Characterization of interfacial mechanical properties using wedge indentation method 6

i
t


F
t
t


d
b
f
o
u
s
t

κ

*
i
nduced str
e
t
aken into c
F
ig. 4.13:
P
t
hickness o

f
t
aken as be
f
The
d
etermine t
h
b
een applie
d
f
ront of the
o
f the wed
g
u
sed to fit t
h
s
hown in F
t
hickness c
a
(
1
f
f
κ
=

⎡
+
⎣

*
Courtesy
o
e
ss. If the
b
onsideratio
n
P
lane view
f
200 nm;
(
f
ore the cra
c
FESEM p
l
h
e curvatur
d
. First, a t
r
delaminati
o
g

e indentati
o
h
e delamin
a
ig.4.14. T
h
a
n then be
d
)
3/2
2
''( )
'( )
x
x
⎤
⎦
.

o
f Ms. Jian
g
b
uckling o
c
n
in the cal
c

of the in
t
(
b) BD fil
m
c
k kinks in
t
l
ane view i
e of a dela
m
r
ansparent
g
o
n crack (b
y
o
n impress
i
a
tion crack
h
e curvatur
e
d
etermined
u

g
Haiyan,
M
c
curs, the
e
c
ulation of
i
t
erfacial cr
a
m
with thic
k
t
o the film
a
mage of a
m
ination cr
a
g
rid paper i
y
defining
t
i
on); then
a

front with
a
e
of interfa
c
u
sing Eq.(4

M
.Sc. stude
n
e
nergy rele
a
i
nterfacial
t
a
ck pattern
k
ness of 50
0
a
nd toward
f
wedge ind
e
a
ck front.
T

s used to o
b
t
he origin o
a
commerci
a
a
ninth-ord
e
c
ial crack
f
.9) and the
n
t of Assoc
i
a
sed due t
o
t
oughness.
by SEM
*
:
0
nm. Inter
f
f
ilm surfac

e
e
ntation i
m
T
he followi
n
b
tain the c
o
f the coord
i
a
l software
e
r polynom
i
f
ront, κ, fo
r
function
f
(
x

i
ate Prof. D
r
o
buckling

(a) BD fi
f
acial crac
k
e
[1].
m
pression is
n
g approac
h
o
ordinates
a
i
nates at th
e
(Origin Pr
o
i
al functio
n
r
different
B
x
) as
(4.9
r
. Zeng Kai

89
must be

lm with
k
front is
used to
h
es have
a
long the
e
middle
o
7.5) is
n
, f(x), as
B
D film
)
yang


F
o
c



F

t

F
ig. 4.14:
F
o
rder poly
n
c
urvature o
f
F
ig. 4.15:
C
t
hickness r
a
F
ESEM pla
n
n
omial fun
c
f
the crack
f
C
urvature
a
nging fro

m
n
e-view im
a
c
tion is fi
t
f
ront [2].
of interfac
i
m
100 to 10
0
a
ge of dela
m
t
ted to the
i
al crack
fr
0
0nm [2].
m
inated are
crack fro
n
fr
ont deter

m
a on 500n
m
n
t in orde
r
m
ined for
t
C

m
BD film.
A
r
to deter
m

t
he BD fil
m

C
hapter 4
90
A
ninth-
m
ine the
m

s with


F
i
B
a

m
1
f
i
t
m
t
r
c
f
F
ig. 4.16: F
i
nterfacial
c
B
D film: a
a
nd (d) the
To
m
easureme

n
1
000nm). F
f
ilm thickn
e
i
nterfacial
c
t
his sugges
t
m
ode, and
t
hickness is
r
eaches a p
l
c
ircular; th
u
f
ilm, the cr
a
ESEM pla
n
c
rack front
o

slightly cu
r
1000 nm B
D
determine
n
ts are ma
d
ig.4.15 sho
w
e
ss. As ca
n
c
rack front
t
s that the
c
the plane
increased
t
l
ateau at a
b
u
s the circu
l
a
ck front is
n

e-view im
a
o
n (a) the 1
0
r
ved crack
f
D
film: al
m
the curvat
u
d
e for eac
h
w
s the rela
t
n
be seen
i
is very str
a
c
ritical
b
uc
k
strain con

d
t
o about 50
0
b
out 0.51 µ
m
l
ar bucklin
g
slightly c
u
a
ges of the
w
0
0 nm BD
f
f
ront; (c) t
h
m
ost circula
r
u
re of the
h
BD fil
m
t

ionship
b
e
t
i
n Fig.4.16
(
a
ight and t
h
k
ling stress
d
ition is f
u
0
nm or mo
r
m
-1
(Fig.4.
1
g
mode sho
u
rved (Fig.
4
w
edge in
d

e
n
f
ilm: a strai
g
h
e 500 nm
B
r
delaminat
i
delaminat
i
thickness
t
ween the c
u
(
a), for a
B
h
e curvatur
should foll
o
u
lfille
d
. In
r
e (Fig.4.1

6
1
5), and th
e
uld be ado
p
4
.16(b)); he
n
n
tation site
s
g
ht crack f
r
B
D film: a
i
on [2].
i
on crack
f
(100nm, 3
0
u
rvature o
f

B
D film ≤

e is closed
o
w the stra
contrast,
w
6
(c) and 4.1
e
delaminat
i
p
ted. For t
h
n
ce the crit
C
s
and the a
s
r
ont; (b) th
e
curved cra
c
f
ront, at l
e
0
0nm, 500
n

f
crack fron
t
100 nm t
h
to zero (F
i
ight-sided
b
w
hen the
B
6(d)), the c
u
i
on shape i
s
h
e 300 nm t
h
ical buckli
n

C
hapter 4
91

sociated
e
300 nm

c
k front,
e
ast five
n
m, and
t
and the
h
ick, the
i
g.4.15);
b
uckling
B
D film
u
rvature
s
almost
h
ick BD
n
g stress