In
d
o
n
e
sian
Jou
r
n
al of
Ele
c
tr
i
c
a
l
En
g
in
e
erin
g
a
n
d
C
om
pu
t
er S
c
ien
ce
Vol.
14, No.
1, April 2019,
pp.
284~289
ISSN: 2502-
4752,
DOI
:
10.115
91/ijeecs.
v
14.
i
1
.
pp284-289
284
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/
i
j
eec
s
Calculatin
g of stress intensity
factors of sol
d
ered join
t
s with
multip
le crack
s
A
l
Emr
an
Ismai
l,
K
am
aru
l
A
zh
ar
Kamar
u
d
in
, M
o
hd
Kh
i
r
Moh
d
N
o
r, A
h
m
ad
M
ub
ara
k
T
aju
l
A
r
i
fin
,
Mohd Fah
r
u
l
Has
s
a
n
, M
oh
d
Rasidi Ib
r
ah
i
m
and M
o
h
a
mmad
Z
ulafif Ra
him
Facu
lt
y of M
echan
ical
a
nd
Man
u
f
act
urin
g
Eng
i
n
e
erin
g, U
ni
versiti
T
u
n
Hu
sse
i
n
On
n Ma
la
ys
ia
,
Ma
l
a
ysia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
2
6
,
2
018
Re
vise
d N
ov
27,
201
8
A
c
c
e
pte
d
D
ec 3,
201
8
Th
is
p
aper
p
res
e
nt
s
th
e
s
o
l
u
t
i
on
o
f
st
ress
i
n
t
ensity
f
actors
o
f
m
u
l
tip
l
e
cracks
at
t
he
j
o
i
nt
b
e
t
ween
t
wo
m
ateria
l
s
.
Bas
e
d
o
n
t
he
l
iterat
ure
s
u
r
vey,
t
here
a
re
trem
en
dou
s
nu
mber
o
f
wo
rks
f
o
u
n
d
on
t
he
s
t
u
d
y
o
f
edg
e
a
n
d
cent
r
al
c
racks
.
On
t
h
e
o
ther han
d, several
p
ap
er
s
o
n
the m
ultip
l
e
crac
k
s
can
b
e
a
ls
o
b
e
f
o
und
in
o
pen
li
terat
u
re.
Ho
wever,
t
h
e
w
ork
on
m
u
l
ti
p
l
e
cr
ack
s
w
i
t
h
d
iff
e
ren
t
c
rack
si
zes
a
re
h
ard
to
f
i
n
d
.
T
heref
o
re,
t
h
is
p
ap
er
f
o
c
us
es
t
o
stu
d
y
t
h
e
crack
in
teracti
o
n
obtained
f
r
o
m
d
iff
e
ren
t
c
rack
s
izes.
ANS
YS
A
PDL
is
us
e
d
t
o
mo
de
l
a
n
d
so
lv
e
th
e
p
r
ob
le
m
s
c
o
n
side
ring
t
he
c
ra
c
k
s
e
m
be
d
d
e
d
in
t
h
e
p
l
a
i
n
st
rain
p
l
a
te
u
nder
tension
stress.
T
he
re
a
re
t
w
o
i
mpor
t
a
nt
p
ar
a
m
e
ters
a
re
con
s
i
d
ered
s
u
c
h
crack
s
izes
a
nd
m
echan
ical
m
ism
a
tches
b
e
tween
j
oi
n
t
a
nd
bas
e
d
m
a
t
e
rial
s
.
S
in
ce
th
e
crack
i
s
s
y
m
m
e
t
r
ical,
only
a
qu
arter
m
odel
i
s
u
sed
and
verifi
ed.
Ba
s
e
d
on
t
he
n
u
m
e
r
ical
s
imu
l
a
t
io
n
,
it
is
f
ou
nd
t
h
a
t
t
w
o
f
a
c
t
o
r
s
are
signifi
cantly
a
f
f
ected
t
he
m
u
ltiple
c
racks
at
t
he
j
oi
n
t
s
su
c
h
a
s
m
ech
ani
c
al
m
i
s
m
a
t
ches
and
relat
iv
e crack s
iz
es
.
K
eyw
ord
s
:
ANSYS
A
P
D
L
C
r
ack
i
nt
e
r
ac
t
i
ons
Mu
lt
ip
l
e
c
rac
k
s
So
ld
er
jo
i
nts
Stress
i
nt
e
n
sity factors
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
Scien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Al Em
r
an Ism
a
il,
D
e
pa
rtme
nt
o
f
En
gine
eri
ng
M
e
c
h
an
ics,
Fac
u
l
t
y
of
M
ech
a
n
i
c
a
l
a
nd
M
an
uf
a
c
t
u
ri
ng
En
g
i
n
ee
rin
g
,
U
n
i
v
ersi
ti
T
un
H
u
ssei
n
O
nn
Ma
lays
ia,
86
4
00
Bat
u
P
a
h
at,
Joh
o
r,
M
al
ay
si
a.
Em
ail:
em
ran@u
t
hm
.edu.
my
/
al_e
m
ra
n
@
ho
t
m
ai
l.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
M
o
st
o
f
el
e
c
t
r
o
n
i
c
d
evi
c
e
s
e
x
p
e
ri
e
n
ced
t
h
e
rmo
-
mec
h
a
n
i
cal
f
at
igu
e
dur
i
ng
se
rv
ices.
Sol
d
er
ed
j
o
i
nt
s
are
used
t
o
co
nne
c
t
d
iffe
rent
e
lec
t
ron
i
c
parts
a
nd
t
h
ere
f
ore
pr
o
v
i
d
e
d
t
he
w
ay
t
o
trans
f
e
r
e
lectric
a
l
c
u
r
rents.
D
u
e
to
t
he
i
m
p
erfect
i
on
of
j
oi
n
t
s,
c
ra
cks
ma
y
appea
r
ed
e
spe
c
i
al
ly
a
t
t
h
e
i
n
terfa
c
e
b
e
t
w
e
e
n
tw
o
ma
t
e
ria
l
s.
