Session H14: Focus Session: Friction, Fracture and Deformation Across Length Scales I: Sliding Friction and Asperities

Nanoscale friction anisotropy controlled by interface inhomogeneous slip and lattice defects

Stick-slip behavior observed from nanoscale asperity friction experiments is often simulated by the one-degree-of-freedom Tomlinson model, which is unable to explain well the effects of lattice structure and interface defects, particularly the friction anisotropy. Using our recently developed Rice-Peierls framework, we study the relative sliding of two elastic half-spaces with a circular contact for two types of interplanar potential: i) triangular lattice potential (3-fold); ii) rectangle potential (2-fold). Our major findings are as follows: first, one can construct friction anisotropy from the interface interaction potential; second, one can modulate the friction anisotropy by controlling the sliding direction and the ratio of contact radius to lattice spacing. We identify that for both cases, when a/b is small, the frictional behavior approaches the Tomlinson limit, while, when a/b is large, the frictional behavior is governed by interface defects. The latter case and its resulting friction anisotropy are very sensitive to the degree of interface incommensurability.   

Frictional Sliding of Amorphous Contacts over Six Decades of Velocity

Our understanding of the nanoscale origins of sliding friction primarily arises from theories of idealized crystalline surfaces in contact. However, many if not most tribological interactions involve one or more surfaces that are disordered in structure. The role that the amorphous nature of these surfaces plays in mediating friction is poorly understood. We apply an emerging simulation methodology, hyperdynamics, for the first time to friction, examining sliding between an oxidized silicon tip and surface over a previously inaccessibly wide range of sliding velocities. The simulations replicate interesting temperature dependent change in the velocity dependence of the friction force observed in this system experimentally, and reveal the nature of the intermediate state-switching transitions responsible for this behavior. A theory based on these transitions is developed and used to describe the experimental and simulated data. We conclude that this type of transition must be quite common in frictional sliding when one or more of the involved surfaces are not perfectly crystalline.   

Sliding Over a Phase Transition

The frictional response experienced by a stick-slip slider when a phase transition occurs in the underlying solid substrate is a potentially exciting, poorly explored problem. We show, based on 2-dimensional simulations modeling the sliding of a nanotip, that indeed friction may be heavily affected by a continuous structural transition. First, friction turns nonmonotonic as temperature crosses the transition, peaking at the critical temperature $T_c$ where fluctuations are strongest. Second, below Tc friction depends upon order parameter directions, and is much larger for those where the frictional slip can cause a local flip. This may open a route towards control of atomic scale friction by switching the order parameter direction by an external field or strain, with possible application to e.g., displacive ferroelectrics such as BaTiO$_3$, as well as ferro- and antiferro-distortive materials.   

Onset of Sliding in Single Asperity Contacts

Continuum models of friction often assume that sliding initiates at the edge of a contact, and gradually spreads across the contact. However these partial slip models make simple assumptions about friction laws and must break down at atomic scales. Molecular dynamics simulations are used to analyze the nature of atomistic effects and the variation of partial slip with length scale. In continuum theory there are singularities in tangential force at the edge of the contact that initiate slip. The discrete spacing between atoms and interfacial elasticity reduce these singularities in small contacts. Elastic coupling within the contact also limits partial slip and favors coherent slip across the interface. The variation of these effects with length scale, atomic geometry and the presence of adsorbed monolayers is described.   

Finite size effects at high speed frictional interfaces

Non-Equilibrium Molecular Dynamics simulations have exhibited characteristic velocity weakening for the tangential frictional force at smooth single crystal interfaces for velocities greater than a critical velocity, v$_{c}$. This behavior has been seen in a number of material pairs including Cu-Ag, Ta-Al and Al-Al. Expressions for v$_{c}$ that characterize this behavior depend on system size. We discuss the size dependence for Al-Al single crystal interfaces for two cases: an Al(111)/Al(001) interface sliding along [1-10],N=1.5M, and an Al(110)[001]/Al(110)[1-10] interface sliding along [001], N=7.5x10$^{6}$ corresponding to a three-fold increase in system size normal to the sliding direction. We find agreement with an inverse size scaling for v$_{c}$. We discuss the similarities in behavior for a highly defective plastically deformed sample with Al(110)[001]/Al(110)[1-10] orientation having the same normal dimension and N= 16.0x10$^{6}$.   

The Tribological Properties of Nanocrystalline Metals

Materials that perform well in electrical contacts usually exhibit high adhesion during frictional contacts. An excellent example of this phenomenon is pure gold, which has extremely low electrical contact resistance, but generally has a high friction coefficient. The exception to this, however, is nanocrystalline gold alloyed with minute amounts of Ni or Co, which in addition to its low contact resistance can also show low friction. The mechanism for this remains poorly understood. We carried out large scale molecular dynamics (MD) simulations to study the tribological response of both single crystal and nanocrystalline gold or silver films in contact with curved probe tips or flat slabs under a variety of sliding conditions. Results show that grain reorientation and coalescence across the contact interface under compressive load or during shearing are responsible for the observed high friction in these contacts. In metallic alloys of silver, the addition of other elements such as copper introduces lattice mismatch and hinders the grain coalescence, which reduces friction during sliding.   

