The onset of the frictional motion of dissimilar materials.

Frictional motion between contacting bodies is governed by propagating rupture fronts that are essentially earthquakes. These fronts break the contacts composing the interface separating the bodies to enable their relative motion. The most general type of frictional motion takes place when the two bodies are not identical. Within these so-called bimaterial interfaces, the onset of frictional motion is often mediated by highly localized rupture fronts, called slip pulses. Here, we show how this unique rupture mode develops, evolves, and changes the character of the interface's behavior. Bimaterial slip pulses initiate as "subshear" cracks (slower than shear waves) that transition to developed slip pulses where normal stresses almost vanish at their leading edge. The observed slip pulses propagate solely within a narrow range of "transonic" velocities, bounded between the shear wave velocity of the softer material and a limiting velocity. We derive analytic solutions for both subshear cracks and the leading edge of slip pulses. These solutions both provide an excellent description of our experimental measurements and quantitatively explain slip pulses' limiting velocities. We furthermore find that frictional coupling between local normal stress variations and frictional resistance actually promotes the interface separation that is critical for slip-pulse localization. These results provide a full picture of slip-pulse formation and structure that is important for our fundamental understanding of both earthquake motion and the most general types of frictional processes.

Dynamics and Properties of the Cohesive Zone in Rapid Fracture and Friction.

The cohesive zone is the elusive region in which material fracture takes place. Here, the putatively singular stresses at a crack's tip are regularized. We present experiments, performed on PMMA, in which we visualize the cohesive zone of frictional ruptures as they propagate. Identical to shear cracks, these ruptures range from slow velocities to nearly the limiting speeds of cracks. We reveal that the cohesive zone is a dynamic quantity; its spatial form undergoes a sharp transition between distinct phases at a critical velocity. The structure of these phases provides an important window into material properties under the extreme conditions that occur during fracture.

How Fast Cracks in Brittle Solids Choose Their Path.

While we fundamentally understand the dynamics of simple cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly perturbed cracks that propagate between 10% and 95% of their limiting velocity within a brittle material. These cracks are deflected by either interaction with sparsely implanted defects or via an intrinsic oscillatory instability in defect-free media. Dense high-speed measurements of the strain fields surrounding the crack tips reveal that crack paths are governed by the direction of maximal strain energy density, even when the near-tip singular fields are highly disrupted. This fundamentally important result may be utilized to either direct or guide running cracks.

Classical shear cracks drive the onset of dry frictional motion.

Frictional processes entail the rupture of the ensemble of discrete contacts defining a frictional interface. There are a variety of views on how best to describe the onset of dry frictional motion. These range from modelling friction with a single degree of freedom, a 'friction coefficient', to theoretical treatments using dynamic fracture to account for spatial and temporal dynamics along the interface. We investigated the onset of dry frictional motion by performing simultaneous high-speed measurements of the real contact area and the strain fields in the region surrounding propagating rupture tips within the dry (nominally flat) rough interfaces formed by brittle polymer blocks. Here we show that the transition from 'static' to 'dynamic' friction is quantitatively described by classical singular solutions for the motion of a rapid shear crack. We find that these singular solutions, originally derived to describe brittle fracture, are in excellent agreement with the experiments for slow propagation, whereas some significant discrepancies arise as the rupture velocity approaches the Rayleigh wave speed. In addition, the energy dissipated in the fracture of the contacts remains nearly constant throughout the entire range in which the rupture velocity is less than the Rayleigh wave speed, whereas the size of the dissipative zone undergoes a Lorentz-like contraction as the rupture velocity approaches the Rayleigh wave speed. This coupling between friction and fracture is critical to our fundamental understanding of frictional motion and related processes, such as earthquake dynamics.

Topological defects govern crack front motion and facet formation on broken surfaces.

Cracks develop intricate patterns on the surfaces that they create. As faceted fracture surfaces are commonly formed by slow tensile cracks in both crystalline and amorphous materials, facet formation and structure cannot reflect microscopic order. Although fracture mechanics predict that slow crack fronts should be straight and form mirror-like surfaces, facet-forming fronts propagate simultaneously within different planes separated by steps. Here we show that these steps are topological defects of crack fronts and that crack front separation into disconnected overlapping segments provides the condition for step stability. Real-time imaging of propagating crack fronts combined with surface measurements shows that crack dynamics are governed by localized steps that drift at a constant angle to the local front propagation direction while their increased dissipation couples to long-ranged elasticity to determine front shapes. We study how three-dimensional topology couples to two-dimensional fracture dynamics to provide a fundamental picture of how patterned surfaces are generated.

