Session H26: Focus Session: Friction, Fracture and Deformation Across Length Scales - Friction Across Length Scales

Rock Friction from the Nanoscale to the San Andreas Fault

Nucleation of earthquakes (EQs) and the resistance of faults to shearing during EQs are determined by nano-to-micro- scale frictional processes that occur on tectonic-scale faults. A first-order observation from rock-friction studies is that of ageing, i.e., the linear increase in friction with the log of the time of stationary contact, manifest as a positive or negative dependence of friction on sliding rate. A necessary condition for EQ nucleation is a negative rate dependence of friction. In spite of the success of friction `laws' which encapsulate the rate and time dependences of friction in fitting experimental data and reproducing natural phenomena in EQ models, these laws lack a physical basis. Atomic force microscope (AFM) experiments on silica-silica contacts explore the physics of ageing, more specifically increases in adhesion of nanometers-sized contacts with time (Li et al., \textit{Nature}, 2011). The experiments reveal prominent ageing which increases with humidity, as in rock friction tests, without increases in contact area due to creep (the canonical explanation for ageing in rock-friction tests). Ageing in the AFM tests is in fact much larger than in rock-friction tests, a discrepancy explained with a simple multi-asperity contact model. At EQ slip rates ($\ge $1 m/s) a variety of dynamic fault-weakening mechanisms may decrease the shear resistance of faults, which would have important consequences for the magnitudes of EQ stress drops, strong ground motions and accelerations, for the EQ energy budget, and for the state of stress on faults. Experiments on rocks found in the Earth's crust for slip rates up to $\sim $0.4 m/s over $\sim $40 mm of slip, reveal a dramatic 1/$V$ decrease in frictional strength above a characteristic weakening velocity $V_{w}$ of $\sim $0.1 m/s (Goldsby and Tullis, \textit{Science}, 2011). Friction is also revealed to be a nearly pure function of slip rate, i.e., it adjusts to the ambient slip rate over only microns of slip. The observations are explained by `flash heating', whereby microscopic asperity contacts become intensely frictionally heated and weakened above $V_{w}$. Dramatically lower friction due to flash heating may explain why heat flow along active faults like the San Andreas Fault is much lower than expected. Strong velocity-weakening friction and the rapid strength recovery with decreasing slip rate from flash heating may explain why EQ ruptures propagate as slip pulses rather than as cracks.   

Avalanche Distributions and the Effect of Inertia in Strained Amorphous Solids

We present results from two and three-dimensional simulations of a disordered, binary Lennard-Jones solid under quasi-static, steady-state shear. The solid responds to the applied shear strain with bursts of particle movement and plasticity. The energy E of these avalanches spans a wide range and follows a power-law distribution $N(E) \propto E^{-\tau}$ with three distinct exponents, depending on the importance of inertia. In the limit of overdamped dynamics, or no inertia, we find $\tau \approx 0.8$, consistent with previous energy minimization simulations. As inertia becomes more important, the system approaches an unstable critical point where $\tau = 1$. In the underdamped limit, where inertia plays a large role, the distribution of avalanches follows a power-law with exponent $\tau = 1.4$ with an excess of system-spanning events. The three regimes have distinct finite-size-scaling exponents. The fact that consistent exponents are found in two and three dimensions indicates that both may be in the mean-field limit. Spatial correlations in avalanches under different damping regimes will be contrasted.   

Dynamic Phase Diagram and Jamming for Driven Dislocation Assemblies

By using large scale numerical simulations for driven dislocations in 2D, we show that the resulting dynamic phase diagram has the same features found for driven vortex matter and charge density waves in the presence of random disorder. For low loads the system is pinned or jammed. Just above the onset of motion we observe strong velocity fluctuations with $1/f$ noise properties and bimodal velocity distributions associated with rapidly fluctuating dislocation structures. At higher loads there is a dynamic reordering into a state of partially ordered domain walls with a pronounced drop in the velocity fluctuations as well as a reduction in the noise power. These features have all the hallmarks observed for dynamic phases such as the pinned, fluctuating, and dynamical reordering transitions found in driven vortex matter. We discuss the implications of work in terms of dynamic phase transitions at the onset of motion and the onset of the dynamical ordering.   

Scale invariant avalanches: a critical confusion

In the last decades considerable efforts have been devoted to understanding single events related to friction, fracture and unjamming transition, commonly denominated avalanches. However, in many different natural scenarios -from subcritical fracture to earthquake dynamics- these events are of all scales; a situation that has often been interpreted within the formalism of critical phenomena, and having as a relevant consequence the inherently unpredictability of scale-invariant avalanches. A revision of this interpretation which departs from standard ideas is presented here, resulting in [1]: (i) critical systems are not necessarily unpredictable; (ii) slowly driven systems evolving through power-law distributed avalanches are not necessarily critical; and (iii) scale-invariant avalanches are not necessarily unpredictable. Simple simulations and granular experiments [2] confirm the findings. \\[4pt] [1] O. Ramos, Scale invariant avalanches: a critical confusion; in B. Veress and J. Szigethy (eds.) Horizons in Earth Science Research. Vol. 3 (Nova Science Publishers) pp 157-188 (2011) arXiv:1104.4991v1. \\[0pt] [2] O. Ramos, E. Altshuler, and K. J. M{\aa}l{\o}y, Avalanche prediction in a self-organized pile of beads, Phys. Rev. Lett. 102, 078701 (2009).   

