Detachment fronts and the onset of dynamic friction

Molecular Probing of the Microscopic Pressure at Contact Interfaces

Obtaining insights into friction at the nanoscopic level and being able to translate these into macroscopic friction behavior in real-world systems is of paramount importance in many contexts, ranging from transportation to high-precision technology and seismology. Since friction is controlled by the local pressure at the contact it is important to be able to detect both the real contact area and the nanoscopic local pressure distribution simultaneously. In this paper, we present a method that uses planarizable molecular probes in combination with fluorescence microscopy to achieve this goal. These probes, inherently twisted in their ground states, undergo planarization under the influence of pressure, leading to bathochromic and hyperchromic shifts of their UV-vis absorption band. This allows us to map the local pressure in mechanical contact from fluorescence by exciting the emission in the long-wavelength region of the absorption band. We demonstrate a linear relationship between fluorescence intensity and (simulated) pressure at the submicron scale. This relationship enables us to experimentally depict the pressure distribution in multiasperity contacts. The method presented here offers a new way of bridging friction studies of the nanoscale model systems and practical situations for which surface roughness plays a crucial role.

How frictional slip evolves

Earthquake-like ruptures break the contacts that form the frictional interface separating contacting bodies and mediate the onset of frictional motion (stick-slip). The slip (motion) of the interface immediately resulting from the rupture that initiates each stick-slip event is generally much smaller than the total slip logged over the duration of the event. Slip after the onset of friction is generally attributed to continuous motion globally attributed to 'dynamic friction'. Here we show, by means of direct measurements of real contact area and slip at the frictional interface, that sequences of myriad hitherto invisible, secondary ruptures are triggered immediately in the wake of each initial rupture. Each secondary rupture generates incremental slip that, when not resolved, may appear as steady sliding of the interface. Each slip increment is linked, via fracture mechanics, to corresponding variations of contact area and local strain. Only by accounting for the contributions of these secondary ruptures can the accumulated interface slip be described. These results have important ramifications both to our fundamental understanding of frictional motion as well as to the essential role of aftershocks within natural faults in generating earthquake-mediated slip.

Controlling Macroscopic Friction through Interfacial Siloxane Bonding

Controlling macroscopic friction is crucial for numerous natural and industrial applications, ranging from forecasting earthquakes to miniaturizing semiconductor devices, but predicting and manipulating friction phenomena remains a challenge due to the unknown relationship between nanoscale and macroscopic friction. Here, we show experimentally that dry friction at multiasperity Si-on-Si interfaces is dominated by the formation of interfacial siloxane (Si─O─Si) bonds, the density of which can be precisely regulated by exposing plasma-cleaned silicon surfaces to dry nitrogen. Our results show how the bond density can be used to quantitatively understand and control the macroscopic friction. Our findings establish a unique connection between the molecular scale at which adhesion occurs, and the friction coefficient that is the key macroscopic parameter for industrial and natural tribology challenges.

Model of Friction with Plastic Contact Nudging: Amontons-Coulomb Laws, Aging of Static Friction, and Nonmonotonic Stribeck Curves with Finite Quasistatic Limit

We introduce a model of friction between two contacting (stationary or cosliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact with each other only pairwise elastic repulsion and dissipative drag. These minimal ingredients are sufficient to capture a static state of jammed, interlocking contacting bumps, below a critical frictional force that is proportional to the normal load and independent of the apparent contact area, consistent with the Amontons-Coulomb laws of friction. However, they fail to capture two widespread observations: (i) that the dynamic friction coefficient (ratio of frictional to normal force in steady sliding) is a roughly constant or slightly weakening function of the sliding velocity U, at low U, with a nonzero quasistatic limit as U→0 and (ii) that the static friction coefficient (ratio of frictional to normal force needed to initiate sliding) increases ("ages") as a function of the time that surfaces are pressed together in stationary contact, before sliding commences. To remedy these shortcomings, we incorporate a single additional model ingredient: that contacting bumps plastically nudge one another slightly sideways, above a critical contact-contact load. With this additional insight, the model also captures observations (i) and (ii).

Laboratory earthquakes decipher control and stability of rupture speeds

Earthquakes are destructive natural hazards with damage capacity dictated by rupture speeds. Traditional dynamic rupture models predict that earthquake ruptures gradually accelerate to the Rayleigh wave speed with some of them further jumping to stable supershear speeds above the Eshelby speed (~[Formula: see text] times S wave speed). However, the 2018 M_w 7.5 Palu earthquake, among several others, significantly challenges such a viewpoint. Here we generate spontaneous shear ruptures on laboratory faults to confirm that ruptures can indeed attain steady subRayleigh or supershear propagation speeds immediately following nucleation. A self-similar analysis of dynamic rupture confirms our observation, leading to a simple model where the rupture speed is uniquely dependent on a driving load. Our results reproduce and explain a number of enigmatic field observations on earthquake speeds, including the existence of stable subEshelby supershear ruptures, early onset of supershear ruptures, and the correlation between the rupture speed and the driving load.

