Christiane Caroli

Solid friction from stick–slip down to pinning and aging

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between macroscopic hard rough solids, whose main dynamical features are well described by the Rice–Ruina rate and state-dependent constitutive law. We show that it results from two combined effects: (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure and (ii) the geometric aging, i.e. slow growth of the real area of contact via asperity creep interrupted by sliding. Closer analysis leads to identifying a second aging-rejuvenation process, at work within the junctions themselves. We compare the effects of structural aging at such multicontact, very highly confined, interfaces with those met under different confinement levels, namely boundary lubricated contacts and extended adhesive interfaces involving soft materials (hydrogels, elastomers). This leads us to propose a classification of frictional junctions in terms of the relative importance of jamming and adsorption-induced metastability. Contents PAGE 1. Introduction 280  1.1. From Amontons--Coulomb to Rate-and-State 281  1.2. Spatial scales 284  1.3. Outline 285  2. Multicontact interfaces (MCIs) 286  2.1. Geometry of MCIs 286   2.1.1. Surface roughness 286   2.1.2. The single microcontact 287   2.1.3. Area of contact between random surfaces 289  2.2. Geometric age: a major state variable for MCIs 292   2.2.1. Time dependence of the static threshold 292   2.2.2. Creep growth of the real area of contact 294   2.2.3. Geometric age as a dynamical state variable 296  2.3. Junction rheology: gross features 298   2.3.1. Junctions at multicontact interfaces 298   2.3.2. A threshold rheology 299   2.3.3. Beyond threshold: rate effects 299    2.3.3.1. Velocity jumps: the direct effect 299    2.3.3.2. Steady sliding friction coefficient 301   2.3.4. Threshold rheology as a signature of multistability 303    2.3.4.1 A toy model for junction rheology 303    2.3.4.2. Monostable contact 304    2.3.4.3. Bistable contact 305    2.3.4.4. Rate effect at finite temperature 307    2.3.4.5. From the toy model to the real junction 308  2.4. Sliding dynamics of an MCIs 311   2.4.1. The Rice--Ruina friction law 311   2.4.2. The RR dynamics of a driven block 311   2.4.3. Limitations of block models for extended MCIs 315  3. Junction rheology: Structural aging/Rejuvenation effects 316  3.1. Accessing junction rheology directly: suitable configurations 317   3.1.1. Rough-on-flat multicontact interfaces 317   3.1.2. Junctions in the Surface Force Apparatus 318   3.1.3. Extended soft contacts 319  3.2. MCIs junctions revisited 319   3.2.1. Structural aging 320   3.2.2. Steady sliding dynamic friction 321   3.2.3. Discussion 321  3.3. Boundary lubrication junctions 322   3.3.1. Confinement-induced solidification 322   3.3.2. Structural aging 324   3.3.3. Sliding dynamics 324  3.4. Extended soft contacts: Gelatin/Glass friction 326   3.4.1. Static threshold 326   3.4.2. Sliding dynamics 327   3.4.3. Rate and state interpretation 329  3.5. Extended soft contacts: Dry elastomer friction 331   3.5.1. Bulk dissipation 331   3.5.2. Interfacial dissipation 331  3.6. A tentative classification: Jammed junction plasticity versus adsorption controlled dynamics 332 4. Conclusion 335 Acronyms 337 Acknowledgments 337 Appendix A: Shear stiffness of a MCIs 338 Appendix B: The viscoelastic GW model 339 Appendix C: The driven block: Linear stability analysis 341 Appendix D: The Schallamach model of adsorption-controlled friction 343 References 346

Solvent control of crack dynamics in a reversible hydrogel

The resistance to fracture of reversible biopolymer hydrogels is an important control factor of the textural characteristics of food gels1 (such as gummy candies and aspic preparations). It is also critical for their use in tissue engineering, for which mechanical protection of encapsulated components is needed2,3. Its dependence on loading rate4 and, recently, on the density and strength of crosslinks3 has been investigated. But, so far, no attention has been paid to solvent or to environment effects. Here we report a systematic study of crack dynamics in gels of gelatin in water/glycerol mixtures. We show in this model system that increasing solvent viscosity slows down cracks; moreover soaking with solvent markedly increases gel fragility; finally tuning the viscosity by adding a miscible liquid affects crack propagation through diffusive invasion of the crack tip vicinity. The results highlight the fact that fracture occurs by viscoplastic chain pull-out. This mechanism, as well as the related phenomenology, should be common to all reversibly crosslinked (physical) gels.

