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

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

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

Scale of the material

heterogeneities

Include the basic mechanisms into

a statistical description

Macroscopic scale

Mechanics of materials


No easy averaging at a crack tip: Strong stress gradient

The most brittle link breaks first Rare events statisticsNo «equivalent effective» material

(r

)

r

Inglis (1913), Griffith (1920)

r

c

r

Kr I

0)( c

0

0


Fractography:

+ 3D observations : Collective effects - History reconstruction

In situ observations:

+ Real time observation of basic mechanisms- Confined to the free surface

Experimental tools


1- Scaling properties of fracture surfaces

2- Statistical model… & model experiment

3- Damage: a general mechanism?

4- Conclusion & Work in progress

OUTLINE


xz

h

zh

1- Scaling properties…

=0.75

Self-affineprofile

<

h2

>1

/2 (n

m)

Slope: =0.75

ζ ~ 0.8 independent of material &loading; depends on material

Ti3Al-basedalloy

= 0.785 nm 0.5mm


Profiles perpendicular to the direction of crack propagation

= 0.78

z

hm

ax(z

)


Aluminumalloy

=0.773nm0.1mm


= 0.77

z

hm

ax(z

)

Profiles perpendicular to the direction of crack propagation


Béton(Profilométrie)

Glass (AFM)

Alliage métallique (SEM+Stéréoscopie)

Quasi-cristaux (STM)

130mm


Δh2D(Δz, Δx) = (<(h(zA+Δz, xA+Δx) - h(zA, xA))2>A)1/2

h (

nm)

z (nm)

A B

ΔxΔz

L. Ponson, D. Bonamy, E.B. PRL 2006L. Ponson et al, IJF 2006

h/

x

z/ x1/ z

)(. /1

x

zfxh

1 si

1 si1)(

u

u

uuf

= 0.75 = 0.6Z= / ~ 1.2

z


Glass (AFM)

Alliage métallique (SEM+Stéréoscopie)

Quasi-crystals(STM)


A B

ΔxΔz 130mm

Quasi-crystalsCourtesy P. Ebert

Coll. L. Barbier, P. Ebert

z

z

)(. /1

x

zfxh

1 si

1 si1)(

u

u

uuf

= 0.75 = 0.6

z = / ~ 1.2

h (

Å)



Glass (AFM)

Aluminum alloy (SEM+Stereo)

Quasi-crystals (STM)


A B

ΔxΔz 130mm

)(. /1

x

zfxh

1 si

1 si1)(

u

u

uuf

= 0.75 = 0.6

z = / ~ 1.2

h/

x

z/ x1/z

h (

Å)


Mortar(Profilometry)

Glass (AFM)

Aluminum alloy (SEM+Stereo)

Quasi-crystals(STM)


A B

ΔxΔz 130mm

)(. /1

x

zfxh

1 si

1 si1)(

u

u

uuf

= 0.75 = 0.6

z= / ~ 1.2

h/

x

z/ x1/z

Mortar

(Coll. S. Morel & G. Mourot)h (

Å)


Mortar(Profilometry)

Glass (AFM)

Metallic alloy (SEM+Stereo)

Quasi-crystals(STM)

A B

ΔxΔz 130mm

z/ x1/z(lz/lx)1/(z/lz)/(x/lx)1/z

h/

x(

h/l

x)/(x

/l x

)

Universal structure functionVery different length scales

h (

Å)


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)


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)



),( 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


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


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


3- Damage…

r « Rc r » Rc

Rc

Damage zonescale

Large scales :elastic domain


=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…


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…


Analytical model of fracture of an elasticlinear disordered material

Out-of-plane roughness

=0.4, =0.5 sintered glass beads,sandstone, wood

logarithmic roughness glass, steel

Length scales >> Process zone size

~ 100 nm20m to 200m

4- Conclusion…


)),(,(''

),(),'(

2

1),( 02

000 tzfzKdzzz

tzftzfKKK

t

tzfIcIIcI

z

c0 +f(z,t)

0 +

Vt

(Santucci, Bonamy, Ponson & Måløy, 07 )In-plane fracture

Dynamic phase transitionStable crack KI<KIc

Propagating crack KI>KIc

4- … & work in progress


PROCESS ZONE REGIMEOut-of-plane roughness

=0.8, =0.6 glasswoodmetallic alloys…

Length scales ‹‹ Process zone size

A model ?

ELASTIC REGIME•Algebraic/logarithmic roughness ?

•« Map » of disorder: ')'(

),()',()(

),(2

dzzz

zxhzxhA

x

zxh

Cavity scale?


4- … & work in progress

•Metallic glasses: isotropic fracture surfaces! Coll. G. Ravichandran (Caltech), D. Boivin & JL Pouchou (Onera)

•Coupled equations: growth of cavities/ line progression

Silicate glasses: damage formation at the crack tipColl. E. Charlaix (Lyon I), M. Ciccotti (Montpellier II)

3- Damage…

300 m 30 m

Zr-based metallic glass(Coll. D. Boivin, J.-L. Pouchou, G. Ravichandran)


?

3- Damage…


4- Conclusion…

3 classes of universality ?

1 Linear elastic region =0.4 =0.52 Intermediate region:

damage = « perturbation » of the front (screening)=0.8 =0.6

3 Cavity scale: isotropic region ==0.5

1 2 3


Models:- in-plane roughness (D. Bonamy, S. Santucci & K.J. Målǿy)- how to take damage into account?