Static friction coefficient depends on the external pressure and block shape due to precursor slip

Amontons' law states that the maximum static friction force on a solid object is proportional to the loading force and is independent of the apparent contact area. This law indicates that the static friction coefficient does not depend on the external pressure or object shape. Here, we numerically investigate the sliding motion of a 3D viscoelastic block on a rigid substrate using the finite element method (FEM). The macroscopic static friction coefficient decreases with an increase in the external pressure, length, or width of the object, which contradicts Amontons' law. Precursor slip occurs in the 2D interface between the block and substrate before bulk sliding. The decrease in the macroscopic static friction coefficient is scaled by the critical area of the precursor slip. A theoretical analysis of the simplified models reveals that bulk sliding results from the instability of the quasi-static precursor slip caused by velocity-weakening local friction. We also show that the critical slip area determines the macroscopic static friction coefficient, which explains the results of the FEM simulation.

Scaling theory for the statistics of slip at frictional interfaces

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress σ^{*}, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a power law corresponding to "avalanches" and a "narrow" distribution of system-spanning "fracture" events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.

Creep fronts and complexity in laboratory earthquake sequences illuminate delayed earthquake triggering

Earthquakes occur in clusters or sequences that arise from complex triggering mechanisms, but direct measurement of the slow subsurface slip responsible for delayed triggering is rarely possible. We investigate the origins of complexity and its relationship to heterogeneity using an experimental fault with two dominant seismic asperities. The fault is composed of quartz powder, a material common to natural faults, sandwiched between 760 mm long polymer blocks that deform the way 10 meters of rock would behave. We observe periodic repeating earthquakes that transition into aperiodic and complex sequences of fast and slow events. Neighboring earthquakes communicate via migrating slow slip, which resembles creep fronts observed in numerical simulations and on tectonic faults. Utilizing both local stress measurements and numerical simulations, we observe that the speed and strength of creep fronts are highly sensitive to fault stress levels left behind by previous earthquakes, and may serve as on-fault stress meters.

Giant fluidic impedance of nanometer-sized water bridges: Shear capillary force at the nanoscale

We analytically show that the interfacial fluid's molecular dynamics of capillary bridges induces both elastic and dissipative forces to the shearing plane. Surprisingly, the nanometer-sized, liquid-solid contact line of the bridges exerts a giant "shear" force on the solid surface, which is 10^{5} higher than the usual viscous interaction and comparable to that of solid-solid direct-contact friction. These results are consistent with previously reported experimental data and may provide clues to longstanding questions on the apparent viscosity of the nanoconfined fluids.

Propagating Schallamach-type waves resemble interface cracks

Intermittent motion, called stick-slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick-slip arises due to the propagation of slow detachment waves at the interface. Here we analyze two distinct detachment waves moving parallel (Schallamach wave) and antiparallel (separation wave) to applied remote sliding. Both waves cause slip in the same direction, travel at speeds much lesser than any elastic wave speed, and are therefore describable using the same perturbative elastodynamic framework with identical boundary conditions. A numerical scheme is used to obtain interface stresses and velocities for arbitrary Poisson ratio, along with closed-form solutions for incompressible solids. Our calculations reveal a close correspondence between moving detachment waves and bimaterial interface cracks, including the nature of the singularity and the functional forms of the stresses. Based on this correspondence, and coupled with a fracture analogy for dynamic friction, we develop a phase diagram showing domains of possible occurrence of stick-slip via detachment waves vis-á-vis steady interface sliding. Our results have interesting implications for sliding and stick-slip phenomena at soft interfaces.

An experimental study on the relation between friction force and real contact area

Classical laws of friction suggest that friction force is proportional to the normal load and independent of the nominal contact area. As a great improvement in this subject, it is now widely accepted that friction force is proportional to the real contact area, and much work has been conducted based on this hypothesis. In present study, this hypothesis will be carefully revisited by measuring the friction force and real contact area in-site and real-time at both normal loading and unloading stages. Our experiments reveal that the linear relation always holds between friction force and normal load. However, for the relation between friction force and real contact area, the linearity holds only at the loading stage while fails at the unloading stage. This study may improve our understanding of the origin of friction.

Superlubric polycrystalline graphene interfaces

The effects of corrugated grain boundaries on the frictional properties of extended planar graphitic contacts incorporating a polycrystalline surface are investigated via molecular dynamics simulations. The kinetic friction is found to be dominated by shear induced buckling and unbuckling of corrugated grain boundary dislocations, leading to a nonmonotonic behavior of the friction with normal load and temperature. The underlying mechanism involves two effects, where an increase of dislocation buckling probability competes with a decrease of the dissipated energy per buckling event. These effects are well captured by a phenomenological two-state model, that allows for characterizing the tribological properties of any large-scale polycrystalline layered interface, while circumventing the need for demanding atomistic simulations. The resulting negative differential friction coefficients obtained in the high-load regime can reduce the expected linear scaling of grain-boundary friction with surface area and restore structural superlubricity at increasing length-scales.

