Local friction of rough contact interfaces with rubbers using contact imaging approaches mm

Transcription

1 mm Local friction of rough contact interfaces with rubbers using contact imaging approaches mm MPa (c) D.T. Nguyen, M.C. Audry, M. Trejo, C. Fretigny and A. Chateauminois Soft Matter Science and Engineering Laboratory - SIMM Ecole Supérieure de Physique et Chimie Industrielles (ESPCI), Paris, France E. Barthel & J.Teisseire Surface du Verre et Interfaces, CNRS Saint Gobain, Aubervilliers A.Prevost & E. Wandersman Jean Perrin Laboratory (LJP), Université P. et M. Curie, Paris ICMCTF 2014 April 29th 2014

2 Steady state friction of dry multi-contact interfaces p Surface geometry, contact mechanics t C s (m 4 ) Roughness PSD q (10 6 m -1 ) Micro-contacts distribution Real contact area?? Non linear material response Adhesion Viscoelasticity. Frictional energy dissipation at micro-asperity scale v Interfacial dissipation Bulk plastic or viscoelastic dissipation Local friction law t(p)??

3 Displacement field measurements within contacts with rubber P Glass lens R cm v R Imposed - normal load, P - velocity, v PDMS rubber (surface marked) 1 mm Surface displacements during steady state friction u x u y Along sliding direction Space resolution ~ 10 x 10 µm 2 Perpendicular to sliding direction

4 Contact stresses : inversion of the displacement field Linear elasticity Green s tensor Incompressible materials, n= Lateral displacements Inversion??? Surface displacement Surface stresses Vertical displacement contact strain Experimentally : large strains! Numerical inversion using FEM x y Neo-Hokean material z u y u x d R D.T. Nguyen, J Adhesion (2011) u z

5 mm mm Contact stresses: single asperity contact Smooth Glass/PDMS contact Contact pressure Surface shear stress mm MPa R=9.3 mm, P=1.4 N, v= mm/s mm MPa PDMS displacement Pressure independent shear stress

6 Contact pressure p (MPa) Shear stress t (MPa) mm mm Contact stresses: rough multi-contact interface Contact pressure mm MPa Gaussian roughness r.m.s roughness ~ 1 µm Shear stress mm MPa 20µm Sand blasted glass lens Space coordinate x (mm) Space coordinate x (mm) Stress profiles at increasing applied normal load

7 C(q) (m 4 ) Local friction law PDMS / self affine rough glass surface Local frictional stress t (MPa) Normal load from 5 N to 17 N H= q (10 6 m -1 ) Ph (1/µm) Roughness PSD Asperity Height (µm) Local contact pressure p (MPa) Non Amontons-Coulomb local friction law D.T Nguyen et al EPL (2014)

8 Spatial fluctuations in the shear stress at low contact pressures mm mm MPa MPa 0 0 MPa 5 P = 5 N P = N P = N Stress fluctuations over length scales of the order of a few tens of micrometers Local changes in the contact stress distribution induced by details of the topography of the rough lens

9 Gaussian vs non Gaussian surface roughness Local shear stress t (MPa) PDMS rubber Sand blasting Sand blasting + etching µm µm Height distribution Local contact pressure p (MPa) Local friction law

10 Additional roughnesses... Cups Sol-gel Replica Bumps Different height distributions P h (1/µm) P h (1/µm) 30µm h (µm) h (µm) 30µm Same roughness power spectrum density

11 Cusps vs bumbs: local friction law Shear stress[mpa] Contact pressure [MPa] All the topographical information relevant to friction is not embedded in the PSD

12 Friction of rubbers with rough surfaces: the role of viscoelastic losses Log Modulus p Viscoelastic modulus E*(w) t Multicontact interface E E Log w v Characteristic frequency w ~ v / a a Single asperity contact Velocity and pressure dependence of the real contact area? Viscoelastic losses at micro-asperity scale?

