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

D.T. Nguyen, M.C. Audry, M. Trejo, C. Fretigny and A. ChateauminoisSoft Matter Science and Engineering Laboratory - SIMMEcole Supérieure de Physique et Chimie Industrielles (ESPCI), Paris, France

E. Barthel & J .TeisseireSurface du Verre et Interfaces , CNRS – Saint Gobain, Aubervilliers

A.Prevost & E. WandersmanJean Perrin Laboratory (LJP), Université P. et M. Curie, Paris

ICMCTF 2014 April 29th 2014

2.5

2.0

1.5

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-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

mm

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0.10

0.00

MP

a

(c)

Steady state friction of dry multi-contact interfaces

Real contact area ??

• Frictional energy dissipation at micro-asperity scale

• Surface geometry, contact mechanics

t

p

Non linear material responseAdhesionViscoelasticity….

v

• Bulk plastic or viscoelastic dissipation

• Interfacial dissipation

Local friction law t(p) ??

10-36

10

-34

10-32

10

-30

10-28

10

-26

10-24

10

-22

10-20

Cs (m

4)

0.01 0.1 1 10 100 1000

q (106 m

-1)

Roughness PSD

Micro-contacts distribution

Displacement field measurements within contacts with rubber

vImposed - normal load, P

- velocity, v

P

1 mm

uy

ux

Along sliding direction Perpendicular to sliding direction

Surface displacements during steady state friction

PDMS rubber(surface marked)

Glass lensR ≈ cm

R

Space resolution ~ 10 x 10 µm2

Contact stresses : inversion of the displacement field

Surface displacement Surface stresses

Inversion???

D.T. Nguyen, J Adhesion (2011)

Lateral displacements

Vertical displacement

• Linear elasticity → Green’s tensor

• Experimentally : large strains ! → Numerical inversion using FEM

x

y

z

uy ux

Neo-Hokeanmaterial

R

uz

d

Incompressible materials, n=0.5

contact strain

Contact stresses: single asperity contact

Surface shear stressContact pressure

R=9.3 mm, P=1.4 N, v=0.5 mm/s

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a

Pressure independent shear stress

PD

MS

dis

pla

ce

men

tSmooth Glass/PDMS contact

Contact stresses: rough multi-contact interface

Contact pressure Shear stress

Gaussian roughnessr.m.s roughness ~ 1 µm

20µm

Sand blasted glass lens

1.5

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0.1

0.0

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a

0.6

0.5

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0.3

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0.1

0.0

Shear

str

ess t

(M

Pa)

-3 -2 -1 0 1 2 3

Space coordinate x (mm)

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Conta

ct pre

ssure

p (

MP

a)

-3 -2 -1 0 1 2 3

Space coordinate x (mm)

Stress profiles at increasing applied normal load

Local friction law

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Lo

ca

l fr

ictio

na

l str

ess t

(M

Pa)

1.21.00.80.60.40.20.0

Local contact pressure p (MPa)

Non Amontons-Coulomb local friction law

D.T Nguyen et al EPL (2014)

• PDMS / self affine rough glass surface

10-36

10-35

10-34

10-33

10-32

10-31

10-30

10-29

10-28

10-27

10-26

10-25

10-24

10-23

10-22

C(q

) (m

4)

0.01 0.1 1 10 100

q (106 m

-1)

0.5

0.4

0.3

0.2

0.1

0.0

Ph

(1

/µm

)

3210-1-2-3

Asperity Height (µm)

Roughness PSDNormal load from 0.05 N to 17 N

H=0.7

-0.8 -0.4 0.0 0.4 0.8

0.250.00

MPa

-0.8 -0.4 0.0 0.4 0.8

mm

0.200.100.00

MPa

0.8

0.4

0.0

-0.4

-0.8

mm

-0.8 -0.4 0.0 0.4 0.8

0.200.100.00

MPa

Spatial fluctuations in the shear stress at low contact pressures

P = 0.05 N P = 0.2 N P = 0.5 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

20µm

20µm

9

0.1

2

3

4

5

6

7

Lo

ca

l sh

ea

r str

ess t

(M

Pa

)

6 7 8 9

0.12 3 4 5 6 7 8 9

1

Local contact pressure p (MPa)

1

0.61

1

0.67

Sand blasting

Sand blasting + etching

Height distribution

Local friction law

• PDMS rubber

Additional roughnesses...