Fracture asperity evolution during the transition from stick slip to stable sliding

Fracture asperities interlock or break during stick slip and ride over each other during stable sliding. The evolution of fracture asperities during the transition between stick slip and stable sliding has attracted less attention, but is important to predict fracture behaviour. Here, we conduct a series of direct shear experiments on simulated fractures in homogeneous polycarbonate to examine the evolution of fracture asperities in the transition stage. Our results show that the transition stage occurs between the stick slip and stable sliding stages during the progressive reduction in normal stress on the smooth and rough fractures. Both the fractures exhibit the alternative occurrence of small and large shear stress drops followed by the deterministic chaos in the transition stage. Our data indicate that the asperity radius of curvature correlates linearly with the dimensionless contact area under a given normal stress. For the rough fracture, a bifurcation of acoustic energy release appears when the dimensionless contact area decreases in the transition stage. The evolution of fracture asperities is stress-dependent and velocity-dependent. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Air mediates the impact of a compliant hemisphere on a rigid smooth surface

Fleeting contact between solids immersed in a fluid medium governs the response of critically important materials, from coffee to soil. Rapid impact of soft solids occurs in systems as diverse as car tires, soft robotic locomotion and suspensions, including soil and coffee. In each of these systems, the dynamics are fundamentally altered by the presence of a fluid layer mediating solid contact. However, observing this class of interactions directly is challenging, as the relevant time and length scales are extremely small. Here we directly image the interface between a soft elastic hemisphere and a flat rigid substrate during rapid impact over a wide range of impact velocities V at high temporal and spatial resolution using the Virtual Frame Technique (VFT). In each experiment, a pocket of air is trapped in a dimple between the impactor and the substrate, preventing direct solid-solid contact at the apex of the hemisphere. Thus, unlike the quasi-static Hertzian solution where contact forms in an ellipse, in each rapid air-mediated impact, contact forms in an annular region which rapidly grows both inward toward the impact axis, and rapidly outward away from the impact axis. We find that the radius of initial contact varies non-monotonically with V, indicating a transition between elastically dominated dynamics to inertially dominated dynamics. Furthermore, we find that for slower impact speeds, where the outer contact front cannot outpace the Rayleigh velocity, contact expands in a patchy manner, indicating an elasto-lubricative instability. These behaviors, observed using the VFT, occur in regimes relevant to a wide variety of soft systems, and might modulate frictional properties during contact. The size of the air pocket varies with V and impactor stiffness. Our measurements reveal an unanticipated, sudden transition of the air pocket's size as V increases beyond 1 m s^-1 and multiple modes of air entrainment at the advancing solid-solid contact front that depend on the front's velocity.

Laboratory earthquake forecasting: A machine learning competition

Earthquake prediction, the long-sought holy grail of earthquake science, continues to confound Earth scientists. Could we make advances by crowdsourcing, drawing from the vast knowledge and creativity of the machine learning (ML) community? We used Google’s ML competition platform, Kaggle, to engage the worldwide ML community with a competition to develop and improve data analysis approaches on a forecasting problem that uses laboratory earthquake data. The competitors were tasked with predicting the time remaining before the next earthquake of successive laboratory quake events, based on only a small portion of the laboratory seismic data. The more than 4,500 participating teams created and shared more than 400 computer programs in openly accessible notebooks. Complementing the now well-known features of seismic data that map to fault criticality in the laboratory, the winning teams employed unexpected strategies based on rescaling failure times as a fraction of the seismic cycle and comparing input distribution of training and testing data. In addition to yielding scientific insights into fault processes in the laboratory and their relation with the evolution of the statistical properties of the associated seismic data, the competition serves as a pedagogical tool for teaching ML in geophysics. The approach may provide a model for other competitions in geosciences or other domains of study to help engage the ML community on problems of significance.

Dynamic stiction without static friction: The role of friction vector rotation

In the textbook formulation of dry friction laws, static and dynamic friction (stick and slip) are qualitatively different and sharply separated phenomena. However, accurate measurements of stick-slip motion generally show that static friction is not truly static but characterized by a slow creep that, upon increasing tangential load, smoothly accelerates into bulk sliding. Microscopic, contact-mechanical, and phenomenological models have been previously developed to account for this behavior. In the present work, we show that it may instead be a systemic property of the measurement apparatus. Using a mechanical model that exhibits the characteristics of typical setups of measuring friction forces-which usually have very high transverse stiffness-and assuming a small but nonzero misalignment angle in the contact plane, we observe some fairly counterintuitive behavior: Under increasing longitudinal loading, the system almost immediately starts sliding perpendicularly to the pulling direction. Then the friction force vector begins to rotate in the plane, gradually approaching the pulling direction. When the angle between the two becomes small, bulk sliding sets in quickly. Although the system is sliding the entire time, macroscopic stick-slip behavior is reproduced very well, as is the accelerated creep during the "stick" phase. The misalignment angle is identified as a key parameter governing the stick-to-slip transition. Numerical results and theoretical considerations also reveal the presence of high-frequency transverse oscillations during the "static" phase, which are also transmitted into the longitudinal direction by nonlinear processes. Stability analysis is carried out and suggests dynamic probing methods for the approaching moment of bulk slip and the possibility of suppressing stick-slip instabilities by changing the misalignment angle and other system parameters.

