Roughness Evolution Induced by Third-Body Wear.

Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently flat surfaces is revealed. Roughness in natural surfaces has been reported to conform to self-affine statistics in a wide variety of settings (ranging from earthquake physics to micro-electro-mechanical devices), meaning that the height profile can be described using a spectrum where the amplitude is proportional to its wavelength raised to a constant power, which is related to a statistical parameter named Hurst exponent. We analyze the roughness evolution in atomistic surfaces during molecular dynamics simulations of wear. Both pairs of initially flat and initially rough surfaces in contact are worn by a third body formed by particles trapped between them during relative sliding. During the first sliding stages, the particles trapped between the first bodies scratch the surfaces. Once the former becomes coated with atoms from the latter, the wear process slows down and becomes "adhesive like." The initial particle sizes are consistent with the minimum size to be expected for the debris, but tend to grow by material removal from the surfaces and to agglomerate. We show that, for the particular configurations under consideration, the surface roughness seems to converge to a steady state characterized by Hurst exponent close to 0.8, independently of the initial conditions. Supplementary Information: The online version contains supplementary material available at 10.1007/s11249-024-01833-9.

Dynamic Crack-Front Deformations in Cohesive Materials.

Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out-of-plane damage. Current models neglect the influence of a finite dissipation length scale behind the crack tip, called the process zone size. The latter introduces scale effects in the deformation of the crack front, that are mitigated by the dynamics of the crack. We provide and numerically validate a theoretical framework for dynamic crack-front deformations in heterogeneous cohesive materials, a key step toward identifying the effective properties of a microstructure.

Explosive fragmentation of Prince Rupert's drops leads to well-defined fragment sizes.

Anyone who has ever broken a dish or a glass knows that the resulting fragments range from roughly the size of the object all the way down to indiscernibly small pieces: typical fragment size distributions of broken brittle materials follow a power law, and therefore lack a characteristic length scale. The origin of this power-law behavior is still unclear, especially why it is such an universal feature. Here we study the explosive fragmentation of glass Prince Rupert's drops, and uncover a fundamentally different breakup mechanism. The Prince Rupert's drops explode due to their large internal stresses resulting in an exponential fragment size distribution with a well-defined fragment size. We demonstrate that generically two distinct breakup processes exist, random and hierarchical, that allows us to fully explain why fragment size distributions are power-law in most cases but exponential in others. We show experimentally that one can even break the same material in different ways to obtain either random or hierarchical breakup, giving exponential and power-law distributed fragment sizes respectively. That a random breakup process leads to well-defined fragment sizes is surprising and is potentially useful to control fragmentation of brittle solids.

Earthquake Nucleation Along Faults With Heterogeneous Weakening Rate.

The transition from quasistatic slip growth to dynamic rupture propagation constitutes one possible scenario to describe earthquake nucleation. If this transition is rather well understood for homogeneous faults, how the friction properties of multiscale asperities may influence the overall stability of seismogenic faults remains largely unclear. Combining classical nucleation theory and concepts borrowed from condensed matter physics, we propose a comprehensive analytical framework that predicts the influence of heterogeneities of weakening rate on the nucleation length L c for linearly slip-dependent friction laws. Model predictions are compared to nucleation lengths measured from 2D dynamic simulations of earthquake nucleation along heterogeneous faults. Our results show that the interplay between frictional properties and the asperity size gives birth to three instability regimes (local, extremal, and homogenized), each related to different nucleation scenarios, and that the influence of heterogeneities at a scale far lower than the nucleation length can be averaged.

Role of interfacial adhesion on minimum wear particle size and roughness evolution.

