D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud GROUPE FRACTURE Service de Physique et Chimie des Surfaces et des Interfaces CEA-Saclay, France Collaboration S. Morel (US2B, Bordeaux, France) H. Auradou, J.-P. Hulin (FAST, Orsay, France) MatGenIV, Cargèse, September 2007 FRACTURE MECHANISMS & SCALING PROPERTIES OF FRACTURE SURFACES
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D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud GROUPE FRACTURE Service de Physique et Chimie des Surfaces et des Interfaces.
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D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud
GROUPE FRACTUREService de Physique et Chimie des Surfaces et des Interfaces
Universal structure functionVery different length scales
h (
Å)
1- Scaling properties…
General result : anisotropic self-affine surface independent of disorder
Crack front= «elastic line» Fracture surface = trace left behind by the frontJ.-P. Bouchaud, EB, G. Lapasset, J. Planès (93)
2- Statistical models
D. Bonamy et al, PRL 2006
)')'(
)()'()(( .exp2
)0(
dzzz
zhzhA
x
hK IKII
Linear elastic material
Weak distorsions
KII = 0
.exp2'
)'(
),()',()(
),(
dz
zz
zxhzxhA
x
zxh
)),(,,( zxhzx
z
x
f(x,z)
KI0
KI0
h(x,z)
2- Statistical models
Principle of local symmetry
.exp2)),(,,('
)'(
),()',()(
),(
zxhzxdz
zz
zxhzxhA
x
zxh
(x,z,h(x,z))=q(z,h(x,z))+t(z,x)
)),(,(')'(
),()',()(
),(.exp2
zxhzdzzz
zxhzxhA
x
zxhq
+t(z,x)
ζ=0.39A. Rosso & W. Krauth (02)
β=0.5 and z=0.8O.Duemmer & W. Krauth (05)
2- Statistical models
MatGenIV, Cargèse, September 2007
),( xzt
Logarithmic roughnessS. Ramanathan, D. Ertaş
& D. Fisher (97)
« Model» material: sintered glass beads (L. Ponson et al, PRL06; coll. H. Auradou, J.-P. Hulin & P. Vié)
Porosity 3 to 25%Grain size 50 to 100 mVitreous grain boudaries
Linear Elastic Material
2- … & model experiment
MatGenIV, Cargèse, September 2007
ζ=0.4 ± 0.05β=0.5 ± 0.05
z=ζ/β=0.8 ±0.05
3 exponent
s
Universal 2D correlation function +
Structure 2DPacking of sintered glass beads
1/z
2- … & model experiment
3- Damage…
What did we
MISS ?Damage !
Amorphous silicaTi3Al-based alloy
Roughness measurements performed within the damaged zone !
damaged zone size
MatGenIV, Cargèse, September 2007
Elisabeth BOUCHAUD
Tous les autres matériaux s'endommagent. Montrer les images.Et leurs surfaces de rupture sont étudiées à des échelles comparables à celles où le matériau s'endommage.
•Disorder line roughness •Elastic restoring forces rigidity of the line
Undamaged materialTransmission of stresses throughundamaged material :long rangelong range interactions (1/r2) very rigid line
3- Damage…
Transmission of stressesthrough a « Swiss cheese »: Screening of elastic interactions lower rigidity
')'(
),()',(2
dzzz
zxhzxh
Long range Short range
MatGenIV, Cargèse, September 2007
3- Damage…
r « Rc r » Rc
Rc
Damage zonescale
Large scales :elastic domain
MatGenIV, Cargèse, September 2007
=0.75, =0.6 =0.4, =0.5 OR log
?
=0.75h ~ logz
=0.75h ~ logz
Rc ~ 30nm
Rc ~ 30nm
75 nm
3- Damage…
Quasi-brittle material: Mortar… … In transient roughening regime
Rc increases with timeRc(x1)
=0.75
=0.4
x1
x2
75n
mRc(x1) Rc(x2)
=0.75
=0.4
Coll. S. Morel
3- Damage…
MatGenIV, Cargèse, September 2007
Steel broken at different temperatures (Coll. S. Chapuilot)2
8
1
Y
Icc
KR
)(TK Ic
)(TY
toughness
yield stressT=20K, Y = 1305MPa , KIc = 23MPa.m1/2
Rc = 20 µm
=0.75
h ~ logz
Rc
T=98K, Y = 772MPa , KIc = 47MPa.m1/2
Rc = 200 µm
=0.75
h ~ logz
Rc
3- Damage…
4- Conclusion…
MatGenIV, Cargèse, September 2007
Analytical model of fracture of an elasticlinear disordered material