Friction is fracture: Slippery surfaces and frustrated cracks · F N F S L = 200 mm 100 mm x y x...
Transcript of Friction is fracture: Slippery surfaces and frustrated cracks · F N F S L = 200 mm 100 mm x y x...
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