In
g
e
n
e
r
al
,
th
e
co
n
c
e
p
t
of
L
in
e
a
r
El
asti
c
Fra
c
t
u
re
M
ech
ani
c
s
(L
EF
M)
i
s
use
d
t
o
cha
r
ac
te
rize
s
uc
h
c
r
ac
ks
i
n
order
to
d
e
t
er
mine
t
he
r
e
l
i
a
b
i
l
i
t
y
o
f
t
he
j
o
i
n
t
s.
F
or
e
xa
mpl
e
H
ua
n
g
e
t
a
l
.
[1]
pro
v
i
ded
a
ge
nera
l
m
e
th
o
d
o
l
og
y
for
ca
l
c
ul
a
t
i
n
g
m
i
xed
mode
s
tress
i
n
te
ns
i
t
y
fac
t
or
o
f
i
n
t
e
rfa
c
i
a
l
c
rac
k
s.
I
n
t
h
i
s
w
ork,
onl
y
a
sin
g
le
c
r
ack
i
s
foc
u
se
d
c
onsi
d
er
i
n
g
s
i
n
g
l
e-
ed
ge
c
r
ack
i
n
p
l
ain
stra
in
c
on
d
i
t
i
on
.
Tsa
i
[
2]
p
e
r
form
ed
a
s
t
udy
o
n
t
he
m
o
d
e
I
ene
r
g
y
r
elease
r
a
te
o
f
sol
d
er
ed
j
o
i
n
t
s
c
o
n
t
a
i
n
i
ng
a
s
i
n
g
l
e
cra
c
k
u
s
in
g
fi
n
i
te
e
lem
e
nt
a
nal
y
s
i
s
c
o
ns
i
d
er
i
n
g
a
me
tho
d
o
f
v
i
rt
ual
cra
c
k
c
l
o
s
u
r
e.
I
t
is
o
nl
y
c
o
ns
i
d
e
r
ed
a
s
in
gle
c
r
a
c
k
b
e
t
w
e
e
n
t
w
o
p
a
r
t
s
.
Anoth
e
r
s
i
m
i
lar
work
ca
n
be
f
o
u
n
d
i
n
[3].
F
unda
m
e
ntal
w
ork
on
t
h
e
i
n
ter
f
a
c
i
a
l
c
rac
k
s
b
e
t
w
e
e
n
t
w
o
d
i
s
s
i
m
i
l
a
r
m
a
t
e
r
i
a
l
s
a
r
e
ava
ila
b
l
e
i
n
[
4
-
7].
M
o
st
o
f
t
h
ese
paper
s
d
isc
u
sse
d
o
n
t
he
e
ffec
t
o
f
d
i
s
s
i
milar
m
a
teria
l
s
o
n
t
he
s
i
n
g
l
e
c
r
ac
k.
It is ha
rd to
find
the w
o
r
k
s o
n
th
e
multipl
e
cracks
or crack in
tera
c
t
i
o
n
s
i
n
di
ffe
re
nt m
ater
ial be
ha
v
i
or
.
C
o
m
n
i
n
ou
[8]
pr
o
v
i
d
e
d
a
n
ov
erview
w
or
k
o
n
t
he
i
n
t
er
fac
i
a
l
c
rac
k
s
b
e
tw
e
e
n
tw
o
d
i
ffe
r
ent
m
a
ter
i
a
l
s
con
s
i
d
eri
ng
t
h
e
LEF
M
.
A
t
k
i
n
so
ns’
f
i
r
s
t
a
n
d
sec
o
n
d
m
o
d
e
l
s
a
re
a
p
p
l
ie
d
in
a
na
l
y
zi
n
g
t
he
i
n
t
e
r
fa
c
i
al
c
ra
cks.
In
t
h
i
s
w
o
rk,
onl
y
a
sin
g
l
e
cra
c
k
i
s
c
on
si
dere
d.
T
he
re
a
re
s
e
v
e
ral
wo
rk
s
f
oun
d
i
n
d
is
cu
ssi
ng
th
e
r
o
l
e
o
f
mu
l
tip
l
e
i
nt
e
r
fa
ci
al
c
rac
k
s
for
an
e
xam
p
l
e
M
o
n
f
a
r
ed
e
t
al.
[9]
s
t
udi
e
d
o
n
th
e
di
ssi
m
i
l
ar
m
at
e
r
i
a
ls
w
it
h
mult
i
p
le
c
rac
k
s.
I
t
is
pos
i
t
i
one
d e
x
ac
tl
y be
t
w
een
t
w
o
m
ateri
a
ls
w
here
the
c
ra
ck ge
o
me
t
r
y
is i
den
t
ical.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Ca
l
c
ul
ati
n
g
of
st
re
ss int
e
nsit
y
f
a
c
t
o
rs of
solde
r
e
d
j
o
int
s
w
i
th
mu
lt
ipl
e
cr
a
c
k
s
(Al
Emra
n
I
s
ma
il
)
28
5
O
n
t
he
o
t
h
er
h
a
nd,
B
id
o
k
h
ti
a
nd
S
h
a
h
an
i
[10]
a
ls
o
stu
d
ie
d
the
m
ul
ti
p
l
e
cr
acks
howe
v
e
r
t
he
c
r
acks
are
non-a
l
i
gne
d.
M
eanw
h
i
l
e,
W
e
n
e
t
a
l
.
[1
1]
a
lso
s
t
u
d
i
ed
t
he
m
u
l
t
iple
s
urfa
ce
c
r
ac
ks
u
n
d
er
f
at
i
gue
l
oad
i
ng.
In
t
his
w
o
r
k
,
cra
c
ks
a
re
c
o-p
l
ana
r
w
i
t
h
bo
t
h
i
de
nti
c
a
l
a
n
d
non-
ide
n
tic
a
l
s
izes
o
f
thre
e-d
i
m
e
ns
io
na
l
m
o
del
s
.