Frictionless Motion of Lattice Defects

Energy dissipation by fast crystalline defects takes place mainly through the resonant interaction of their cores with periodic lattice. We show that the resultant effective friction can be reduced to zero by appropriately tuned acoustic sources located on the boundary of the body. To illustrate the general idea, we consider three prototypical models describing the main types of strongly discrete defects: dislocations, cracks, and domain walls. The obtained control protocols, ensuring dissipation-free mobility of topological defects, can also be used in the design of metamaterial systems aimed at transmitting mechanical information.

Dynamics and Properties of the Cohesive Zone in Rapid Fracture and Friction

The cohesive zone is the elusive region in which material fracture takes place. Here, the putatively singular stresses at a crack's tip are regularized. We present experiments, performed on PMMA, in which we visualize the cohesive zone of frictional ruptures as they propagate. Identical to shear cracks, these ruptures range from slow velocities to nearly the limiting speeds of cracks. We reveal that the cohesive zone is a dynamic quantity; its spatial form undergoes a sharp transition between distinct phases at a critical velocity. The structure of these phases provides an important window into material properties under the extreme conditions that occur during fracture.

Subsonic to Intersonic Transition in Sliding Friction for Soft Solids

We perform friction experiments between a compliant gel and a rigid cylinder at sliding velocities comparable to the Rayleigh wave or secondary wave velocity of the gel. We find that, when the sliding velocity exceeds the wave velocities, the contact state transitions from Hertzian like to flat punch like, resulting in the breakdown of the lubricating oil film and the abrupt increase in the friction coefficient. We succeed in deriving theoretical solutions for the contact pressure distributions and the deformation profiles in the presence of friction, which are consistent with our experimental observations.

The onset of the frictional motion of dissimilar materials

Frictional motion between contacting bodies is governed by propagating rupture fronts that are essentially earthquakes. These fronts break the contacts composing the interface separating the bodies to enable their relative motion. The most general type of frictional motion takes place when the two bodies are not identical. Within these so-called bimaterial interfaces, the onset of frictional motion is often mediated by highly localized rupture fronts, called slip pulses. Here, we show how this unique rupture mode develops, evolves, and changes the character of the interface's behavior. Bimaterial slip pulses initiate as "subshear" cracks (slower than shear waves) that transition to developed slip pulses where normal stresses almost vanish at their leading edge. The observed slip pulses propagate solely within a narrow range of "transonic" velocities, bounded between the shear wave velocity of the softer material and a limiting velocity. We derive analytic solutions for both subshear cracks and the leading edge of slip pulses. These solutions both provide an excellent description of our experimental measurements and quantitatively explain slip pulses' limiting velocities. We furthermore find that frictional coupling between local normal stress variations and frictional resistance actually promotes the interface separation that is critical for slip-pulse localization. These results provide a full picture of slip-pulse formation and structure that is important for our fundamental understanding of both earthquake motion and the most general types of frictional processes.

Transition from Static to Dynamic Friction in an Array of Frictional Disks

The nature of an instability that controls the transition from static to dynamical friction is studied in the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit and Newtonian dynamics can be employed without any phenomenological assumptions. We show that an oscillatory instability that had been discovered recently is responsible for the transition, allowing individual disks to spontaneously reach the Coulomb limit and slide with dynamic friction. The transparency of the model allows a full understanding of the phenomenon, including the speeds of the waves that travel from the trailing to the leading edge and vice versa.

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius [Formula: see text] governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding [Formula: see text] presents a pseudogap [Formula: see text], where θ is a nonuniversal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudogap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite-size effect, while the slip nucleation radius [Formula: see text] diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation—the macroscopic friction law—and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of a minimal macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the system’s geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g., rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially extended frictional systems.

Minimal model for slow, sub-Rayleigh, supershear, and unsteady rupture propagation along homogeneously loaded frictional interfaces

In nature and experiments, a large variety of rupture speeds and front modes along frictional interfaces are observed. Here, we introduce a minimal model for the rupture of homogeneously loaded interfaces with velocity strengthening dynamic friction, containing only two dimensionless parameters; τ[over ¯], which governs the prestress, and α[over ¯], which is set by the interfacial viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, supershear fronts, slip pulses, cracks, arresting fronts, and fronts that alternate between arresting and propagating phases. Our results indicate that this wide range of front types is an inherent property of frictional systems with velocity strengthening branches.

Periodic buckling and grain boundary slips in a colloidal model of solid friction

The intermittent 'stick-slip' dynamics in frictional sliding of solid bodies is common in everyday life and technology. This dynamics has been widely studied on a macroscopic scale, where the thermal motion can usually be neglected. However, the microscopic mechanisms behind the periodic stick-slip events are yet unclear. We employ confocal microscopy of colloidal spheres, to study the frictional dynamics at the boundary between two quasi-two-dimensional (2D) crystalline grains, with a single particle resolution. Such unprecedentedly-detailed observations of the microscopic-scale frictional solid-on-solid sliding have never been previously carried out. At this scale, the particles undergo an intense thermal motion, which masks the avalanche-like nature of the underlying frictional dynamics. We demonstrate that the underlying sliding dynamics involving out-of-plane buckling events, is intermittent and periodic, like in macroscopic friction. However, unlike in the common models of friction, the observed periodic frictional dynamics is promoted, rather than just suppressed, by the thermal noise, which maximizes the entropy of the system.

