Tristan Baumberger

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

Shear stiffness of a solid–solid multicontact interface

The macroscopic multicontact between two rough nominally flat surfaces is a common object whose physics is only partially understood. This paper is aimed at giving experimental evidence for the linear elastic response of a multicontact interface to a moderate shear force, i.e. below the threshold for incipient sliding. Non–intuitive properties of the interfacial shear stiffness are exhibited, in the spirit of macroscopic friction laws, which should be of practical interest when evaluating the performances of a built–up system. These are explained qualitively within the random surface framework prevailing in multicontact mechanics, and a numerical treatement of the three–dimensional profile of a real rough surface is proposed, which enables a direct quantitative simulation of the elastic stiffness. This is found to be compatible with experimental data on a polymer glass and an aluminium alloy. The sensitivity of interfacial stiffness measurements is discussed, and illustrated by the experimental evidence of the plastic deformation of aluminium alloy asperities under light nominal pressure. This emphasizes the need for an elastoplastic description of asperity deformation within a multicontact.

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.

Contact dynamics and friction at a solid-solid interface: Material versus statistical aspects

Abstract We describe some selected experimental and theoretical features of dry, sliding friction at a multicontacts interface. Special emphasis is put on features and concepts which preserve the universal — at least widely material independent - spirit of the Amontons-Coulomb laws. Stability analysis of the sliding motion is proposed as a powerful tool for the characterization of the frictional properties of an interface between rough solids in contact.

Non-Amontons behavior of friction in single contacts

Abstract.We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to a widely spread belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plasticity of a glass-like interfacial layer in the former case, and by pinning of polymer chains on the substrate in the latter one.

Microstructuration stages during gelation of gelatin under shear

We study gelation under shear of aqueous gelatin by measuring the evolution of the apparent viscosity, thus extending the previous study by de Carvalho and Djabourov (W. de Carvalho, M. Djabourov, Rheol. Acta 36, 591 (1997)). From a set of experiments under constant stress, we deduce that the microstructure evolves through the following succession of regimes: i) nucleation and growth until crowding of a microgel suspension; ii) coalescence into strata parallel to the flow; iii) gradual thickening of these strata via transverse cross-linking until the flow finally localizes into two interfacial sliding bands which close sequentially. The transition between these regimes occurs at characteristic viscosity values. This scenario is fully confirmed by experiments performed at constant shear rates. We expect it to be relevant for all materials forming thermoreversible gels.