Fifty years of Schallamach waves: from rubber friction to nanoscale fracture.

The question of how soft polymers slide against hard surfaces is of significant scientific interest, given its practical implications. Specifically, such systems commonly show interesting stick-slip dynamics, wherein the interface moves intermittently despite uniform remote loading. The year 2021 marked the 50th anniversary of the publication of a seminal paper by Adolf Schallamach (Wear, 1971), which first revealed an intimate link between stick-slip and moving detachment waves, now called Schallamach waves. We place Schallamach's results in a broader context and review subsequent investigations of stick-slip, before discussing recent observations of solitary Schallamach waves. This variant is not observable in standard contacts so that a special cylindrical contact must be used to quantify its properties. The latter configuration also reveals the occurrence of a dual wave-the so-called separation pulse-that propagates in a direction opposite to Schallamach waves. We show how the dual wave and other, more general, Schallamach-type waves can be described using continuum theory and provide pointers for future research. In the process, fundamental analogues of Schallamach-type waves emerge in nanoscale mechanics and interface fracture. The result is an ongoing application of lessons learnt from Schallamach-type waves to better understand these latter phenomena. This article is part of the theme issue 'Nanocracks in nature and industry'.

Propagating Schallamach-type waves resemble interface cracks.

Intermittent motion, called stick-slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick-slip arises due to the propagation of slow detachment waves at the interface. Here we analyze two distinct detachment waves moving parallel (Schallamach wave) and antiparallel (separation wave) to applied remote sliding. Both waves cause slip in the same direction, travel at speeds much lesser than any elastic wave speed, and are therefore describable using the same perturbative elastodynamic framework with identical boundary conditions. A numerical scheme is used to obtain interface stresses and velocities for arbitrary Poisson ratio, along with closed-form solutions for incompressible solids. Our calculations reveal a close correspondence between moving detachment waves and bimaterial interface cracks, including the nature of the singularity and the functional forms of the stresses. Based on this correspondence, and coupled with a fracture analogy for dynamic friction, we develop a phase diagram showing domains of possible occurrence of stick-slip via detachment waves vis-á-vis steady interface sliding. Our results have interesting implications for sliding and stick-slip phenomena at soft interfaces.

Microbial induced calcite precipitation can consolidate martian and lunar regolith simulants.

We demonstrate that Microbial Induced Calcite Precipitation (MICP) can be utilized for creation of consolidates of Martian Simulant Soil (MSS) and Lunar Simulant Soil (LSS) in the form of a 'brick'. A urease producer bacterium, Sporosarcina pasteurii, was used to induce the MICP process for the both simulant soils. An admixture of guar gum as an organic polymer and NiCl2, as bio- catalyst to enhance urease activity, was introduced to increase the compressive strength of the biologically grown bricks. A casting method was utilized for a slurry consisting of the appropriate simulant soil and microbe; the slurry over a few days consolidated in the form of a 'brick' of the desired shape. In case of MSS, maximum strength of 3.3 MPa was obtained with 10mM NiCl2 and 1% guar gum supplementation whereas in case of LSS maximum strength of 5.65 Mpa was obtained with 1% guar gum supplementation and 10mM NiCl2. MICP mediated consolidation of the simulant soil was confirmed with field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD) and thermogravimetry (TG). Our work demonstrates a biological approach with an explicit casting method towards manufacturing of consolidated structures using extra-terrestrial regolith simulant; this is a promising route for in situ development of structural elements on the extra-terrestrial habitats.

Diffusion of water in palm leaf materials.

Diffusion of water into plant materials is known to decrease their mechanical strength and stiffness but improve formability. Here, we characterize water diffusion through areca palm leaf-sheath-a model plant material, with hierarchical structure, used in eco-friendly foodware. The diffusion process is studied using mass gain measurements and in situ imaging of water transport. By treating the areca sheath as homogeneous ensemble, and incorporating effects of material swelling due- to water absorption, a factor typically neglected in prior studies, the diffusion coefficient Dw for water is estimated as (6.5 ± 2.2) × 10-4 mm2 s-1. It is shown that neglecting the swelling results in gross underestimation of Dw. Microstructural effects (e.g. fibre, matrix) on the diffusion are characterized using in situ imaging of the water transport at high resolution. The observations show that the water diffuses an order of magnitude faster in the matrix (8.63 × 10-4 mm2 s-1) than in the fibres (7.19 × 10-5 mm2 s-1). This non-uniformity is also reflected in the swelling-induced strain in the leaf, mapped by image correlation. Lastly, we vary salt concentration by controlled additions of NaCl and note a non-monotonic dependence of the diffusion on concentration. Implications of the results for improving foodware manufacturing processes and product life are discussed.

