Velocity-weakening and -strengthening friction at single and multiasperity contacts with calcite single crystals

Nanotribological properties of bulk metallic glasses

Injection of fluids for geothermal stimulation has often caused seismic events that have raised concern and resulted in discontinuing the operations. Consequently, a safe and effective geothermal operation requires an assessment of the potential for induced seismicity. Rate and state friction (RSF) is well-established as a robust description of rock friction. It is, however, strictly empirical and extension to hydrothermal conditions relevant to geothermal stimulation is problematic. We extend a microphysical model to hydrothermal conditions by incorporating thermally activated processes in fault gouges. We use a simple spring-slider model to simulate steady-state friction at a typical range of temperatures and load-point velocities. Numerical simulations show that, consistent with experimental observations, the simulated steady-state friction of granite gouges in wet conditions rises slightly with temperature, and the friction rate parameter (a − b) transitions from velocity-strengthening at low temperatures to velocity-weakening behaviors at high temperatures of about 300°C. This transition indicates the possibility of change from stable to unstable (seismic) slip near this temperature. These results also suggest that the dominant deformation mechanisms may evolve from frictional granular flow with intergranular pressure solution at low temperatures to grain boundary sliding (GBS) with solid-state diffusion creep at high temperatures. INTRODUCTION Induced seismicity in enhanced geothermal systems is generally detected in a depth range from a few hundreds of meters to several kilometers below the Earth surface where temperature and pore fluid pressure are elevated (Tomac and Sauter, 2018; Johnson et al., 2016; Atkinson, 2015; Eberhart-Phillips and Oppenheimer, 1984). The correlation between induced seismicity and geothermal production has been proposed based on many field observations, such as the Utah FORGE geothermal system (Moore et al., 2019), the Reykjanes and Svartsengi geothermal areas (Keiding et al., 2010), the Geysers geothermal field (Eberhart-Phillips and Oppenheimer, 1984), and the Geoven deep geothermal site (Schmittbuhl et al., 2021). The injection of cold fluids and extraction of hot fluids from the subsurface may cause the pressure imbalance and trigger the seismic slip in the seismogenic zone (Xing et al., 2020). Extensive studies suggest that the aseismic-seismic transition in the seismogenic zone is thermally controlled (Currie et al., 2002; Tichelaar and Ruff, 1993; Blanpied et al., 1995; Niemeijer et al., 2016; Den Hartog and Spiers, 2013; Toy et al., 2010). In addition, the seismic slip behaviors are probably linked with temperature dependence of effective frictional properties, rock composition, porosity, and plasticity in fault gouges (Tullis and Yund, 1980; Boettcher et al., 2007; Giger et al., 2007; Barbot, 2022; Scholz, 2019). The complex frictional behaviors are often captured by a standard RSF that uses a state variable to represent the structural evolution within the fault zone (Dieterich, 1979; Ruina, 1983).

We performed laboratory experiments to investigate the processes responsible for rate and state friction (RSF) behavior in fault rocks. We focused on the symmetry of the frictional constitutive response to velocity changes and the mechanics of the critical friction slip distance Dc. Experiments were conducted in double direct shear at 1 and 25 MPa normal stress, at room temperature, and for shearing velocity from 1 to 300 µm/s. We studied three granular materials and bare surfaces of Westerly granite. Ruina's law, which predicts frictional symmetry between velocity increases and decreases, better matches our data than Dieterich's law, which predicts that velocity decreases should evolve to steady state at a smaller displacement. However, for granular shear, in some cases Dc is smaller for velocity increases than for velocity decreases, contrary to expectations from either law. On bare granite surfaces, the frictional response is symmetric for velocity increases/decreases. Two distinct length scales for Dc and two‐state variables are required for granular shear in some cases. We hypothesize that asymmetry and two‐state behavior are caused by shear localization and changes in shear fabric in fault gouge. Our measurements show that during steady state frictional shear, dilation after a velocity increase is smaller than compaction after a decrease. Normal stress oscillations cause a marked decrease in Dc. Reduction of Dc reduces frictional stability, enhancing the possibility of seismic slip. Our experiments show that shear localization and fabric within the fault gouge can influence the RSF parameters that dictate earthquake nucleation and dynamic rupture.