The
re
su
lts
a
r
e
t
he
n
c
o
m
p
are
d
w
i
t
h
A
S
ME,
BS
79
1
0
,
A
P
I57
9
a
nd
G
B
/
T
1
9
6
24
c
o
de
s
o
f
s
ta
n
d
a
r
d.
T
he
n,
t
he
y
sug
g
es
t
e
d
a
ne
w
c
o
mb
ina
t
io
n
r
u
l
e
a
nd
c
o
n
c
l
ude
d
t
h
a
t
it
a
l
w
a
ys
y
ie
l
d
s
a
re
aso
n
ab
le
e
st
i
m
a
t
io
n
w
ith
n
e
c
e
ssary
c
o
nse
r
v
a
ti
sm
f
o
r
v
ariou
s
i
ni
t
i
a
l
c
ra
ck
d
ept
h
,
ma
t
e
ri
al
c
on
sta
n
t
a
nd
re
la
ti
v
e
s
i
z
es
o
f
tw
o
c
r
ac
ks.
Isma
i
l
[
1
2
]
in
ves
tiga
t
e
d
n
u
m
erica
lly
t
he
m
ult
i
pl
e
cr
ack in
t
e
r
ac
ti
on in
b
i-m
aterials p
l
a
te
u
n
d
e
r
m
ode
I
t
ens
i
o
n
.
T
w
o
pla
t
es
of
d
if
fere
n
t
m
ateria
l
s
a
re
p
e
r
fec
tly
b
onde
d
a
s
sum
i
ng
tha
t
t
her
e
i
s
n
o
c
hem
i
ca
l
rea
c
t
i
o
n
a
t
the
in
te
rface
.
Tw
o
cra
c
ks
a
re
posit
i
o
n
e
d
at
a
d
ista
nce
o
f
b
f
or
t
he
i
nterf
acia
l
bo
u
ndar
y
.
In
t
his
w
o
rk,
ide
n
tic
a
l
c
rac
k
l
e
n
gth
is
u
sed
to
s
t
u
d
y
t
he
c
rac
k
i
n
t
era
c
ti
ons
w
he
n
di
ffe
ren
t
m
echa
n
i
c
al
m
i
s
matc
h
i
s
u
sed
.
T
h
e
e
f
f
ect
o
f
me
cha
n
i
cal
mism
atch
c
a
n
a
l
s
o
be
f
ou
n
d
i
n
[1
3,
1
4].
A
z
l
a
n
a
nd
I
s
m
a
i
l
[
13]
s
t
u
d
i
e
d
t
he
i
nc
li
ned
cr
ack
i
n
b
i
-m
ater
i
a
l
pla
t
es
and
I
s
ma
il
[1
4]
e
xam
i
ne
d
t
h
e
c
r
ac
k
ec
ce
ntr
i
ci
t
y
a
t
differ
e
nt
d
i
sta
n
ce
m
e
a
sured
fro
m
t
he
i
nter
fac
i
a
l
l
i
n
e
.
H
o
w
e
ve
r,
bot
h
w
o
rks
foc
u
s
e
d
o
n
t
he
e
ffe
c
t
o
f
m
echa
n
ic
al
m
isma
t
c
h
on
the
s
i
ng
le
c
r
ack.
Based
on
the
lite
rat
u
re
f
o
u
n
d
a
bo
ve,
i
t
i
s
see
m
e
d
t
ha
t
t
h
e
st
udy
o
n
t
he
c
ra
c
k
i
n
tera
ct
i
o
n
w
h
en
t
he
c
r
ack
s
iz
es
a
r
e
u
n-
ide
n
ti
c
a
l a
r
e
hard
t
o
fi
n
d
.
The
r
ef
ore,
t
his
pa
per
n
u
m
e
ric
a
l
l
y
presen
t
s
t
he
r
ole
of
m
ul
t
i
p
l
e
c
rac
k
s
e
m
be
dde
d
a
t
t
he
j
o
i
nt.
There
are
t
w
o
c
r
ac
ks
o
f
u
n
-
i
d
e
ntica
l
c
rac
k
l
e
n
g
t
h
an
d
e
m
be
dde
d
at
t
he
j
o
i
nt
m
ate
r
ia
l.
A
NS
YS
f
i
n
i
t
e
el
em
ent
p
r
og
ram
i
s
a
p
p
li
ed
t
h
r
ou
gh
t
h
e
use
of
ANSYS
P
a
r
a
m
e
t
ri
c
D
e
si
gn
L
ang
u
a
g
e
(A
P
D
L).
T
w
o
importa
nt
p
a
ramet
e
rs
a
re
u
se
d
t
o
s
t
udy
t
h
e
c
r
a
c
k
i
n
t
e
ra
c
t
io
n
s
s
u
c
h
mec
h
a
n
i
c
a
l
p
roper
t
ie
s
mi
sm
atch
a
n
d
c
rac
k
l
en
g
t
h.
J-i
n
t
e
g
r
al
i
s
u
s
ed
t
o
ca
l
c
ul
at
e
t
h
e
c
r
a
c
k
d
riv
i
ng
f
o
r
ce
s
and
t
h
e
n
c
o
nver
t
i
n
t
o
s
t
ress
i
n
tens
i
t
y
fac
t
ors.
It is sel
e
cted
s
ince t
he
u
se of si
ng
u
l
a
r
e
lem
e
nt ar
o
un
d
t
h
e c
r
a
ck
t
ip
i
s u
n
n
ece
ssa
ry
.
2.
RESEARCH
M
ETH
O
D
I
n
t
h
i
s
w
o
r
k
,
thr
ee
m
u
l
t
i
p
le
c
rac
k
s
a
r
e
m
odelle
d
us
in
g
A
N
S
YS
A
P
D
L
f
in
ite
e
lem
e
nt
p
rogra
m
a
s
in
F
i
gure
1.