Continuously Sheared Granular Matter Reproduces in Detail Seismicity Laws

We introduce a shear experiment that quantitatively reproduces the main laws of seismicity. By continuously and slowly shearing a compressed monolayer of disks in a ringlike geometry, our system delivers events of frictional failures with energies following a Gutenberg-Richter law. Moreover, foreshocks and aftershocks are described by Omori laws and interevent times also follow exactly the same distribution as real earthquakes, showing the existence of memory of past events. Other features of real earthquakes qualitatively reproduced in our system are both the existence of a quiescence preceding some main shocks, as well as magnitude correlations linked to large quakes. The key ingredient of the dynamics is the nature of the force network, governing the distribution of frictional thresholds.

Simple Law for Third-Body Friction

A key difficulty to understanding friction is that many physical mechanisms contribute simultaneously. Here we investigate third-body frictional dynamics in a model experimental system that eliminates first-body interaction, wear, and fracture, and concentrates on the elastic interaction between sliding blocks and third bodies. We simultaneously visualize the particle motion and measure the global shear force. By systematically increasing the number of foreign particles, we find that the frictional dissipation depends only on the size ratio between surface asperities and the loose particles, irrespective of the particle's size or the surface's roughness. When the particles are comparable in size to the surface features, friction increases linearly with the number of particles. For particles smaller than the surface features, friction grows sublinearly with the number of particles. Our findings suggest that matching the size of surface features to the size of potential contaminants may be a good strategy for reliable lubrication.

Frictional weakening of slip interfaces

When two objects are in contact, the force necessary to overcome friction is larger than the force necessary to keep sliding motion going. This difference between static and dynamic friction is usually attributed to the growth of the area of real contact between rough surfaces in time when the system is at rest. We directly measure the area of real contact and show that it actually increases during macroscopic slip, despite the fact that dynamic friction is smaller than static friction. This signals a decrease in the interfacial shear strength, the friction per unit contact area, which is due to a mechanical weakening of the asperities. This provides a novel explanation for stick-slip phenomena in, e.g., earthquakes.

The virtual frame technique: ultrafast imaging with any camera

Many phenomena of interest in nature and industry occur rapidly and are difficult and cost-prohibitive to visualize properly without specialized cameras. Here we describe in detail the virtual frame technique (VFT), a simple, useful, and accessible mode of imaging that increases the frame acquisition rate of any camera by several orders of magnitude by leveraging its dynamic range. The VFT is a powerful tool for capturing rapid phenomena where the dynamics facilitate a transition between two states, and are thus binary. The advantages of the VFT are demonstrated by examining such dynamics in five physical processes at unprecedented rates and spatial resolution: fracture of an elastic solid, wetting of a solid surface, rapid fingerprint reading, peeling of adhesive tape, and impact of an elastic hemisphere on a hard surface. We show that the performance of the VFT exceeds that of any commercial high-speed camera not only in rate of imaging but also in field of view, achieving a 65MHz frame rate at 4MPx resolution. Finally, we discuss the performance of the VFT with several commercially available conventional and high-speed cameras. In principle, modern cell phones can achieve imaging rates of over a million frames per second using the VFT.

Bending to Kinetic Energy Transfer in Adhesive Peel Front Microinstability

We report an extensive experimental study of a detachment front dynamics instability, appearing at microscopic scales during the peeling of adhesive tapes. The amplitude of this instability scales with its period as A_{mss}∝T_{mss}^{1/3}, with a prefactor evolving slightly with the peel angle θ, and increasing systematically with the bending modulus B of the tape backing. Establishing a local energy budget of the detachment process during one period of this microinstability, our theoretical model shows that the elastic bending energy stored in the portion of tape to be peeled is converted into kinetic energy, providing a quantitative description of the experimental scaling law.

Evidence of friction reduction in laterally graded materials

In many biological structures, optimized mechanical properties are obtained through complex structural organization involving multiple constituents, functional grading and hierarchical organization. In the case of biological surfaces, the possibility to modify the frictional and adhesive behaviour can also be achieved by exploiting a grading of the material properties. In this paper, we investigate this possibility by considering the frictional sliding of elastic surfaces in the presence of a spatial variation of the Young's modulus and the local friction coefficients. Using finite-element simulations and a two-dimensional spring-block model, we investigate how graded material properties affect the macroscopic frictional behaviour, in particular, static friction values and the transition from static to dynamic friction. The results suggest that the graded material properties can be exploited to reduce static friction with respect to the corresponding non-graded material and to tune it to desired values, opening possibilities for the design of bio-inspired surfaces with tailor-made tribological properties.