Same roughness power spectrum density

Different height distributions

30µm30µm

Ph(1/µm)

h (µm)h (µm)

Ph(1/µm)

Sol-gel Replica‘Cups’ ‘Bumps’

Cusps vs bumbs: local friction law

0.5

0.4

0.3

0.2

0.1

0.0

Shear

str

ess[M

Pa]

0.350.300.250.200.150.100.050.00

Contact pressure [MPa]

All the topographical information relevant to friction is not embedded in the PSD

t

p

Characteristic frequency w ~ v / a

v

a

• Velocity and pressure dependence of the real contact area ?

• Viscoelastic losses at micro-asperity scale ?

E*(w)

Friction of rubbers with rough surfaces: the role of viscoelastic losses

Multicontact interface

Single asperity contact

Log w

Log

Mo

du

lus

E’

E’’

Viscoelastic modulus

Local friction of viscoelastic rubbers with randomly rough surfaces

1 mm

Torsional contacts

Linear sliding

A. Chateauminois et al Phys Rev E 81 (2010)

10-36

10-34

10-32

10-30

10-28

10-26

10-24

10-22

10-20

Cs (m

4)

0.01 0.1 1 10 100 1000

q (106 m

-1)

6

810

5

2

4

6

810

6

2

4

Mo

du

lus (

Pa

)

10-2

10-1

100

101

102

103

104

Frequency (Hz)

Epoxy rubber Tg = - 42°C

G’

G”

Bulk viscoelastic dissipation at contact scale !

Sand blasted glass surface

rms roughness µm

Torsional contact : displacement & stress field

0.35

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0.05

0.00

Sh

ea

r st

ress

t

(MP

a)

2.01.51.00.50.0

Radial coordinate (mm)

Indentation depth (µm) 60 100 140

0.25

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Azim

uth

al d

ispla

ce

me

nt

u(

mm

)

2.01.51.00.50.0

Radial coordinate (mm)

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mm

Azimuthal displacement u

Frictional shear stress

r

velocity

pressure

Inve

rsio

n

Light transmission through rough multi-contact interfaces

Light transmitted through the interface more efficientlywhen only one interface is present

Dieterich et al. Pageoph,143 (1994)

Static indentation experiments

Transmitted light intensity I(x,y) Proportion of area in contact A/Ao(x,y)

Incre

asin

gco

nta

ct lo

ad

1.4

1.2

1.0

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Norm

aliz

ed

inte

nsity

2.52.01.51.00.50.0

Radial coordinate r (mm)

14

12

10

8

6

4

2

0No

rma

lize

din

ten

sity

/ p

m(M

Pa

-1)

1.21.00.80.60.40.20.0

Non dimensional radial coordinate r/a

1 pixel = 5.1 µm

Velocity dependence of the shear stress

Angular velocity Transmitted light intensity

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0N

orm

aliz

ed

in

ten

sity

2.01.51.00.50.0

Radial coordinate (mm)

Angular velocity (deg s-1

)

0.01 0.03 0.1 0.3 1

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0.05

0.00

Sh

ea

r st

ress

t

(MP

a)

2.01.51.00.50.0

Radial coordinate (mm)

Angular velocity (deg s-1

) 0.01 0.03 0.1 0.3 1

Dependence of the shear stress on the actual contact area :

???