Adhesion between two bodies is a key parameter in wear processes. At the macroscale, strong adhesive bonds are known to lead to high wear rates, as observed in clean metal-on-metal contact. Reducing the strength of the interfacial adhesion is then desirable, and techniques such as lubrication and surface passivation are employed to this end. Still, little is known about the influence of adhesion on the microscopic processes of wear. In particular, the effects of interfacial adhesion on the wear particle size and on the surface roughness evolution are not clear and are therefore addressed here by means of molecular dynamics simulations. We show that, at short timescales, the surface morphology and not the interfacial adhesion strength dictates the minimum size of wear particles. However, at longer timescales, adhesion alters the particle motion and thus the wear rate and the surface morphology.

Emergence of self-affine surfaces during adhesive wear.

Friction and wear depend critically on surface roughness and its evolution with time. An accurate control of roughness is essential to the performance and durability of virtually all engineering applications. At geological scales, roughness along tectonic faults is intimately linked to stick-slip behaviour as experienced during earthquakes. While numerous experiments on natural, fractured, and frictional sliding surfaces have shown that roughness has self-affine fractal properties, much less is known about the mechanisms controlling the origins and the evolution of roughness. Here, by performing long-timescale molecular dynamics simulations and tracking the roughness evolution in time, we reveal that the emergence of self-affine surfaces is governed by the interplay between the ductile and brittle mechanisms of adhesive wear in three-body contact, and is independent of the initial state.

Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition.

The onset of rapid slip along initially quiescent frictional interfaces, the process of "earthquake nucleation," and dissipative spatiotemporal slippage dynamics play important roles in a broad range of physical systems. Here we first show that interfaces described by generic friction laws feature stress-dependent steady-state slip pulse solutions, which are unstable in the quasi-1D approximation of thin elastic bodies. We propose that such unstable slip pulses of linear size L^{*} and characteristic amplitude are "critical nuclei" for rapid slip in a nonequilibrium analogy to equilibrium first-order phase transitions and quantitatively support this idea by dynamical calculations. We then perform 2D numerical calculations that indicate that the nucleation length L^{*} exists also in 2D and that the existence of a fracture mechanics Griffith-like length L_{G}

Asperity-Level Origins of Transition from Mild to Severe Wear.

Wear is the inevitable damage process of surfaces during sliding contact. According to the well-known Archard's wear law, the wear volume scales with the real contact area and as a result is proportional to the load. Decades of wear experiments, however, show that this relation only holds up to a certain load limit, above which the linearity is broken and a transition from mild to severe wear occurs. We investigate the microscopic origins of this breakdown and the corresponding wear transition at the asperity level. Our atomistic simulations reveal that the interaction between subsurface stress fields of neighboring contact spots promotes the transition from mild to severe wear. The results show that this interaction triggers the deep propagation of subsurface cracks and the eventual formation of large debris particles, with a size corresponding to the apparent contact area of neighboring contact spots. This observation explains the breakdown of the linear relation between the wear volume and the normal load in the severe wear regime. This new understanding highlights the critical importance of studying contact beyond the elastic limit and single-asperity models.

Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks.

Using an elastodynamic boundary integral formulation coupled with a cohesive model, we study the problem of a dynamic rupture front propagating along an heterogeneous plane. We show that small-scale heterogeneities facilitate the supershear transition of a mode-II crack. The elastic pulses radiated during front accelerations explain how microscopic variations of fracture toughness change the macroscopic rupture dynamics. Perturbations of dynamic fronts are then systematically studied with different microstructures and loading conditions. The process zone size is the intrinsic length scale controlling heterogeneous dynamic rupture. The ratio of this length scale to asperity size is proposed as an indicator to transition from quasihomogeneous to heterogeneous fracture. Moreover, we discuss how the shortening of the process zone size with increasing crack speed brings the front to interact with smaller details of the microstructure. This study shines new light on recent experiments reporting perturbations of dynamic rupture fronts, which intensify with crack propagation speed.

On the debris-level origins of adhesive wear.