Simultaneous improvements of strength and toughness in topologically interlocked ceramics

Topologically interlocked materials (TIMs) are an emerging class of architectured materials based on stiff building blocks of well-controlled geometries which can slide, rotate, or interlock collectively providing a wealth of tunable mechanisms, precise structural properties, and functionalities. TIMs are typically 10 times more impact resistant than their monolithic form, but this improvement usually comes at the expense of strength. Here we used 3D printing and replica casting to explore 15 designs of architectured ceramic panels based on platonic shapes and their truncated versions. We tested the panels in quasi-static and impact conditions with stereoimaging, image correlation, and 3D reconstruction to monitor the displacements and rotations of individual blocks. We report a design based on octahedral blocks which is not only tougher (50×) but also stronger (1.2×) than monolithic plates of the same material. This result suggests that there is no upper bound for strength and toughness in TIMs, unveiling their tremendous potential as structural and multifunctional materials. Based on our experiments, we propose a nondimensional "interlocking parameter" which could guide the exploration of future architectured systems.

Chemical aging of large-scale randomly rough frictional contacts

It has been shown that contact aging due to chemical reactions in single asperity contacts can have a significant effect on friction. However, it is currently unknown how chemically induced contact aging of friction depends on roughness that is typically encountered in macroscopic rough contacts. Here we develop an approach that brings together a kinetic Monte Carlo model of chemical aging with a contact mechanics model of rough surfaces based on the boundary element method to determine the magnitude of chemical aging in silica-silica contacts with random roughness. Our multiscale model predicts that chemical aging for randomly rough contacts has a logarithmic dependence on time. It also shows that friction aging switches from a linear to a nonlinear dependence on the applied load as the load increase. We discover that surface roughness affects the aging behavior primarily by modifying the real contact area and the local contact pressure, whereas the effect of contact morphology is relatively small. Our results demonstrate how understanding of chemical aging can be translated from studies of single asperity contacts to macroscopic rough contacts.

Recent highlights in nanoscale and mesoscale friction

Friction is the oldest branch of non-equilibrium condensed matter physics and, at the same time, the least established at the fundamental level. A full understanding and control of friction is increasingly recognized to involve all relevant size and time scales. We review here some recent advances on the research focusing of nano- and mesoscale tribology phenomena. These advances are currently pursued in a multifaceted approach starting from the fundamental atomic-scale friction and mechanical control of specific single-asperity combinations, e.g., nanoclusters on layered materials, then scaling up to the meso/microscale of extended, occasionally lubricated, interfaces and driven trapped optical systems, and eventually up to the macroscale. Currently, this "hot" research field is leading to new technological advances in the area of engineering and materials science.

The equation of motion for supershear frictional rupture fronts

The rupture fronts that mediate the onset of frictional sliding may propagate at speeds below the Rayleigh wave speed or may surpass the shear wave speed and approach the longitudinal wave speed. While the conditions for the transition from sub-Rayleigh to supershear propagation have been studied extensively, little is known about what dictates supershear rupture speeds and how the interplay between the stresses that drive propagation and interface properties that resist motion affects them. By combining laboratory experiments and numerical simulations that reflect natural earthquakes, we find that supershear rupture propagation speeds can be predicted and described by a fracture mechanics-based equation of motion. This equation of motion quantitatively predicts rupture speeds, with the velocity selection dictated by the interface properties and stress. Our results reveal a critical rupture length, analogous to Griffith's length for sub-Rayleigh cracks, below which supershear propagation is impossible. Above this critical length, supershear ruptures can exist, once excited, even for extremely low preexisting stress levels. These results significantly improve our fundamental understanding of what governs the speed of supershear earthquakes, with direct and important implications for interpreting their unique supershear seismic radiation patterns.

Nonmonotonic Aging and Memory in a Frictional Interface

We measure the static frictional resistance and the real area of contact between two solid blocks subjected to a normal load. We show that following a two-step change in the normal load the system exhibits nonmonotonic aging and memory effects, two hallmarks of glassy dynamics. These dynamics are strongly influenced by the discrete geometry of the frictional interface, characterized by the attachment and detachment of unique microcontacts. The results are in good agreement with a theoretical model we propose that incorporates this geometry into the framework recently used to describe Kovacs-like relaxation in glasses as well as thermal disordered systems. These results indicate that a frictional interface is a glassy system and strengthen the notion that nonmonotonic relaxation behavior is generic in such systems.

Molecular probes reveal deviations from Amontons' law in multi-asperity frictional contacts

Amontons’ law defines the friction coefficient as the ratio between friction force and normal force, and assumes that both these forces depend linearly on the real contact area between the two sliding surfaces. However, experimental testing of frictional contact models has proven difficult, because few in situ experiments are able to resolve this real contact area. Here, we present a contact detection method with molecular-level sensitivity. We find that while the friction force is proportional to the real contact area, the real contact area does not increase linearly with normal force. Contact simulations show that this is due to both elastic interactions between asperities on the surface and contact plasticity of the asperities. We reproduce the contact area and fine details of the measured contact geometry by including plastic hardening into the simulations. These new insights will pave the way for a quantitative microscopic understanding of contact mechanics and tribology.

