Stick-slip Events Research Articles

Mechanisms of Tactile Information Transmission through Whisker Vibrations

In their natural environment, rodents use their whiskers to locate and distinguish between objects of different textures and shapes. They do so by moving their whiskers actively as well as passively, through body and head movements. To determine the mechanisms by which surface coarseness is translated into neuronal discharges through passive whisker movements, we monitored head movements of awake behaving rats while approaching objects. We then replayed these movements in anesthetized rats, monitored the whiskers' movements across various surfaces, and concurrently recorded the activity of first-order sensory neurons. We found that whiskers, being the first stage of sensory information translation, shape transduction by amplifying small-amplitude high-frequency signals. Thus, surface coarseness is transmitted through high-velocity micromotions. Consistent with this, we find that during surface contact, discrete high-velocity movements, or stick-slip events, evoke first-order neuronal discharge. Transient ringing in whiskers, which primarily represents resonance vibrations, follows these events, but seldom causes neurons to discharge. These sensory transformations are influenced by the whiskers' biomechanical properties. To determine the resemblance of these tactile transformations during passive whisker movements and active whisking, we induced artificial whisking across various surface textures. We found that the processes by which tactile information becomes available to the animal are similar for these different modes of behavior. Together, these findings indicate that the temporal bandpass properties for spike generation in first-order neurons are matched by the biomechanical characteristics of whiskers, which translate surface coarseness into high-frequency whisker micromotions. These properties enable rodents to acquire tactile information through passive and active movements of their whiskers.

Fiber bundle model with stick-slip dynamics

We propose a generic model to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can gradually increase their relaxed length with a stick-slip mechanism activated by the increasing load. We determine the constitutive equation of the system and show by analytical calculations that on the macroscale a plastic response emerges followed by a hardening or softening regime. Releasing the load, an irreversible permanent deformation occurs which depends on the properties of sliding events. For quenched and annealed disorder of the failure thresholds the same qualitative behavior is found, however, in the annealed case the plastic regime is more pronounced.

Nanoindentation of model diamond nanocomposites: Hierarchical molecular dynamics and finite-element simulations

Complementary molecular dynamics (MD) and finite-element (FE) simulations of model diamond nanocomposites (MDN) subjected to nanoindentation were undertaken to understand how contact behavior pertaining to the surface morphology of MDN surfaces can be spanned from the molecular to the continuum scale. The MD simulations determined that the behavior inside the contact region is influenced by atomic-scale features on the tip and surface, indent location, grain tilt and roughness of the MDN surfaces. In addition, if the atomic-scale surface morphology is treated as a surface roughness within the FE simulations, the same grain orientations, and similar elastic properties are used for both MD and FE simulations, there is reasonable agreement between the contact pressures for relatively low indentation loads and shallow substrates. For larger loads, the contact pressures from the FE simulations deviate somewhat from the MD results near the center of the contact. The contact behavior for length scales that are prohibitive for MD models (e.g., deep substrates) was also examined using FE simulations. This allowed for a detailed investigation of how contact conditions and stick-slip events within the contact evolve as a function of contact pressure and continuum surface stresses.

High-order synchronization of stick–slip process: experiments on spring–slider system

In the last years it has been shown that the synchronization and triggering of dynamic events by weak external forcing is ubiquitous and is observed in biological systems, lasers, electronic networks, etc. In the present paper, new experimental data on the phase synchronization in frictional system induced by a weak electromagnetic or mechanical periodic forcing are analyzed. For quantitative analysis of stick–slip time series, modern tools of nonlinear dynamics were used. Stick–slip events were identified by recording acoustic emissions, which accompany slip displacements. The spring–slider system in stick–slip regime is considered as a proxy of active tectonic fault, generating earthquakes.

