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.     

基于滑动势能面的二维材料原子尺度摩擦行为的量化计算

近年来,二维材料优异的摩擦特性成为人们关注的焦点,然而目前缺乏理论上对其摩擦力进行快速、有效、精确的计算预测方法.本文提出采用密度泛函理论计算真实体系的滑动势能面,利用得到的"数值型势能面"替代传统的解析势函数,并结合Prandtl-Tomlinson模型,量化求解具有复杂形状势能面的真实二维材料体系的摩擦行为.基于该方法,揭示了原子力显微镜实验中观察到的石墨烯Moire纹超晶格结构的双周期"黏-滑"摩擦现象;理论预测了二维材料异质结构的层间超低摩擦现象,相对于同质材料,其静摩擦力和滑动摩擦力均成数量级降低,发现势能面起伏和驱动弹簧刚度均会影响层间相对滑动路径,进而对层间的摩擦行为产生影响.该方法同样可拓展到其他van der Waals作用主导的界面摩擦体系.     

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.     

Stabilizing stick-slip friction

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.     

Normal and Lateral Force Calibration Techniques for AFM Cantilevers

Atomic force microscopy (AFM) is a useful tool, not only for imaging but also for quantification of normal and lateral forces exerted on the AFM tip while interacting with the surface of materials. In order to measure these forces, an accurate determination of the normal and lateral forces exerted on the AFM cantilever is necessary. To date, there is no generally accepted technique for the force calibration of AFM cantilevers. In this paper, we present a critical review of various techniques for measuring cantilever stiffness in the normal and lateral/torsional directions in order to calibrate the normal and lateral forces exerted on AFM cantilevers. The key concepts of each technique are presented, along with a discussion of their advantages and disadvantages. An understanding of the issues involved in the determination of the stiffness is needed for the proper choice and implementation of any given technique.     

Unsteady processes in machines

Couplings in machines and mechanisms always have play and friction. While under loading, stick-slip phenomena and impact events can take place. Such processes are modeled as multibody systems whose structure is time variant or unsteady. The time-variant number of degrees of freedom is due to stick-slip contacts. The coupling characteristics become unsteady, for instance there exist jumps in the loads, if impacts occur. For establishing a uniform theory for such phenomena we use a Lagrangian approach connecting the additional constraint equations and the equations of motion by Lagrange multipliers, which are proportional to the constraint forces. Stick-slip and impact events are evaluated by indicator functions leading to special numerical algorithms for the search of switching points. Contact problems are formulated as a complementarity problem which can be solved by efficient algorithms. The theory is applied to rattling in gears, impact drilling machines, turbine blade dampers, and a woodpecker toy. In some of these applications, chaos as a result of bifurcations is possible, which results from variations in the parameters. (c) 1994 American Institute of Physics.     

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.     

Transition from stick-slip to smooth sliding: an earthquakelike model

We present a detailed study of an earthquakelike model that exhibits a "transition" from stick-slip motion to smooth sliding at a velocity of the order of those observed in experiments. This contrasts with the many previous microscopic models in which the transition velocity is many orders of magnitude too large. The results show that experimentally observed smooth sliding at the macroscopic scale must correspond to microscopic-scale stick-slip motion.     

On the conditions of strain localization and microstructure fragmentation under high-rate loading

The paper reports on research in the deformation and fragmentation mechanisms of coarse- and fine-grained materials under high-rate loading. The study was performed by an experimental procedure based on collapse of thick-walled hollow cylinders and by molecular dynamics simulation. The key issue was to study the formation of plastic strain localization bands. It is found that the pattern of plastic deformation is governed by loading conditions and characteristic grain sizes. For a coarse-grained material, the governing mechanism is dislocation deformation resulting in localization bands. For a fine-grained material, the governing mechanism is grain boundary sliding with attendant fragmentation of the material. A dependence of the strain rate and degree on the critical grain size was disclosed. The computer simulation revealed mechanisms of grain boundary sliding on the scales studied.     

Reconstruction of bowing point friction force in a bowed string

A method is presented for reconstructing the friction force and the velocity at the bowing point of a string excited by a rosined bow sliding transverse to the string. Two versions of the method of reconstruction are presented, each approximate in different ways, but both capable of sufficient accuracy to allow useful application to problems of understanding frictional interactions in this dynamical system. The method is illustrated with simulated data to verify its accuracy, and results are shown for two contrasting cases of observed stick-slip string motion. As has been found in other investigations, the friction force during sliding is not determined by the instantaneous sliding speed. The results seem to be compatible with a thermally based model of rosin friction.     

Effect of inertia and elasticity on stick-slip motion

A hybrid simulation method is used to study the transition from stick-slip motion to steady sliding as the sliding velocity increases above a critical value v(c). The effects of the geometry, elasticity, and mass M of the sliding object are varied to test competing theories. When the slider has a tapered geometry, v(c) scales as M(-1/2), and the elasticity of the slider is irrelevant. When the slider has a constant columnar cross section, elasticity dominates, and v(c) is independent of mass as M--> infinity. The tapered geometry is more typical of existing measurements, but the columnar geometry could be realized using a nanotube.     

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.     

