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.