Rheological aging and rejuvenation in solid friction contacts

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).

Dynamics of Sliding Friction between Laser-Induced Periodic Surface Structures (LIPSS) on Stainless Steel and PMMA Microspheres

In this work, we investigated the sliding friction measured between poly(methyl methacrylate) (PMMA) colloidal probes with two different diameters D (1.5 and 15 μm) and laser-induced periodic surface structures (LIPSS) on stainless steel with periodicities Λ of 0.42 and 0.9 μm, when the probes are elastically driven along two directions, perpendicular and parallel to the LIPSS. The time evolution of the friction shows the characteristic features of a reverse stick-slip mechanism recently reported on periodic gratings. The morphologies of colloidal probes and modified steel surfaces are geometrically convoluted in the atomic force microscopy (AFM) topographies simultaneously recorded with the friction measurements. The LIPSS periodicity is only revealed with smaller probes (D = 1.5 μm) and when Λ takes the largest value of 0.9 μm. The average value of the friction force is found to be proportional to the normal load, with a coefficient of friction μ varying between 0.23 and 0.54. The values of μ are rather independent of the direction of motion, and they reach their maximum when the small probe is scanned on the LIPSS with the larger periodicity. The friction is also found to decrease with increasing velocity in all cases, which is attributed to the corresponding decrease of the viscoelastic contact time. These results can be used to model the sliding contacts formed by a set of spherical asperities of different sizes driven on a rough solid surface.

Sliding friction perturbed by shear ultrasound vibrations: dynamic lubrication and overaging

Reduction of the effective static coefficient of friction by shear ultrasound has been shown recently to be due to the partial lubrication of the solid-solid contact. Here, we study the effect of ultrasound perturbation on a multicontact interface at imposed drive velocity. We show that, together with the partial lubrication similar to the static case, ultrasound vibrations enhance structural aging and the emergence of stick-slip.

Beyond quality and quantity: Spatial distribution of contact encodes frictional strength

Classically, the quantity of contact area A_{R} between two bodies is considered a proxy for the force of friction. However, bond density across the interface-quality of contact-is also relevant, and contemporary debate often centers around the relative importance of these two factors. In this work, we demonstrate that a third factor, often overlooked, plays a significant role in static frictional strength: The spatial distribution of contact. We perform static friction measurements, μ, on three pairs of solid blocks while imaging the contact plane. By using linear regression on hundreds of image-μ pairs, we are able to predict future friction measurements with three to seven times better accuracy than existing benchmarks, including total quantity of contact area. Our model has no access to quality of contact, and we therefore conclude that a large portion of the interfacial state is encoded in the spatial distribution of contact, rather than its quality or quantity.

The evolution of rock friction is more sensitive to slip than elapsed time, even at near-zero slip rates

Nearly all frictional interfaces strengthen as the logarithm of time when sliding at ultra-low speeds. Observations of also logarithmic-in-time growth of interfacial contact area under such conditions have led to constitutive models that assume that this frictional strengthening results from purely time-dependent, and slip-insensitive, contact-area growth. The main laboratory support for such strengthening has traditionally been derived from increases in friction during "load-point hold" experiments, wherein a sliding interface is allowed to gradually self-relax down to subnanometric slip rates. In contrast, following step decreases in the shear loading rate, friction is widely reported to increase over a characteristic slip scale, independent of the magnitude of the slip-rate decrease-a signature of slip-dependent strengthening. To investigate this apparent contradiction, we subjected granite samples to a series of step decreases in shear rate of up to 3.5 orders of magnitude and load-point holds of up to 10,000 s, such that both protocols accessed the phenomenological regime traditionally inferred to demonstrate time-dependent frictional strengthening. When modeling the resultant data, which probe interfacial slip rates ranging from 3 .[Formula: see text]. to less than [Formula: see text], we found that constitutive models where low slip-rate friction evolution mimics log-time contact-area growth require parameters that differ by orders of magnitude across the different experiments. In contrast, an alternative constitutive model, in which friction evolves only with interfacial slip, fits most of the data well with nearly identical parameters. This leads to the surprising conclusion that frictional strengthening is dominantly slip-dependent, even at subnanometric slip rates.