Understanding the relationship between sliding velocity, temperature, friction, and wear is of fundamental importance in materials science and engineering. Here, we explore sliding friction and wear of a silicon carbide nano-asperity sliding over a silicon carbide substrate for a broad range of temperatures and velocities using molecular dynamics simulations. Our study reveals three distinct friction regimes over four velocity decades: velocity-weakening at moderate velocities, velocity-strengthening at high velocities, and an additional velocity-strengthening behavior at very low velocities and elevated temperatures. We theoretically describe these findings with physics-based friction models. For the low-velocity regime, we refine the Prandtl-Tomlinson model by incorporating a logarithmic aging mechanism that accounts for surface diffusion-driven contact evolution. For the high-velocity regime, we introduce a linear viscous friction model with an Arrhenius temperature dependence. These models demonstrate strong agreement with the molecular dynamics simulation results in their respective velocity regimes. We then explore wear mechanisms, distinguishing between atomic attrition at low velocities and collective material removal at high velocities, thus providing a comprehensive framework for understanding the velocity and temperature dependence of nanoscale friction and wear of silicon carbide.

Earthquake rupture propagation inferred from the spatial distribution of fault rock frictional properties

The velocity dependence of nanoscale friction is studied for the first time over a wide range of velocitiesbetween 1 µm s−1 and10 mm s−1 on large scanlengths of 2 and 25 µm. High sliding velocities are achieved by modifying an existing commercial atomic forcemicroscope (AFM) setup with a custom calibrated nanopositioning piezo stage. Thefriction and adhesive force dependences on velocity are studied on four different samplesurfaces, namely dry (unlubricated), hydrophilic Si(100); dry, partially hydrophobicdiamond-like carbon (DLC); a partially hydrophobic self-assembled monolayer(SAM) of hexadecanethiol (HDT); and liquid perfluoropolyether lubricant, Z-15.The friction force values are seen to reverse beyond a certain critical velocity forall the sample surfaces studied. A comprehensive friction model is developed toexplain the velocity dependence of nanoscale friction, taking into consideration thecontributions of adhesion at the tip–sample interface, high impact velocity-relateddeformation at the contacting asperities and atomic scale stick–slip. A molecular springmodel is used for explaining the velocity dependence of friction force for HDT.

It has been shown that contact aging due to chemical reactions in single asperity contacts can have a significant effect on friction. However, it is currently unknown how chemically induced contact aging of friction depends on roughness that is typically encountered in macroscopic rough contacts. Here we develop an approach that brings together a kinetic Monte Carlo model of chemical aging with a contact mechanics model of rough surfaces based on the boundary element method to determine the magnitude of chemical aging in silica-silica contacts with random roughness. Our multiscale model predicts that chemical aging for randomly rough contacts has a logarithmic dependence on time. It also shows that friction aging switches from a linear to a nonlinear dependence on the applied load as the load increase. We discover that surface roughness affects the aging behavior primarily by modifying the real contact area and the local contact pressure, whereas the effect of contact morphology is relatively small. Our results demonstrate how understanding of chemical aging can be translated from studies of single asperity contacts to macroscopic rough contacts.

Micro∕nanoelectromechanical system devices and components often operate at high sliding velocities, and it requires the investigation of friction at high velocities. In this study, the velocity dependence of friction and the rest time effect on friction of hard diamondlike carbon films, soft perfluorodecyltrichlorosilane, and perfluoropolyether films were investigated up to 2×105μm∕s using an ultrahigh velocity stage and a high velocity stage. The velocity dependence of friction was found to vary with films and involve different mechanisms including adhesion due to solid-solid interaction, adhesion due to formation of meniscus bridges, atomic-scale stick slip, high velocity impact of the contacting asperities∕molecules, phase transformation∕tip jump, and viscoelastic shear. The increase in friction as a function of rest time was caused by continued growth and formation of water menisci bridges for the hydrophilic surfaces and continued deformation of soft films.

