Friction is fracture:

Top Block

PMMA

NF

SF

Low-Friction Surface

Bottom Block

PMMA

SF

Low-Friction Surface

Bottom Block

PMMA

Elsa Bayart, Ilya Svetlizky and Jay FinebergThe Racah Institute of Physics

The Hebrew University of Jerusalem, Israel

Slippery surfaces

frustrated cracks

and

1480 - Da Vinci 1699 - Amontons

1785 - Coulomb

F = μ N

F is independent of the area of contact

μstatic ≠ μdynamic

Small scales: technological challenges

Reducing friction (MEMS).

Reducing wearing of surfaces.

Improving lubricants efficiency and durability.

Biomimetic approach.

Large scales: geophysical challenges

Earthquakes and landslide mechanisms.

Predictability.

Effect of heterogeneities of interfaces (water,

melted rocks, roughness).

500 μmwww.memx.com

Peng and Gomberg,Nature Geoscience 3, 599 - 607 (2010)

K. Autumn

What we usually know about frictionDa Vinci, Amontons, Coulomb

𝐹𝑆 < 𝜇𝑠𝐹𝑁 ⇒ no motion

𝐹𝑆 = 𝜇𝑠𝐹𝑁 ⇒ motion

𝐹𝑆

𝐹𝑁

𝐹𝑆

time

𝜇𝑠𝐹𝑁

What actually happens at the interface

𝐹𝑆

EARTHQUAKE !

Net contact area = A << Nominal contact area

Pressure = yield stress, sY A = FN / sY

A is proportional to the normal load

Huge pressures deform the contacts

F.P. Bowden and D. Tabor (1950)

S. M. Rubinstein et al (2004)

The onset of friction

fracture of the discrete contacts that form

the interface

Interface slip is mediated by crack-like rupture fronts

Fronts have been observed experimentally in many different systems:

PMMA : Rubinstein et al (2004)

Homalite: Xia et al (2004)

Granite: Passelègue et al (2013)

Gels: Baumberger et al (2002), Latour (2011)

PDMS: Chateauminois et al (2008) , Prévost et al (2013)

𝐹𝑆

We’ll show that: The stresses driving these fronts are described by Fracture Mechanics

Outlines

1. The experiment

2. Previous work: Friction is fracture, I.Svetlizky and J. Fineberg, Nature, 509 205–

208 (2014)

3. Arrested ruptures: Predictability of “laboratory earthquakes”

4. Lubricated interfaces: Slippery can be tough

Experimental setupReal contact area measurement

2D-strain tensor measurement at 1 MSamples/s

FN

FS

~ 10 mm

~ 3 mm

x

y

Fast Camera

580,000 fps

PMMA

PMMA

100 mm

FN

5.5mm

z

x

y

S. M. Rubinstein et al (2004)

Svetlizky and Fineberg (2014)

A typical experiment

FN ~300-700 kg

FS ~100-500 kg

x

y

0

200

400

0 100 400

FN , FS (kg)

time (s)

m= FS / FN

300 350

0 200x (mm)

319

326

tim

e (s

)

A/A0

1

0.9

0.8

1.1

time (s)319 326

0.9

1

A/A

0

0.4

0.5

0.6

0 200x (mm)

Block detachment is mediated by propagating crack-like fronts

Rupture Fronts

0 200x (mm)

319

326

tim

e (s

)

A/A0

1

0.9

0.8

1.1

CR: Rayleigh wave speed (1255m/s for PMMA)

Each line = snapshot of the real area of contact along the entire interface

1.5msec between lines

At long ( sec) time scales:

0 200x (mm)

x (mm)

t (m

s)

A/A0

At shorter time scales:

s(r) ~ r -1/2

Shear (sxy)Tension (syy)

Fracture MechanicsLinear Elastic Fracture Mechanics (LEFM)

• Linear elasticity → singular stress at a crack’s tip

•Energy balance → Dissipation = Energy flux into the crack tip

• Speed limit: CR ,Rayleigh wave speed (1255m/s for PMMA)

CfCf

Svetlizky and Fineberg, Nature 509, 205–208 (2014)

Δ휀𝑖𝑗 =𝐾

𝑟 1 2𝑓(𝜃, 𝑣)

Fracture mechanics solution (LEFM):

𝐾 ↔energy flux 𝐺

energy to break a unit area of

contacts𝐺 = ΓPropagation condition Γ =

𝐾 ↔ Γ Γ~1 J/m2

Detachment fronts are shear cracks

Strain field measurements ↔ Γ

Rupture propagation

q

×10-3

De x

y

x-xtip(mm)

y(m

m)

x-xtip (mm)

