the existence of a new velocity scale and a "forbidden gap" of rupture velocities. We highlight the role played by interfacial elasticity and supplement our analysis with 2D scaling arguments.     

Dry friction in the Frenkel-Kontorova-Tomlinson model: dynamical properties

Wearless friction is investigated in a simple mechanical model called Frenkel-Kontorova-Tomlinson model. We have introduced this model in [Phys. Rev. B, 53, 7539 (1996)] where the static friction has already been considered. Here the model is treated for constant sliding speed. The motion of the internal degrees of freedom is regular for small sliding velocities or weak interaction between the sliding surfaces. The regular motion for large velocities is strongly determined by normal and superharmonic resonance of phonons excited by the so-called “washboard wave”. The kinetic friction has maxima near these resonances. For increasing interaction strength the regular motion becomes unstable due to parametric resonance leading to quasistatic and chaotic motion. For sliding velocities beyond first-order parametric resonance bistability occurs between the strongly chaotic motion (fluid sliding state), where friction is large and a regular motion (solid sliding state), where friction is weak. The fluid sliding state is mainly determined by the density of decay channels of m washboard waves into n phonons. This density describes qualitatively the effectiveness of the energy transfer from the uniform sliding motion into the microscopic, irregular motion of the degrees of freedom at the sliding interface. For a narrow interval of the sliding velocities we also found enhanced friction due to coherent motion. In the regime of coherent motion nondestructive interactions of dark envelope solitons occur.     

Nanoscale interaction mechanism between a solid tip and a layered material while in relative motion: the boric acid case

The interaction occurring between a layered material (boric acid) and an atomic force microscope tip is discussed. It is shown that images containing the periodicity of a boric acid crystal, and the low friction occurring between the tip and the crystal surface, are caused by an effective tip composed of boric acid molecules. The friction at the sliding system decreases with an increase of the scanning velocity, suggesting that the dependence of friction on the velocity can be caused by a change of the energy dissipation regime from the nonlinear dynamics of a sliding system to phonon excitation.     

Friction and wear of a spherical indenter under influence of out-of-plane ultrasonic oscillations

This paper presents an experimental and theoretical investigation of friction and wear of a spherical indenter. With the pin-on-disc-tribometer the out-of-plane oscillations are applied to the sliding indenter. Oscillations lead to a decrease of the coefficient of friction, and this effect is also related to the sliding velocity and oscillation amplitude. During the sliding movement, the contact area of indenter increases due to the wear of material. This radius of the worn spherical cap is measured after each sliding period. It is found that the radius of the wear flat increases with sliding distance according to a power law with the power 1/4 and is independent of the sliding velocity. It further is practically insensitive to the presence of oscillations. A theoretical analysis and a numerical simulation based on the method of dimensionality reduction are carried out, both describing the experimental data very well.     

Ice internal friction: Standard theoretical perspectives on friction codified,adapted for the unusual rheology of ice,and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials.

We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.     

3 GPa熔融盐固体介质三轴高温压力容器的轴压摩擦力标定

 在温度标定和围压标定的基础上,采用轴压循环方法,对3 GPa固体介质三轴高温高压实验系统的轴压摩擦力进行了标定,分析了围压、温度、轴向位移速率、装样方式（盐套类型）等实验条件对轴压摩擦力的影响。结果表明：静摩擦力、挤压摩擦力和滑动摩擦力3种轴压摩擦力对轴向应力的影响不同,其中静摩擦力和挤压摩擦力对轴向应力的影响很小,影响应力精度的主要是滑动摩擦力。静摩擦力及滑动摩擦力与围压正相关;静摩擦力与轴向位移速率正相关,但受其影响较小,滑动摩擦力不受其影响;静摩擦力和滑动摩擦力与温度负相关,并且受其影响较显著;盐套类型对轴压摩擦力的影响较大,当实验条件接近盐套熔点时,轴压摩擦力显著降低,当样品周围的盐套处于熔融状态时,轴压摩擦力最小。基于此,确定了标定轴压摩擦力的具体步骤,并对角闪岩的应力-应变曲线进行了轴压摩擦力标定。对比轴压摩擦力校正前、后的应力-应变曲线发现,经过轴压摩擦力校正的应力-应变曲线能更好地反映样品的实际变形情况。     