I
t
is
a
ssum
e
d
t
h
a
t
t
he
m
ode
l
fu
lfi
l
le
d
a
p
l
ai
n
strain
c
on
d
iti
on
a
nd
s
u
b
j
ec
t
e
d
to
a
xia
l
t
e
n
s
i
o
n
.
Since
the
m
o
d
e
l
is
s
ym
me
t
r
ical,
o
n
ly
a
q
ua
rter
m
odel
is
c
onsi
d
e
red
a
n
d
m
o
d
e
l
l
e
d
a
s
i
n
F
igure
2
w
h
er
e
t
h
e
v
e
rti
c
al
l
e
f
t
si
de
i
s
as
sign
e
d
a
s
a
sy
mmet
ri
ca
l
l
i
n
e
a
nd
o
n
the
o
t
h
e
r
h
a
n
d
t
h
e
b
o
t
t
o
m
l
i
n
e
i
s
a
l
s
o
a
s
s
i
g
n
e
d
a
s
a
symm
etrica
l si
de e
xce
p
t
the
c
r
ac
k fa
ces.
F
i
gure
3
s
h
ow
s
the
qua
rter
f
ini
t
e
e
l
e
m
e
n
t
m
ode
l
o
f
m
u
l
t
i
ple
cra
ck
u
n
d
er
t
e
n
sio
n
f
orc
e
.
It
i
s
m
e
shed
us
i
n
g
P
L
A
N
E
18
3
elem
en
t
ty
pe
a
ssumi
n
g
t
o
ful
f
il
l
the
p
l
a
i
n
strai
n
co
nd
i
t
i
on.
T
he
m
ode
l
is
c
ons
t
r
uc
te
d
using
ANSYS
P
arametric
De
si
g
n
L
ang
u
a
g
e
(AP
D
L).
I
n
t
h
i
s
w
o
rk,
J-
i
n
tegr
a
l
i
s use
d
a
s
a
cr
ack
d
riv
i
n
g
f
or
ce
bef
o
r
e
i
t
i
s
c
on
ve
rt
ed
i
nt
o
St
ress
I
nte
n
si
t
y
F
ac
to
r
(SI
F
)
a
s
i
n
(1
).
S
ince
J
-i
n
t
egr
a
l
i
s
u
sed,
it
i
s
not
r
eq
u
i
re
d
t
o
u
se
sing
u
l
ar
e
lem
e
nt
s
a
r
ou
n
d
t
he
c
rac
k
t
ip.
F
i
g
u
r
e
4
s
how
s
th
e
defo
r
m
e
d
p
l
a
t
e
c
o
n
t
a
i
n
e
d
m
u
l
t
i
p
l
e
c
r
a
c
k
s
u
n
d
e
r
ten
s
ile
f
orc
e
.
In
o
rde
r
t
o
stud
y
t
h
e
effect
o
f
d
i
ss
imilar
ma
t
e
r
ials,
th
e
fac
t
or
o
f
m
e
c
h
an
ica
l
m
is
ma
t
c
h,
e
is use
d
as in (
2). Thre
e
va
l
u
e
s
o
f e ar
e
use
d
s
uch a
s
1
,
5
and
1
0.
I
n
t
h
is w
ork,
t
he he
i
g
h
t
ra
tio of j
o
i
n
t is ke
p
t
c
o
nst
a
nt
wh
e
re
h/
W
= 0.
02
an
d
Tab
l
e 1
summ
ar
i
z
ed the
cr
ack
p
ara
m
e
t
ers use
d
.
2
1
J
E
K
v
(1)
wher
e,
J
i
s
t
h
e
va
l
u
e
of
J
-
i
nte
g
r
a
l,
K
i
s
a
stre
ss
in
tens
i
t
y
f
ac
tor
,
E
i
s
a
m
o
d
u
l
u
s
o
f
e
l
a
s
t
i
c
i
t
y
a
n
d
v
i
s
a
Poiss
on’s ra
tio
.
1
2
E
e
E
(2)
wher
e,
e
i
s
a
mi
s
m
a
t
c
h
f
acto
r
,
E
1
i
s
a
m
o
d
u
l
u
s of
e
las
tic
it
y for
p
l
a
t
e
m
a
te
r
i
al
a
n
d
E
2
is
a
m
odu
lus of
e
la
st
i
c
it
y
for
so
l
d
er
ed
m
ater
i
a
l.
B
efo
r
e
a
n
y
further
anal
ys
is,
it
is
i
m
por
ta
n
t
t
o
val
i
d
at
e
t
h
e
pr
ese
n
t
m
ode
l
w
i
t
h
t
he
exi
s
ti
ng
s
olu
t
i
ons.
It
i
s
har
d
t
o
fi
n
d
t
he
m
u
l
t
i
p
l
e
c
r
ac
ks
i
n
d
issimi
lar
or
s
ol
der
jo
i
n
ts.
T
h
en,
it
i
s
assumed
that
the
so
l
u
t
i
o
n
o
bt
a
i
ne
d
fr
om
h
omoge
nou
s
p
l
a
t
e
a
n
d
si
ngle
cr
ack
(
L
an
e
t
al
.
[
7
]
and
Yan
&
Mi
ao
[
15
])
a
s
i
n
F
i
gure
s
5
a
nd
6.
I
t
is
obser
v
e
d
t
h
at
f
or
b
ot
h
type
o
f
cra
c
ks
(
d
o
u
b
l
e
e
d
g
e
a
nd
c
e
n
t
ral
cr
acks),
t
h
e
p
r
esent
cra
c
ks a
re w
ell
a
g
ree
d
w
ith t
h
e
e
xis
t
i
n
g sol
u
t
i
o
n
s a
n
d ve
rifi
ed
for the
f
urt
h
er
appl
ica
t
i
o
n
s
.