0.04CR<Cf<0.3CR

×10-3

De x

xD

e xy

×10-3

De y

y

Cf

×10-3

x (mm)

t (m

sec)

A/A0

J.H. Dieterich, B.D. Kilgore Tectonophysics 256 (1996)

Real area of contact - PMMA

Under our conditions: A ~ 0.005A0

100mm

x-xtip(mm)

A/A

(t=

0)

~20%

Cf

Gbulk = G A0/DA = 1 / (0.2 × 0.005) ~ 1000 J/m2

Gbulk ~ the measured bulk fracture energy for

PMMA!

G(J

.m-2

)

σyy (MPa)

0

2

1 73

1

5

G is proportional to A

A is proportional to σyy

G is proportional to σyy ?

About the value of G

We will now use this to describe related phenomena/questions

1. Arrested rupture fronts How far will an earthquake extend when will a rupture stop?

2. Lubrication of the interfaceIs friction still fracture?Effect of lubricants on rupture onset/dissipation…

Friction rupture fronts are essentially shear cracks(at least when they are moving)

ARRESTED RUPTURE FRONTS

Bayart, Svetlizky and Fineberg, Nature Physics (2016)

200 400

t (s)

FS

(k

g)

20

200

300

VIV

IIIIV

III

I

II

III

IV

V

VI

t (m

s)

20000

0.4

1

x (mm)

A/A0

0.9

Transition from stick to slip is mediated by a rupture front

Partial ruptures occur before the transition: no macroscopic sliding

What controls the arrest of the rupture?

EARTHQUAKE !

EARTHQUAKES !

FN

FS

L = 200 mm

100 m

mx

y

x (mm)

0

16

σyy(M

Pa

)

0200100

σxy(M

Pa

)

0

5

Arrested ruptures can result from inhomogeneous stress distributions

Several observations of these partial ruptures: Rubinstein 2007, Maegawa 2010, Katano 2014

Numerical studies of the existence of such ruptures:

Braun 2009, Scheibert 2010, Tromborg 2011, Taloni 2015, Bar-Sinai 2015

2001000

x (mm)

Recent study proposed a CRACK ARREST CRITERION

D. S. Kammer, M. Radiguet, J. P. Ampuero, & J. F. Molinari, Tribology Letters 57, 23 (2015).

Our work: Experimental verification of the validity of a crack arrest criterion

𝐾𝑠𝑡𝑎𝑡 < 𝐾𝑐 = Γ𝐸

How can fracture mechanics help?

q

×10-3

x-xtip(mm)

y(m

m)

We have seen thatStresses are singular at the crack tip

Propagation criterion: Energy flux = Fracture energy

xyeD

Arrest criterion:

At the arrest: 𝐺 𝑣, 𝑙𝑣→0

𝐺𝑠𝑡𝑎𝑡 𝑙 = 𝐾𝑠𝑡𝑎𝑡 𝑙

2

𝐸

𝐺𝑠𝑡𝑎𝑡 < Γ ⇒

𝐸 is the Young’s modulus

Δ𝜎𝑖𝑗 =𝐾

𝑟 1 2𝑓(𝜃, 𝑣)

𝐺~ 𝐾2 𝐸 = Γ

Griffith (1920)

Freund (1990)

Kammer et al (2015)

Griffith criterion

Arrest criterion:

Fracture Mechanics: 𝐾𝑠𝑡𝑎𝑡 is determined by the stress drop Δσ(x) for all 𝑥 < 𝒍

𝐾𝑠𝑡𝑎𝑡 𝒍 =2

𝜋 0

𝑙 Δ𝜎(𝑥)

𝒍 − 𝑥𝑑𝑥

𝒍 = prospective (predicted) crack length

l

Δσ(x) = stored stress ahead of the crack

0.1

σxy

(MP

a)

-0.1 0t (ms)

1.4

1.8

1.6

Γ

𝜎𝑥𝑦𝑟𝑒𝑠

𝜎𝑥𝑦0 Δ𝜎(𝑥)𝐾𝑠𝑡𝑎𝑡 < 𝐾𝑐 = Γ𝐸

Determination of 𝐾𝑐 We know how to determine Γ

Calculation of 𝐾𝑠𝑡𝑎𝑡

I

IIIIIIVVVI

+

x

SLOPE 1 !Excellent agreement!

Can we predict crack arrest?