Rate-dependent frictional adhesion in natural and synthetic gecko setae

Geckos owe their remarkable stickiness to millions of dry, hard setae on their toes. In this study, we discovered that gecko setae stick more strongly the faster they slide, and do not wear out after 30,000 cycles. This is surprising because friction between dry, hard, macroscopic materials typically decreases at the onset of sliding, and as velocity increases, friction continues to decrease because of a reduction in the number of interfacial contacts, due in part to wear. Gecko setae did not exhibit the decrease in adhesion or friction characteristic of a transition from static to kinetic contact mechanics. Instead, friction and adhesion forces increased at the onset of sliding and continued to increase with shear speed from 500 nm s(-1) to 158 mm s(-1). To explain how apparently fluid-like, wear-free dynamic friction and adhesion occur macroscopically in a dry, hard solid, we proposed a model based on a population of nanoscopic stick-slip events. In the model, contact elements are either in static contact or in the process of slipping to a new static contact. If stick-slip events are uncorrelated, the model further predicted that contact forces should increase to a critical velocity (V*) and then decrease at velocities greater than V*. We hypothesized that, like natural gecko setae, but unlike any conventional adhesive, gecko-like synthetic adhesives (GSAs) could adhere while sliding. To test the generality of our results and the validity of our model, we fabricated a GSA using a hard silicone polymer. While sliding, the GSA exhibited steady-state adhesion and velocity dependence similar to that of gecko setae. Observations at the interface indicated that macroscopically smooth sliding of the GSA emerged from randomly occurring stick-slip events in the population of flexible fibrils, confirming our model predictions.

Tribological performance of MoS 2 coatings in liquid helium and at high loads

The main part of a narrow support element (NSE) of the W7-X superconducting coil system is an aluminium bronze pad, PVD coated on its spherical surface with MoS 2, which slides against the flat surface of the stainless steel coil housing, coated with MoS 2 spray. The operational requirements of the NSEs are: vacuum of p < 10 −6 mbar, temperature T ∼ 4 K, maximum load P ∼1500 kN, typical displacement ≤5 mm, smooth sliding and no stick-slip events. The paper describes test results obtained with a downscaled NSE at T = 4.2 and 77 K. During the test the NSEs were submerged in liquid helium and nitrogen, respectively. Whereas the LN 2 test ran smoothly for up to ∼15,000 cycles, the test in LHe showed stick-slip from the very first cycle. The stick-slip disappeared after ∼50 cycles. Post mortem analysis of the tested parts revealed that in case of LHe the sprayed MoS 2 film was removed during the first 30–100 cycles by blistering and flaking. The reason for the loss of adhesion at LHe temperature is not known, several possible causes are under discussion. Further experiments under vacuum and at T ∼4 K are being prepared which are expected to help in clarifying the issue.

Cryogenic vacuum tests of scaled down narrow support elements for the W7-X coil system

The narrow support elements (NSEs) between the casings of the superconducting coils of the Wendelstein 7-X magnet system consist of pads made of Al–bronze, which can slide and tilt against stainless-steel counter-faces. Static friction peaks or stick–slip events during sliding may cause disturbances to the magnet system and have to be avoided. Because the NSEs are operated at a temperature of ≈4 K and in vacuum at a residual pressure of p < 10 −6 mbar, only solid lubricants, in particular MoS 2, are applicable. Therefore, the static and dynamic friction behaviour of MoS 2-coatings was tested in liquid helium at 4.2 K and in vacuum at room temperature under high contact pressures and very low sliding velocities. In model tests with small Al–bronze pins, sliding in reciprocating motion against a PVD–MoS 2-coating on a steel substrate, very stable sliding behaviour without coating failure, and a friction coefficient below 0.1 was observed. However, tests with downscaled samples in original geometry showed stable sliding in liquid nitrogen, but unexpected stick–slip behaviour in liquid helium at 4.2 K. For further investigations and because in actual service the NSEs are not immersed into a liquid cryogen, tests under vacuum at low temperatures are being prepared.

Subglacial clast behaviour and its implication for till fabric development: new results derived from wireless subglacial probe experiments

