3. fracture mechanisms in real materials fracture of crystals: different fracture mechanisms

$: 3. Fracture mechanisms in real materials Fracture of crystals: Different fracture mechanisms$
3. Fracture mechanisms in real materials Fracture of crystals:

Different fracture mechanismsThe importance of plasticity

Quasi-brittle fracture: R-curve and size effect Sub-critical fracture in silicate glasses: stress corrosion… Brittle or quasi-brittle?

OUTLINE

The Chinese University of Hong-Kong, September 2008

3- Fracture mechanisms in real materials

Cleavage of single crystals: rapid, crystallographic

(M. Marder, Austin University, USAsingle silicon crystal)

Metallic alloys:

Cleavage Ductile Intergranular

Plasticity in metals


Edge dislocation


Stress corrosion in metallic alloys: 316L steel &liquid mercury (L. Medina, D. Gorse et al., 07)


Void formation by fracture of brittle precipitatesIn an aluminum alloy (C. Prioul, Centrale Paris, France)

Dimples around Si particles in an AlSi alloy(C. Prioul, Centrale Paris, France)


Ti3Al-based alloy

Fracture surface polycristalline Ni3Al




Irwin’s estimate of the plastic zone size

- Perfect plasticity (no work hardening)- No angular dependence- Plane stress

Elastic Plastic

yS

Effective (notional) elastic crack :

y

x

Plastic zone size

yS

a

Actual stress field afterlocal yieldingan ry

r

aa n

2

(


RC=2ry= ------ (------- )1 KIc

yS

2an=ry

KI= (a+an)

Dugdale’s estimate of the plastic zone size

RC=2ry= ------ (------- )8

KIc

yS

2

Shape of the plastic zone

Von Mises criterion:(1-2)2+ (+ (3-1)2=2yS

2

No intrinsic plasticityExtended FPZ: microcracks

• release of stored energy • stress redistribution


Quasi-brittle fracture: wood, concrete, rocks…

E. Landis & al.

S. Morel & al.




Paper creep(Santucci, Vanel & Ciliberto)



Screening of the external stress field

FPZ size

Quasi-brittle case:R-curve behaviourPerfectly brittle case



Experimental resistance curves for spruce(S. Morel et al. 01)

a(mm)

R(J

/m2)



Size effect on the stress to failure: (Bažant 04)

)(2 n

Icc

aa

K

:naa Size of the notional crack

yn ra : FPZ size{Short cracks: constant: cy ar

Long cracks: a

1: cy ar

a

L2a

2L

Lc

c

1 :samples Large

Constant :samples Small

(L/L0)

Limestone Sea Ice

SiC

ConcreteCarbonComposite Vinyl Foam

Concrete

Concrete


Stress corrosion fracture of silicate glassesBrittle or quasi-brittle?


KIc=0.8MPa m Intrinsic strength: Vacuum c≈10-12GPa

Humid air c≈3-4GPa

RC ≈1.5-2nmRC ≈13-23nm


Wiederhorn et al. (1967,1970)

KIcKI

10-13 m/s

10-5 m/s

mMPa8.0mMPa4.03.0

I

III

II

Chemically controlled

Diffusion controlled

Transition to dynamicfracture

Higher humidity rate

Crack propagation in a humid environmentSame behaviour for mica, sapphire…Same ammonia on glass


Stress corrosion: classical theory (Charles & Hillig 65, Wiederhorn 67, Michalske & Freiman 82)

Hydrolysis: H2O+(-Si-O-Si-)(-Si-OH.HO-Si-)



Si

Si

O

Si

Si

O

Si

Si

O

H

HO

O

H

H

O

H

H


Molecular reaction rate at the tip:

kT

F

kT

Fexpexp0

Energy barrierto break the SiO bond

Energy barrierto reform the SiO bond

F±=F∙

±(G-*)+o(G-*)

))(

(sinh)exp(2 000 kT

G

kT

FaaV

kTkT

FaV

kT

GVV

expexp :with

)exp(

000

0>~G *

Stage I chemically controlled



45% humidity



Griffith’s criterion: G= at the onset of fracture

In humid air, G=* V=0

G=*: replaces Griffith’s criterion

*<: easier to break in the presence of water!

crack

s

5 mm

2,5

cm

In situAFM

observations

Collaboration with F. Célarié, L. Ferrero & C. Marlière (LdV , Montpellier University)

75 n

m

In situ

AFM

ob

serv

atio

ns

am

orp

hou

s a

lum

inosilic

ate

V=

3. 1

0-

10

m/s

In situ

AFM

ob

serv

atio

ns

Pu

re s

ilica g

lass

V=

3. 1

0-1

1 m/s


FRASTA METHOD(Kobayachi & Schokey 87)

Final image: definition of contours

Relative movement of the contours: going back in time.



Exp

eri

ment

FRA

STA

reco

nst

ruct

ion

d d0 (VstageII / V)1/3

0 exp (K2I/K2

0)

V V0 exp (K2I/K2

0)

0 for V > VstageII

Nucleation sitesLow fracture toughness regions

= 1/d3

0 = 1/d03

+ H20

Elastic energy G ~ KI

2

VstageII 10-5 m/s(Wiederhorn et al., 67)

Dynamic fractured0 ~ 1 nm (C. Rountree et al)

Stress corrosionV=10-10 m/s => d ~ 40 nmV=10-11 m/s => d ~ 100 nm

0 V / V 0



z r -0.5

Plane stress linear elasticity :1

m

x (nm)

z (

nm)

x (nm)

z (

nm)

r (nm)

z (

nm)

80 nm

r (nm)

z (

nm)

20 nm

Departure from r-0.5

within the damage zone(20nmx80nm)



x

yz

Rc

Crack tip

z

x

280 nm



120nm

120n

m

-2.77

0.48

NotchDepression

0.7479

0.2263100

log[

u z(n

m)]

r(nm)

0.1

log[

u z(n

m)]

Cum

ula

ted

poro

sity

r (nm)

1/r



Process zone size

V (m/s)

Rc

(nm

)Along the direction

of crack propagation

Perpendicular to the directionof crack propagation

ln(V*/V)


3 - Fracture mechanisms in real materials

1.5 nm

-1.5 nm

x

Image 146

Kinematics of cavity growth

Image 50

x

AB

C

x

Image 1

A

24

6

t (h

)

100 200 300x (nm)

A B C



Front arrière de la cavitéV = 8 ± 5 10-12 m/s

Intermittency of propagation

C (foreward front cavity)V = 9 ± 8 10-12 m/s

A (main crack front)V = 3 ± 0.8 10-12 m/s

Posit

ion

s o

f fr

on

ts A

, B

, C

(n

m)

B (rear front cavity)V= 8 ± 5 10-12 m/s

“Macroscopic” velocity 3 10-11 m/s!



Posi

tion

of

the m

ain

cra

ck f

ron

t (A

)

Time

1st coalescence

2nd coalescence

Velocity 3 10-12 m/s

Velocity 3 10-11 m/s




(J.-P. Guin & S. Wiederhorn)

No plasticity, but what about nano-cracks?…Fracture surfaces…

Summary

- Dissipative processes: damage formation∙ Fracture of metallic alloys: the importance of plasticity ∙ Quasi-brittle materials: brittle damage ∙ Stress corrosion of silicate glasses: brittle or quasi-brittle?

- From micro-scale mechanisms to a macroscopic description:∙ Morphology of cracks and fracture surfaces∙ Dynamics of crack propagation


3. fracture mechanisms in real materials fracture of crystals: different fracture mechanisms

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