Evolution of ductility: steel(C. Guerra/S. Chapuilot)

Metallic glasses Silicate glasses

( C. Rountree, D. Bonamy)

4- … & Work in progress

T

UCLA, May 31, 2007

NLE zone size

3- Damage…D

. B

on

am

y e

t al.

, (0

6)

V (m/s)

Rc

(nm

)Correlation length

Velocity (m/s)

(n

m)

and Rc decrease with v

‹=Rc

z x

Endommagement en pointe de fissure

Ecrantage des interactionsentre deux points du front

')'(

)()'().( dz

zz

zhzhA

x

h

KI0

KI0

3- Endommagement…

> 2=0.75; =0.6; z=1.2

3- Endommagement

Verres métalliques (Xi et al, PRL 94, 2005)

Base-Ce

KIc=10MPa√mBase-Mg

KIc=2MPa√m

Si z > 1 mm ζ ~ 0.4

Si z < 1 mm ζ ~ 0.8

Collaboration avecS. Morel & G. Mourot,Bordeaux I, France

Log (

Δh)

(mm

)

10010-1 101

10-2

10-1

100

log(Δz) (mm)

3- Endommagement

3- Des surfaces de rupture “anormalement” rugueuses: les céramiques de verre

Exposant de rugosité indépendant de la microstructure: ζ = 0.40 ± 0.04

Analyse 1D

Matériau modèle dont on peut moduler:-la porosité -la taille des billes d



ζ=0.4 ± 0.05β=0.5 ± 0.05 z=ζ/β=0.8 ±0.05L. Ponson, H. Auradou et J.P. Hulin, soumis à Phys. Rev. E

Les 3 exposants

Analyse 2D

Forme universelle de la fonction de corrélation

2D

+


Diamètre des billes: 100 µmPorosité: 5%

Analyse 2D

= 1 mm

3- Des surfaces de rupture “anormalement” rugueuses: le mortier à grande échelle

Si z > 1 mm ζ ~ 0.4

Si z < 1 mm ζ ~ 0.8

CollaborationS. Morel et G. Mourot,LRBB, Bordeaux

Si z > 100 nm ζ ~ 0.4

3- Des surfaces de rupture “anormalement” rugueuses: le verre à grande échelle

= 100 nm

Si z < 100 nm ζ ~ 0.8

S. Wiederhorn et al. 05

vv

tip

Au(111) film(~150 nm)

mica plate

Sample holder

Z-piezo

It

wedge

preamplifier

feedbacksystem of STM

PC

Vibration isolation system

Ut

Humid air

n-tetradecane

l

a

δ=h2-h1

s

vh1

h2

B

A

h

STM tip

C1D

C2

D1

D2

wedge

12

)(1800)()( sttha

fltv

l

alh

tsl

atslht

)(

)(

)()(

smv

vvvP

O

O

/10

)/exp()(6

9.2)(

vvP

Topothesies lz and lx:

mortar

glass

metal

Crossover function is also universal

1- Scaling properties …

2- Fracture surfaces “abnormally” rough:

glass ceramics

Δz

ΔhDistribution of ΔhΔz

Δh/Δzζ

P(Δh) ~ Δz-ζ g(Δh/Δzζ)

Mono-affine

ζ = 0.40 ± 0.04

P.Δ

zζ

Gaussian distribution

2- Fracture surfaces “abnormally” rough:

glass ceramics

Δz

ΔhDistribution of ΔhΔz

Δh/Δzζ

P.Δ

zζ

f(z)z

x

ft

= KI - KIc

+ fz( )

2μ

KI0

KI0

3- Towards one scenario for all the materials?

For an homogeneous and elastic material: H. Gao and

J. Rice, 89

)')'(

)()'(1()(

20 dz

zz

zfzfKzK II

In-plane displacement of the crack front:

f(z)z

x

ft

= KI - KIc

+ fz( )

2μ

KI0

KI0

3- Towards one scenario for all the materials?

For an homogeneous and elastic material: H. Gao and

J. Rice, 89

)')'(

)()'(1()(

20 dz

zz

zfzfKzK II

))(,(')'(

)()'(.)(

2002 zfzdz

zz

zfzfKKK

h

f

t

fIIcI

Equation of pinning/depinning of an elastic line

In-plane displacement of the crack front:

(r

)Zone

endommagée

Introduction

cmi

n

cmax

Dis

trib

uti

on

des s

eu

ils

de r

up

ture

2

min

min

C

IC

CI

KR

r

K

exposant

angleAlliage métallique

zdirection du front

xdirection depropagation

Demande française et américaine de brevet (2005)

direction de propagation ζ = 0.75

β = 0.6

Matériau « modèle »: fritté de verre (L. Ponson, H. Auradou & J.-P. Hulin, 06)

- Porosité contrôlée (3 to 25%)- Taille de grains (50 to 200 m)- Joints vitreux- Rupture mixte inter/trans-granulaire- Taille zone de processcomparable verre << taille grains

2- Modèles statistiques…

Journées de Physique Statistique- 25 janvier 2007

Examen des surfaces de rupture

Johnson et Holloway (1968) 0.5 mm

Principle of local symmetry:

KII=0


UCLA, May 31, 2007

Documents

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