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.     

Effect of C60 molecular rotation on nanotribology

The effect of C60 molecular rotation on the nanotribological properties of C60 single crystal surfaces has been studied by atomic/frictional force microscopy. The orientational order-disorder phase transition, in which the high temperature C60 free rotation is reduced to a low temperature hindered rotation, is shown to give rise to an abrupt change in friction and adhesion. This change in frictional force is quantitatively consistent with the observed change in adhesion. The similar slopes of the friction versus load curves in both phases indicate that the friction coefficient in the two phases remains about the same. Hence the C60 rotation does not provide an additional energy dissipation channel in the friction process.     

Micro/macro-slip damping in beams with frictional contact interface

Friction in contact interfaces of assembled structures is the prime source of nonlinearity and energy dissipation. Determination of the dissipated energy in an assembled structure requires accurate modeling of joint interfaces in stick, micro-slip and macro-slip states. The present paper proposes an analytical model to evaluate frictional energy loss in surface-to-surface contacts. The goal is to develop a continuous contact model capable of predicting the dynamics of friction interface and dissipation energy due to partial slips. To achieve this goal, the governing equations of a frictional contact interface are derived for two distinct contact states of stick and partial slip. A solution procedure to determine stick–slip transition under single-harmonic excitations is derived. The analytical model is verified using experimental vibration test responses performed on a free-frictionally supported beam under lateral loading. The theoretical and experimental responses are compared and the results show good agreements between the two sets of responses.     

Superlubricity of graphite

Using a home-built frictional force microscope that is able to detect forces in three dimensions with a lateral force resolution down to 15 pN, we have studied the energy dissipation between a tungsten tip sliding over a graphite surface in dry contact. By measuring atomic-scale friction as a function of the rotational angle between two contacting bodies, we show that the origin of the ultralow friction of graphite lies in the incommensurability between rotated graphite layers, an effect proposed under the name of "superlubricity" [Phys. Rev. B 41, 11 837 (1990)]].     

Static friction of sinusoidal surfaces: a discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.     

Stick-slip friction and energy dissipation in boundary lubrication

Shearing of a simple nonpolar film, right after the liquid-to-solid phase transition under nanometer confinement, is studied by using a liquid-vapor molecular dynamics simulation method. We find that, in contrast with the shear melting and recrystallization behavior of the solidlike phase during the stick-slip motion, interlayer slips within the film and wall slips at the wall-film interface are often observed. The ordered solidified film is well maintained during the slip. Through the time variations of the frictional force and potential energy change within the film, we find that both the friction dissipation during the slip and the potential energy decay after the slip in the solidified film take a fairly large portion of the total energy dissipation.     

External dissipation in driven two-dimensional turbulence

Turbulence in a freely suspended soap film is created by electromagnetic forcing and measured by particle tracking. The velocity fluctuations are shown to be adequately described by the forced Navier-Stokes equation for an incompressible two-dimensional fluid with a linear drag term to model the frictional coupling to the surrounding air. Using this equation, the energy dissipation rates due to air friction and the film's internal viscosity are measured, as is the rate of energy injection from the electromagnetic forcing. Comparison of these rates demonstrates that the air friction is a significant energy dissipation mechanism in the system.     

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.     

界面羟基对碳纳米管摩擦行为和能量耗散的影响

本文采用分子动力学模拟研究了羟基对碳纳米管摩擦和能量耗散方式的影响.研究结果表明:由于界面间氢键的形成,碳纳米管所受的平均摩擦力明显增大;随着羟基比例的改变,界面间氢键的数量与摩擦力的变化趋势一致;碳纳米管的手性角对摩擦力有一定的影响,扶手椅型碳纳米管所受的摩擦力比其他类型的碳纳米管的大;直径对摩擦力的影响较大,直径越大界面间的摩擦力越大,其原因是大直径的碳纳米管底部变平导致界面接触面积增大;界面接枝羟基后,体系的声子态密度中出现羟基的振动峰;随羟基比例的增加,羟基的振动在能量耗散中起到更为重要的作用,当碳纳米管和硅基底的羟基比例为10%/20%时,体系能量耗散的主要途径由碳纳米管和硅基底的振动转变为羟基的振动.     

计入固液界面作用的润滑热力学模型与分析

摩擦与润滑过程是典型的能量耗散过程, 在机理上与非平衡热力学中的熵增、耗散结构等理论颇有相似之处. 通过热力学分析可以对一些典型的摩擦磨损过程做出合理的机理揭示与推测. 本文利用热力学理论对典型的润滑过程进行了建模分析. 采用分离压模型表征和计入了微尺度下的固液界面作用, 揭示分析了润滑热力学模型与润滑状态Stribeck曲线的联系. 从分析计算结果来看, 润滑Stribeck曲线的摩擦系数最低点与系统热力学上的熵增率最低点具有相当好的对应关系, 而润滑状态从弹流润滑向薄膜润滑的转变过程, 可以用耗散结构理论加以机理解释. 文中的热力学模型和方法能够有效地体现出润滑过程中多物理要素跨尺度非线性耦合的作用, 对实际工程与实验有着重要的指导作用.     

Dynamic sliding friction between concentric carbon nanotubes

Molecular dynamics simulations are used to study mechanical energy dissipation in carbon nanotube oscillators of lengths of tens of nanometers. The principal source of friction is found to be the ends of the tubes and hence dynamical friction is virtually independent of the overlap area between tubes. As a result of this, tube commensuration does not lead to significantly increased frictional forces. The friction force is found to depend strongly and nonlinearly on the relative velocity of the tubes. It is suggested that a strong velocity dependence and strong contributions from surface edges may be quite general features of friction at the nanoscale.     

