Statistics of the separation between sliding rigid rough surfaces: Simulations and extreme value theory approach

When a rigid rough solid slides on a rigid rough surface, it experiences a random motion in the direction normal to the average contact plane. Here, through simulations of the separation at single-point contact between self-affine topographies, we characterize the statistical and spectral properties of this normal motion. In particular, its rms amplitude is much smaller than that of the equivalent roughness of the two topographies, and depends on the ratio of the slider's lateral size over a characteristic wavelength of the topography. In addition, due to the non-linearity of the sliding contact process, the normal motion's spectrum contains wavelengths smaller than the smallest wavelength present in the underlying topographies. We show that the statistical properties of the normal motion's amplitude are well captured by a simple analytic model based on the extreme value theory framework, extending its applicability to sliding-contact-related topics

On the speed of fast and slow rupture fronts along frictional interfaces

The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasi-static fronts with speeds proportional to external loading rates, via fronts much slower than the Rayleigh wave speed, and fronts that propagate near the Rayleigh wave speed, to fronts that travel faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic 2D spring--block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that a proportionality between material slip speed and rupture front speed, previously reported for slow fronts, actually holds across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even in homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Lastly, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically-based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.Comment: 29 pages, 21 figure

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

To study the microscopic origins of friction, we build a framework to describe the collective behaviour of a large number of individual micro-junctions forming a macroscopic frictional interface. Each micro-junction 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 micro-junction 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. We show how this framework represents an overarching structure for important models existing in the friction literature. We then use it to study systematically the effect of the time-scale that controls the duration of the slipping state. We first find the steady-state friction force as a function of the sliding velocity. As the framework allows for a whole family of micro-junction behaviour laws, we show how these laws can be chosen to obtain monotonic (strengthening or weakening) or non-monotonic velocity dependence at the macroscale. By then considering transient situations, we predict that the macroscopic static friction coefficient is strongly influenced by the way the interface was prepared, in particular by the slip dynamics of the previous sliding event. We also show that slow slip spontaneously occurs in the framework for a wide range of behaviour laws.Comment: 20 pages, 10 figure

Slow slip and the transition from fast to slow fronts in the rupture of frictional interfaces

The failure of the population of micro-junctions forming the frictional interface between two solids is central to fields ranging from biomechanics to seismology. This failure is mediated by the propagation along the interface of various types of rupture fronts, covering a wide range of velocities. Among them are so-called slow fronts, which are recently discovered fronts much slower than the materials' sound speeds. Despite intense modelling activity, the mechanisms underlying slow fronts remain elusive. Here, we introduce a multi-scale model capable of reproducing both the transition from fast to slow fronts in a single rupture event and the short-time slip dynamics observed in recent experiments. We identify slow slip immediately following the arrest of a fast front as a phenomenon sufficient for the front to propagate further at a much slower pace. Whether slow fronts are actually observed is controlled both by the interfacial stresses and by the width of the local distribution of forces among micro-junctions. Our results show that slow fronts are qualitatively different from faster fronts. Since the transition from fast to slow fronts is potentially as generic as slow slip, we anticipate that it might occur in the wide range of systems in which slow slip has been reported, including seismic faults.Comment: 35 pages, 5 primary figures, 6 supporting figures. Post-print version with improvements from review process include

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

International audienceIn 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, which governs the prestress, and ᾱ which is set by the dynamic viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, super-shear 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

Numerical Modelling of the Dynamics of the Onset of Sliding

Nous utilisons un modèle multi-échelles de la transition entre frottement statique et frottement dynamique, pour étudier la vitesse des fronts de rupture le long d'interfaces multi-contact étendues. Nous montrons que la vitesse des fronts est directement contrôlée par la vitesse de glissement associée, pour toute la gamme de vitesses explorée. Nous proposons ensuite un classement, basé sur les mécanismes en jeu, pour les différents types de fronts observés. Nous montrons finalement comment le coefficient de frottement statique local est contrôlé par l'histoire du glissement, au même endroit, mais lors de la rupture précédente de l'interface

Precursors to sliding and static friction threshold of heterogeneous frictional interfaces

Nous utilisons un modèle multi-échelles de la transition entre frottement statique et frottement dynamique, pour étudier la vitesse des fronts de rupture le long d'interfaces multi-contact étendues. Nous montrons que la vitesse des fronts est directement contrôlée par la vitesse de glissement associée, pour toute la gamme de vitesses explorée. Nous proposons ensuite un classement, basé sur les mécanismes en jeu, pour les différents types de fronts observés. Nous montrons finalement comment le coefficient de frottement statique local est contrôlé par l'histoire du glissement, au même endroit, mais lors de la rupture précédente de l'interface

1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments

We study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38, 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.Comment: 13 pages, 14 figures, accepted in Tribology Letter

Modeling the Onset of Dynamic Friction : Contact Mechanics

A one-dimensional mesoscopic spring block model with Amontons-Coulomb friction is introduced in order to investigate if some features of recent friction experiments can be understood. Our results suggest that the model too simple to reproduce the main features of the experiment. A two dimensional model and a different local friction law is needed. In order to test the latter, a two dimensional quasi-static discrete element method is developed to find the tangential loading curve of a thin surface layer. A single asperity is modeled as a semi-circle, in agreement with Hertz and Cattaneo-Mindlin theory. A scaling behavior of the shear stiffness of an asperity with the compression and the dynamic friction coefficient is found, and used to develop a theoretical model for the shear strength of a rough surface assuming elastic independence of asperities. The discrete element method is further used to model a self affine surface and a gradient percolation surface. Our results suggest that the qualitative behavior of the shear stiffness for the self affine surface is in agreement with the theory, while the behavior of the gradient percolation surface is not