S
t
ress inte
ns
ity
f
ac
tors,
K
obta
i
ne
d fr
om
A
NS
YS
fi
n
i
t
e
ele
m
ent pr
o
g
ram
is n
orm
a
lize
d
as
fo
ll
o
w
:
K
F
a
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
250
2-
4
7
5
2
In
do
n
e
sia
n
J
Elec Eng
&
C
o
mp
S
ci,
Vo
l. 1
4
,
No
. 1
,
Ap
r
i
l
2
0
1
9
:
284
–
2
8
9
28
6
wh
ere,
F
i
s
a
nor
m
a
l
i
zed
S
I
F
o
r
geom
etr
i
c
a
l
c
or
r
ecti
on
f
a
c
t
or
s,
K
i
s
t
h
e
S
I
F
,
i
s
the
applied
stress
and
a
is
the
cr
ack len
g
t
h
.
I
n
or
der
to
s
tu
d
y
t
he
i
nt
e
r
a
c
t
i
o
n
am
on
g
t
h
e
c
r
a
cks,
a
n
inte
r
a
c
t
ion
fa
c
t
or
,
is
t
h
e
n
i
n
t
r
o
d
u
c
e
d
as
b
e
l
o
w
:
cen
t
r
al
c
rack
ed
g
e
c
rack
F
F
(4
)
wh
ere
F
centr
al_crack
a
nd
F
edge_c
rack
are
th
e
n
o
r
malized
SIFs
o
btain
e
d
f
r
o
m
c
en
t
r
al
c
rack
(
crack
l
e
ng
th,
a
1
)
an
d
ed
g
e
cra
ck
(cra
c
k
l
e
ngt
h
,
a
2
),
r
esp
e
c
t
i
v
ely
.
F
i
gur
e 1.
Mu
l
t
i
ple
t
h
r
e
e
cr
ack
a
t the
s
o
lde
r
jo
i
n
t
F
i
gur
e
2.
Q
ua
r
t
er
m
ode
l
o
f
t
he
s
ol
d
e
r
j
o
i
n
t
w
i
th
mult
ipl
e
cr
acks
F
i
gur
e
3.
F
i
n
i
t
e
e
lem
e
nt
m
od
el
o
f
m
u
lt
ip
le
c
r
a
c
k
s
F
i
gur
e
4.
F
ini
t
e
ele
m
e
n
t
r
e
sul
t
s
of
m
ul
t
i
ple
c
r
acks
Table
1
.
S
u
m
m
a
ry
o
f Crack
P
a
ramet
e
rs
a
1
/
W a
2
/
W W
h
/
W a
1
a
2
0.
1
0.
1
50
1
5
5
0.
2
0.
1
50
1
1
0
5
0.
3
0.
1
50
1
1
5
5
0.
4
0.
1
50
1
2
0
5
0.
5
0.
1
50
1
2
5
5
0.
6
0.
1
50
1
3
0
5
0.
7
0.
1
50
1
3
5
5
0.
8
0.
1
50
1
4
0
5
*
N
ot
e:
Th
e
p
a
r
amet
er
a
2
/W
i
s
a
l
s
o
v
ar
ied
s
t
a
r
tin
g
fr
om
0
.
1
t
o
0.
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesia
n
J
Elec Eng
&
C
o
m
p
S
ci
ISSN:
2502-
4752
C
a
lc
u
l
a
tin
g of st
re
ss in
ten
s
i
t
y
fac
t
ors
o
f
so
l
d
ere
d
j
o
in
ts
w
ith mul
t
i
p
le crac
ks (Al
Emran Ismai
l
)
28
7
F
i
gur
e
5.
M
o
d
e
l
val
i
d
a
tio
n
of
dou
b
l
e
edge
c
r
ack
un
der
t
e
ns
ion
f
o
r
c
e
F
i
gur
e
6.
M
od
e
l
v
al
i
d
a
t
i
on
of
centr
a
l
c
r
ack
u
nder
tension
fo
rce
3.
RESULTS
A
ND
A
NAL
YS
IS
Th
i
s
s
e
c
t
i
o
n
i
s
d
i
v
i
d
ed
i
nt
o
tw
o
se
par
a
t
e
s
ec
tio
ns.
The
f
i
r
s
t
s
e
c
t
i
on
dea
l
s
w
ith
t
he
e
ff
ec
t
o
f
nor
m
a
l
i
ze
d
e
d
ge
c
r
ack
l
en
g
t
h,
a
2
/W
o
n
the
i
n
te
r
a
c
t
i
on
fac
t
o
r
,
.
The
secon
d
p
a
r
t
on
th
e
e
ffe
ct
o
f
me
chan
ic
a
l
mi
s
m
a
t
ch
,
e
on
t
h
e
in
tera
ct
ion
fac
t
or,
.
3
.
1
.
E
f
fect
o
f
No
rmali
z
ed
Edg
e
Cra
c
k
L
e
ng
th,
a
2/
W
o
n
the I
nter
a
c
tion
F
a
c
to
r,
.
F
i
gur
e
7
sh
ow
s
the
r
o
l
e
s
of
n
or
m
a
lize
d
c
en
t
r
a
l
c
r
a
c
k
l
e
n
g
t
h,
a
1
/W
on
t
h
e
in
ter
a
ct
i
on
fac
t
or
,
w
h
e
n
m
e
c
h
a
n
i
c
a
l
m
i
s
m
a
t
c
h
i
s
k
e
p
t
a
s
a
c
o
n
s
t
a
n
t
p
a
r
a
m
e
t
e
r
.
A
s
s
h
o
w
n
i
n
(
4
)
,
t
he
f
act
or
o
f
cr
a
c
k
i
n
t
e
r
a
c
t
i
o
n
is
d
e
fin
e
d
as
t
h
e
r
atio
b
etween
SIFs
o
f
central
c
r
a
ck
s
ov
er
t
h
e
e
d
ge
c
r
acks.
H
ig
her
t
h
e
in
t
e
r
a
c
t
i
on
f
a
c
t
or
in
d
i
cat
i
n
g
t
h
at
t
he
SIF
s
of
centra
l
c
r
acks
a
r
e
hig
h
er
t
ha
n
the
S
I
F
s
f
or
e
dge
c
r
a
ck
s.