A numerical analysis of the heavy-ion reaction based on the linear response theory

Taking the relative distanceR and the deformationδ of each nucleus as the collective variables, we solve the two dimensional coupled dynamical equations of motion with friction in the framework of the linear response theory. In solving the equations of motion, we approximately replace the inertia tensor with the hydrodynamical one and use the modified liquid-drop one as the collective potential energy. As the frictional coefficients we use the microscopically calculated ones in the previous paper. The calculation is done for the reaction of²⁸Si+²⁰Ne, in which the incident energy of²⁰Ne is 120 MeV. Results show that our microscopically calculated friction gives the large value of energy dissipation which amounts to the “completely damped” collision. Besides it, growths of the oblate deformation in the entrance channel and the prolate deformation in the exit channel are clearly seen. They give a large influence on the time development of the energy dissipation. We compare our calculated results with the experimental data for the reactions of 120 MeV²⁰Ne with²⁷Al. The agreement between them is found to be reasonably good.     

Molecular origin of friction

The wearless friction originating from molecular interactions has been discussed in this paper. We find that the frictional properties are closely related to the structural match of two surfaces in relative motion. For the surfaces with incommensurate structure and week inter-surface interaction, zero static and kinetic friction can be achieved. In a sliding considered as in a quasi-static state, the energy dissipation initiates when interfacial particles move in a discontinuous fashion, which gives rise to a finite kinetic friction. The state of superlubricity is a result of computer simulations, but the prediction will encourage people to look for a technical approach to realizing the state of super low friction.     

Atomic scale friction between clean graphite surfaces

We investigate atomic scale friction between clean graphite surfaces by using molecular dynamics. The simulation reproduces atomic scale stick-slip motion and a low frictional coefficient, both of which are observed in experiments using frictional force microscope. It is made clear that the microscopic origin of low frictional coefficients of graphite lies on the honeycomb structure of each layer, not only on the weak interlayer interaction as believed so far.     

稠密气固流动二阶矩摩擦应力模型和模拟

基于统一二阶矩两相湍流应力模型和稠密颗粒动力学理论,建立了欧拉-欧拉双流体二阶矩颗粒摩擦应力模型。模型充分反映各向异性的气固两相相间雷诺应力相互作用,并引入有效颗粒弹性恢复系数,考虑了因颗粒表面不光滑产生的摩擦力对湍流流动结构和颗粒弥散特性的影响,对于下降管的计算结果与实验吻合较好。因颗粒摩擦产生能量耗散降低了颗粒温度和导致颗粒雷诺应力再分布。在入口和出口区域因颗粒碰撞频率较高而产生的能量耗散对流动结构影响明显。     

欧拉圆盘不同能量耗散机理之间的关联

本文研究了欧拉圆盘运动过程中盘厚度以及盘面与水平面夹角α两因素对能量耗散的影响. 得出圆盘厚度与直径之比x对能量变化中各项因子的影响: x很小时, 质心在竖直方向上的动能变化和重力势能变化是系统能量耗散的主要因素; 当x>0.4142时, 圆盘绕与之平行的轴的转动动能变化成为主要因素, 并给出圆盘厚度可忽略的条件. 模拟了滚动摩擦、空气黏滞等不同能量耗散方式与x,α的关系, 导出各种耗散方式在圆盘运动的过程中的转变规律, 并指出x=0.1733, α>18°时能量耗散形式为纯滚动摩擦, 这修正了文献[26]结论.     

Influence of wall friction on granular column

Granular packings under gravity in frictional and frictionless silos were simulated and the influence of the wall friction on the normal force distribution was investigated. Although there is an obvious Janssen effect in frictional silos, only a slight influence on the geometry of packing was found. The law of normal force distribution is different for frictional and frictionless walls, which is related to the pressure profile. A modified formula with consideration of the pressure profile was well fitted to the simulation results.     

One- and two-body dissipation in heavy-ion collisions

A microscopic theory has been formulated for one- and two-body dissipation in collisions between two heavy nuclei. With a nucleon-nucleon interaction as the basic perturbation in a density matrix approach with “linear response” approximations, the one- and two-body nuclear friction coefficients for the ⁴⁰Ca + ⁴⁰Ca system have been calculated and their dependence on relative kinetic energy and smearing of nuclear single-particle states was obtained. The results of our calculation show that: (a) the combined one- and two-body friction coefficients compare favourably with phenomenological values, (b) the one-body dissipation is more effective than two-body in kinetic energy damping, while both the mechanisms are comparable for the damping of relative angular momentum, (c) the importance of the two-body friction compared to one-body increases at higher relative kinetic energies and (d) the effect of introducing a smearing in nuclear levels appears as a lowering of nuclear friction.     

Molecular origin of friction

The wearless friction originating from molecular interactions has been discussed in this paper. We find that the frictional properties are closely related to the structural match of two surfaces in relative motion. For the surfaces with incommensurate structure and week inter-surface interaction, zero static and kinetic friction can be achieved. In a sliding considered as in a quasi-static state, the energy dissipation initiates when interfacial particles move in a discontinuous fashion, which gives rise to a finite kinetic friction. The state of superlubricity is a result of computer simulations, but the prediction will encourage people to look for a technical approach to realizing the state of super low friction.

     

Memory effects in the energy dissipation for slow collective nuclear motion

The energy dissipation in slow collective nuclear motion is considered as a combined effect of the diabatic production of particle-hole excitations and the subsequent equilibration by two-body collisions. Memory effects due to the long mean free path of the nucleons are treated analytically for an interacting Fermi gas within moving walls leading to a friction kernel (frequency-dependent friction coefficient) in the classical equation of collective motion.