Self-healing slip pulses along a gel/glass interface

We present experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity: steady sliding at high velocity (>V(c) approximately 100--125 microm/s), characterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a "healing instability" occurring when the local sliding velocity reaches the macroscopic transition velocity V(c). At driving velocities close below V(c), the system exhibits complex spatiotemporal behavior.     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V = V _c. For V > V _c, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than V _c, hence with the existence of the healing instability. Received: 7 March 2003 / Accepted: 2 May 2003 / Published online: 11 June 2003 RID="b" ID="b"e-mail: ronsin@gps.jussieu.fr     

Mesomechanics of shear resistance along a filled crack

The paper reports on laboratory experiments with the aim of studying the effect of microstructural and macromechanical properties of a crack filled with discrete material on the formation of a sliding mode. It is shown that the spectrum of possible deformation events on the discontinuity is governed by both the macroscopic characteristics of the gouge and its mesoscale structure. The evolution of force bridges which are formed and collapsed in shear along the crack, their length and number fully control the type of deformation—stable sliding, stick-slip, and intermediate modes with low-velocity motion of the crack edges. The variation of the Coulomb strength affects mainly the stress drop value in dynamic failure or a slip event with low displacement velocity and little affects the deformation mode. Consideration is also given to the regularities by which the macroscopic characteristics of contact vary in shear.     

The mobility of the amorphous phase in polyethylene as a determining factor for slow crack growth

Polyethylene (PE) pipes generally exhibit a limited lifetime, which is considerably shorter than their chemical degradation period. Slow crack growth failure occurs when pipes are used in long-distance water or gas distribution though being exposed to a pressure lower than the corresponding yield stress. This slow crack growth failure is characterized by localized craze growth and craze fibril rupture. In the literature, the lifetime of PE pipes is often considered as being determined by the density of tie chains connecting adjacent crystalline lamellae. But this consideration cannot explain the excellent durability of the recent bimodal grade PE for pipe application. We show in this paper the importance of the craze fibril length as the determining factor for the pipe lifetime. The conclusions are drawn from stress analysis. It is found that longer craze fibrils sustain lower stress and are deformed to a lesser degree. The mobility of the amorphous phase is found to control the amount of material that can be sucked in by the craze fibrils and thus the length of the craze fibrils. The mobility of the amorphous phase can be monitored by dynamic mechanical analysis measurements. Excellent agreement between the mobility thus derived and lifetimes of PE materials as derived from FNCT (full notch creep test) is given, thus providing an effective means to estimate the lifetime of PE pipes by considering well-defined physical properties.     

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

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

Force fluctuations in a vertically pushed granular column

We present series of experiments on the resistance force encountered by a bottom piston pushing a vertical granular column confined in a two-dimensional cell. We show that, due to the presence of friction at the boundaries and between the grains, the signal shows many complex features. At slow driving velocities, we observe a transition to a stick-slip dynamic instability. Depending on the granular material used, the elementary stick-slip events may either be well characterized or largely distributed. We present a statistical study on the waiting time between events and the distribution of energy release as a function of the spring stiffness and the driving velocity. Received 5 August 1998 and Received in final form 22 October 1998     

Experimental study of different modes of block sliding along interface. Part 1. Laboratory experiments

This paper is the first part of an experimental work on studying the formation of different deformation modes of rock discontinuities under laboratory and field conditions. The formation conditions of different sliding modes were studied under laboratory conditions for several types of discontinuities, such as rigid surface contact and cracks filled with quartz sand, talc, and clay. A wide range of shear deformation modes were experimentally reproduced—from dynamic slip with a maximum velocity of tens of mm/s to stable sliding with a velocity of 1 µm/s. The behavior of a crack with a clay-containing gouge drastically changes after its wetting. The larger is the content of clay, the longer is the slip duration. The motion of a block consists of a long phase (~100 s) in which displacement velocity smoothly increases, and a retardation phase of almost the same duration in which displacement velocity decreases down to a few tens of µm/s. The used sensors detected no acoustic emission prior to the beginning of block sliding as well as on all stages of block motion until its full stop. It is shown that slow slip events have all stages typical for stick-slip motion: acceleration, long sliding, retardation, arrest, and quiescence. The conducted laboratory experiments substantiate the earlier statement that all types of deformation processes in the Earth’s crust produce a common range of phenomena.     

Fatigue Crack Nucleation at Σ3(1 1 2) Boundary in a Ferritic Stainless Steel

The effect of a geometrical relationship between a grain boundary (GB) plane and a tensile axis on intergranular fatigue cracking along 3(1 1 2) twin boundaries has been investigated in Fe-30%Cr alloy crystals. Fatigue experiments were carried out on the three kinds of the specimens containing the 3(1 1 2) twin boundary. It was found that the fatigue cracking behavior was sensitive to the geometry of the GB plane. In a specimen where both the GB plane and a slip vector lying in the GB plane in adjacent grains are inclined to the tensile axis at 45°, the fatigue cracks were nucleated preferentially along the twin boundary at a stress amplitude of 170 MPa. The specimen with the GB plane normal to the tensile axis showed that the fatigue crack was initiated from a slip band formed within a constituent grain at a stress amplitude of 300 MPa. When the GB plane was inclined to the tensile axis but the slip vector lying in the GB plane was normal to the tensile axis, development of additional slips formed perpendicular to the GB plane were observed at a specific site of the GB. Initiation of intergranular fatigue cracks at the site was recognized at a stress amplitude of 250 MPa. It can be suggested that the GB plane normal to the tensile axis provides the highest fatigue performance among them. The difference in the cracking property among these specimens could be understood in terms of the effective Schmid factor derived from elastically incompatible stress.     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.     