I
t
is
o
bser
v
e
d
t
h
at
a
s
i
n
F
i
gur
e
7,
i
nt
e
r
ac
tio
n
fac
t
or
s
inc
r
ea
sed
a
s
t
he
f
u
n
c
t
i
on
of
t
he
l
e
ng
th
o
f
cen
t
r
al
c
ra
c
k
s.
M
an
y
re
se
arc
h
w
o
r
k
s
ha
v
e
r
ep
or
ted
sim
i
l
a
r
r
e
sul
t
s
a
nd
c
a
n
be
f
oun
d
in
[
7-
1
4
]
.
(a
)
(b
)
Fi
g
u
re
7
.
E
f
f
e
ct
o
f
n
o
r
m
al
i
zed
e
d
g
e
c
r
a
c
k
l
e
n
g
t
h
,
a
1
/W
on
th
e SIF
s
w
hen
differ
en
t m
e
c
h
an
ical
m
ism
a
tc
he
s,
e
are
v
a
ried
,
(a)
e
= 1
.
0
,
(b
)
e
=
5.
0
a
nd
(
c
)
e
= 1
0
.
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
250
2-
4
7
5
2
In
do
n
e
sia
n
J
Elec Eng
&
C
o
mp
S
ci,
Vo
l. 1
4
,
No
. 1
,
Ap
r
i
l
2
0
1
9
:
284
–
2
8
9
28
8
O
n
t
he
o
t
h
er
w
hen
t
h
e
n
o
r
m
alize
d
e
d
g
e
cr
a
c
ks
i
ncr
e
ased
t
he
i
nte
r
a
c
t
i
o
n
fa
ct
ors
ar
e
a
l
s
o
d
e
c
re
ased.
Th
is
i
s
d
u
e
t
o
t
he
f
ac
t
th
at
f
or
t
he
c
ase
of
E
1
> E
2
,
the
r
e
sis
t
ance
o
f
jo
i
n
t
is
l
ow
er
t
ha
n
th
e
up
per
an
d
b
o
t
t
o
m
p
l
at
e
s
.
Th
is
c
o
ndi
tio
n
cre
a
te
d
a
l
a
rg
e
jo
i
n
t
d
e
f
o
rmat
i
on
a
n
d
t
h
e
r
ef
or
e
pr
o
duc
i
n
g
hi
gher
va
lue
s
o
f
S
I
F
s
.
In
c
o
m
p
a
riso
n
th
ese
S
IFs
a
re
h
ig
h
e
r
th
an
t
h
e
SIF
s
wh
en
E
1
< E
2
.
F
i
gures
7
(a)
-
7(c
)
r
eve
a
l
the
in
te
r
acti
o
n
fa
ct
ors for d
i
f
f
ere
n
t val
u
es of me
chan
ica
l
m
ism
a
tc
h
,
e
=
1
.
0
,
5.
0 and
10.
0,
r
espe
ct
iv
e
l
y
.
I
t
is obser
ved t
h
at th
e
m
e
c
h
ani
cal
m
i
s
m
a
t
c
h
p
l
a
y
e
d
a
n
imp
o
r
t
a
n
t
r
o
l
e
i
n
de
ter
m
inin
g
the
i
nt
era
c
t
i
on
f
ac
to
rs
e
s
p
eci
a
lly
f
o
r
t
h
e
c
a
s
e
of
a
2
/W
= 0.
1
a
nd 0.2
where
i
n
cr
easi
ng t
h
e
mism
atch
v
a
l
u
e
s c
a
pab
l
e
to
re
duce
t
h
e i
n
tera
cti
o
n fa
ct
ors.
3.
2.
E
f
f
ect
o
f
M
ech
an
ical
M
ism
a
t
c
h
,
e
o
n
t
h
e
In
t
era
ction Fa
cto
r
,
.
Figure
8
sh
ow
s
t
h
e
e
f
fe
ct
o
f
me
chani
c
a
l
m
i
s
ma
t
c
hes,
e
on
th
e
in
t
e
ra
c
t
i
on
f
act
o
r
,
w
h
e
n
no
rma
l
i
z
e
d
e
d
g
e
c
r
acks,
a
2
/
W
a
r
e
v
ar
ie
d.
I
n
gener
a
l
,
w
he
n
the
v
a
lue
o
f
m
ech
a
n
i
c
a
l
m
i
s
m
a
t
c
h
inc
r
ea
se
d,
t
her
e
i
s
in
sig
n
i
f
ic
a
n
t
e
f
fec
t
o
n t
h
e in
t
e
rac
tion
fac
t
or
s espe
c
i
al
ly whe
n
h
i
ghe
r
va
l
u
e of
a
2
/W
is
u
s
ed.
On
t
h
e
o
th
er h
and
,
low
e
r
in
te
r
a
c
t
i
on
fa
c
t
or
s
ca
n
be
o
bser
ve
d
w
h
en
l
on
ger
e
d
g
e
c
r
a
c
ks
a
r
e
i
n
t
r
o
duce
d
.
Th
is
i
s
in
d
i
ca
te
d
th
a
t
t
he
in
ter
a
ct
ion
f
a
c
t
or
i
s
s
i
gn
i
f
ic
a
n
t
l
y
r
e
late
d
to
t
he
r
ela
t
i
v
e
l
e
n
g
t
h
be
twee
n
t
w
o
in
ter
acte
d
c
rac
k
s.
F
igu
r
e
6(a)
show
s
t
h
e
be
h
a
vi
or
o
f
i
n
te
r
a
c
t
i
o
n
fac
t
or
f
o
r
t
he
c
ase
of
a
2
/W
=
0
.
1
w
h
e
r
e
b
o
t
h
c
r
a
c
k
s
a
r
e
s
i
m
i
l
a
r
i
n
s
i
z
e
.