Unjamming of amorphous films probed with a transverse shear ultrasonic oscillator

Friction between solids depends essentially on the response of the interfacial amorphous layer to shear and compressive stresses. Hence, the transition from static to dynamic friction corresponds to the unjamming transition of confined amorphous materials [1]. With a shear ultrasonic oscillator, we study the boundary lubrication due to molecular films confined between a plane and a sphere [2]. We observe a linear viscoelastic behaviour at low oscillation amplitude and a nonlinear frictional microslip regime at high amplitude. In a new set of experiments, the system is brought near the unjamming transition by applying a static force. The interfacial layer softens before unjamming, as indicated by the linear response of the oscillator. We suggest an interpretation based on a stress-induced decrease of the free volume, and propose a corresponding heuristic model. Last, we show how ultrasonic in-plane oscillations of $\sim 10$ nm amplitude can trigger unjamming, and we discuss the possible related mechanisms. \\[4pt] [1] P. Thomson and G. Grest and M.O. Robbins, Phys. Rev. Lett \textbf{68}, 3448 (1992)\\[0pt] [2] J. L\'eopold\`es and X. Jia, Phys. Rev. Lett \textbf{105}, 266101 (2010)   

Universality of Deformation Down to the Nanoscale

Deformation on macroscopic scales is often modeled as a continuous process, which in reality occurs via a sequence of nanometer-sized discrete slips. We report statistical analyses of slip size distributions obtained by uniaxial compression experiments on nano-crystals of different crystal structures and sizes down to 75 nm. We show that a simple mean field theory (MFT) correctly predicts the statistical behavior by collapsing data using the MFT exponents and scaling function. This study demonstrates that a simple model captures the statistics and universality class of discrete deformation events in a variety of metallic nano-crystals down to the smallest experimentally accessed length scales.   

Boundary lubrication under pressure: could the friction jump down, instead of up?

The sliding friction during pressure squeezout of a boundary lubricated contact has been shown [1,2] to undergo upward jumps every time a lubricant atomic layer is expelled. Here we ask the question whether the jump could not be downward. Whereas most studies focus on the layered structure which the confined lubricant takes in the normal direction, the element we wish to consider is a possible change of parallel periodicity occurring at the squeezout transition. Such changes have been reported in simulations [3], but their effect has not been discussed so far. One possible effect could be a transition of the slider-lubricant interface commensurability, producing a switch of the frictional mechanism, from lubricant melting-freezing in a commensurate state, to superlubric in an incommensurate one -- in this case with a drop of friction for increasing load. We exemplify this effect by MD simulations, where we replace for convenience the open squeezout system with a closed system, where the lubricant is sealed between the sliders. As the number of layers drops under pressure, the planar lubricant structural lattice parameter also drops. This change reflects in a sliding friction jump, which is easily observed to be downwards. The potential observability of load-induced friction drops will be discussed. \\[4pt] [1] J.N. Israelachvili et al., Science 240, 189 (1988). \\[0pt] [2] J. Gao et al., J. Phys. Chem. B 102, 5033 (1998). \\[0pt] [3] U. Tartaglino et al., J. Chem. Phys. 125, 014704 (2006).   

Plasticity as a Depinning Phase Transition

Crystalline materials deform in an intermittent way via slip-avalanches, which exhibit a variety of scale-invariant behaviors that have been interpreted as a pinning-depinning transition. We use discrete dislocation dynamics at zero temperature to resolve the temporal profiles of slip-avalanches and extract the finite-size scaling properties of the dislocation system, thus going beyond gross aggregate statistics. We provide a comprehensive set of scaling exponents, which establishes that the dynamics of plasticity, in the absence of hardening, is consistent with the mean field interface depinning universality class, even though there is no quenched disorder. Finally, we show how Phase Field Crystal simulations shed light on the effect of temperature on intermittent dislocation dynamics and its critical scaling behavior.   