I

II

III

IV

V

VI

t (m

s)

20000

0.4

1

x (mm)

A/A0

0.9

(Pa.m

1/2

)

x105

0

3

0 200100

x (mm)

-1

1

0

Δσ

(MP

a)

0 200100

x (mm)

0 2000

200

lmeasured (mm)l p

red

icte

d(m

m)

< 𝜎𝑦𝑦>(MPa)

Γ (J.m-2)

8.2-8.5 3.5

5.2-5.8 2.5

6 1.5

3.8-4 1.1

3 0.75

2 0.4

1.3 0.2

We have predicted crack arrest once ... is it general?

l pre

dic

ted

(mm

)

20 18020

180

100

100

lmeasured (mm)

G(J

.m-2

)

σyy (MPa)

0

2

1 73

1

5

Bayart et al (2016)

is deterministic.The location of a rupture arrest

can be simply defined with a crack arrest criterion.

We have shown that

Confirmation of the fracture-paradigm for understanding friction.

Friction coefficient = force balanceFracture mechanics = energy balance

WHY ARE WE INTERESTED IN ARRESTED RUPTURES ?

Prediction of earthquake’s size

An earthquake is a finite size rupture in an infinite size system

LUBRICATED FRICTION

Bayart, Svetlizky and Fineberg, arXiv:1602.00085 (2016)

Coated lubricated interfaces = Interfaces coated with a film of lubricant

What about lubricated interfaces ?

LUBRICANT KINEMATIC VISCOSITY (cSt)

Silicone oil 5

Silicone oil 100

Silicone oil 104

Hydrocarbon oil (TKO-77) 200

𝐹𝑆

𝐹𝑁

0

1

1500

t (m

s)

x (mm)

0.5

1

A

A0

For slippery interfaces, we observe STICK-SLIP

and propagating RUPTURE FRONTS !

Coated with a thin layer of oil

Fully lubricated

Dry interface

F S/

F N

0

0.3

0.6

t (s)

100 200

It is more slippery …

… BUT

x-xtip(mm)

Δ εxyΔ εxx Δ εyy

x-xtip(mm)

Γlubricated = 23 J/m2 >> Γdry = 2.6 J/m2 !!

DRY FRICTION

×10-3 ×10-3 ×10-3

×10-3 ×10-3 ×10-3

LUBRICATED FRICTION

-0.2

0

0

0.06 0.1

0

0

-0.50

0.2

0

0.3

0 40-40 0 40-40 0 40-40

0 40-400 40-400 40-40

Fracture energy vs normal stress

• G is always proportional to normal stress• Different lubricants have different influence on G• Viscosity does not affect G…

Dry interface

Silicone oil 5 cSt

Silicone oil 10000 cSt

Hydrocarbon oil 200cSt

4 6 8 10

30

20

10

<syy> (MPa)

G (

J/m

²)

0

Silicone oil 100 cSt

2

Γlub ~ 23 J/m2 >> Γdry ~ 3 J/m2 !!

Coated lubrication

A WEAKER interface – smaller friction coefficient

A STRONGER interface – higher fracture energy

Coated with a thin

layer of oil

Dry

?

How to explain a high fracture energy G ?

r

Dissipative zone

𝜎𝑥𝑦 ∝ 1/ 𝑟𝜎𝑥𝑦

LEFM: intermediate scaleSmall scale: dissipative zone

𝜎𝑥𝑦𝑝𝑒𝑎𝑘

G

slip

𝜎𝑥𝑦𝑝𝑒𝑎𝑘

𝜎𝑥𝑦𝑟𝑒𝑠

𝑑𝑐

Frictional crack – Linear slip-weakening modelPalmer and Rice 1973

𝑑𝑐 : slip distance over which stresses are reduced (asperity size)

Γ =1

2𝜎𝑥𝑦𝑝𝑒𝑎𝑘

− 𝜎𝑥𝑦𝑟𝑒𝑠 𝑑𝑐

Increase of Γ:

- increase of 𝜎𝑥𝑦𝑝𝑒𝑎𝑘

- decrease of 𝜎𝑥𝑦𝑟𝑒𝑠

- increase of 𝑑𝑐

measured

not measured

not measured

x-xtip (mm)

0 10-10

Dro

p o

f co

nta

ct a

rea

-1

0

-0.6

𝑋𝑐 is the distance behind the crack tip over which contact are broken

dry

silicone oil

hydrocarbon (TKO-77)

𝑋𝑐~3mm

-40

1

0 40

2

3

𝜎𝑥𝑦

(MPa

)

x-xtip (mm)