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.

How Supertough Gels Break.

Fracture of highly stretched materials challenges our view of how things break. We directly visualize rupture of tough double-network gels at >50% strain. During fracture, crack tip shapes obey a x∼y^{1.6} power law, in contrast to the parabolic profile observed in low-strain cracks. A new length scale ℓ emerges from the power law; we show that ℓ scales directly with the stored elastic energy and diverges when the crack velocity approaches the shear wave speed. Our results show that double-network gels undergo brittle fracture and provide a testing ground for large-strain fracture mechanics.

Nonlinear Focusing in Dynamic Crack Fronts and the Microbranching Transition.

Cracks in brittle materials produce two types of generic surface structures: facets at low velocities and microbranches at higher ones. Here we observe a transition from faceting to microbranching in polyacrylamide gels that is characterized by nonlinear dynamic localization of crack fronts. To better understand this process we derive a first-principles nonlinear equation of motion for crack fronts in the context of scalar elasticity. Its solution shows that nonlinear focusing coupled to rate dependence of dissipation governs the transition to microbranching.

Frictional Resistance within the Wake of Frictional Rupture Fronts.

Frictional resistance to slip, τ, is determined by the real area of contact, A, and the shear strength of the contacts forming the frictional interface. We perform simultaneous high-speed local measurements of τ and A at the tail of propagating rupture fronts. Rate dependence is investigated over 2 orders of magnitude of local slip velocities which reach up to ∼1 m/s. A critical slip velocity is observed that signifies a transition in the frictional behavior: enhanced velocity weakening of A and τ. These measurements enable us to infer the contact shear strength, an otherwise elusive quantity, and show that the contact shear strength persistently increases with slip rate. This, surprisingly, contrasts with expected contact softening at the high temperatures induced by rapid sliding.

Brittle Fracture Theory Predicts the Equation of Motion of Frictional Rupture Fronts.

We study rupture fronts propagating along the interface separating two bodies at the onset of frictional motion via high-temporal-resolution measurements of the real contact area and strain fields. The strain measurements provide the energy flux and dissipation at the rupture tips. We show that the classical equation of motion for brittle shear cracks, derived by balancing these quantities, well describes the velocity evolution of frictional ruptures. Our results demonstrate the extensive applicability of the dynamic brittle fracture theory to friction.

Slip-stick and the evolution of frictional strength.

The evolution of frictional strength has great fundamental and practical importance. Applications range from earthquake dynamics to hard-drive read/write cycles. Frictional strength is governed by the resistance to shear of the large ensemble of discrete contacts that forms the interface that separates two sliding bodies. An interface's overall strength is determined by both the real contact area and the contacts' shear strength. Whereas the average motion of large, slowly sliding bodies is well-described by empirical friction laws, interface strength is a dynamic entity that is inherently related to both fast processes such as detachment/re-attachment and the slow process of contact area rejuvenation. Here we show how frictional strength evolves from extremely short to long timescales, by continuous measurements of the concurrent local evolution of the real contact area and the corresponding interface motion (slip) from the first microseconds when contact detachment occurs to large (100-second) timescales. We identify four distinct and inter-related phases of evolution. First, all of the local contact area reduction occurs within a few microseconds, on the passage of a crack-like front. This is followed by the onset of rapid slip over a characteristic time, the value of which suggests a fracture-induced reduction of contact strength before any slip occurs. This rapid slip phase culminates with a sharp transition to slip at velocities an order of magnitude slower. At slip arrest, 'ageing' immediately commences as contact area increases on a characteristic timescale determined by the system's local memory of its effective contact time before slip arrest. We show how the singular logarithmic behaviour generally associated with ageing is cut off at short times. These results provide a comprehensive picture of how frictional strength evolves from the short times and rapid slip velocities at the onset of motion to ageing at the long times following slip arrest.

Crack front dynamics: the interplay of singular geometry and crack instabilities.

When fast cracks become unstable to microscopic branching (microbranching), fracture no longer occurs in an effective 2D medium. We follow in-plane crack front dynamics via real-time measurements in brittle gels as microbranching unfolds and progresses. We first show that spatially local energy balance quantitatively describes crack dynamics, even when translational invariance is badly broken. Furthermore, our results explain microbranch dynamics; why microbranches form along spatially localized chains and how finite-time formation of cusps along the crack front leads to their death.