This study has investigated the three-dimensional movement of clasts within deformation till, using embedded wireless probes. These probes were part of an environmental sensor network, which measured subglacial properties (temperature, water pressure, resistivity, case strain and tilt) six times a day, and relayed that data via radio to the glacier surface, where they were forwarded and broadcast on-line. The system was installed at Briksdalsbreen, Norway and operated from August 2004 until August 2006. Approximately 2000 probe days worth of data were collected, with an increase in performance (41% more readings) during the second year. The probes showed similar patterns of water pressure rises throughout the two years, but with slightly different magnitudes and timings. These changes in water pressure could be related to clast behaviour. The probes decreased their dip over the year, and the rate of change was related to an increase in glacier velocity. After initial changes in dip, the probes experienced changes in orientation, followed by rotation about the a-axis. This continuous rotation was similar to the motion suggested by Jeffery [1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London, Series A 102, 161–179] for the behaviour of clasts within a viscous material. In addition, some probes also showed short, frequent dip oscillations in spring and autumn, which were interpreted to reflect stick-slip events, similar to lodging; and demonstrated how local conditions can interrupt the predicted rotation pattern. Overall, it is demonstrated that when water pressures were high, decoupling occurred associated with basal sliding and dip oscillations; and when water pressures fell, the ice and sediment were coupled and till deformation occurred. These events happened during summer and autumn. It is this combination of “lodgement” and deformation that builds up both a complex (but predictable) fabric and a resultant composite till sedimentology.

Modelling polymer interactions of the ‘molecular Velcro’ type in wood under mechanical stress

Trees withstand wind and snow loads by synthesising wood that varies greatly in mechanical properties: flexible in twigs and in the stem of the sapling, and rigid in the outer part of the mature stem. The ‘molecular Velcro’ model of Keckes et al. [2003. Cell-wall recovery after irreversible deformation of wood. Nat. Mater. 2, 810–814] permits the simulation of the tensile properties of water-saturated wood as found in living trees. A basic feature of this model is the presence of non-covalent interactions between hemicellulose chains attached to adjacent cellulose microfibrils, which are disrupted above a threshold level of interfibrillar shear. However, other evidence does not confirm the importance of hemicellulose–hemicellulose association in the cohesion of the interfibrillar matrix. Here, we present an alternative model in which hemicellulose chains bridging continuously from one microfibril aggregate (macrofibril) to the next provide most of the cohesion. We show that such hemicellulose bridges exist and that the stripping of the bridging chains from the cellulose surfaces under the tensile stress component normal to the macrofibrils can provide an alternative triggering mechanism for shear deformation between one macrofibril and the next. When one macrofibril then slides past another, a domain of the wood cell wall can extend but simultaneously it twists until the spacing between macrofibrils is reduced again and contact through hemicelluloses bridges is restored. Overall deformation therefore takes place through a series of local stick–slip events involving temporary twisting of small domains within the wood cell wall. Modelled load–deformation curves for this modified ‘molecular Velcro’ model are similar, although not identical, to those for the original model. However, the mechanism is different and more consistent with current views of the structure of wood cell walls, providing a framework within which the developmental control of rigidity in wood synthesised in different parts of a tree may be considered.

Electromagnetic signals associated with stick–slip of quartz-free rocks

We recorded clear transients in the electric and magnetic fields upon sudden slip in stick–slip experiments on dry, cylindrically shaped, quartz-free rock specimens of basalt and peridotite with a 30° saw-cut (representing a fault) at confining pressures of up to 120 MPa. The amplitudes of the measured electric field signals were always higher at the electrode pair oriented parallel to the strike of the fault than at the pair oriented perpendicular. This anisotropy suggests a preferred electric polarization normal to the slip surface. The transients in the electric and magnetic fields were observed only when the fault slip occurred by stick–slip mode, not by a stable mode of the sliding, and the amplitudes of the electric field signals increased with increasing stress drop. It is suggested that the generation process of the electromagnetic signals is closely related to the characteristic behavior of the fault at the time of the initiation of slip during stick–slip events, probably with respect to the intensity of the signals. We propose that one or both of the following two processes characteristic of the fault at the time of the initiation of slip during stick–slip events are essential for the generation of detectable electromagnetic signals: rapid slip along the simulated fault and separation of the rock masses across the fault.

Stick-Slip Motions in the Friction Force Microscope: Effects of Tip Compliance

When a microcantilever with a nanoscale tip is scanned laterally over a surface to measure the nanoscale frictional forces, the onset of stick-slip tip motions is an extremely important phenomenon that signals the onset of lateral friction forces. In this article, we investigate theo- retically the influence of tip and microcantilever compliance on this phenomenon. We show that static considerations alone cannot predict uniquely the onset of single or multiple atom slip events. Instead, the nonlinear dynamics of the tip during a slip event need to be carefully investigated to determine if the tip evolves to a single or multiple atom stick-slip motions. The results suggest that the relative compliances of the tip and microcantilever can be engineered to induce single or multiple atom stick-slip events and thus control lateral friction forces at the nanoscale.