𝜎𝑑𝑟𝑦𝑟𝑒𝑠

𝜎𝑇𝐾𝑂𝑟𝑒𝑠

𝜎𝑠𝑖𝑙𝑟𝑒𝑠

Linear slip-weakening model relates 𝜎𝑥𝑦𝑝𝑒𝑎𝑘

to the dissipative zone size XC: 𝜎𝑥𝑦𝑝𝑒𝑎𝑘

= 𝜎𝑥𝑦𝑟𝑒𝑠 +

9𝜋

32

𝛤𝐸

1 − 𝜈2 𝑋𝑐

𝑑𝑐𝑇𝐾𝑂

𝜎𝑇𝐾𝑂𝑟𝑒𝑠

𝜎𝑇𝐾𝑂𝑝𝑒𝑎𝑘

𝜎𝑠𝑖𝑙𝑟𝑒𝑠

𝜎𝑠𝑖𝑙𝑝𝑒𝑎𝑘

𝑑𝑐𝑠𝑖𝑙

𝑑𝑐𝑑𝑟𝑦

𝜎𝑑𝑟𝑦𝑟𝑒𝑠

𝜎𝑑𝑟𝑦𝑝𝑒𝑎𝑘

𝜎𝑥𝑦

(MPa

)

4

slip (mm)

0 8

Γ𝑑𝑟𝑦

Γ𝑠𝑖𝑙

Γ𝑇𝐾𝑂

Increase of Γ:

- increase of 𝜎𝑥𝑦𝑝𝑒𝑎𝑘

- decrease of 𝜎𝑥𝑦𝑟𝑒𝑠

- increase of 𝑑𝑐

YES

YES

YES

0

4

8

Γ =1

2𝜎𝑥𝑦𝑝𝑒𝑎𝑘

− 𝜎𝑥𝑦𝑟𝑒𝑠 𝑑𝑐

Peak stress is not reduced, even increased:

Possibly: Huge pressures at the contacts cause…

Layering transition of the highly compressed liquid (e.g. layering -Israelachvili, Klein, Granick…) ?

Coated lubrication: Some questions…

Residual strength is significantly lower.

Possibly: Once motion initiates…

Lubrication of contacts? Lubricant recovers a liquid behavior

PMMA

PMMA

PMMA

PMMA

Solidification followed by melting could be the answer

Questions do remain:

Why doesn’t fluid viscosity matter?

Why does lubricant composition matter so much?

High fracture energy = high dissipation high wear of lubricated machine parts at the onset of motion

NO PARADOX between a low static friction coefficient and a high fracture energy

friction coefficient = nucleation process

fracture energy = interface property, related to propagation

SUMMARY

They are ruled by FRACTURE MECHANICS while propagating and at the ARREST

At the onset of motion, RUPTURE FRONTS propagate along the frictional interface

Along a LUBRICATED interface, fracture mechanics provide a way to observe the complex dynamics of the lubricant layer

Nucleation = crack initiation ?

What about more complex interfaces ?

What about sliding ?

NOT A CLOSED PROBLEM

probably not

non-cohesive interfaces, textured

APPLICATIONCan be a rupture arrested by a local increase of the fracture energy ?

• 0 < x < 75mm : non-lubricated surface

• 75mm < x < 150mm: surfaces coated with hydrocarbon oil (TKO-77).

• <syy>= 4MPa

𝐹𝑆

𝐹𝑁

x (mm)0 75 150

Spontaneous nucleation

What will happen to the propagating rupture while entering in the lubricated part ?

4 6 8 10

40

30

20

10

<syy> (MPa)

G (

J/m

²)

0

Dry interface

Silicone oil 5 cSt

Silicone oil 100000 cSt

Hydrocarbon oil 200cSt TKO-77

0 75 150

0

x (mm)

KII

(Pa.

m1

/2)

2

4x105

GDRY (<syy>= 4MPa ) = 1 J/m2

GTKO-77 (<syy>= 4MPa ) = 10 J/m2

A

B

075 1500

0.2

0.4

0.6

x (mm)

t(m

s)

A

075 1500

0.2

0.4

0.6

x (mm)

t(m

s)

B

THANK YOU

𝜇 =𝐹𝑆𝐹𝑁

Silicone oil 5 cSt

Silicone oil 100 cSt

Silicone oil 105 cSt

Summary

Rupture fronts mediating the onset of sliding are shear cracks

Spontaneously arrested ruptures: arrest location is defined by a crack arrest criterion

Lubricated interfaces: the interface fracture energy is increased.

