Work hardening in colloidal crystals.

Colloidal crystals exhibit interesting properties1-4 that are in many ways analogous to their atomic counterparts. They have the same crystal structures2,5-7, undergo the same phase transitions8-10, and possess the same crystallographic defects11-14. In contrast to these structural properties, the mechanical properties of colloidal crystals are quite different from those of atomic systems. For example, unlike in atomic systems, the elasticity of hard-sphere colloidal crystals is purely entropic15; as a result, they are so soft that they can be melted just by stirring16,17. Moreover, crystalline materials deform plastically when subjected to increasing shear and become stronger because of the ubiquitous process of work hardening18; but this has so far never been observed in colloidal crystals, to our knowledge. Here we show that hard-sphere colloidal crystals exhibit work hardening. Moreover, despite their softness, the shear strength of colloidal crystals can increase and approach the theoretical limit for crystals, a value reached in very few other materials so far. We use confocal microscopy to show that the strength of colloidal crystals increases with dislocation density, and ultimately reaches the classic Taylor scaling behaviour for atomic materials19-21, although hard-sphere interactions lack the complexity of atomic interactions. We demonstrate that Taylor hardening arises through the formation of dislocation junctions22. The Taylor hardening regime, however, is established only after a transient phase, and it ceases when the colloidal crystals become so hard that the strain is localized within a thin boundary layer in which slip results from an unconventional motion of dislocations. The striking resemblance between colloidal and atomic crystals, despite the many orders of magnitude difference in particle size and shear modulus, demonstrates the universality of work hardening.

Spatial Crossover Between Far-From-Equilibrium and Near-Equilibrium Dynamics in Locally Driven Suspensions.

We examine the response of a quasi-two-dimensional colloidal suspension to a localized circular driving induced by optical tweezers. This approach allows us to resolve over 3 orders of magnitude in the Péclet number (Pe) and provide a direct observation of a sharp spatial crossover from far- to near-thermal-equilibrium regions of the suspension. In particular, particles migrate from high to low Pe regions and form strongly inhomogeneous steady-state density profiles with an emerging length scale that does not depend on the particle density and is set by Pe≈1. We show that the phenomenological two phase fluid constitutive model is in line with our results.

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.

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.

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.

Dislocation interactions during plastic relaxation of epitaxial colloidal crystals.

The severe difficulty to resolve simultaneously both the macroscopic deformation process and the dislocation dynamics on the atomic scale limits our understanding of crystal plasticity. Here we use colloidal crystals, imaged on the single particle level by high-speed three-dimensional (3D) confocal microscopy, and resolve in real-time both the relaxation of the epitaxial misfit strain and the accompanying evolution of dislocations. We show how dislocation interactions give rise to the formation of complex dislocation networks in 3D and to unexpectedly sharp plastic relaxation. The sharp relaxation is facilitated by attractive interactions that promote the formation of new dislocations that are more efficient in mediating strain. Dislocation networks form fragmented structures, as dislocation growth is blocked by either attractive interactions, which result in the formation of sessile dislocation junctions, or by repulsion from perpendicular segments. The strength of these blocking mechanisms decreases with the thickness of the crystal film. These results reveal the critical role of dislocation interactions in plastic deformation of thin films and can be readily generalized from the colloidal to the atomic scale.

The equation of motion for supershear frictional rupture fronts.

The rupture fronts that mediate the onset of frictional sliding may propagate at speeds below the Rayleigh wave speed or may surpass the shear wave speed and approach the longitudinal wave speed. While the conditions for the transition from sub-Rayleigh to supershear propagation have been studied extensively, little is known about what dictates supershear rupture speeds and how the interplay between the stresses that drive propagation and interface properties that resist motion affects them. By combining laboratory experiments and numerical simulations that reflect natural earthquakes, we find that supershear rupture propagation speeds can be predicted and described by a fracture mechanics-based equation of motion. This equation of motion quantitatively predicts rupture speeds, with the velocity selection dictated by the interface properties and stress. Our results reveal a critical rupture length, analogous to Griffith's length for sub-Rayleigh cracks, below which supershear propagation is impossible. Above this critical length, supershear ruptures can exist, once excited, even for extremely low preexisting stress levels. These results significantly improve our fundamental understanding of what governs the speed of supershear earthquakes, with direct and important implications for interpreting their unique supershear seismic radiation patterns.

The near-tip fields of fast cracks.

In a stressed body, crack propagation is the main vehicle for material failure. Cracks create large stress amplification at their tips, leading to large material deformation. The material response within this highly deformed region will determine its mode of failure. Despite its great importance, we have only a limited knowledge of the structure of this region, because it is generally experimentally intractable. By using a brittle neo-Hookean material, we overcame this barrier and performed direct and precise measurements of the near-tip structure of rapid cracks. These experiments reveal a hierarchy of linear and nonlinear elastic zones through which energy is transported before being dissipated at a crack's tip. This result provides a comprehensive picture of how remotely applied forces drive material failure in the most fundamental of fracture states: straight, rapidly moving cracks.