Memory effects in friction: the role of sliding heterogeneities

We report on memory effects involved in the unsteady-state frictional response of a contact interface between a silicone rubber and a spherical glass probe when it is perturbed by changes in the orientation of the driving motion or by velocity steps. From measurements of the displacement fields at the interface, we show that observed memory effects can be accounted for by the non-uniform distribution of the sliding velocity within the contact interface. As a consequence of these memory effects, the friction force may no longer be aligned with respect to the sliding trajectory. In addition, stick–slip motions with a purely geometrical origin are also evidenced. These observations are adequately accounted for by a friction model that takes into account heterogeneous displacements within the contact area. When a velocity dependence of the frictional stress is incorporated in this model, unsteady-state regimes induced by velocity steps are also adequately described. The good agreement between the model and experiments outlines the role of space heterogeneities in memory effects involved in soft matter friction.

Shear Controls Frictional Aging by Erasing Memory

We simultaneously measure the static friction and the real area of contact between two solid bodies. These quantities are traditionally considered equivalent, and under static conditions both increase logarithmically in time, a phenomenon coined aging. Here we show that the frictional aging rate is determined by the combination of the aging rate of the real area of contact and two memory-erasure effects that occur when shear is changed (e.g., to measure static friction.) The application of a static shear load accelerates frictional aging while the aging rate of the real area of contact is unaffected. Moreover, a negative static shear-pulling instead of pushing-slows frictional aging, but similarly does not affect the aging of contacts. The origin of this shear effect on aging is geometrical. When shear load is increased, minute relative tilts between the two blocks prematurely erase interfacial memory prior to sliding, negating the effect of aging. Modifying the loading point of the interface eliminates these tilts and as a result frictional aging rate becomes insensitive to shear. We also identify a secondary memory-erasure effect that remains even when all tilts are eliminated and show that this effect can be leveraged to accelerate aging by cycling between two static shear loads.

Ageing of Polymer Frictional Interfaces: The Role of Quantity and Quality of Contact

When two objects are in contact, the force necessary for one to start sliding over the other is larger than the force necessary to keep the sliding motion going. This difference between static and dynamic friction is thought to result from a reduction in the area of real contact upon the onset of slip. Here, we resolve the structure in the area of contact on the molecular scale by means of environment-sensitive molecular rotors using (super-resolution) fluorescence microscopy and fluorescence lifetime imaging. We demonstrate that the macroscopic friction force is not only controlled by the area of real contact but also controlled by the "quality" of that area of real contact, which determines the friction per unit contact area. We show that the latter is affected by the local density of the contacting surfaces, a parameter that can be expected to change in time at any interface that involves glassy, amorphous materials.

Slow dynamic nonlinearity in unconsolidated glass bead packs

Slow dynamic nonlinearity describes a poorly understood, creeplike phenomena that occurs in brittle composite materials such as rocks and cement. It is characterized by a drop in stiffness induced by a mechanical conditioning, followed by a log(time) recovery. A consensus theoretical understanding of the behavior has not been developed. Here we introduce an alternative experimental venue with which to inform theory. Unconsolidated glass bead packs are studied rather than rocks or cement because the structure and internal contacts of bead packs are less complex and better understood. Slow dynamics has been observed in such systems previously. However, the measurements to date tend to be irregular. Particular care is used here in the experimental design to overcome the difficulties inherent in bead pack studies. This includes the design of the bead pack support, the use of low-frequency conditioning, and the use of ultrasonic waves as a probe with coda wave interferometry to assess changes. Slow dynamics is observed in our system after three different methods for low-frequency conditioning, one of which has not been reported in the literature previously.