Hot cracks in rubber: origin of the giant toughness of rubberlike materials

We study crack propagation in rubberlike materials and show that the nonuniform temperature distribution which occurs in the vicinity of the crack tip has a profound influence on the crack propagation, and may strongly enhance the crack propagation energy G(v) for high crack velocities v. At very low crack-tip velocities, the heat produced at the crack tip can diffuse away, but already at moderate crack-tip velocities a very large temperature increase occurs close to the crack tip resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt and may result in unstable crack motion, e.g., stick-slip motion or catastrophic failure.     

Shear-induced adhesive failure of a rigid slab in contact with a thin confined film

A rigid-glass prism (square or rectangular base, rectangular cross-section) is sheared off a thin film of silicone elastomer bonded to a glass plate by applying a tangential force at various distances above the prism/elastomer interface. At a given tangential force, the prism starts to slide on the elastomeric film. As the sliding velocity, thus the frictional force, is progressively increased, an elastic instability develops at the interface that results in the formation of numerous bubbles. These bubbles, the lateral dimension of which is comparable to the thickness of the film, move across the interface with speeds 1000 times faster than the overall sliding speed of the glass prism against the PDMS film. It is found that the glass prism continues to slide on the elastomeric film as long as the applied shear stress is less than a critical value. During sliding, however, a normal stress is developed at the interface that decays from the front (i.e. where the force is applied) to the rear end of the prism. When the normal stress reaches a critical value, the prism comes off the film. The critical shear stress of fracture increases with the modulus of the film, but decreases with the thickness following a square root relationship, as is the case with the removal of rigid punches from thin elastomeric films by normal pull-off forces.     

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

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

Slip dynamics at a patterned rubber/glass interface during stick-slip motions

We report on an experimental study of heterogeneous slip instabilities generated during stick-slip motions at a contact interface between a smooth rubber substrate and a patterned glass lens. Using a sol-gel process, the glass lens is patterned with a lattice of parallel ridges (wavelength, 1.6 μm, amplitude 0.35 μm). Friction experiments using this patterned surface result in the systematic occurrence of stick-slip motions over three orders of magnitude in the imposed driving velocity while stable friction is achieved with a smooth surface. Using a contact imaging method, real-time displacement fields are measured at the surface of the rubber substrate. Stick-slip motions are found to involve the localized propagation of transverse interface shear cracks whose velocity is observed to be remarkably independent on the driving velocity.     

Nonlinear Dynamics of a Sliding Chain in a Periodic Potential

Nonlinear dynamics of the sliding process of a chain driven with a constant velocity at one end in a periodic substrate potential is investigated. The driven chain exhibits distinctly different dynamical characteristics at different velocities. In the low velocity region, the chain moves in a stick-slip manner. When the driving velocity is increased, the stick-slip behaviour is replaced by complicated and regular oscillatory motions. The dependence of the dynamics on the coupling strength is studied and the step-like behaviour is found, where different steps correspond to different dynamical phases.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Critical Velocity of Controllability of Sliding Friction by Normal Oscillations for an Arbitrary Linear Rheology

The application of ultrasonic vibrations is an established procedure in industry in order to significantly reduce and control sliding friction. One of the main characteristics of this phenomenon is that, beyond a certain critical sliding velocity, the friction is no longer controllable—although oscillations are still being externally applied. an a previous series of related studies, closed-form solutions of the critical velocity have been derived with respect to pure elastic and specific viscoelastic models. In the present paper we present a universal formula of the critical velocity which is valid for arbitrary linear rheology. The derivation relies on the same theoretical basis of the previous studies, where the reduction of friction is ascribed to a stick-slip motion of the contact. Therefore, all previous results represent limiting and special cases of this universal equation. In the second part of this paper we pursue the numerical analysis of the previous studies by investigating the reduction of friction for a viscoelastic Kelvin material for the first time.     

Kinetics and dynamics of frictional stick-slip in mesoscopic boundary lubrication

The kinetics and dynamics of frictional stick-slip motion of a slider of size extending from mesoscopic upward is analyzed within the framework of a multi-contact, earthquake-like model. The microscopic contacts are characterized by a distribution of static thresholds for individual breaking. The condition for an overall elastic instability leading to stick-slip sliding are derived and details of the slip motion are studied theoretically. The crucial model parameters emerging from this analysis include the delay time for each micro-contact to reform after breaking, the strength of elastic interaction between the contacts, the elasticity of contacts and of the slider, and the distribution of static thresholds for their breaking. The dynamics is also studied with the help of a scaling procedure. As a prototype application, we adopt parameters appropriate to describe recent surface force apparatus (SFA) boundary lubrication experiments. Despite suggestions of extremely large lubricant viscosities, the experimental data are shown to be fully compatible with ordinary, bulk-like viscosity values once the multi-contact aspects are taken into account.