Surface-Stress Induced Embrittlement of Metals.

Environment-assisted fracture phenomena in metals are usually associated with surface energy reduction due to an adsorbed film. Here we demonstrate a unique embrittlement effect in Al that is instead mediated by surface stress, induced by an adsorbed organic monolayer. Atomistic simulations show that the adsorbate carbon-chain length lc controls the surface stress via van der Waals forces, being compressive for lc < 8 and tensile otherwise. For lc > 8, we demonstrate experimentally that the nanoscale film causes a ductile-to-brittle transition on the macroscale. Concomitant with this transition is a nearly 85% reduction in deformation forces. Additional simulations reveal that the microscopic mechanism for the embrittlement is via suppression of dislocation emission at incipient crack-tips. In addition to challenging long-held views on environment-assisted fracture, our findings pertaining to surface-stress induced embrittlement suggest profitable utility in manufacturing processes such as machining and comminution.

Organic monolayers disrupt plastic flow in metals.

Adsorbed films often influence mechanical behavior of surfaces, leading to well-known mechanochemical phenomena such as liquid metal embrittlement and environment-assisted cracking. Here, we demonstrate a mechanochemical phenomenon wherein adsorbed long-chain organic monolayers disrupt large-strain plastic deformation in metals. Using high-speed in situ imaging and post facto analysis, we show that the monolayers induce a ductile-to-brittle transition. Sinuous flow, characteristic of ductile metals, gives way to quasi-periodic fracture, typical of brittle materials, with 85% reduction in deformation forces. By independently varying surface energy and molecule chain length via molecular self-assembly, we argue that this "embrittlement" is driven by adsorbate-induced surface stress, as against surface energy reduction. Our observations, backed by modeling and molecular simulations, could provide a basis for explaining diverse mechanochemical phenomena in solids. The results also have implications for manufacturing processes such as machining and comminution, and wear.

The cutting of metals via plastic buckling.

The cutting of metals has long been described as occurring by laminar plastic flow. Here we show that for metals with large strain-hardening capacity, laminar flow mode is unstable and cutting instead occurs by plastic buckling of a thin surface layer. High speed in situ imaging confirms that the buckling results in a small bump on the surface which then evolves into a fold of large amplitude by rotation and stretching. The repeated occurrence of buckling and folding manifests itself at the mesoscopic scale as a new flow mode with significant vortex-like components-sinuous flow. The buckling model is validated by phenomenological observations of flow at the continuum level and microstructural characteristics of grain deformation and measurements of the folding. In addition to predicting the conditions for surface buckling, the model suggests various geometric flow control strategies that can be effectively implemented to promote laminar flow, and suppress sinuous flow in cutting, with implications for industrial manufacturing processes. The observations impinge on the foundations of metal cutting by pointing to the key role of stability of laminar flow in determining the mechanism of material removal, and the need to re-examine long-held notions of large strain deformation at surfaces.

Slow wave propagation in soft adhesive interfaces.

Stick-slip in sliding of soft adhesive surfaces has long been associated with the propagation of Schallamach waves, a type of slow surface wave. Recently it was demonstrated using in situ experiments that two other kinds of slow waves-separation pulses and slip pulses-also mediate stick-slip (Viswanathan et al., Soft Matter, 2016, 12, 5265-5275). While separation pulses, like Schallamach waves, involve local interface detachment, slip pulses are moving stress fronts with no detachment. Here, we present a theoretical analysis of the propagation of these three waves in a linear elastodynamics framework. Different boundary conditions apply depending on whether or not local interface detachment occurs. It is shown that the interface dynamics accompanying slow waves is governed by a system of integral equations. Closed-form analytical expressions are obtained for the interfacial pressure, shear stress, displacements and velocities. Separation pulses and Schallamach waves emerge naturally as wave solutions of the integral equations, with oppositely oriented directions of propagation. Wave propagation is found to be stable in the stress regime where linearized elasticity is a physically valid approximation. Interestingly, the analysis reveals that slow traveling wave solutions are not possible in a Coulomb friction framework for slip pulses. The theory provides a unified picture of stick-slip dynamics and slow wave propagation in adhesive contacts, consistent with experimental observations.