Slow dynamics in a single glass bead

Slow dynamic nonlinearity is ubiquitous amongst brittle materials, such as rocks and concrete, with cracked microstructures. A defining feature of the behavior is the logarithmic-in-time recovery of stiffness after a mechanical conditioning. Materials observed to exhibit slow dynamics are sufficiently different in microstructure, chemical composition, and scale (ranging from the laboratory to the seismological) to suggest some kind of universality. A consensus of theoretical understanding of the universality in general and the log(time) recovery in particular is lacking. Seminal studies were focused on sandstones and other natural rocks, but in recent years other experimental venues have been introduced with which to inform theory. One such system is unconsolidated glass bead packs. However, bead packs still contain many contact points. The force distribution amongst the contacts is unknown. Here, we present slow dynamics measurements on a yet simpler system-a single glass bead confined between two large glass plates. The system is designed with a view towards rapid control of the contact zone environment. Ultrasonic waves are used as a probe of the system, and changes are assessed with coda wave interferometry. Three different methods of low-frequency conditioning are applied; all lead to slow dynamic recoveries. Results imply that force chains do not play an essential role in granular media slow dynamics, as they are absent in our system.

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.

Interface bonding in silicon oxide nanocontacts: interaction potentials and force measurements

The interface bonding between two silicon-oxide nanoscale surfaces has been studied as a function of atomic nature and size of contacting asperities. The binding forces obtained using various interaction potentials are compared with experimental force curves measured in vacuum with an atomic force microscope. In the limit of small nanocontacts (typically <10³ nm²) measured with sensitive probes the bonding is found to be influenced by thermal-induced fluctuations. Using interface interactions described by Morse, embedded atom model, or Lennard-Jones potential within reaction rate theory, we investigate three bonding types of covalent and van der Waals nature. The comparison of numerical and experimental results reveals that a Lennard-Jones-like potential originating from van der Waals interactions captures the binding characteristics of dry silicon oxide nanocontacts, and likely of other nanoscale materials adsorbed on silicon oxide surfaces. The analyses reveal the importance of the dispersive surface energy and of the effective contact area which is altered by stretching speeds. The mean unbinding force is found to decrease as the contact spends time in the attractive regime. This contact weakening is featured by a negative aging coefficient which broadens and shifts the thermal-induced force distribution at low stretching speeds.

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.

Universal Aging Mechanism for Static and Sliding Friction of Metallic Nanoparticles

The term "contact aging" refers to the temporal evolution of the interface between a slider and a substrate usually resulting in increasing friction with time. Current phenomenological models for multiasperity contacts anticipate that such aging is not only the driving force behind the transition from static to sliding friction, but at the same time influences the general dynamics of the sliding friction process. To correlate static and sliding friction on the nanoscale, we show experimental evidence of stick-slip friction for nanoparticles sliding on graphite over a wide dynamic range. We can assign defined periods of aging to the stick phases of the particles, which agree with simulations explicitly including contact aging. Additional slide-hold-slide experiments for the same system allow linking the sliding friction results to static friction measurements, where both friction mechanisms can be universally described by a common aging formalism.

History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework

To study how macroscopic friction phenomena originate from microscopic junction laws, we introduce a general statistical framework describing the collective behavior of a large number of individual microjunctions forming a macroscopic frictional interface. Each microjunction can switch in time between two states: a pinned state characterized by a displacement-dependent force and a slipping state characterized by a time-dependent force. Instead of tracking each microjunction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. This framework allows for a whole family of microjunction behavior laws, and we show how it represents an overarching structure for many existing models found in the friction literature. We then use this framework to pinpoint the effects of the time scale that controls the duration of the slipping state. First, we show that the model reproduces a series of friction phenomena already observed experimentally. The macroscopic steady-state friction force is velocity dependent, either monotonic (strengthening or weakening) or nonmonotonic (weakening-strengthening), depending on the microscopic behavior of individual junctions. In addition, slow slip, which has been reported in a wide variety of systems, spontaneously occurs in the model if the friction contribution from junctions in the slipping state is time weakening. Next, we show that the model predicts a nontrivial history dependence of the macroscopic static friction force. In particular, the static friction coefficient at the onset of sliding is shown to increase with increasing deceleration during the final phases of the preceding sliding event. We suggest that this form of history dependence of static friction should be investigated in experiments, and we provide the acceleration range in which this effect is expected to be experimentally observable.