The prediction and characterization of multilength-scale tribological phenomena is challenging, yet essential for the advancement of micro- and nanomachine technology. Here, we consider theoretical underpinnings of multiasperity friction, review various approaches to measure micro- and nanoscale friction and discuss the effect of monolayer coatings to reduce friction and wear. We then overview a theoretical framework known as rate-and-state friction (RSF ), in which friction is considered to be a continuous function of velocity and interface state. A microscale test platform that is used to measure friction over multiple decades of velocity and normal load is presented and results are reported. Using the RSF framework, we quantitatively predict and validate the transition from stick-slip to steady sliding, enabling the creation of a microscale kinetic phase diagram. Next, we take a brief look at continued progress in spinning micromachine motor technology. Finally, we discuss wear- and tribopolymer-related phenomena in micro- and nanoswitches, which are promising devices to complement transistors due to their low on resistance and steep subthreshold swing. We anticipate great progress towards reliable, contacting micro- and nanomachines by linking theory and experiment to nano- and microscale tribological phenomena and by improving the testing, materials and processing methods used to characterize these phenomena.

The influence of surface roughness in elliptical contacts

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl–Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip–sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

Earthquake nucleation is a crucial preparation process of the following coseismic rupture propagation. Under the framework of rate‐and‐state friction (RSF), it was found that the ratios of to parameters control whether earthquakes nucleate as an expanding crack or with a fixed length prior to the dynamic instability. However, the characteristic weakening distance controls the weakening efficiency of state variables in RSF and can influence the nucleation styles as well. Here we investigate the effects of on nucleation styles in the context of fully dynamic seismic cycles by evaluating the evolution of the nucleation zone quantitatively when it accelerates from the tectonic loading rate to seismic slip velocity. A larger (>0.75) is needed to produce expanding crack nucleation styles for relatively small , which suggests that fixed length nucleation styles may dominate on natural and laboratory faults. Furthermore, we find a more complex nucleation style when the nucleation site is not in the center of the asperity and identify a twin‐like nucleation style which includes two initial acceleration phases. We conclude that the earthquake nucleation style is strongly controlled by the value of . The possible dominance of fixed length nucleation styles suggests that the minimum size of earthquake rupture may be estimated at the early stage of the nucleation phase.

Subsea pipeline walking with velocity dependent seabed friction

Dry sliding friction is a complex but ubiquitous phenomenon. Experimental studies of friction produce large amounts of data, while most models are phenomenological rather than deduced from fundamental principles. Proper identification of relevant degrees of freedom is crucial for the development of adequate frictional models, such as the state-and-rate models. Topological data analysis is a mathematical method for dimensionality reduction for datasets characterizing surface roughness, contact of rough surfaces, and frictional sliding. We study tribological systems including the surface roughness and multi-asperity contacts using 33, 44, and 55 pixel patches. Depending on whether the surface is isotropic or anisotropic with particular lay directions, the data tends to concentrate at certain “primary” and “secondary” circles yielding different values of the Betti numbers. Scale dependency of corresponding structures is analyzed with persistence diagrams. Moreover, statistics of stick-slip zones can provide insights into relevant internal degrees of friction.

: The mechanical behavior of contacts plays a critical role in the function of devices from aircraft engines to microelectromechanical systems. As the demands for performance from these devices increase or their size shrinks, traditional continuum models of contact behavior become inadequate. This project developed methods for including atomistic effects in systems with up to micrometer dimensions. The methods were used to examine contact, friction, adhesion and stiffness of single and multiasperity contacts. The interfacial stiffness was found to scale linearly with contact area and load and to obey a simple scaling law with a universal prefactor. A simple predictive relation for the contact area between adhesive surfaces was developed and tested. It explains why adhesion is not observed between most macroscopic surfaces, but can be seen with elastomeric materials. Thermal fluctuations were shown to produce instantaneous pressures that are comparable to the ideal hardness. Simulations of large single asperity contacts showed large decreases in friction coefficient with increasing size, but did not show the partial slip predicted by continuum models. The widely used bearing area model was tested and found to give incorrect predictions for contact-contact correlations.