mm 2.5 2.0 1.5 - - -1.5-2.0-2.5 Local friction of rough contact interfaces with rubbers using contact imaging approaches mm -2.5-2.0-1.5 - - 1.5 2.0 2.5 0.30 0 0 0 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
Steady state friction of dry multi-contact interfaces p Surface geometry, contact mechanics t 10-20 C s (m 4 ) 10-22 10-24 10-26 10-28 10-30 10-32 10-34 10-36 Roughness PSD 1 1 10 100 1000 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)??
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
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
mm 2.5 2.0 1.5 - - -1.5-2.0-2.5 mm 2.5 2.0 1.5 - - -1.5-2.0-2.5 Contact stresses: single asperity contact Smooth Glass/PDMS contact Contact pressure Surface shear stress mm -2.5-2.0-1.5 - - 1.5 2.0 2.5 0.3 MPa R=9.3 mm, P=1.4 N, v= mm/s mm -2.5-2.0-1.5 - - 1.5 2.0 2.5 0.30 0 0 0 MPa PDMS displacement Pressure independent shear stress
Contact pressure p (MPa) Shear stress t (MPa) mm 1.5 - - -1.5 mm 1.5 - - -1.5 Contact stresses: rough multi-contact interface Contact pressure mm -1.5 - - 1.5 0.3 MPa Gaussian roughness r.m.s roughness ~ 1 µm Shear stress mm -1.5 - - 1.5 0.3 MPa 20µm Sand blasted glass lens 1.2 0.8 0.6 0.6 0.3-3 -2-1 0 1 2 3 Space coordinate x (mm) -3-2 -1 0 1 2 3 Space coordinate x (mm) Stress profiles at increasing applied normal load
C(q) (m 4 ) Local friction law PDMS / self affine rough glass surface Local frictional stress t (MPa) 0.6 0.3 Normal load from 5 N to 17 N 10-22 10-23 10-24 10-25 10-26 10-27 10-28 10-29 10-30 10-31 10-32 10-33 10-34 10-35 H=0.7 10-36 1 1 10 100 q (10 6 m -1 ) Ph (1/µm) 0.3-3 Roughness PSD -2-1 0 1 2 Asperity Height (µm) 3 0.6 0.8 1.2 Local contact pressure p (MPa) Non Amontons-Coulomb local friction law D.T Nguyen et al EPL (2014)
Spatial fluctuations in the shear stress at low contact pressures mm 0.8 - -0.8-0.8-0.8 mm -0.8-0.8-0.8-0.8 0 0 MPa 0 0 0 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
Gaussian vs non Gaussian surface roughness Local shear stress t (MPa) PDMS rubber 7 6 5 Sand blasting Sand blasting + etching 4 3 20µm 2 0.61 0.67 1 1 9 20µm 6 7 8 9 2 3 4 5 6 7 8 9 1 Height distribution Local contact pressure p (MPa) Local friction law
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
Cusps vs bumbs: local friction law Shear stress[mpa] 0.3 0 5 0 5 0 5 0.30 0.35 Contact pressure [MPa] All the topographical information relevant to friction is not embedded in the PSD
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?
Local friction of viscoelastic rubbers with randomly rough surfaces C s (m 4 ) Modulus (Pa) 10-20 10-22 10-24 10-26 10-28 10-30 10-32 10-34 10-36 Sand blasted glass surface 1 1 10 100 1000 q (10 6 m -1 ) rms roughness µm 4 2 10 6 8 6 4 2 10 5 8 6 Epoxy rubber Tg = - 42 C G G 10-2 10-1 10 0 10 1 10 2 10 3 10 4 Frequency (Hz) Torsional contacts Linear sliding Bulk viscoelastic dissipation at contact scale! 1 mm A. Chateauminois et al Phys Rev E 81 (2010)
Torsional contact : displacement & stress field mm 1.2 0.8 - -0.8-1.2 Inversion Shear stress t (MPa) Azimuthal displacement u mm -1.2-0.8-0.8 1.2 Frictional shear stress 0.35 0.30 5 Indentation depth (µm) 60 100 140 0 0 5 5 0 mm 0 5 0 5 Azimuthal displacement u (mm) 5 0 5 0 5 0 1.5 Radial coordinate (mm) 2.0 0 1.5 Radial coordinate (mm) velocity pressure r 2.0
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 1.4 1.2 0.8 0.6 1.5 2.0 Radial coordinate r (mm) 2.5 14 12 10 8 6 Dieterich et al. Pageoph,143 (1994) 4 Light transmitted through the interface more efficiently when only one interface is present 2 0 0.6 0.8 Non dimensional radial coordinate r/a 1.2 Transmitted light intensity I(x,y) Proportion of area in contact A/Ao(x,y)
Shear stress t (MPa) Velocity dependence of the shear stress Normalized intensity Angular velocity Transmitted light intensity 0.30 5 0 Angular velocity (deg s -1 ) 1 3 0.3 1 1.4 1.2 Angular velocity (deg s -1 ) 1 3 0.3 1 5 0.8 0 0.6 5 0 1.5 Radial coordinate (mm) 2.0 Radial coordinate (mm) 1.5 2.0 Dependence of the shear stress on the actual contact area :???
Pressure and velocity dependence of the frictional shear stress 60 100 140 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)
Unsteady state friction: Stick-slip motions within patterned glass/pdms contacts
Stiction of patterned glass surfaces : stick-slip motions Lateral force (N) [nm] 360 nm 3.5 3.0 v = 50 µm/s 2.5 2.0 1.5 1.5 2.0 2.5 3.0 Displacement (mm) Patterned glass lenses 1.6 µm Sol-gel process, Saint Gobain 300 200 100 0 0 2 4 [µm] 6 8 M.-C. Audry EPJE (2012)
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=23.5 2 Q=11.5 1 Q=10 0 Q=3 0 10 20 30 40 Time (s) Stick-slip generated by localized stress fluctuations
Lateral force (N) Friction traces : velocity dependence Stick-slip frequency (Hz) 2.5 2.0 1.5 100 2.8 v = 5 µm s -1 10 2.6 2.4 1 2.2 2.0 1.8 2.8 2.6 2.4 v = 1 mm s -1 1 1 Sliding velocity (mm/s) 2.2 2.0 1.8 v = 2 mm s -1 0.3 Imposed displacement (mm) Characteristic length: l = v/f ~ 70 µm
Stiction with patterned lenses Surface velocity field Crack-like precursors to friction
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) 3.0 2.0 mm / s Displacement profile 80 D Crack propagation 60 Crack velocity ~ 100 mm s -1 40 d slip C d slip ~ 70 µm 20 B A 0 1 2 3 4 5 6 Position (mm)
Established stick-slip regime : high velocity regime Surface velocity field - v = mm s -1
Stick slip regimes : high velocity Displacement (x 10-3 mm) Slip velocity field (a) (b) (c) (d) A B C D 3.0 2.0 mm / s Displacement profile 80 D 60 40 C Crack velocity ~ 100 mm s -1 d slip ~ 70 µm 20 d slip B A 0 1 2 3 4 Position (mm) 5 6
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?
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) 0.6 0.8 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????