Evolution of grain contacts in a granular sample under creep and stress relaxation

This article deals with the characterization, using an acoustic technique, of the mechanical behavior of a dry dense granular medium under quasistatic loading. Ultrasound propagation through the contact-force network supporting the external load offers a noninvasive probe of the viscoelastic properties of such heterogeneous media. First the response of a glass bead packing is studied in an oedometric configuration during creep and relaxation tests. Quasilogarithmic increases of sound velocities are found in both mechanical tests. A model based on the mechanics of microcontacts between rough grains adequately reproduces our experimental results, especially for the evolution of elastic modulus. Another main experimental finding is that collective grain rearrangements within the packing also play a crucial role at the early stage of creep and relaxation.

Aging and stiction dynamics in confined films of a star polymer melt

The stiction properties of a star polyisoprene (PIP) melt (having 22 arms and an arm molecular weight of around 5000, M(w) ≈ 110,000) confined between mica surfaces were investigated using the surface forces apparatus. Stop-start experiments were carried out and the stiction spike was measured as a function of surface stopping (aging) time t and applied pressure P; the time constants of the phase transitions in the stiction dynamics (freezing on stopping and melting on starting) were obtained from the force relaxation behaviors. The results were compared with those of a confined linear-PIP melt (M(w) ≈ 48,000) and other confined fluid systems; the effect of star architecture on the phase transitions in confinement during aging is discussed. Estimation of the molecular size gives that the confined star-PIP films consist of three molecular layers; a non-adsorbed layer sandwiched between two layers adsorbed on opposed mica surfaces. There are (at least) four time constants in the freezing transition of the confined star-PIP melt; fast (τ(1)) and slow (τ(2)) time constants for lateral force relaxation on stopping, critical aging time for freezing (τ(f)), and the logarithmic increase of the spike height against t. The three time constants on stopping, τ(1), τ(2), and τ(f), increase with the increase of P (decrease of the thickness D). As regards the melting transition on starting, spike force decay was fitted by a single exponential function and one time constant was obtained, which is insensitive to P (D). Comparison of the time constants between freezing and melting, and also with the results of linear-PIP reveals that the stiction dynamics of the star-PIP system involves the relaxation and rearrangement of segmental-level and whole molecular motions. Lateral force relaxation on stopping is governed by the individual and cooperative rearrangements of local PIP segments and chain ends of the star, which do not directly lead to the freezing of the system. Instead, geometrical rearrangements of the soft star-PIP spheres into dense packing between surfaces (analogous to the concept of a colloidal glass transition) are the major mechanism of the freezing transition (stiction) after aging. Interdigitation of PIP segments/chain ends between neighboring star molecules also contributes to the spike growth along with aging, and the melting transition on starting.

Aging of the frictional properties induced by temperature variations

The dry frictional contact between two solid surfaces is well known to obey Coulomb friction laws. In particular, the static friction force resisting the relative lateral (tangential) motion of solid surfaces, initially at rest, is known to be proportional to the normal force and independent of the area of the macroscopic surfaces in contact. Experimentally, the static friction force has been observed to slightly depend on time. Such an aging phenomenon has been accounted for either by the creep of the material or by the condensation of water bridges at the microscopic contact points. By studying a toy model, we show that the small uncontrolled temperature changes of the system can also lead to a significant increase of the static friction force.