Every contacting surface inevitably experiences wear. Predicting the exact amount of material loss due to wear relies on empirical data and cannot be obtained from any physical model. Here, we analyze and quantify wear at the most fundamental level, i.e., wear debris particles. Our simulations show that the asperity junction size dictates the debris volume, revealing the origins of the long-standing hypothesized correlation between the wear volume and the real contact area. No correlation, however, is found between the debris volume and the normal applied force at the debris level. Alternatively, we show that the junction size controls the tangential force and sliding distance such that their product, i.e., the tangential work, is always proportional to the debris volume, with a proportionality constant of 1 over the junction shear strength. This study provides an estimation of the debris volume without any empirical factor, resulting in a wear coefficient of unity at the debris level. Discrepant microscopic and macroscopic wear observations and models are then contextualized on the basis of this understanding. This finding offers a way to characterize the wear volume in atomistic simulations and atomic force microscope wear experiments. It also provides a fundamental basis for predicting the wear coefficient for sliding rough contacts, given the statistics of junction clusters sizes.

Damage cluster distributions in numerical concrete at the mesoscale.

We investigate the size distribution of damage clusters in concrete under uniaxial tension loading conditions. Using the finite-element method, the concrete is modeled at the mesoscale by a random distribution of elastic spherical aggregates within an elastic mortar paste. The propagation and coalescence of damage zones are then simulated by means of dynamically inserted cohesive elements. Dynamic failure analysis shows that the size distribution of damage clusters follows a power law when a system-spanning cluster is first observed, with an exponent close to that of percolation theory. This is found for a range of selected mesostructural parameters, material defects, and applied strain rates. In all cases, the system-spanning cluster occurs prior to the onset of local decohesion, a regime of crack nucleation and propagation, and eventual material failure. The resulting fully damaged crack surfaces after failure are found to be only weakly correlated with the percolated damage region structures.

Critical length scale controls adhesive wear mechanisms.

The adhesive wear process remains one of the least understood areas of mechanics. While it has long been established that adhesive wear is a direct result of contacting surface asperities, an agreed upon understanding of how contacting asperities lead to wear debris particle has remained elusive. This has restricted adhesive wear prediction to empirical models with limited transferability. Here we show that discrepant observations and predictions of two distinct adhesive wear mechanisms can be reconciled into a unified framework. Using atomistic simulations with model interatomic potentials, we reveal a transition in the asperity wear mechanism when contact junctions fall below a critical length scale. A simple analytic model is formulated to predict the transition in both the simulation results and experiments. This new understanding may help expand use of computer modelling to explore adhesive wear processes and to advance physics-based wear laws without empirical coefficients.

Avalanches in dry and saturated disordered media at fracture.

This paper analyzes fracturing in inhomogeneous media under dry and fully saturated conditions. We adopt a central force model with continuous damage to study avalanche behavior in a two-dimensional truss lattice undergoing dilation. Multiple fractures can develop at once and a power-law distribution of the avalanche size is observed. The values for the power-law exponent are compared with the ones found in the literature and scale-free behavior is suggested. The fracture evolves intermittently in time because only some avalanches correspond to fracture advancement. A fully saturated model with continuous damage based on the extended Biot's theory is developed and avalanche behavior is studied in the presence of fluid, varying the fluid boundary conditions. We show that power-law behavior is destroyed when the fluid flux governs the problem. Fluid pressure behavior during intermittent crack tip advancement is studied for the continuous-damage fully saturated model. It is found that when mechanical loading prevails, the pressure rises when the crack advances, while when fluid loading prevails, the pressure drops when the crack advances.

Properties of the shear stress peak radiated ahead of rapidly accelerating rupture fronts that mediate frictional slip.

