TELKOM
NIKA
, Vol.12, No
.3, Septembe
r 2014, pp. 5
89~596
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i3.107
589
Re
cei
v
ed Ma
rch 5, 2
014;
Re
vised
Ma
y 26, 2014; Accepted June 1
5
, 2014
Strain Transfer and Test Research of Stick-up Fiber
Bragg Grating Sensors
Wang Bing*
1
,
Wang Xiaoli
2
Huai
ha
i Institute Of
T
e
chnolo
g
y
, L
i
an
yu
n
gan
g, Chin
a
Mecha
n
ica
l
En
gin
eeri
ng Sch
o
o
l
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hrb
w
b
200
1@
163.com
,
w
a
n
g
x
i
aol
i-dr
eam@
163.com
A
b
st
r
a
ct
Becaus
e
of the
flaw
s of fi
ber
Bragg
grati
ng,
nee
ds
to
set
u
p
pr
otective
lay
e
r b
e
tw
een th
e
structur
e
and fib
e
r lay
e
r
to protect the fiber grati
ng. F
i
rstly
the strain transferri
ng
rules of the
F
B
G sensors is
ana
ly
z
e
d, car
e
fully an
aly
z
e
th
e ma
in factors
influ
enci
ng the
fiber Bragg gr
ating strai
n
se
nsor transfer, an
d
ana
ly
z
e
c
oncr
e
tely
effect of
each
factor, th
e fib
e
r
Br
agg
gratin
g s
ensor
s e
m
b
e
d
ded
a
ngl
e d
e
vi
ation
i
s
ana
ly
z
e
d a
nd i
n
flue
nce o
n
the me
asur
ed re
sults. F
i
nally
, b
y
a series of repe
ated, coh
e
r
ent, dyna
mic a
n
d
fatigue ch
aract
e
ristic test, it is proved
that th
e F
B
G sensor has ap
pli
ed va
l
ue.
Ke
y
w
ords
:
fib
e
r Bragg gr
atin
g sensors, strai
n
transfer, ang
l
e
devi
a
tio
n
1. Introduc
tion
To opti
c
al fib
e
r Bragg g
r
a
t
ing optical fiber
g
r
atin
g sensor, its
ad
vantage i
s
th
at: the
measuri
ng si
gnal
s from th
e optical fib
e
r bendin
g
lo
ss, loss of
con
nectio
n
, the influen
ce of li
ght
sou
r
ce fluctu
ation and det
ector a
g
ing fa
ctors, to
avoid the phase measuri
ng interferomete
r
fuzzy
probl
em
s of fi
ber optic
sen
s
or;
In mo
re
than
se
rie
s
o
n
a
singl
e fibe
r Brag
g g
r
atin
g, the fibe
r
op
tic
embed
ded
st
ick (or to)
st
ructu
r
e
to
be
tested,
can
be
obtain
e
d
at the
sam
e
time,
seve
ral
measuri
ng ta
rget'
s
info
rm
ation, an
d
ca
n rea
lize
qua
si di
stri
buted
mea
s
u
r
em
e
n
t, for exa
m
ple
throug
h re
al-t
ime mea
s
u
r
e
m
ent of stre
ss, tempe
r
ature, vibration a
nd othe
r sen
s
or i
n
form
ation
[1].
Interface tra
n
s
missio
n
cha
r
acte
ri
stics of
optic
al fibe
r
sen
s
o
r
h
a
ves attra
c
ted
attention,
and
som
e
u
s
eful re
sult
s a
r
e o
b
taine
d
.
Senso
r
with
optical fib
e
r coating laye
r i
s
p
r
e
s
ente
d
[
5
],
the matrix structure, the matrix st
ru
cture
to the stress
of the fiber
optic se
nsor transitive rel
a
tion.
Analysis of th
e ela
s
tic mo
d
u
lus an
d thi
c
kne
s
s of
coat
ing laye
r'
s infl
uen
ce
on th
e
stress t
r
an
sf
er
and stress (concentratio
n
).
Explores the
claddi
ng [6
],
the cha
r
a
c
teri
stics of optical fiber se
nso
r
s
embed
ded
concrete
and
its impo
rtan
ce, and i
n
vie
w
of the
out
side l
oad
pa
rallel to the
fiber
dire
ction a
ppl
ied to con
c
ret
e
memb
ers, the cl
addin
g
o
f
fiber optic
sensor m
a
teria
l
prop
ertie
s
a
n
d
t
h
ick
n
e
ss
of
con
c
r
e
t
e
int
e
rnal st
re
ss co
nce
n
t
r
at
ion
chara
c
te
risti
c
s of some research a
r
e ma
de.