Thermal Precursory Pattern of Fault Unstable Slip: An Experimental Study of En Echelon Faults

AbstractWe have measured synchronously the variation of temperature and infrared radiation fields before and after unstable slip events on compressive and extensional en echelon faults by using an infrared thermal image system and a contact‐type thermometric apparatus in the laboratory. From the experiment records we found that the temperature and thermal radiation values drop first in the inner flank of the jog before they begin to jump along the fault. The relative rising of temperature along the fault occurs 2~3 seconds before a stick‐slip, while the drop of temperature in the jog area happens about 20 seconds before the stick‐slip, meaning a time lead about an order of magnitude. This kind of thermal field pattern “drop first and rise afterwards” is ubiquitous to some extent for stick slip events during the deformation of en echelon faults. Therefore, it can be regarded as a heat precursor pattern of instability. The temporal process and the characteristics in spatial structure of the thermal field are described based on the results of the experiment. The mechanism of precursory pattern is discussed. The generation condition of remarkable anomalies and favorable sites of observations for this precursory phenomenon are analyzed. Moreover, the significance in exploring of earthquake precursory and application of satellite infrared information is discussed.

Near-Fault Peak Ground Velocity from Earthquake and Laboratory Data

We test the hypothesis that peak ground velocity (pgv) has an upper bound independent of earthquake magnitude and that this bound is controlled primarily by the strength of the seismogenic crust. The highest pgvs, ranging up to several meters per second, have been measured at sites within a few kilometers of the causative faults. Because the database for near-fault pgv is small, we use earthquake slip models, laboratory experiments, and evidence from a mining-induced earthquake to investigate the factors influencing near-fault pgv and the nature of its scaling. For each earthquake slip model we have calculated the peak slip rates for all subfaults and then chosen the maximum of these rates as an estimate of twice the largest near-fault pgv. Nine slip models for eight earthquakes, with magnitudes ranging from 6.5 to 7.6, yielded maximum peak slip rates ranging from 2.3 to 12 m/ sec with a median of 5.9 m/sec. By making several adjustments, pgvs for small earthquakes can be simulated from peak slip rates measured during laboratory stick- slip experiments. First, we adjust the pgv for differences in the state of stress (i.e., the difference between the laboratory loading stresses and those appropriate for faults at seismogenic depths). To do this, we multiply both the slip and the peak slip rate by the ratio of the effective normal stresses acting on fault planes measured at 6.8 km depth at the KTB site, Germany (deepest available in situ stress measurements), to those acting on the laboratory faults. We also adjust the seismic moment by replacing the laboratory fault with a buried circular shear crack whose radius is chosen to match the experimental unloading stiffness. An additional, less important adjustment is needed for experiments run in triaxial loading conditions. With these adjustments, peak slip rates for 10 stick-slip events, with scaled moment magnitudes from −2.9 to 1.0, range from 3.3 to 10.3 m/sec, with a median of 5.4 m/sec. Both the earthquake and laboratory results are consistent with typical maximum peak slip rates averaging between 5 and 6 m/sec or corresponding maximum near-fault pgvs between 2.5 and 3 m/sec at seismogenic depths, independent of magnitude. Our ability to replicate maximum slip rates in the fault zones of earthquakes by adjusting the corresponding laboratory rates using the ratio of effective normal stresses acting on the fault planes suggests that the strength of the seismogenic crust is the important factor limiting the near-fault pgv.