13 Local friction of viscoelastic rubbers with randomly rough surfaces C s (m 4 ) Modulus (Pa) Sand blasted glass surface q (10 6 m -1 ) rms roughness µm Epoxy rubber Tg = - 42 C G G Frequency (Hz) Torsional contacts Linear sliding Bulk viscoelastic dissipation at contact scale! 1 mm A. Chateauminois et al Phys Rev E 81 (2010)

14 Torsional contact : displacement & stress field mm Inversion Shear stress t (MPa) Azimuthal displacement u mm Frictional shear stress Indentation depth (µm) mm Azimuthal displacement u (mm) Radial coordinate (mm) Radial coordinate (mm) velocity pressure r 2.0

15 Light transmission through rough multi-contact interfaces Normalized intensity / p m (MPa -1 ) Normalized intensity Increasing contact load 1 pixel = 5.1 µm Static indentation experiments Radial coordinate r (mm) Dieterich et al. Pageoph,143 (1994) 4 Light transmitted through the interface more efficiently when only one interface is present Non dimensional radial coordinate r/a 1.2 Transmitted light intensity I(x,y) Proportion of area in contact A/Ao(x,y)

16 Shear stress t (MPa) Velocity dependence of the shear stress Normalized intensity Angular velocity Transmitted light intensity Angular velocity (deg s -1 ) Angular velocity (deg s -1 ) Radial coordinate (mm) 2.0 Radial coordinate (mm) Dependence of the shear stress on the actual contact area :???

17 Pressure and velocity dependence of the frictional shear stress Smooth contact Average shear stress within micro-asperity contacts Real contact area: density of micro-contacts Interface dissipation predominates over bulk viscoelastic dissipation M. Trejo Phys Rev E (2013)

18 Unsteady state friction: Stick-slip motions within patterned glass/pdms contacts

19 Stiction of patterned glass surfaces : stick-slip motions Lateral force (N) [nm] 360 nm v = 50 µm/s Displacement (mm) Patterned glass lenses 1.6 µm Sol-gel process, Saint Gobain [µm] 6 8 M.-C. Audry EPJE (2012)

20 Friction traces vs ridges orientation Friction force (N) Q Critical angle for the occurrence of stick slip Q c ~ 11 v = 20 µm/s Q= Q= Q=10 0 Q= Time (s) Stick-slip generated by localized stress fluctuations

21 Lateral force (N) Friction traces : velocity dependence Stick-slip frequency (Hz) v = 5 µm s v = 1 mm s Sliding velocity (mm/s) v = 2 mm s Imposed displacement (mm) Characteristic length: l = v/f ~ 70 µm

22 Stiction with patterned lenses Surface velocity field Crack-like precursors to friction

23 Siding direction Displacement ( x 10-3 mm) Lateral force (N) Established stick-slip regime : low velocity regime Slip phase - v=5 µm s -1 Slip velocity field Imposed displacement (mm) A B C D (a) (b) (c) (d) mm / s Displacement profile 80 D Crack propagation 60 Crack velocity ~ 100 mm s d slip C d slip ~ 70 µm 20 B A Position (mm)

24 Established stick-slip regime : high velocity regime Surface velocity field - v = mm s -1

25 Stick slip regimes : high velocity Displacement (x 10-3 mm) Slip velocity field (a) (b) (c) (d) A B C D mm / s Displacement profile 80 D C Crack velocity ~ 100 mm s -1 d slip ~ 70 µm 20 d slip B A Position (mm) 5 6

26 Stick-slip as a crack-like motion d s v c & d s independent on the driving velocity v c v < v c < V Rayleigh Mode III Typical propagation time: Low velocity : High velocity: d s cst Stick slip frequency linearly related to the driving velocity V c cst Fracture energy G c? Parameters setting the slip length?? How do the surfaces re-stick?? Threshold stress for crack nucleation >> Threshold stress for quasi-static crack propagation Reduced velocity dependence of G c due to the interplay with friction?

27 Local shear stress [MPa] Conclusion /Outlook Local friction law from displacement field measurements Multi-contact interface with rigid randomly rough surface Non linear local friction law Relevance of spectral description of surface topography? Contribution of viscoelasticity to friction 0.3 Crack-like precursors to friction during stick slip regime (c) Local contact pressure [MPa] Ongoing work: friction of model randomly rough surfaces with A. Prevost and E. Wandersman, Paris Univ M. Chaudhury, Leighigh University Elastic coupling between micro-asperity contacts????