Origin of the microbranching instability in rapid cracks.

The origin of the microbranching instability is a long-standing unresolved issue in the fracture of brittle amorphous materials. We investigate the onset of this instability by measuring the real-time dynamics and symmetries of the strain fields produced by rapid tensile cracks in brittle gels. We find that once a simple tensile crack is subjected to shear perturbations, cracks undergo the microbranching instability above a finite velocity-dependent threshold. We further reveal a distinct relation between the microbranching and the oscillatory instabilities of rapid cracks.

The dynamics of rapid fracture: instabilities, nonlinearities and length scales.

The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation-the dynamic process of fracture-couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the almost singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, namely linear elastic fracture mechanics (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined 'weakly nonlinear fracture mechanics', where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, ℓnl. These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of ℓnl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wavelength is determined by ℓnl. We conclude by delineating outstanding challenges in the field.

Tensile cracks can shatter classical speed limits.

Brittle materials fail by means of rapid cracks. Classical fracture mechanics describes the motion of tensile cracks that dissipate released elastic energy within a point-like zone at their tips. Within this framework, a "classical" tensile crack cannot exceed the Rayleigh wave speed, [Formula: see text]. Using brittle neo-hookean materials, we experimentally demonstrate the existence of "supershear" tensile cracks that exceed shear wave speeds, [Formula: see text]. Supershear cracks smoothly accelerate beyond [Formula: see text], to speeds that could approach dilatation wave speeds. Supershear dynamics are governed by different principles than those guiding "classical" cracks; this fracture mode is excited at critical (material dependent) applied strains. This nonclassical mode of tensile fracture represents a fundamental shift in our understanding of the fracture process.

How frictional slip evolves.

Earthquake-like ruptures break the contacts that form the frictional interface separating contacting bodies and mediate the onset of frictional motion (stick-slip). The slip (motion) of the interface immediately resulting from the rupture that initiates each stick-slip event is generally much smaller than the total slip logged over the duration of the event. Slip after the onset of friction is generally attributed to continuous motion globally attributed to 'dynamic friction'. Here we show, by means of direct measurements of real contact area and slip at the frictional interface, that sequences of myriad hitherto invisible, secondary ruptures are triggered immediately in the wake of each initial rupture. Each secondary rupture generates incremental slip that, when not resolved, may appear as steady sliding of the interface. Each slip increment is linked, via fracture mechanics, to corresponding variations of contact area and local strain. Only by accounting for the contributions of these secondary ruptures can the accumulated interface slip be described. These results have important ramifications both to our fundamental understanding of frictional motion as well as to the essential role of aftershocks within natural faults in generating earthquake-mediated slip.

Intrinsic nonlinear scale governs oscillations in rapid fracture.

When branching is suppressed, rapid cracks undergo a dynamic instability from a straight to an oscillatory path at a critical velocity v(c). In a systematic experimental study using a wide range of different brittle materials, we first show how the opening profiles of straight cracks scale with the size ℓ(nl) of the nonlinear zone surrounding a crack's tip. We then show, for all materials tested, that v(c) is both a fixed fraction of the shear speed and, moreover, that the instability wavelength is proportional to ℓ(nl). These findings directly verify recent theoretical predictions and suggest that the nonlinear zone is not passive, but rather is closely linked to rapid crack instabilities.

Static friction coefficient is not a material constant.

The static friction coefficient between two materials is considered to be a material constant. We present experiments demonstrating that the ratio of shear to normal force needed to move contacting bodies can, instead, vary systematically with controllable changes in the external loading configuration. Large variations in both the friction coefficient and consequent stress drop are tightly linked to changes in the rupture dynamics of the rough interface separating the two bodies.

Stabilizing stick-slip friction.

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.

Localized instability on the route to disorder in Faraday waves.

We experimentally investigate how disorder comes about in parametrically excited waves on a fluid surface (Faraday waves). We find that the transition from an ordered pattern to disorder corresponding to "defect-mediated turbulence" is mediated by a spatially incoherent oscillatory phase. This phase consists of highly damped waves that propagate through the effectively elastic lattice defined by the pattern. They have a well-defined frequency, velocity, and transverse polarization. As these waves decay within a few lattice spaces, they are spatially and temporally uncorrelated at larger scales.