9 research outputs found
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
Modelling the onset of frictional sliding: Rupture fronts, slow slip, and time-dependent junction laws
Friction is scientifically interesting and technologically important. We can characterize friction well, but even the friction force between macroscopic surfaces of known chemistry and topography under known loading conditions cannot yet be predicted from the bottom up. A major obstacle to predicting frictional properties is to link the macroscopic observations to the behavior of the myriad microscopic connections that make up the interaction.
The onset of frictional sliding occurs through the breaking of the contacts that were keeping the interface stuck. Recent experiments performed with high spatial and temporal resolution show that rupture nucleates at weak or highly stressed points and propagates outwards from there. Understanding how the rupture travels is an important step towards understanding friction. This thesis presents simulations and theory aimed at improving our understanding of this onset of sliding in dry friction systems. The principal model combines 2D elasticity with an asperity level description of the interface and reproduces and explains many of the experimental results. Analytical calculations provide additional insights
Steady-state propagation speed of rupture fronts along one-dimensional frictional interfaces
The rupture of dry frictional interfaces occurs through the propagation of fronts breaking the contacts at the interface. Recent experiments have shown that the velocities of these rupture fronts range from quasistatic velocities proportional to the external loading rate to velocities larger than the shear wave speed. The way system parameters influence front speed is still poorly understood. Here we study steady-state rupture propagation in a one-dimensional (1D) spring-block model of an extended frictional interface for various friction laws. With the classical Amontons-Coulomb friction law, we derive a closed-form expression for the steady-state rupture velocity as a function of the interfacial shear stress just prior to rupture. We then consider an additional shear stiffness of the interface and show that the softer the interface, the slower the rupture fronts. We provide an approximate closed form expression for this effect. We finally show that adding a bulk viscosity on the relative motion of blocks accelerates steady-state rupture fronts and we give an approximate expression for this effect. We demonstrate that the 1D results are qualitatively valid in 2D. Our results provide insights into the qualitative role of various key parameters of a frictional interface on its rupture dynamics. They will be useful to better understand the many systems in which spring-block models have proved adequate, from friction to granular matter and earthquake dynamics