Thin Film Cracking Modulated by Underlayer Creep
Rui Huang
The University of Texas at Austin
Collaborators: J. Liang, J.H. Prevost, Z. Suo
Creep and ratcheting induced cracks in thin films
SiN film on Al (ratcheting)Huang, Suo, Ma, J. Mech. Phys. Solids 50, 1079 (2002)
SiGe film on glassHuang, et al., Acta Mechanica Sinica (2002).
h
l ~ a
aa
EG
2
1 ~
Free-standing film
Gradual loss of constraint due to creep
hE
G2
2 ~
Film on elastic substrate
l ~ Zh
a
h
Viscous layer
Film on viscous layerStress relaxes in crack wake,but intensifies at crack tip;Gradual loss of constraint (G2 G1)
Cracking of a brittle film on a viscous layer
• Will a pre-exist crack grow?
• When will a pre-exist crack grow?
• How fast will a crack grow?
Viscous layer
2D Shear Lag Model
dxx
dx
H
h
Diffusion-like equations, DE Hh /
Elsasser, 1969.Rice, 1980.Freund and Nix, 1999.Xia and Hutchinson, 2000.Huang et al., 2001.
,, 2
1
2
1uu
HhE
t
u
t
u
H
Viscous layer: pure shear
h ,
Elastic film: plane stress
1E
,,2
1uu
Gradual loss of constraint:•When t = 0, K = 0•When t ∞, K ∞
Long crack will grow after a delay (when K = Kc)
Stationary long crack
Length scale =
Dimensional consideration:
Analytical solution:(Laplace transform)
K Dt 1/ 4
2/1Dt
4/121103.1 DtK
K
Stationary short crack
Longer cracks are subject to delayed fracture.
K a
fDt
a2
1/ 4
,
Dt / a2 1/ 4
a
K
0
When t 0,
K 1.103 1 2 Dt 1/ 4
1
When t = ∞,
K a
Very short cracks will never grow, cKa
2a
Delayed fracture
Kc
a
Delayed fracture
Cracks never grow K a
0
a
Crack growst
0 ac
tm
,2
a
Kg
D
at c
4
22 )1(48.1
1
c
m
K
Dt
21
cc
Ka
Effect of edge relaxation
x
y
L
L
L L
2a
0.1 1 10 1000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized time, t * D/a2
No
rma
lize
d s
tre
ss in
ten
sity
fa
cto
r
L = 5a
L = 10a
L = 20a
Eq. (12)
Equilibrium value
K a
time
t = 0.05
K = 0.264
t = 1.0
K = 0.604
t = 3.0
K = 0.722
t = 10.0
K = 0.441
Huang, et al., Acta Mater. 50, 4137 (2002).
Growing Cracks
K KcCrack growth criterion:
Time scale: t0 2
D
Kc
4 HhE
Kc
2
Length scale:
= 500 MPam1MPaKc E = 100 GPa, = 10 GPa-s, h = 0.1 m, and H = 1 m
Representative values
= 4 m, t0 = 16 s
Numerical simulation of crack growth
0 0.5 1 1.5 2 2.5 30
0.5
1K
/Kc
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
a /
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
Vt 0 /
t / t0
Transient state
Stationary crack
4/10)()( DttK
Steady state growth
0tV
Steady state velocity of crack growth
2
2
0
5.0c
ss K
HhE
tV
V
Steady velocity is approached after the crack grows by a distance ~
Crack velocity can be readily measured experimentally, and can be use to determine the viscosity of the underlayer.
Viscous layer
hH
Liang, Huang, Prévost, Suo, Experimental Mechanics. In press.
Subcritical cracking
•Know the subcritical cracking V-K curve of the brittle film•Measure crack velocity to determine the underlayer viscosity.
Stress Intensity Factor, K
Crack Velocity, V
Vss 0.5E Hh 2
Kss2
Kth
Kc
Subcritical V-K curve Vss
Kss
Steady state set by two kinetic processes:
•underlayer creep
•Subcritical bond break
Crack in a micro-bridge
Viscous layer
Substrate
Brittle film
L L
0
Stress Intensity Factor, KCrack Velocity, V
0
,t
LfVss
LKeq21
Crack Velocity, V
Bridge length, LLc
2
2
5.0c
ss K
HhEV
2
21
1
th
c
KLCritical legnth:
Viscoelastic underlayer
Elastic underlayer(Xia and Hutchinson, 2000)
4/1
21
hHE
K
rubbery
glassy
viscoelstaicK
106
105
days weeks years
Kc
a
No initiation
0
Delayed fracture
Instant initiation
4/1
21
g
fgg
hHEK
4/1
21
r
frr
hHEK
Suo, prevost, Liang, submitted.
Nonlinear creep
Power law creep: nBt
u
H
1
Stationary long crack: )1(2
113, nnn HBtEhntK
Steady state velocity: n
c
nn
SS KHBEhnV
2
13
,
Measure crack velocity to determine the creep law (B, n) for the underlayer.
Liang, Zhang, Prevost, Suo, submitted to Acta Mater.
Thin Film Ratcheting
Huang, Suo, Ma, Acta Materialia 49, 3039-3049 (2001).
Y3
pStrain per cycle
E f s TH TL 1 Y
2
Uni-directional shear
substrate
metal film
cyclic temperature
cyclic stress Y
strain
stress
E
Rdt
d
dN
d,
Ratching-creep analogy:
,/ Rp R
Em
12(1 vm)EmT(1 vm)Y
2
1
Ratcheting-induced crack
Liang, Huang, Prevost, Suo, Experimental Mechanics, in press.
Tensile Film
Ratcheting Layer
Cyclic temperature
Stress intensity factor of a stationary long crack:4/1
21103.1)(
N
hHENK
R
dadN0.5
E Hh 2
RKc2
Steady state growth rate:
Summary• Underlayer creep induces loss of constraint on cracks in
thin films.– A long crack starts to grow after a delay.
– Subcritical cracking, modulated by underlayer creep, attains a steady state crack velocity.
• Extensions to viscoelastic and nonlinear creep underlayers.
• Ratcheting-induced crack by analogy.
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