Amontons’ law assumes that friction and normal forces depend linearly on the contact area. Here, the authors use a new contact detection method to show that the law is broken because asperities interact and deform in the contact area to change it, thereby also changing the friction force.

Evolution of real contact area under shear and the value of static friction of soft materials

The frictional properties of a rough contact interface are controlled by its area of real contact, the dynamical variations of which underlie our modern understanding of the ubiquitous rate-and-state friction law. In particular, the real contact area is proportional to the normal load, slowly increases at rest through aging, and drops at slip inception. Here, through direct measurements on various contacts involving elastomers or human fingertips, we show that the real contact area also decreases under shear, with reductions as large as 30[Formula: see text], starting well before macroscopic sliding. All data are captured by a single reduction law enabling excellent predictions of the static friction force. In elastomers, the area-reduction rate of individual contacts obeys a scaling law valid from micrometer-sized junctions in rough contacts to millimeter-sized smooth sphere/plane contacts. For the class of soft materials used here, our results should motivate first-order improvements of current contact mechanics models and prompt reinterpretation of the rate-and-state parameters.

Atomic-Scale Front Propagation at the Onset of Frictional Sliding

Macroscopic frictional sliding emerges from atomic-scale interactions and processes at the contact interface, but bridging the gap between micro and macro scales still remains an unsolved challenge. Direct imaging of the contact surface and simultaneous measurement of stress fields during macroscopic frictional slip revealed the formation of crack precursors, questioning the traditional picture of frictional contacts described in terms of a single degree of freedom. Here we study the onset of frictional slip on the atomic scale by simulating the motion of an aluminum block pushed by a slider on a copper substrate. We show the formation of dynamic slip front propagation and precursory activity that resemble macroscopic observations. The analysis of stress patterns during slip, however, reveals subtle effects due to the lattice structures that hinder a direct application of linear elastic fracture mechanics. Our results illustrate that dynamic front propagation arises already on the atomic scales and shed light on the connections between atomic-scale and macroscopic friction.

A phase-plane analysis of localized frictional waves

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick–slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

Slip Morphology of Elastic Strips on Frictional Rigid Substrates

The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which-when the bending elasticity dominates over the effect of gravity-are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and the coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thus complements recent work on elastic rope coiling and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

Brittle Fracture Theory Predicts the Equation of Motion of Frictional Rupture Fronts

We study rupture fronts propagating along the interface separating two bodies at the onset of frictional motion via high-temporal-resolution measurements of the real contact area and strain fields. The strain measurements provide the energy flux and dissipation at the rupture tips. We show that the classical equation of motion for brittle shear cracks, derived by balancing these quantities, well describes the velocity evolution of frictional ruptures. Our results demonstrate the extensive applicability of the dynamic brittle fracture theory to friction.

Hierarchical Spring-Block Model for Multiscale Friction Problems

A primary issue in biomaterials science is to design materials with ad hoc properties, depending on the specific application. Among these properties, friction is recognized as a fundamental aspect characterizing materials for many practical purposes. Recently, new and unexpected frictional properties have been obtained by exploiting hierarchical multiscale structures, inspired by those observed in many biological systems. In order to understand the emergent frictional behavior of these materials at the macroscale, it is fundamental to investigate their hierarchical structure, spanning across different length scales. In this article, we introduce a statistical multiscale approach, based on a one-dimensional formulation of the spring-block model, in which friction is modeled at each hierarchical scale through the classical Amontons-Coulomb force with statistical dispersion on the friction coefficients of the microscopic components. By means of numerical simulations, we deduce the global statistical distributions of the elementary structure at micrometric scale and use them as input distributions for the simulations at the next scale levels. We thus study the influence of microscopic artificial patterning on macroscopic friction coefficients. We show that it is possible to tune the friction properties of a hierarchical surface and provide some insight on the mechanisms involved at different length scales.

Slow wave propagation in soft adhesive interfaces

Stick-slip in sliding of soft adhesive surfaces has long been associated with the propagation of Schallamach waves, a type of slow surface wave. Recently it was demonstrated using in situ experiments that two other kinds of slow waves-separation pulses and slip pulses-also mediate stick-slip (Viswanathan et al., Soft Matter, 2016, 12, 5265-5275). While separation pulses, like Schallamach waves, involve local interface detachment, slip pulses are moving stress fronts with no detachment. Here, we present a theoretical analysis of the propagation of these three waves in a linear elastodynamics framework. Different boundary conditions apply depending on whether or not local interface detachment occurs. It is shown that the interface dynamics accompanying slow waves is governed by a system of integral equations. Closed-form analytical expressions are obtained for the interfacial pressure, shear stress, displacements and velocities. Separation pulses and Schallamach waves emerge naturally as wave solutions of the integral equations, with oppositely oriented directions of propagation. Wave propagation is found to be stable in the stress regime where linearized elasticity is a physically valid approximation. Interestingly, the analysis reveals that slow traveling wave solutions are not possible in a Coulomb friction framework for slip pulses. The theory provides a unified picture of stick-slip dynamics and slow wave propagation in adhesive contacts, consistent with experimental observations.