Structural aging and stiction dynamics in confined liquid films

The static friction (stiction) of the molecularly thin films of an irregularly shaped molecule 1,3-dimethylbutyl octyl ether (DBOE) confined between mica surfaces was investigated using the surface forces apparatus. Stop-start experiments were carried out and the stiction spike was measured as a function of surface stopping (aging) time t and applied pressure P. The results show two relaxation processes, one on stopping and one on starting, where each process has a fast and a slow time constant. For stopping mode, there is no stiction spike when t is shorter than a characteristic nucleation time, tau(n) (fast time constant). When t exceeds tau(n), stiction spike appears whose height increases logarithmically with t. With regard to starting, the relaxation behavior was evaluated by a double exponential fit of the slipping regime (force decay) of the spike and two time constants (tau(1) and tau(2)) were obtained. The fast time constant on starting tau(1) is almost equal to that on stopping tau(n). To the best of our knowledge, this is the first direct observation of the agreement of the time constant on stopping and that on starting, indicative of a reversible structural transition (solid-liquid transition) in the stop-start stiction dynamics. The two fast time constants exhibit exponential dependence on P, which implies a glasslike nature of the transition. Comparison with the stick-slip friction reveals that the solid-liquid transition involved in stiction and that in stick-slip dynamics is different for DBOE; first-order-like discontinuous transition is suggested for stick-slip friction. Origins of the different solid-liquid transition dynamics in stiction and in stick-slip friction are discussed by comparing with the dynamics of other confined liquid systems.

Ultrasonic excitation affects friction interactions between food materials and cutting tools

In the food industry, ultrasonic cutting is used to improve separation by a reduction of the cutting force. This reduction can be attributed to the modification of tool-workpiece interactions at the cutting edge and along the tool flanks because of the superposition of the cutting movement with ultrasonic vibration of the cutting tool. In this study, model experiments were used to analyze friction between the flanks of a cutting tool and the material to be cut. Friction force at a commercial cutting sonotrode was quantified using combined cutting-friction experiments, and sliding friction tests were carried out by adapting a standard draw-off assembly and using an ultrasonic welding sonotrode as sliding surface. The impact of material parameters, ultrasonic amplitude, and the texture of the contacting food surface on friction force was investigated. The results show that ultrasonic vibration significantly reduces the sliding friction force. While the amplitude showed no influence within the tested range, the texture of the contact surface of the food affects the intensity of ultrasonic transportation effects. These effects are a result of mechanical interactions and of changes in material properties of the contact layer, which are induced by the deformation of contact points, friction heating and absorption heating because of the dissipation of mechanical vibration energy.

Mechanisms for acoustic absorption in dry and weakly wet granular media

The dissipation of an elastic wave in dry and wet glass bead packings is measured using multiple sound scattering. The interplay of a linear viscoelastic loss and a nonlinear frictional one is observed in dry media. The Mindlin model provides a qualitative description of the experiment, but fails to quantitatively account for the data due to grain roughness. In weakly wet media, we find that the dissipation is dominated by a linear viscous loss due to the liquid films trapped at the grain surface asperities. Adding more liquid enables us to form the capillary menisci but does not increase the energy loss.

Frictional dissipation and interfacial glass transition of polymeric solids

We present single contact friction experiments between a glassy polymer and smooth silica substrates grafted with alkylsilane layers of different coverage densities and morphologies. This allows us to adjust the polymer-substrate interaction strength. We find that, when going from weak to strong interaction, the response of the interfacial junction where shear localizes evolves from that of a highly viscous threshold fluid to that of a plastically deformed glassy solid. This we analyze as resulting from an interaction-induced "interfacial glass transition" helped by pressure.

Contact area measurements reveal loading-history dependence of static friction

We perform quantitative measurements of the actual area of contact, A, formed by two rough solids that are subjected to different normal loading protocols. We show that microscopic motion, induced by Poisson contraction or expansion, produces a strong memory dependence of on the loading history with a large corresponding influence on the system's frictional strength. These effects, together with accompanying transient dynamics, are independent of humidity, loading rates, and material contrast across the interface.