Propagation and Structure of Planar Streamer Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations. In the present long paper, you find the physics of the model and the interfacial approach further explained. As a first ingredient of this approach, we here analyze planar fronts, their profile and velocity. We encounter a selection problem, recall some knowledge about such problems and apply it to planar streamer fronts. We make analytical predictions on the selected front profile and velocity and confirm them numerically. (abbreviated abstract)

Fracture of a biopolymer gel as a viscoplastic disentanglement process

Abstract.We present an extensive experimental study of mode-I, steady, slow crack dynamics in gelatin gels. Taking advantage of the sensitivity of the elastic stiffness to gel composition and history we confirm and extend the model for fracture of physical hydrogels which we proposed in a previous paper (Nature Mater. 5, 552 (2006)), which attributes decohesion to the viscoplastic pull-out of the network-constituting chains. So, we propose that, in contrast with chemically cross-linked ones, reversible gels fracture without chain scission.

Elasticity and onset of frictional dissipation at a non-sliding multi-contact interface

We measure the elastic and dissipative responses of a multi‐contact interface, formed between the rough surfaces of two contacting macroscopic solids, submitted to a biased oscillating shear force. We evidence that, beyond a linear viscoelastic regime, observed at low shear amplitude, the interface response exhibits a dissipative component that corresponds to the onset of frictional dissipation. The latter regime exists, whereas the tangential force applied, far from the nominal static threshold, does not provoke any sliding. This result, akin to that of Mindlin for a single contact, leads us to extend his model of ‘microslip’ to the case of an interface composed of multiple microcontacts. While describing satisfactorily the elastic response, the model fails to account quantitatively for the observed energy dissipation, which, we believe, results from the fact that the key assumption of local Coulomb friction in Mindlins model is not legitimate at the sub‐micrometre scale of the microslip zones within microcontacts between surface asperities.

Magic angles and cross-hatching instability in hydrogel fracture.

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasistatic crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at V-independent symmetry-preserving angles and (ii) a subcritical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities. Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger than low strain moduli.

Plastic response of a two-dimensional amorphous solid to quasistatic shear: transverse particle diffusion and phenomenology of dissipative events.

We perform extensive simulations of a two-dimensional Lennard-Jones glass subjected to quasistatic shear deformation at T=0. We analyze the distribution of nonaffine displacements in terms of contributions of plastic, irreversible events, and elastic, reversible motions. From this, we extract information about correlations between plastic events and about the elastic nonaffine noise. Moreover, we find that nonaffine motion is essentially diffusive, with a clearly size-dependent diffusion constant. These results, supplemented by close inspection of the evolving patterns of the nonaffine tangent displacement field, lead us to propose a phenomenology of plasticity in such amorphous media. It can be schematized in terms of elastic loading and irreversible flips of small, randomly located shear transformation zones, elastically coupled via their quadrupolar fields.

Universal Additive Effect of Temperature on the Rheology of Amorphous Solids

Extensive measurements of macroscopic stress in a 2D Lennard-Jones glass, over a broad range of temperatures (T) and strain rates (γ), demonstrate a very significant decrease of the flowing stress with T, even much below the glass transition. A detailed analysis of the interplay between loading, thermal activation, and mechanical noise leads us to propose that over a broad (γ, T) region, the effect of temperature amounts to a mere lowering of the strains at which plastic events occur, while the athermal avalanche dynamics remains essentially unperturbed. Up to the vicinity of the glass transition, temperature is then shown to correct the athermal stress by a (negative) additive contribution which presents a universal form, thus bringing support to and extending an expression proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)].

Interplay between Shear Loading and Structural Aging in a Physical Gelatin Gel

We show that the aging of the mechanical relaxation of a gelatin gel exhibits the same scaling phenomenology as polymer and colloidal glasses. In addition, gelatin is known to exhibit logarithmic structural aging (stiffening). We find that stress accelerates this process. However, this effect is definitely irreducible to a mere age shift with respect to natural aging. We suggest that it is interpretable in terms of elastically aided elementary (coil --> helix) local events whose dynamics gradually slows down as aging increases geometric frustration.

Ultrafast spherulitic crystal growth as a stress-induced phenomenon specific of fragile glass-formers

We propose a model for the abrupt emergence, below temperatures close to the glass transition, of the ultrafast (glass-to-crystal) steady mode of spherulitic crystal growth in deeply undercooled liquids. We interpret this phenomenon as controlled by the interplay between the generation of stresses by crystallization and their partial release by flow in the surrounding amorphous visco-elastic matrix. Our model is consistent with both the observed ratios (∼10(4)) of fast-to-slow velocities and the fact that fast growth emerges close to the glass transition. It leads us to conclude that the existence of a fast growth regime requires both (i) a high fragility of the glassformer; (ii) the fine sub-structure specific of spherulites. It finally predicts that the transition is hysteretic, thus allowing for an independent experimental test.