Geometric flow control of shear bands by suppression of viscous sliding.

Shear banding is a plastic flow instability with highly undesirable consequences for metals processing. While band characteristics have been well studied, general methods to control shear bands are presently lacking. Here, we use high-speed imaging and micro-marker analysis of flow in cutting to reveal the common fundamental mechanism underlying shear banding in metals. The flow unfolds in two distinct phases: an initiation phase followed by a viscous sliding phase in which most of the straining occurs. We show that the second sliding phase is well described by a simple model of two identical fluids being sheared across their interface. The equivalent shear band viscosity computed by fitting the model to experimental displacement profiles is very close in value to typical liquid metal viscosities. The observation of similar displacement profiles across different metals shows that specific microstructure details do not affect the second phase. This also suggests that the principal role of the initiation phase is to generate a weak interface that is susceptible to localized deformation. Importantly, by constraining the sliding phase, we demonstrate a material-agnostic method-passive geometric flow control-that effects complete band suppression in systems which otherwise fail via shear banding.

Stick-slip at soft adhesive interfaces mediated by slow frictional waves.

Stick-slip is a friction instability that governs diverse phenomena from squealing automobile brakes to earthquakes. At soft adhesive interfaces, this instability has long been attributed to Schallamach waves, which are a type of slow frictional wave. We use a contact configuration capable of isolating single wave events, coupled with high speed in situ imaging, to demonstrate the existence of two new stick-slip modes. It is shown that these modes also correspond to the passage of slow waves-separation pulse and slip pulse-with distinct nucleation and propagation characteristics. The slip pulse, characterized by a sharp stress front, propagates in the same direction as the Schallamach wave. In contrast, the separation pulse, involving local interface detachment and resembling a tensile neck, travels in exactly the opposite direction. A change in the stick-slip mode from the separation to the slip pulse is effected simply by increasing the normal force. Taken together, the three waves constitute all possible stick-slip modes in low-velocity sliding. The detailed observations enable us to present a phase diagram delineating the domains of occurrence of these waves. We suggest a direct analogy between the observed slow frictional waves and well known muscular locomotory waves in soft bodied organisms. Our work answers basic questions about adhesive mechanisms of frictional instabilities in natural and engineered systems, with broader implications for slow surface wave phenomena.

Sinuous flow in metals.

Annealed metals are surprisingly difficult to cut, involving high forces and an unusually thick "chip." This anomaly has long been explained, based on ex situ observations, using a model of smooth plastic flow with uniform shear to describe material removal by chip formation. Here we show that this phenomenon is actually the result of a fundamentally different collective deformation mode--sinuous flow. Using in situ imaging, we find that chip formation occurs via large-amplitude folding, triggered by surface undulations of a characteristic size. The resulting fold patterns resemble those observed in geophysics and complex fluids. Our observations establish sinuous flow as another mesoscopic deformation mode, alongside mechanisms such as kinking and shear banding. Additionally, by suppressing the triggering surface undulations, sinuous flow can be eliminated, resulting in a drastic reduction of cutting forces. We demonstrate this suppression quite simply by the application of common marking ink on the free surface of the workpiece material before the cutting. Alternatively, prehardening a thin surface layer of the workpiece material shows similar results. Besides obvious implications to industrial machining and surface generation processes, our results also help unify a number of disparate observations in the cutting of metals, including the so-called Rehbinder effect.

Nucleation and propagation of solitary Schallamach waves.

We isolate single Schallamach waves--detachment fronts that mediate inhomogeneous sliding between an elastomer and a hard surface--to study their creation and dynamics. Based on measurements of surface displacement using high-speed in situ imaging, we establish a Burgers vector for the waves. The crystal dislocation analogs of nucleation stress, defect pinning, and configurational force are demonstrated. It is shown that many experimentally observed features can be quantitatively described using a conventional model of a dislocation line in an elastic medium. We also highlight the evolution of nucleation features, such as surface wrinkles, with consequences for interface delamination.