Non-Amontons behavior of friction in single contacts

We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to a widely spread belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plasticity of a glass-like interfacial layer in the former case, and by pinning of polymer chains on the substrate in the latter one.

Direct mechanical force measurements during the migration of Dictyostelium slugs using flexible substrata

We use the flexible substrate method to study how and where mechanical forces are exerted during the migration of Dictyostelium slugs. This old and contentious issue has been left poorly understood so far. We are able to identify clearly separate friction forces in the tip and in the tail of the slug, traction forces mostly localized in the inner slug/surface contact area in the prespore region and large perpendicular forces directed in the outward direction at the outline of contact area. Surprisingly, the magnitude of friction and traction forces is decreasing with slug velocity indicating that these quantities are probably related to the dynamics of cell/substrate adhesion complexes. Contrary to what is always assumed in models and simulations, friction is not of fluid type (viscous drag) but rather close to solid friction. We suggest that the slime sheath confining laterally the cell mass of the slug experiences a tension that in turn is pulling out the elastic substrate in the direction tangential to the slug profile where sheath is anchored. In addition, we show in the appendix that the iterative method we developed is well adapted to study forces over large and continuous fields when the experimental error is sufficiently low and when the plane of recorded bead deformations is close enough to the elastomer surface, requirements fulfilled in this experimental study of Dictyostelium slugs.

Anomalous acoustic reflection on a sliding interface or a shear band

We study the reflection of an acoustic plane wave from a steadily sliding planar interface with velocity-strengthening friction or a shear band in a confined granular medium. The corresponding acoustic impedance is utterly different from that of the static interface. In particular, the system being open, the energy of an in-plane polarized wave is no longer conserved, the work of the external pulling force being partitioned between frictional dissipation and gain (of either sign) of coherent acoustic energy. Large values of the friction coefficient favor energy gain, while velocity strengthening tends to suppress it. An interface with infinite elastic contrast (one rigid medium) and v-independent (Coulomb) friction exhibits spontaneous acoustic emission, as already shown by Nosonovsky and Adams [Int. J. Eng. Sci. 39, 1257 (2001)]. But this pathology is cured by a moderately large V strengthening of friction, or, for systems with not too large friction coefficients, by any finite elastic contrast. We show that (i) positive gain should be observable for rough-on-flat multicontact interfaces and (ii) a sliding shear band in a granular medium should give rise to sizable reflection, which opens a promising possibility for the detection of shear localization.

Shearing of a confined granular layer: tangential stress and dilatancy

We study the behavior of a confined granular layer under shearing, in an annular cell, at low velocity. We give evidence that the response of the granular layer under shearing is described by characteristic length scales. The tangential stress reaches its steady state on the same length scale as the dilatancy. Stop-and-go experiments performed at several driving velocities show a logarithmic increase of the static friction coefficient with waiting time, followed by rejuvenation on a characteristic length of the order of the magnitude of a Hertz contact between adjacent grains. The dilatancy does not evolve during the stop, neither during the elastic reloading when the driving is resumed. There is a small variation when sliding sets anew, which corresponds to the rejuvenation of the layer, and this variation is independent of the waiting time. We argue that aging is due to the behavior of individual contacts between grains, not global evolution of the piling. Under an instantaneous increase of the velocity, the tangential stress reaches a new steady state, exhibiting velocity strengthening behavior. An increase of dilatancy is also observed. It is much larger than fluctuations in the steady state, variations in a stop and-go-experiment, but much less than for shearing of freshly poured grains. The dilatancy variation during a velocity jump is not due to structural rearrangements of the piling. The evolutions of tangential stress and dilatancy are logarithmic in the ratio of upper and lower velocities.

Boundary lubrication with a glassy interface

Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo nonaffine deformations in response to stress. The generalization we study phenomenologically incorporates the effects of aging and glassy relaxation. Under experimental conditions associated with typical transitions from stick-slip to steady sliding and stop-start tests, these effects can be dominant, although the full STZ description is necessary to account for more complex, chaotic transitions.