Creep to inertia dominated stick-slip behavior in sliding friction modulated by tilted non-uniform loading

Comprehension of stick-slip motion is very important for understanding tribological principles. The transition from creep-dominated to inertia-dominated stick-slip as the increase of sliding velocity has been described by researchers. However, the associated micro-contact behavior during this transition has not been fully disclosed yet. In this study, we investigated the stick-slip behaviors of two polymethyl methacrylate blocks actively modulated from the creep-dominated to inertia-dominated dynamics through a non-uniform loading along the interface by slightly tilting the angle of the two blocks. Increasing the tilt angle increases the critical transition velocity from creep-dominated to inertia-dominated stick-slip behaviors. Results from finite element simulation disclosed that a positive tilt angle led to a higher normal stress and a higher temperature on blocks at the opposite side of the crack initiating edge, which enhanced the creep of asperities during sliding friction. Acoustic emission (AE) during the stick-slip has also been measured, which is closely related to the different rupture modes regulated by the distribution of the ratio of shear to normal stress along the sliding interface. This study provided a more comprehensive understanding of the effect of tilted non-uniform loading on the local stress ratio, the local temperature, and the stick-slip behaviors.

Partial squeeze film levitation modulates fingertip friction

When touched, a glass plate excited with ultrasonic transverse waves feels notably more slippery than it does at rest. To study this phenomenon, we use frustrated total internal reflection to image the asperities of the skin that are in intimate contact with a glass plate. We observed that the load at the interface is shared between the elastic compression of the asperities of the skin and a squeeze film of air. Stroboscopic investigation reveals that the time evolution of the interfacial gap is partially out of phase with the plate vibration. Taken together, these results suggest that the skin bounces against the vibrating plate but that the bounces are cushioned by a squeeze film of air that does not have time to escape the interfacial separation. This behavior results in dynamic levitation, in which the average number of asperities in intimate contact is reduced, thereby reducing friction. This improved understanding of the physics of friction reduction provides key guidelines for designing interfaces that can dynamically modulate friction with soft materials and biological tissues, such as human fingertips.

A reciprocating optical in situ tribometer with high-speed data acquisition

Tribology is the science of interacting surfaces in relative motion. Processes like the transition from static to dynamic friction are fast and complex, especially as the contacting interface is buried. A direct view at the interface, in order to gain a deeper understanding of the interaction between the materials, is therefore of great interest. The reciprocating optical in situ tribometer introduced here observes the interface of two contacting materials (one of them being optical transparent) with a high-speed camera, taking up to 230 000 frames per second. The camera is attached to an optical microscope with a magnification of up to 2500 times. Friction forces are measured by an analog laser detection setup, with a maximum sampling rate of 500 kHz. The sliding motion of the materials is realized by two displacement units. A linear positioning stage allows velocities between 500 nm/s and 100 mm/s for a maximum distance of 200 mm. For smaller velocities, and to exclude breakaway torque, a piezo actuator can be used. The maximum displacement distance of the piezo actuator is 120 μm. The smallest applicable normal load on the samples is 0.5 N which is applied by the dead weights. Tribological experiments to investigate the transition from static to dynamic friction have been performed with morphologically textured brass hemispheres in contact with the sapphire discs. Sapphire was chosen for its high hardness and optical transparency. These experiments revealed, due to the high data acquisition possible with the new setup, a so far unobserved effect during the transition from static to dynamic friction.

Friction and nonlinear dynamics

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.

Stick-slip at soft adhesive interfaces mediated by slow frictional waves

Stick-slip is a friction instability that governs diverse phenomena from squealing automobile brakes to earthquakes. At soft adhesive interfaces, this instability has long been attributed to Schallamach waves, which are a type of slow frictional wave. We use a contact configuration capable of isolating single wave events, coupled with high speed in situ imaging, to demonstrate the existence of two new stick-slip modes. It is shown that these modes also correspond to the passage of slow waves-separation pulse and slip pulse-with distinct nucleation and propagation characteristics. The slip pulse, characterized by a sharp stress front, propagates in the same direction as the Schallamach wave. In contrast, the separation pulse, involving local interface detachment and resembling a tensile neck, travels in exactly the opposite direction. A change in the stick-slip mode from the separation to the slip pulse is effected simply by increasing the normal force. Taken together, the three waves constitute all possible stick-slip modes in low-velocity sliding. The detailed observations enable us to present a phase diagram delineating the domains of occurrence of these waves. We suggest a direct analogy between the observed slow frictional waves and well known muscular locomotory waves in soft bodied organisms. Our work answers basic questions about adhesive mechanisms of frictional instabilities in natural and engineered systems, with broader implications for slow surface wave phenomena.

Stable and unstable development of an interfacial sliding instability

Examining a nonlinear instability of sliding rate on a frictional interface of elastic bodies, we investigate whether laboratory-constrained frictional relations suggest universal scaling under even the simplest of configurations. We find blowup solutions by solving an equivalent, classical problem in fracture mechanics. The solutions are fixed points of a dynamical system and we show that their stability is lost by a cascade of Hopf bifurcations as a single problem parameter is increased, leading to chaotic dynamics.