Wh
e
n
bot
h
cr
a
c
ks
a
r
e
i
de
nt
i
c
al,
t
h
e
ef
fec
t
o
f
m
e
c
h
an
ica
l
m
i
s
m
a
t
ch
o
n
t
h
e
cr
ack
i
ntera
c
t
io
n
is
o
b
v
i
o
u
s
w
here
it i
s
dec
re
ased
w
hen t
h
e
m
i
sm
atch
f
ac
tor
is de
c
re
ased.
(a
)
(b
)
(c
)
Fi
g
u
re
8
.
E
f
f
e
ct
o
f
m
e
c
h
a
n
i
c
al
m
i
s
ma
t
c
h
e
s
,
e
on
t
h
e
i
n
ter
a
cti
on
fa
ct
or
,
f
or
d
iff
e
r
e
n
t
n
or
ma
li
z
e
d
e
dge
c
r
a
ck,
(a)
a
2
/W
=
0.
1,
(
b)
a
2
/W
=
0.
2
a
nd
(
c
)
a
2
/W
=
0
.
3
4.
CONCLUSION
B
a
se
d
on
the
n
u
m
e
r
i
ca
l
simu
l
a
ti
o
n
s,
s
e
v
er
a
l
m
a
i
n
conc
lus
i
o
n
s
ca
n
be
l
ist
e
d
as
b
e
l
ow
:
a)
I
t
i
s
obse
r
ve
d
i
n
g
ene
r
a
l
t
ha
t
the
in
ter
a
ct
i
o
n
f
a
ctor
r
educe
d
w
hen
t
h
e
m
e
c
h
anica
l
m
ism
a
tc
h
i
s
i
nc
r
e
a
s
ed.
b)
I
t
i
s
a
l
so
o
bse
r
ve
d
t
h
at
t
he
i
nte
r
ac
t
i
o
n
f
ac
tor
c
o
nv
er
ge
d
i
n
t
o
a
s
i
ngl
e
va
l
u
e
wh
en
t
h
e
a
2
/W
i
s
g
r
e
a
t
e
r
th
an
0
.3
.
ACKNOWLEDGE
ME
N
T
S
Author
s
ac
k
now
l
e
d
g
e
U
n
i
v
er
siti
T
u
n
H
usse
i
n
O
n
n
M
a
l
ays
i
a
(UTHM)
an
d
K
e
m
e
nter
ian
P
e
nga
j
i
a
n
Ti
ng
g
i
(
K
P
T)
f
or
f
i
n
a
n
c
i
a
l
l
y
s
po
ns
or
i
n
g
t
h
is
w
or
k
thr
o
u
g
h
the
F
un
d
a
me
nta
l
R
es
ea
rch
G
r
a
n
t
Sc
h
e
me
(
F
R
GS)
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Ca
l
c
ul
ati
n
g
of
st
re
ss int
e
nsit
y
f
a
c
t
o
rs of
solde
r
e
d
j
o
int
s
w
i
th
mu
lt
ipl
e
cr
a
c
k
s
(Al
Emra
n
I
s
ma
il
)
28
9
vo
t. 15
92.
REFE
RENCES
[1]
Z.
H
u
a
ng,
P
.
K
u
m
a
r,
I
.
D
u
tta,
J
.
H
.
L
P
a
n
g
a
nd
R.
S
i
dhu
,
“A
g
ener
al
m
e
t
ho
do
lo
gy
f
o
r
cal
cul
a
tin
g
m
i
x
e
d
m
o
de
s
tre
s
s
intens
ity
f
actors
and
f
r
acture
t
o
u
g
hness
of
s
ol
der
joints
w
it
h
i
n
terf
aci
al
c
racks
”
,
Eng
i
n
eerin
g F
r
ac
t
u
r
e
M
echa
n
i
c
s
,
vo
l.
131
,
p
p
.
9-25,
2
01
4.
[2]
G
.
C
,
T
s
a
i
,
“
P
a
r
a
m
t
e
r
i
c
s
t
u
d
y
o
f
m
o
d
e
I
e
n
e
r
g
y
r
e
l
e
a
s
e
r
a
t
e
o
f
s
old
e
red
joi
n
ts”,
Fi
n
ite E
l
emen
ts
i
n
A
nalys
is
an
d
Des
i
gn
,
v
o
l
.
3
8,
pp.
6
7
1
-6
89,
2002
.
[3]
M
.
O
A
l
a
m
,
H
.
L
u
,
C
.
B
a
i
l
e
y
a
n
d
Y
.
C
C
h
a
n
,
“
F
i
n
i
t
e
-
e
l
e
m
e
n
t
s
i
m
u
l
a
t
i
on
o
f
stress
i
ntens
ity
f
act
ors
in
s
older
joi
n
t
inter
m
etalli
c co
mpound”,
IEEE
T
r
ans
actio
n
o
n
D
evice a
n
d
M
a
ter
i
als Reli
ab
ilit
y
, v
o
l
. 9
,
p
p
. 4
0-4
8
, 2
00
9.
[4]
D.
S
utul
a,
P
.
Kerf
rid
e
n,
T
.
van
Dam
and
S
.
P
.
A
Bo
rdas
,
“M
i
n
i
m
um
e
n
ergy
m
u
l
t
i
ple
cra
c
k
prop
agat
ion
.
Part 1
:
T
h
eory
and
stat
e
o
f
t
h
e
art
revi
ew”,
E
ngineerin
g F
r
actu
re
M
echan
ics,
v
o
l
.
191
,
p
p.
205
-224,
2
0
18.
[5]
J.R
Ri
ce,
“
El
as
tic
f
ractu
r
e
m
ech
anics
con
cepts
f
or
i
n
t
erf
aci
al
cracks
”
,
Jou
r
n
a
l
of A
ppli
e
d M
e
ch
an
ics
,
v
o
l
.
5
5
,
pp
.
9
8-10
3,
1
9
8
8
.
[6]
C.
H
w
u
a
n
d
T
.