Two-dimensional stick–slip on a soft elastic polymer: pattern generation using atomic forcemicroscopy

It has been demonstrated that it is possible to create laterally differentiated frictionalpatterning and three-dimensional structures using an atomic force microscope(AFM) probe on the surface of a soft elastic polymer, poly(dimethylsiloxane)(PDMS). The resulting effect of contact mode imaging at low loading forces(<100 nN), observed in the lateral force mode, revealed a homogeneous pattern on the PDMSsurface exhibiting higher friction. With higher loading forces ( nN) the effect is non-uniform, resulting in structures with depths on the nanometre scale.The topographic and frictional data revealed stick–slip responses in both the fast(orthogonal to the long axis of the lever) and slow (parallel to the long axis of the lever)directions of probe travel from scanning in a raster pattern. The stick–slip events aremanifested in the form of a series of shallow channels spaced evenly apart on the polymersurface. Detailed friction loop analysis acquired during the manipulation process showedthat the lateral force changed according to the strength of trapping of the tip with thepolymer surface exhibiting significant in-plane deformation due to lateral forces beingimposed. An incremental increase in the initial loading force resulted in an increase inin-plane displacement and a greater spacing between the stick lines/channels inthe slow-scan direction. A decrease in channel length in the fast-scan directionis also observed as a result of an increase in static friction with normal force,resulting in greater surface deformation and shorter track length for sliding friction.

Electric dipoles perpendicular to a stick-slip plane

Stick-slip tests of pre-cut quartz pegmatite cylinders under tri-axial compression were conducted with a solenoid or toroidal coil near or surrounding the stick-slip plane. The solenoid coil detected damped oscillating signals during stick-slip events. The toroidal coil detected similar oscillations but on an exponential decay. The damped oscillating component is the induced electromotive force (emf) voltage due to piezoelectric polarizations of individual quartz crystals or due to the Earth's magnetostatic field when the coils vibrate. The exponentially decaying component is the induced emf voltage due to electric dipoles approximately perpendicular to the stick-slip plane. These perpendicular dipoles can be explained by the formation of surface charges on separate asperities. The exponential decay of the perpendicular dipoles is due to exponential diffusion and recombination of the separate charges. Electric dipoles on separated asperities may also exist on the geophysical scale: on fault planes during faulting.

A laboratory experiment to monitor the contact state of a fault by transmission waves

We performed a series of laboratory experiments in which elastic waves were transmitted across a simulated fault. Two types of experiments were carried out: (1) Normal Stress Holding Test (NSHT): normal stress was kept constant for about 3 h without shear stress and transmission waves were observed. (2) Shear Stress Increasing Test (SSIT): shear stress was gradually increased until a stick-slip event occurred. Transmission waves were continuously observed throughout the process of stress accumulation. We focused on the change in transmission waves during the application of shear stress and especially during precursory slips. It was found in NSHT that the amplitude of transmission waves linearly increased with the logarithm of stationary contact time. The increase amounted to a few percent after about 3 h. Creep at asperity contacts is responsible for this phenomenon. From a theoretical consideration, it was concluded that the real contact area increased with the logarithm of stationary contact time. We observed in SSIT a significant increase in wave amplitude with shear stress application. This phenomenon cannot be attributed to the time effect observed in NSHT. Instead, it can be explained by the mechanism of “junction growth” proposed by Tabor. Junction growth yields an increase in real contact area. It is required for junction growth to occur that the material in contact is already plastic under a purely normal loading condition. A computer simulation confirmed that this requirement was satisfied in our experiments. We also found that the rate at which the amplitude increased was slightly reduced prior to a stick-slip event. The onset time of the reduction well coincides with the onset of precursory slip. The cause of the reduction is attributed to the reset of stationary contact time due to displacement. This interpretation is supported by the result of NSHT. Taking the time of stationary contact in SSIT into account, we may expect the change in wave amplitude to be, at most, only a few percent. The observed slight reduction in increasing rate is, in this sense, reasonable. The static stiffness of the fault also decreases with precursory slip. It was also found that low frequency waves are a better indicator of precursory slip than high frequency waves. This might suggest that low frequency waves with longer wavelength are a better indicator of average behavior of faults. The problem, however, merits a further investigation. The shifts in phase were also found to be a good indicator of the change in contact state of the fault. The changes in both amplitude and phase of transmission waves are unifyingly understood through the theory of transmission coefficient presented by Pyrak-Nolte et al. Rough surfaces have a tendency to give larger stick-slips than smooth surfaces. The amount of precursory slip is larger for rough surfaces than for smooth surfaces. Although it was confirmed by a computer simulation that rough surfaces have larger contact diameters than smooth surfaces, the rigorous relationship between the surface roughness (contact diameter) and the amount of precursory slips was not established.