What does friction really depend on? Robust governing parameters in contact mechanics and friction

It is known that the coefficient of friction generally depends on a large number of system and loading parameters. Already Coulomb presented experimental evidence that the static coefficient of friction may depend on time, on normal force, on the contact size, on the nature of contacting materials, and on the presence of intermediate lubricant layers. For the sliding coefficient of friction, he observed the dependence on the sliding velocity as well as the force and size dependencies. Later research has shown that the friction coefficient is very sensitive to the presence of oscillations (including self-excited vibrations). In spite of the practical importance of the problem, no generalized laws of friction or empirical procedures for measuring and representing the law of friction have been developed so far, which included at least the following four parameters: contacting body velocity, normal force, shape (and thus implicitly size), and time. In the present paper, we discuss the question of how the dimension of space of governing parameters can be reduced and if a small set of “robust governing parameters” of friction can be identified. We argue that one of such robust governing parameters is the indentation depth (or relative approach) of contacting bodies and discuss further candidates for the role of robust governing parameters.     

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.     

Friction between α-Al2O3(0 0 0 1) surfaces and the effects of surface hydroxylation

Molecular dynamics simulations were performed to study the friction between hydroxylated α-Al₂O₃(0 0 0 1) surfaces at the temperature of 300 K. Effects of the degree of surface hydroxylation and sliding velocity have been discussed. Results indicate that the friction coefficient decreases with increased degrees of hydroxylation. For all degrees of surface hydroxylation, the friction law crosses over from thermal activation to viscous damping at sliding velocity of 80 m/s.     

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.     

Giant wave-drag enhancement of friction in sliding carbon nanotubes

Molecular dynamics simulations of coaxial carbon nanotubes in relative sliding motion reveal a striking enhancement of friction when phonons whose group velocity is close to the sliding velocity of the nanotubes are strongly excited. The effect is analogous to the dramatic increase in air drag experienced by aircraft flying close to the speed of sound but differs in that it can occur in multiple velocity ranges with varying magnitude, depending on the atomic level structures of the nanotubes. The phenomenon is a general one that may occur in other nanoscale mechanical systems.     

Multimode Active Control of Friction,Dynamic Ratchets and Actuators

Active control of friction by ultrasonic vibration is a well-known effect with numerous technical applications ranging from press forming to micromechanical actuators. Reduction of friction is observed with vibration applied in any of the three possible directions (normal to the contact plane, in the direction of motion and in-plane transverse). In this work, we consider the multi-mode active control of sliding friction, where phase-shifted oscillations in two or more directions act at the same time. Our analysis is based on a macroscopic contact-mechanical model that was recently shown to be well-suited for describing dynamic frictional processes. For simplicity, we limit our analysis to a constant, load-independent normal and tangential stiffness and two superimposed phase-shifted harmonic oscillations, one of them being normal to the plane and the other in the direction of motion. As in previous works utilizing the present model, we assume a constant local coefficient of friction, with reduction of the observed force of friction arising entirely from the macroscopic dynamics of the system. Our numerical simulations show that the resulting law of friction is determined by just three dimensionless parameters. Depending on the values of these parameters, three qualitatively different types of behavior are observed: (a) symmetric velocity-dependence of the coefficient of friction (same for positive and negative velocities), (b) asymmetric dependence with respect to the sign of the velocity, but with zero force at zero velocity, and (c) asymmetric dependence with nonzero force at zero velocity. The latter two cases can be interpreted as a "dynamic ratchet" (b) and an actuator (c).     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.     

Observed transition from linear to non-linear friction-load behavior using a lateral force microscope

The most commonly observed friction behavior for sliding systems is that described by Amontons laws of friction. In this case, sliding friction is independent of the gross or apparent area of contact between the materials and a linear function of the applied normal load, where the constant of proportionality is called the friction coefficient. However, for dry sliding solids in contact via a single-asperity junction, Amontons (linear) friction-load behavior is not strictly relevant. In experiments measuring sliding friction between a silicon tip and a quartz surface using an atomic force microscope (AFM), a transition from linear to non-linear friction-load behavior has been observed. This is proposed to result from a nanoscale ‘conditioning’ of a multiple-contact tip-surface interface to form a single-asperity contact.