We study rapidly accelerating rupture fronts at the onset of frictional motion by performing high-temporal-resolution measurements of both the real contact area and the strain fields surrounding the propagating rupture tip. We observe large-amplitude and localized shear stress peaks that precede rupture fronts and propagate at the shear-wave speed. These localized stress waves, which retain a well-defined form, are initiated during the rapid rupture acceleration phase. They transport considerable energy and are capable of nucleating a secondary supershear rupture. The amplitude of these localized waves roughly scales with the dynamic stress drop and does not decrease as long as the rupture front driving it continues to propagate. Only upon rupture arrest does decay initiate, although the stress wave both continues to propagate and retains its characteristic form. These experimental results are qualitatively described by a self-similar model: a simplified analytical solution of a suddenly expanding shear crack. Quantitative agreement with experiment is provided by realistic finite-element simulations that demonstrate that the radiated stress waves are strongly focused in the direction of the rupture front propagation and describe both their amplitude growth and spatial scaling. Our results demonstrate the extensive applicability of brittle fracture theory to fundamental understanding of friction. Implications for earthquake dynamics are discussed.

Survival of heterogeneous stress distributions created by precursory slip at frictional interfaces.

We study the dynamics of successive slip events at a frictional interface with finite-element simulations. Because of the viscous properties of the material, the stress concentrations created by the arrest of precursory slip are not erased by the propagation of the following rupture but reappear with the relaxation of the material. We show that the amplitude of the stress concentrations follows an exponential decay, which is controlled by the bulk material properties. These results highlight the importance of viscosity in the heterogeneous stress state of a frictional interface and reveal the "memory effect" that affects successive ruptures.

Direct visualization of single ions in the Stern layer of calcite.

Calcite is among the most abundant minerals on earth and plays a central role in many environmental and geochemical processes. Here we used amplitude modulation atomic force microscopy (AFM) operated in a particular regime to visualize single ions close to the (1014) surface of calcite in solution. The results were acquired at equilibrium, in aqueous solution containing different concentrations of NaCl, RbCl, and CaCl(2). The AFM images provide a direct and atomic-level picture of the different cations adsorbed preferentially at certain locations of the calcite-water interface. Highly ordered water layers at the calcite surface prevent the hydrated ions from directly interacting with calcite due to the energy penalty incurred by the necessary restructuring of the ions' solvation shells. Controlled removal of the adsorbed ions from the interface by the AFM tip provides indications about the stability of the adsorption site. The AFM results show the familiar "row pairing" of the carbonate oxygen atoms, with the adsorbed monovalent cations located adjacent to the most prominent oxygen atoms. The location of adsorbed cations near the surface appears better defined for monovalent ions than for Ca(2+), consistent with the idea that Ca(2+) ions remain further away from the surface of calcite due to their larger hydration shell. The precise distance between the different hydrated ions and the surface of calcite is quantified using MD simulation. The preferential adsorption sites found by MD as well as the ion residence times close to the surface support the AFM findings, with Na(+) ions dwelling substantially longer and closer to the calcite surface than Ca(2+). The results also bring new insights into the problem of the Stern and electrostatic double layer at the surface of calcite, showing that parameters such as the thickness of the Stern layer can be highly ion dependent.

Contact between representative rough surfaces.

A numerical analysis of mechanical frictionless contact between rough self-affine elastic manifolds was carried out. It is shown that the lower cutoff wave number in surface spectra is a key parameter controlling the representativity of the numerical model. Using this notion we demonstrate that for representative surfaces the evolution of the real contact area with load is universal and independent of the Hurst roughness exponent. By introducing a universal law containing three constants, we extend the study of this evolution beyond the limit of infinitesimal area fractions.

The autocorrelation function for island areas on self-affine surfaces.

The spatial distribution of regions that lie above contours of constant height through a self-affine surface is studied as a function of the Hurst exponent H. If the surface represents a landscape, these regions correspond to islands. When the surface represents the height difference for contacting surfaces, the regions correspond to mechanical contacts in the common bearing area model. The autocorrelation function C(Δr) is defined as the probability that points separated by Δr are both within islands. The scaling of C has important implications for the stiffness and conductance of mechanical contacts. We find that its Fourier transform C(q) scales as a power of the wavevector magnitude q: [Formula: see text] with µ = 2 + H rather than the value µ = 2 + 2H reported previously. An analytic argument for µ = 2 + H is presented using the distribution of areas contained in disconnected islands.