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The Chinese University of Hong-Kong, September 2008. OUTLINE. 3. Fracture mechanisms in real materials Fracture of crystals: Different fracture mechanisms The importance of plasticity Quasi-brittle fracture: R-curve and size effect - PowerPoint PPT Presentation
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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
3- Fracture mechanisms in real materials
Edge dislocation
3- Fracture mechanisms in real materials
Stress corrosion in metallic alloys: 316L steel &liquid mercury (L. Medina, D. Gorse et al., 07)
3- Fracture mechanisms in real materials
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)
3- Fracture mechanisms in real materials
Ti3Al-based alloy
Fracture surface polycristalline Ni3Al
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
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
(
3- Fracture mechanisms in real materials
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
3- Fracture mechanisms in real materials
Quasi-brittle fracture: wood, concrete, rocks…
E. Landis & al.
S. Morel & al.
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
Paper creep(Santucci, Vanel & Ciliberto)
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
Screening of the external stress field
FPZ size
Quasi-brittle case:R-curve behaviourPerfectly brittle case
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
Experimental resistance curves for spruce(S. Morel et al. 01)
a(mm)
R(J
/m2)
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
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
3- Fracture mechanisms in real materials
Stress corrosion fracture of silicate glassesBrittle or quasi-brittle?
The Chinese University of Hong-Kong, September 2008
KIc=0.8MPa m Intrinsic strength: Vacuum c≈10-12GPa
Humid air c≈3-4GPa
RC ≈1.5-2nmRC ≈13-23nm
3- Fracture mechanisms in real materials
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
3- Fracture mechanisms in real materials
Stress corrosion: classical theory (Charles & Hillig 65, Wiederhorn 67, Michalske & Freiman 82)
Hydrolysis: H2O+(-Si-O-Si-)(-Si-OH.HO-Si-)
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
Si
Si
O
Si
Si
O
Si
Si
O
H
HO
O
H
H
O
H
H
3- Fracture mechanisms in real materials
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
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
45% humidity
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
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
3- Fracture mechanisms in real materials
FRASTA METHOD(Kobayachi & Schokey 87)
Final image: definition of contours
Relative movement of the contours: going back in time.
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
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
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
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)
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
x
yz
Rc
Crack tip
z
x
280 nm
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
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
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
Process zone size
V (m/s)
Rc
(nm
)Along the direction
of crack propagation
Perpendicular to the directionof crack propagation
ln(V*/V)
The Chinese University of Hong-Kong, September 2008
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
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
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!
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
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
3- Fracture mechanisms in real materials
The Chinese University of Hong-Kong, September 2008
3- Fracture mechanisms in real materials
(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
The Chinese University of Hong-Kong, September 2008