Tribo-induced melting and temperature gradients at sliding asperity contacts

Tribo-induced nanoscale surface melting mechanisms have been investigated by means of a combined QCM-STM technique [1] for a range of Au and Au-Ni alloys with varying compositional percentages and phases. The QCM-STM setup allows studies to be performed at sliding speeds of up to m/s, and also reveals valuable information concerning tip-substrate temperature gradients.[3] A transition from solid-solid to solid-``liquid like'' contact was observed for each sample at sufficiently high asperity sliding speeds. Pure gold, solid-solution and two-phase Au-Ni (20 at.{\%} Ni) alloys were compared, which are materials of great relevance to MEMS RF switch technology.[2] The transition points agree favorably with theoretical predictions for their surface melting characteristics. We acknowledge NSF and AFOSR support for this research. \\[4pt] [1] B. D. Dawson, S. M. Lee, and J. Krim, Phys. Rev. Lett. 103, 205502 (2009) \\[0pt] [2] Zhenyin Yang; Lichtenwalner, D.J.; Morris, A.S.; Krim, J.; Kingon, A.I, Journal of Microelectromechanical Systems, April 2009, Volume: 18 Issue:2, 287-295 \\[0pt] [3] C.G. Dunkle, I.B. Altfeder, A.A. Voevodin, J. Jones, J. Krim and P.Taborek, J. Appl. Phys., 107, art{\#}114903, (2010)   

Formation of Stable Metallic Nanocontacts by mechanical annealing

Metallic nanocontacts (NC) can be fabricated using STM or related techniques. In these experiments the size of the NC can be followed, down to the atomic contact, by measuring its electrical conductance. Such evolution will normally differ for each experimental realization and therefore conductance histograms are used to identify preferential configurations. It can be shown that occasionally there are some atomic configurations that can be repeated during consecutive cycles of mechanical deformation of the contacts. Here we report experiments for gold NC where the same trace of conductance can be obtained for hundreds of cycles of formation and rupture. We have studied the process leading to such repetitiveness of the traces and found that this is obtained when limiting the indentation depth between the two surfaces to a conductance value of approximately 5-6 G$_{0}$. Using molecular dynamics simulations we have obtained the same behaviour and observed how, after repeated indentations, the two metallic contacts are shaped into a stable configuration by mechanical annealing. This confirms and explains the fact that repeated indentation of a tip into a metallic substrate can be used as a method to sharpen or clean STM tips, but only when such indentation does not exceed a limit.   

Scaling in earthquake models with inhomogeneous damage

We study the scaling of earthquake models that are variations of Olami-Feder-Christensen and Burridge-Knopoff models, in order to explore the effect of spatial inhomogeneities on earthquake-like systems when interaction ranges are long, but not necessarily longer than the distances associated with the inhomogeneities of the system. For long ranges and without inhomogeneities, such models have been found to produce scaling similar to GR scaling found in real earthquake systems. In the earthquake models discussed here, damage is distributed inhomogeneously throughout and the interaction ranges, while long, are not longer than all of the damage length scales. We find that the scaling depends not only on the amount of damage, but also on the spatial distribution of that damage.   

Stress Corrosion Fracture of Silicate Glasses: How Far Can Water Penetrate?

Although glass can be considered as homogeneous at scales as small as a few tens of nanometers, since it exhibits no density fluctuations beyond, its amorphous structure makes it a disordered material with respect to fracture properties. Fluctuations of the orientations of Si-O bonds with respect to the external stress make it unlikely that bonds closest to the crack tip break first, despite the high stress concentration. As a consequence, glass behaves in a quasi-brittle manner rather than in a purely elastic way. \textit{In situ} Atomic Force Microscopy experiments tracking the slow progression of a stress corrosion crack seemed to show indeed the opening and growth of nano size flaws ahead of the tip. However, these results are controversial, because of artifacts which may seriously affect the observations. Furthermore, the low diffusion coefficient of water in silica should forbid hydrolysis at a distance from the crack tip, except at the free surface. Nevertheless, our recent neutron reflectivity experiments show that water actually penetrates into the material during stress corrosion fracture. Comparing two experiments performed for different crack velocities shows that the diffusion coefficient is hugely increased under stress, allowing for bond breakings at $\sim $ten nanometers ahead of the main crack tip.   

Magnetic friction: From Stokes to Coulomb behavior

We demonstrate that in a ferromagnetic substrate, which is continuously driven out of equilibrium by a field moving with constant velocity $v$, at least two types of friction may occur when $v$ goes to zero: The substrate may feel a friction force proportional to $v$ (Stokes friction), if the field changes on a time scale which is longer than the intrinsic relaxation time. On the other hand, the friction force may become independent of $v$ in the opposite case (Coulomb friction). These observations are analogous to e.g.\ solid friction. The effect is demonstrated in both, the Ising (one spin dimension) and the Heisenberg model (three spin dimensions), irrespective which kind of dynamics (Metropolis spin-flip dynamics or Landau-Lifshitz-Gilbert precessional dynamics) is used. For both models the limiting case of Coulomb friction can be treated analytically. Furthermore we present an empiric expression reflecting the correct Stokes behavior and therefore yielding the correct cross-over velocity and dissipation. arXiv:1111.2494