60

100

140 Smooth contact

Real contact area: density of micro-contactsAverage shear stress within micro-asperity contacts

Interface dissipation predominates over bulk viscoelastic dissipation

M. Trejo Phys Rev E (2013)

Pressure and velocity dependence of the frictional shear stress

Unsteady state friction:

Stick-slip motions within patterned glass/PDMS contacts

Stiction of patterned glass surfaces : stick-slip motions

3.5

3.0

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2.0

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1.0

0.5

0.0

Late

ral fo

rce (

N)

3.02.52.01.51.00.50.0

Displacement (mm)

v = 50 µm/s

Sol-gel process, Saint Gobain

300

200

100

0

[nm

]

86420[µm]

1.6 µm

360 n

m

M.-C. Audry EPJE (2012)

Patterned glass lenses

2

1

0

Frictio

n fo

rce

(N

)

403020100

Time (s)

Q=3°

Q=10°

Q=11.5°

Q=23.5°

Friction traces vs ridges orientation

Q

Critical angle for the occurrence of stick slip Qc ~ 11°

v = 20 µm/s

Stick-slip generated by localized stress fluctuations

Friction traces : velocity dependence

2.8

2.6

2.4

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2.0

1.8

La

tera

lfo

rce (

N)

2.8

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2.0

1.80.50.40.30.20.10.0

Imposed displacement (mm)

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1.0

0.5

v = 1 mm s-1

v = 2 mm s-1

v = 5 µm s-1

0.1

1

10

100

Stick-s

lip f

requ

en

cy

(Hz)

0.01 0.1 1

Sliding velocity (mm/s)

Characteristic length: l= v/F ~ 70 µm

Stiction with patterned lenses

• Surface velocity field

Crack-like precursors to friction

3.0

2.0

1.0

0.0

mm

/ s

(a) (b) (c) (d)

Late

ralfo

rce (

N)

Imposed displacement (mm)

Established stick-slip regime : low velocity regime

• ‘Slip phase’ - v=5 µm s-1

A B C D

80

60

40

20

0

654321

Position (mm)

Dis

pla

ce

ment (

x 1

0-3

mm

)

Crack propagation

AB

C

D

Slip velocity field

Displacement profile

Crack velocity ~ 100 mm s-1

Sid

ing d

irection

d slip ~ 70 µm d slip

• Surface velocity field - v =0.5 mm s-1

Established stick-slip regime : high velocity regime

(a)

3.0

2.0

1.0

0.0

mm

/ s

(b) (c) (d)

Stick slip regimes : high velocity

Slip velocity field

Displacement profile

A B C D

80

60

40

20

0

Dis

pla

ce

ment (x

10

-3m

m)

654321Position (mm)

AB

C

D

Crack velocity ~ 100 mm s-1

d slip ~ 70 µm

d slip

Stick-slip as a crack-like motion

vc

ds

Mode III

vc & ds independent on the driving velocity

• ds ≈ cst → Stick slip frequency linearly related to the driving velocity

Parameters setting the slip length ?? How do the surfaces re-stick ??

• Vc ≈ cst → Fracture energy Gc?

Threshold stress for crack nucleation >> Threshold stress for quasi-static crack propagation

Reduced velocity dependence of Gc due to the interplay with friction ?

• Typical propagation time:

Low velocity :

High velocity:

v < vc < VRayleigh

Conclusion /Outlook

with A. Prevost and E. Wandersman, Paris Univ

M. Chaudhury, Leighigh University

Ongoing work: friction of model randomly rough surfaces

Local friction law from displacement field measurements

Multi-contact interface with rigid randomly rough surface

Non linear local friction lawRelevance of spectral description of surface topography ?Contribution of viscoelasticity to friction

Crack-like precursors to friction during stick slip regime

0.5

0.4

0.3

0.2

0.1

0.0

Loca

l sh

ea

r str

ess [

MP

a]

1.00.80.60.40.20.0

Local contact pressure [MPa]

Elastic coupling between micro-asperity contacts ????

(c)