Chains of oscillators with negative stiffness elements

Negative stiffness is not allowed by thermodynamics and hence materials and systems whose global behaviour exhibits negative stiffness are unstable. However the stability is possible when these materials/systems are elements of a larger system sufficiently stiff to stabilise the negative stiffness elements. In order to investigate the effect of stabilisation we analyse oscillations in a chain of n linear oscillators (masses and springs connected in series) when some of the springs? stiffnesses can assume negative values. The ends of the chain are fixed. We formulated the necessary stability condition: only one spring in the chain can have negative stiffness. Furthermore, the value of negative stiffness cannot exceed a certain critical value that depends upon the (positive) stiffnesses of other springs. At the critical negative stiffness the system develops an eigenmode with vanishing frequency. In systems with viscous damping vanishing of an eigenfrequency does not yet lead to instability. Further increase in the value of negative stiffness leads to the appearance of aperiodic eigenmodes even with light damping. At the critical negative stiffness the low dissipative mode becomes non-dissipative, while for the high dissipative mode the damping coefficient becomes as twice as high as the damping coefficient of the system. A special element with controllable negative stiffness is suggested for designing hybrid materials whose stiffness and hence the dynamic behaviour is controlled by the magnitude of applied compressive force.     

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.     

A numerical study on stick-slip motion of a brake pad in steady sliding

A numerical model for an elastic brake pad sliding under constant load and with constant velocity over a rigid surface is investigated by finite element analysis. The geometry is taken to be two-dimensional, the contact is assumed to follow the laws of continuum mechanics and temporal and spatial resolution are such that dynamical effects localized at the interface are resolved. It turns out that at the contact interface localized slip events occur either in the form of long-lasting slip pulses, or in the form of brief local relaxations. Macroscopically steady sliding, macroscopic stick-slip motion or slip-separation dynamics occurs, depending on the macroscopic relative velocity. While structural oscillations of the brake pad do not seem to play a significant role during steady sliding at least one structural oscillation mode becomes synchronized with the interfacial dynamics during stick-slip or slip-separation motion. Assuming a given friction law for the interface, the macroscopically observed friction coefficient depends considerably on the underlying dynamics on the interface.     

An Investigation of Cricoarytenoid Joint Mechanics Using Simulated Muscle Forces

Rotational and translational stiffnesses were calculated for arytenoid motion about the cricoarytenoid joint. These calculations were obtained from measurements on five excised human larynxes. For each larynx, known forces were applied to the arytenoid cartilage, and three markers were tracked as a function of applied forces. Assuming rigid body motion, arytenoid translations and rotations were computed for each applied force. Translational stiffnesses were obtained by plotting force versus displacement, and rotational stiffnesses were calculated by plotting torque versus angular rotation. A major finding was that the translational stiffness along the anterior-posterior direction was three times as great as the translational stiffnesses in the other two directions. This nonisotropic nature of the stiffnesses may be an important consideration for phonosurgeons who wish to avoid subluxation of the cricoarytenoid joint in patients. The computed rotational and translational stiffnesses currently are being implemented in 2D and 3D models. These stiffness parameters play a vital role in prephonatory glottal shaping, which in turn exerts a majorinfluence on all aspects of vocal fold vibration, including fundamental frequency, voice quality, voice register, and phonation threshold pressure.     

Numerical modelling of longitudinal vibrations of a sucker rod string

A new technique for analyzing the dynamic behavior of a sucker rod string used in the oil well industry is presented. The main difficulty in the numerical calculation of the examined structure is a multivalued velocity—force relation determined by Coulomb's friction and by loads generated during operation of pump valves. Both the monotonic and nonmonotonic velocity—force relations are considered. A quasi-variational inequality formulation of the problem is proposed. The solution of the inequality amounts to finding the minimum of a convex nonsmooth functional at each time step by means of the Newmark difference time scheme, successive iterations and finite element discretization. The problem of functional minimization is reduced to construction of a sequence of smooth nonlinear programming problems by introducing the auxiliary variables and applying the augmented Lagrangian method. The proposed approach is used to study the longitudinal vibrations of sucker rod strings under near-real conditions. In such systems the most commonly occurring vibration modes are the stick-slip vibrations and the vibrations with natural force excited twice a cycle. The nonmonotonic character of the friction law leads to intensification of these vibrations. In the case of nonmonotonic friction law the stick-slip vibrations can occur even under the action of constant external forces.     

Ultrasound elastomicroscopy using water jet and osmosis loading: potentials for assessment for articular cartilage

Research in elasticity imaging typically relies on 1-10 MHz ultrasound. Elasticity imaging at these frequencies can provide strain maps with a resolution in the order of millimeters, but this is not sufficient for applications to skin, articular cartilage, or other fine structures. In this paper, we introduced two methods of ultrasound elastomicroscopy using water jet and osmosis loading for imaging the elasticity of biological soft tissues with high resolutions. In the first system, the specimens were compressed using water jet compression. A water jet was used to couple a focused 20 MHz ultrasound beam into the specimen and meanwhile served as a "soft" indenter. Because there was no additional attenuation when propagating from the ultrasound transducer to the specimen, the ultrasound signal with high signal-to-noise ratio could be collected from the specimens simultaneously with compressing process. The compression was achieved by adjusting the water flow. The pressure measured inside the water pipe and that on the specimen surface was calibrated. This system was easily to apply C-scan over sample surfaces. Experiments on the phantoms showed that this water jet indentation method was reliable to map the tissue stiffness distribution. Results of 1D and 2D scanning on phantoms with different stiffness are reported. In the second system, we used osmotic pressure caused by the ion concentration change in the bathing solutions for the articular cartilage to deform them. When bovine articular cartilage specimens were immerged in solutions with different salt concentration, a 50 MHz focused ultrasound beam was used to monitor the dynamic swelling or shrinkage process. Results showed that the system could reliably map the strain distribution induced by the osmotic loading. We extract intrinsic layered material parameters of the articular cartilage using a triphasic model. In addition to biological tissues, these systems have potential applications for the assessment of bioengineered tissues, biomaterials with fine structures, or some engineering materials. Further studies are necessary to fully realize the potentials of these two new methods.