L
K
u
o
,
“
A
unif
i
ed
d
e
f
i
n
iti
on
f
o
r
s
t
ress
i
n
t
e
nsity
f
acto
r
s
of
i
nterf
ace
corn
ers
an
d
crack
s
”
,
In
te
rn
at
io
na
l J
o
urna
l o
f
S
o
l
i
d
s
a
n
d
St
ru
c
t
ure
s
,
vol
.
44
,
p
p
.
63
40-6
3
5
9
,
200
7.
[7]
X.
L
an,
N.A
N
o
da,
K.
M
ithin
ak
a,
Y
.
Z
h
an
g,
“
The
eff
ect
o
f
materi
al
c
om
binations
a
nd
r
elativ
e
crack
s
ize
t
o
t
he
st
ress
intensit
y
f
act
ors
a
t
t
he
c
rack
o
f
a
b
i
-m
ateri
a
l
b
o
n
d
ed
s
trip”,
En
gin
eeri
n
g
Fr
acture M
echa
n
i
c
s
,
vo
l.
7
8,
pp
.
2
572
-25
8
4
, 2
011
.
[8]
M
. Comnin
o
u
,
“An
ov
e
rvi
e
w of in
t
erf
ace cracks
”
,
E
ngineer
in
g F
r
a
c
tur
e
M
ech
an
ics
,
vol.
37,
pp.
1
9
7
-208
,
1
99
0.
[9]
M.M
.
M
on
fa
re
d
,
M
.
Ay
a
t
o
lla
hi,
R.
B
a
g
he
ri,
“In
-
pla
n
e
stre
s
s
a
n
a
l
ysis
o
f
d
i
s
s
imil
a
r
m
ateri
a
ls
w
i
t
h
mult
i
p
l
e
i
n
t
erf
ace
cracks
”
,
Applied Mathema
t
ical
M
odell
i
n
g
,
v
o
l.
40
,
p
p.
8
46
4-8
4
7
4
,
2
01
6.
[10]
A.A.
B
i
dok
h
ti,
A
.R.
S
h
ahan
i,
“
In
teracti
o
n
analy
s
i
s
o
f
no
n-ali
g
n
ed
c
ra
cks
us
in
g
ex
tend
ed
f
i
n
ite
el
emen
t
m
e
t
h
o
d
”,
Latin Amer
ican
J
o
urnal
o
f
So
lid
s an
d S
t
ruc
t
ure
s
,
v
o
l
.
12,
pp.
2
439-24
59
,
2
015
.
[11]
J
-
F
.
W
e
n
,
Y
.
Z
h
a
n
,
S
-
T
.
T
u
,
F
-
Z
.
X
u
a
n
,
“
A
c
o
m
b
i
n
a
t
i
o
n
r
u
l
e
f
o
r
mu
ltip
le
s
urface
cra
c
ks
b
as
e
d
o
n
f
a
ti
gu
e
cra
c
k
gro
w
th
lif
e”,
AI
MS Ma
te
ria
l
s
S
c
ie
nc
e
s
,
v
o
l
. 3
, pp
. 16
4
9
-
16
6
4
,
20
16
.
[12]
A
.
E
.
I
s
m
a
i
l
,
“
M
u
l
t
i
p
l
e
c
r
a
c
k
i
n
t
eracti
on
in
b
i
-
material
p
lates
under
m
ode
I
t
en
s
i
on
lo
adin
g”,
Ap
pl
ied M
echa
n
i
c
s
an
d M
a
t
e
ria
l
s
,
vol
.
6
29,
p
p
.
5
7-6
1
,
2
01
4.
[13]
M
.
A
.
A
z
l
an
,
A
.
E.
I
s
m
a
il,
“
Eff
e
ct
o
f
m
echani
cal
m
i
s
m
a
tch
on
t
he
st
re
s
s
i
n
t
ens
i
t
y
f
acto
r
s
of
i
n
c
l
i
n
e
d
crack
s
un
de
r
m
o
d
e
I
ten
si
on lo
adi
ng”,
App
lie
d
Me
c
h
an
ic
s
an
d
Ma
te
ria
l
s
,
vol.
7
7
3
-
77
4,
pp.
1
2
9
-1
33,
2
0
1
5
.
[14]
A.E.
I
sm
ail,
“
S
t
res
s
i
nt
ensity
f
act
ors
of
eccen
tric
c
rack
s
i
n
b
i-m
a
t
e
rials
p
l
at
e
un
der
m
o
de
I
l
oad
i
n
g
”,
AIP Con
f
eren
ce
Pr
ocee
d
i
ng
s,
v
o
l
.
166
0,
0
7
002
9,
20
1
5
.
[15]
X.
Y
an,
C.
M
ia
o
,
“
In
teract
io
n
o
f
m
ulti
pl
e
crack
s
in
a
r
ect
angu
l
a
r
p
l
a
te”,
Ap
p
l
ie
d Ma
th
e
m
a
tic
s
Mo
de
ll
in
g
,
vol.
36,
pp
.
5
727
-57
4
0
.
BIOGRA
P
HY OF A
U
THOR
D
r
.
Al
E
mran
I
s
m
ail
i
s
a
n
as
soci
ate
p
r
of
es
sor
in
t
h
e
f
acul
t
y
of
m
ech
ani
c
al
a
n
d
m
anu
f
actu
r
ing
en
gin
eerin
g,
U
niv
e
rsiti
T
un
H
u
s
s
ei
n
On
n
M
a
lay
s
i
a
(
U
T
HM
).
H
is
f
o
cus
areas
a
re
f
ractu
r
e
m
echan
ics
,
f
i
n
ite
e
lem
e
nt
a
n
a
ly
s
i
s
and
cras
h
w
o
r
th
i
n
es
s.
F
or
m
or
e
det
a
il,
pleas
e
v
i
si
t:
h
t
t
p
s://
comm
un
it
y.
uthm
.
e
du
.m
y/em
ran
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