Can we use it?

Could we deduce G along a fault by recording the displacement field during a rupture propagation ?

Comparison of the measured value with the estimation by the drop of stress and the event size ?

Rupture arrest: knowing the averaged drop of stress for small earthquakes along a fault, could this

criterion used to evaluate local G along a fault?

Increased of G by lubrication: increase of the wear of the material?

BUT Γdried=20 J/m2 >> Γdry ~ 2 J/m2 !!

Coated lubrication

Why a Stronger interface?

• Layering transition of the highly compressed liquid (e.g. layering -Israelachvili, Klein, Granick…)

• Effect of the pore pressure on the residual stress

List of propositions including ideas of GRC participants:

• Piezoviscosity (increase of the viscosity withthe pressure and shear rate )

• Suction of the liquid at the onset of motion (negative pressure due to capillary bridges)

• Viscous disspation in the cohesive zone

Ginterface = real area of contact

apparent area of contact×number of broken contactstotal number of contacts

× Gbulk

NO PARADOX between a low static friction coefficient and a high fracture energy

friction coefficient = nucleation process

fracture energy = interface property, related to propagation

Dry interface

Silicone oil 5 cSt

Silicone oil 105 cSt

Hydrocarbon oil TKO-77

Silicone oil 100 cSt

0 75 150

4

2

0(M

Pa)

x (mm)

𝜎𝑥𝑦𝑟𝑒𝑠

What we usually know about friction

𝐹𝑆 < 𝜇𝑠𝐹𝑁 ⇒ no motion

𝐹𝑆 = 𝜇𝑠𝐹𝑁 ⇒ motion𝐹𝑆

𝐹𝑁

𝐹𝑆

time

𝜇𝑠𝐹𝑁

What actually happens here

𝐹𝑆 The onset of friction

fracture of the discrete

contacts that form the

interfaces(r ~K∙r -1/2

𝜇𝑑𝐹𝑁

Svetlizky and Fineberg, Nature 509, 205–208 (2014)

EARTHQUAKE !

Net contact area = A << Nominal contact area

Huge pressures at the contact points deform the contacts

Pressure = yield stress, sY A = FN / sY

F. Philip Bowden and David Tabor (1950)

A is proportional to the normal load

About the area of contact

𝐹𝑆

𝐹𝑁

De x

y

×10-3

)

A/A0

De x

x

×10-3

x-xtip(mm)

×10-3

De y

y

Svetlizky and Fineberg, Nature 509, 205–208 (2014)

Δ휀𝑖𝑗 =𝐾

𝑟 1 2𝑓(𝜃, 𝑣)

Fracture mechanics solution (LEFM):

𝐾 ↔energy flux 𝐺

energy to break a unit area of

contacts𝐺 = ΓPropagation condition Γ =

𝐾 ↔ Γ Γ~1 J/m2

Detachment fronts are shear cracks

Strain field measurements ↔ Γ

Rupture propagation

LEFM solution at the measurement point (3 mm above the interface)

q

×10-3

De x

y

x-xtip(mm)

y(m

m)

Coated lubricated interfaces =

Interfaces coated with a film of lubricant

r

sxy sxy 1/r

Dissipative zone

slip distance, d

Gdrysxy

peak

sdryresidual

sxypeak

slubricated

residual

Glubricated >> Gdry

slip distance, d

An interpretation of the role of the lubricant:

On a coated surface: slubricated is lower resulting in longer slip, dresidual

Coated lubrication: Why a Stronger interface?

𝜎𝑙𝑢𝑏𝑟𝑖𝑐𝑎𝑡𝑒𝑑𝑝𝑒𝑎𝑘

≤ 𝜎𝑑𝑟𝑦𝑝𝑒𝑎𝑘

𝜎𝑙𝑢𝑏𝑟𝑖𝑐𝑎𝑡𝑒𝑑𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 ≪ 𝜎𝑑𝑟𝑦

𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙

⇒ Γ𝑙𝑢𝑏𝑟𝑖𝑐𝑎𝑡𝑒𝑑 ~ Δ𝜎 ∙ 𝛿 ≫ Γ𝑑𝑟𝑦

Palmer and Rice (1973)

Large improvements this last two decades

Development of AFM and SFA: measurements for one single contact (Israelachvili, Klein,…)

Biomimetic approach for both dry and lubricated friction

Development of high-sensitivity seismic captors allowing detection of a large range of types of events (silent to supershear earthquakes)

K. Autumn

Peng and Gomberg