Tribo-induced melting transitions at sliding tungsten/gold-nickel asperity contacts

Tribo-induced nanoscale surface melting mechanisms have been investigated by means of a combined QCM-STM technique [1] for a range of Au and Au-Ni alloys with varying compositional percentages and phases. A transition from solid- solid to solid-``liquid like'' contact[1] was observed for each sample at sufficiently high asperity sliding speeds. Pure gold, solid-solution and two-phase Au-Ni (20 at.\% Ni) alloys were compared, which are materials of great relevance to MEMS RF switch technology [2]. The transition points agree favorably with theoretical predictions for their surface melting characteristics. We acknowledge NSF and AFOSR support for this research. \\[4pt] [1] B. D. Dawson, S. M. Lee, and J. Krim, Phys. Rev. Lett. 103, 205502 (2009)\\[0pt] [2] Zhenyin Yang; Lichtenwalner, D.J.; Morris, A.S.; Krim, J.; Kingon, A.I, Journal of Microelectromechanical Systems, April 2009, Volume: 18 Issue:2, 287-295   

\textit{In-situ }study of AFM tip wear by contact resonance force microscopy

The size and shape of an atomic force microscope (AFM) tip strongly influence the resolution and accuracy of the instrument. Here we present a new means to directly measure tip wear \textit{in situ} during contact-mode AFM scanning. Tip wear is observed from changes in contact radius determined by contact resonance force microscopy (CR-FM). In CR-FM, a flexural eigenmode of the cantilever is excited and tracked while the tip is in contact with a sample. As the tip wears, the resonant frequency increases, corresponding to increased contact radius. We demonstrate excellent agreement between quantitative tip wear results from CR-FM and from established \textit{ex-situ} techniques such as scanning electron microscope imaging. Even for compliant cantilevers scanned at very low forces, we are able to resolve subnanometer changes in contact radius. Overall, benefits of our wear-monitoring approach are that CR-FM provides quantitative values of contact radius, allows continuous measurements, affords high spatial resolution, and does not adversely influence the wear rate.   

A physical basis for frictional ageing using single-asperity measurements

Rate and state friction laws are widely used to model laboratory data and reproduce a variety of phenomena in earthquake modeling, and in other multi-asperity contacts. However, these laws lack a physical basis. To identify mechanisms underlying the time dependence of friction, especially the ageing effect, atomic force microscopy (AFM) was employed to probe friction for nanometer-scale single asperity contacts between oxidized silicon AFM tips and a set of substrates. Similar to macroscopic rock friction experiments, `slide-hold-slide' (SHS) experiments on silica revealed a linear increase in friction with the log of the hold time. However, SHS experiments on chemically inert substrates showed little to no ageing. This indicates that the ageing mechanism is related to interfacial chemical reactions, and not plastic deformation of asperities. Ageing in silica-silica contacts is more than an order of magnitude higher than for macroscopic interfaces. However, modeling of slip in multi-asperity contacts suggests that the single- and multi-asperity results agree, since the magnitude of the ageing effect in multi-asperity contacts is reduced by asperity interactions. These results provide the first asperity-level insights into possible mechanisms behind rate and state friction laws.   

Friction at the nanoscale:theory and experiment

Bowden and Tabor established more than 50 years ago that friction is due to populations of asperities. In recent years, increasingly detailed experiments have begun to document the dynamics of these asperities during sliding, and to show that several different modes of motion are possible. I will discuss experiments that probe slipping motion of macroscopic samples down to the nanoscale, and show that the small slow slipping motions are described by the rate and state theory of friction that was developed for very different length and time scales.   

Stiffness of Contacts of Self-Affine Surfaces

The presence of roughness on a wide range of scales has a profound effect on the contact area and interfacial stiffness between contacting surfaces. In turn, the interfacial stiffness dominates the response of many macroscopic systems. Molecular dynamics simulations are used to characterize contacts between self-affine fractal surfaces with different roughness exponents. A unified framework describes the relation between roughness, system size, surface separation, stiffness, and contact area for a wide variety of systems. The contact area and normal stiffness rapidly approach Persson's continuum theory with increasing system size [1]. The lateral stiffness and friction are much more sensitive to atomic-scale effects. Atomic scale displacements at the interface can greatly reduce lateral stiffness and may explain the low lateral stiffness observed in some experiments.\\[4pt] [1] B. N. J. Persson Phys. Rev. Lett. 99, 125502 (2007).   

Stick-Slip and the Transition to Sliding in a 2D Granular Medium and a Fixed Particle Lattice

We report an experimental study of stick-slip to steady sliding for a solid object pulled via a spring across 2D granular substrates of photoelastic disks that are either fixed in a solid lattice or unconstrained, i.e. a disordered granular bed. We observe a progression of friction regimes with increasing sliding speed: single, mixed, and double slip-stick regimes, steady sliding, and inertial oscillations. For the granular bed, we characterize frictional behavior for the low speed stick-slip regime, including spring and elastic energy dependencies. For the granular solid, we explore friction with/without externally applied vibrations, and compare to sliding on a granular bed. We find that external vibration reduces transition values for both the single to double slip transition and the stick-slip to steady sliding transition. Moreover, we observe that the effect of packing disorder on granular friction appears similar to the effect of vibration induced disorder, a result that to our knowledge has not been reported previously in the experimental literature.   

A simple model fault system

The Gutenberg-Richter distribution, which characterizes the frequency-magnitude statistics collected over earthquake fault systems, has lead seismologists as well as physicists and geophysicists to propose various simple models to explain this empirical scaling relation. To date, these models have been limited to the description of a single fault. We discuss a model of an earthquake fault system made up of non-interacting faults that are represented as damaged, Olami-Feder-Christensen models. The frequency-magnitude statistics do not, in general, scale on a single fault with some realization of damage; however, these statistics follow a simple distribution that can also be used to describe the data collected from actual earthquake faults. What is more, by varying the amount of damage on each fault in the system, as well as the relative frequency with which a fault with a given amount of damage occurs within the system, we obtain a one-parameter family of models, all of which produce Gutenberg-Richter-like statistics. This parameter is a measure of the stress dissipation within the fault system, a quantity known to vary with various geological properties, and offers an explanation for the range of $b$-values observed by seismologists.