Stick slip and wear on metal surfaces

Molecular dynamics (MD) simulations of ploughing friction are performed on fcc crystalline Ag and the results compared to experiments on polycrystalline Ag. For the simulations, a sharp pyramidal diamond tip is inserted into the (1 0 0) surface at various depths and for different temperatures and pulled across the surface. The mechanisms behind the stick slip and wear events are investigated. The forces and friction coefficients vary with tip orientation and linear distance travelled by the tip over the surface. The simulations show that dislocations propagate in the 〈1 1 0〉 direction from the tip as the scratch develops. Dislocations can also be linked to the stick events, with the emission of a dislocation in the substrate region near the tip, when slip occurs after stick. The pile-up patterns are shown to be in good qualitative agreement with experimental observations in the scanning force microscope. Higher temperature simulations in silver show less pronounced dislocation emission than at 0K and pile up which is spread further away from the scratch.

Slip event propagation direction in transition region of low surface slope

AbstractThe base of the ice in the transition zone between an ice stream and an ice shelf is likely to be well lubricated by broadly distributed water, a condition which should permit fast sliding motion. It has been observed that motion takes place not smoothly but by localized stick–slip events that propagate in the downstream direction towards the ice shelf and at velocities approximately that expected for shear wave velocity of the basal till. Thus slip packets of gliding edge dislocations are likely to move at the base. I show here that subsonic dislocations should move upstream, rather than downstream, if frictional resistance is determined by normal traction stress change at the base. Transonic dislocations are expected to move in the downstream direction. However, if frictional resistance is lowered by hydrostatic pressure reduction at the base, the subsonic dislocation should move downstream.

Modeling of stick-slip phenomena using molecular dynamics

Molecular dynamics simulations are performed to investigate the atomic-scale stick-slip phenomenon of a pyramidal diamond tip inserted into the Ag(010) surface. The mechanisms behind the stick-slip events are investigated by considering sliding speeds between 1.0 and $5.0{\mathrm{ms}}^{\ensuremath{-}1}$ and vertical support displacements of 5 and 15 \AA{}. The analysis of the dynamic features of the substrate shows that dislocations are extrinsically linked to the stick events, with the emission of a dislocation in the substrate region near the tip, when slip occurs after stick. For small vertical displacements, the scratch in the substrate is not continuous because the tip can jump over the surface when slipping, whereas at 15 \AA{}, a continuous scratch is formed. The dynamic friction coefficient increases from $\ensuremath{\sim}0.13$ to $\ensuremath{\sim}0.46$ with increasing depth, but the static friction coefficient increases only from $\ensuremath{\sim}0.32$ to $\ensuremath{\sim}0.54.$ At the larger depths the tip does not come to a halt during stick as it does for shallow indents. Instead the tip motion is more continuous with stick and slip manifested by periods of faster and slower motion. Although the exact points of stick and slip depend on the sliding speed, the damage to the substrate, the atomistic stick-slip mechanisms, and the friction coefficients are relatively independent of speed over the range of values considered.

Maximum Slip in Earthquake Fault Zones, Apparent Stress, and Stick-Slip Friction

The maximum slip, observed or inferred, for a small patch within the larger fault zone of an earthquake is a remarkably well-constrained function of the seismic moment. A large set of maximum slips, mostly derived from slip models of major earthquakes, indicate that this parameter increases according to the cube root of the seismic moment. Consistent with this finding, neither the average slip rate for the patches of maximum slip nor the apparent stresses of earthquakes show any systematic dependence on seismic moment. Maximum average slip rates are several meters per second independent of moment and, for earthquakes in continental crustal settings, the apparent stress is limited to about 10 MPa. Results from stick-slip friction experiments in the laboratory, combined with information about the state of stress in the crust, can be used to predict, quite closely, the maximum slips and maximum average slip rates within the fault zones of major earthquakes as well as their apparent stresses. These findings suggest that stick-slip friction events observed in the laboratory and earthquakes in continental settings, even with large magnitudes, have similar rupture mechanisms. Manuscript received 24 February 2003.