Fiber o
p
tic se
nso
r
test st
rai
n
and con
c
rete strai
n
relati
onship
s
wa
s
roug
hly got [7],also gives t
he
corre
s
p
ondin
g
optical fibe
r sen
s
in
g me
cha
n
ics
mod
e
l was give
n
[8], but not
con
s
id
erin
g the
influen
ce of t
he pa
ste laye
r thickn
ess, p
a
ckagi
ng ma
t
e
rial
s, not e
a
s
y to an
alyze
issue
s
of o
p
tical
fiber sen
s
o
r
encap
sulatio
n
, setting p
r
oce
s
s. The
optical fib
e
r
sen
s
in
g mod
e
l co
nsi
dere
d
the
influen
ce of paste
layer, but
did
not consi
der
lon
g
e
r fibe
r
affect the ge
omet
ric prope
rties of
sub
s
trate m
a
t
e
rial [9]. It did not discu
ss base
d
on th
e pra
c
tical ap
plicatio
n of grating, also
ca
n't
solv
e
ef
f
e
ct
s
su
ch
a
s
p
r
o
t
ect
i
v
e
lay
e
r,
en
cap
s
ulatio
n, adh
esive
s
,
etc.
Und
e
r
t
he con
d
ition of
material
and
middle laye
rs i
n
the el
a
s
tic
st
age [1
0], give improvement of t
he tran
smi
s
si
on
formula of st
rain [11], get more a
c
curate opt
ical fibe
r strain
sen
s
o
r
transfe
r form
ula.
2. Strain tran
sfer an
aly
s
is
2.1 Strain tra
n
sfer a
nal
ysi
s of fiber Brag
g grating
sen
s
ors
The ba
sic a
s
sumption
s
are stu
d
ied:
1) all materi
als (in
c
lu
din
g
the fiber core, the
stru
cture of t
he
coatin
g la
yer a
nd
su
bst
r
ate) a
r
e li
ne
ar
elasti
c m
a
terial, inte
rfa
c
e combin
ed
with
perfe
ct no rel
a
tive slip. 2) I
gnori
ng the di
fferences
bet
wee
n
the mat
e
rial p
r
op
erti
es of the opti
c
al
fiber co
re a
n
d
fiber co
re
cov
e
r, the fib
e
r co
re
can
be se
en a
s
a kind of gla
ss fibe
r whi
c
h is
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 58
9 – 596
590
comp
osed of
a single ma
terial. 3) Coa
t
ing layer co
mposed of a
polymer onl
y endure
sh
ear
stre
ss. 4
)
Ma
trix structu
r
e
endu
re
axial
norm
a
l
st
re
ss, parallel to
t
he o
p
tical
fib
e
r
co
ating l
a
yer
and the
opti
c
al fiber is
not
dire
ct force. 5
)
In t
he
midp
oint of opti
c
al
fiber
se
nsor,
sup
p
o
s
e o
p
tical
fiber, coatin
g layer and
sub
s
trate
stru
cture at the same
strain [12].
The o
p
tical
fibers first u
s
e
d
by fibe
r Bragg
gratin
g sensor and
ordinary co
mm
unication
optical
fib
e
r basi
c
same, all
are co
mp
ose
d
by
the
fiber core, the cla
dding
a
nd coating la
yers
form the rig
h
t total internal
reflectio
n
co
ndition limit light in the fiber core, the
waveg
u
ide o
p
tica
l
fiber for light tran
sfer its d
e
c
isive role [13
]
.
g
g
g
r
r
x
dx
d
)
,
(
2
(1)
On the middl
e tier take out
the period a
n
d
analyze:
dx
d
r
r
r
r
x
r
r
r
x
c
g
g
g
g
2
)
,
(
)
,
(
2
2
(2)
Put equation
(
2) into
(1),
dx
d
r
r
r
dx
d
r
r
r
x
p
g
g
g
2
2
)
,
(
2
2
2
(3)
Becau
s
e fibe
r radial defo
r
m
a
tion is sm
all, the Poisso
n effect can b
e
ignored (assu
m
ing
sum of the ci
rcumfe
rential
and ra
dial st
ress is zero
), then
)
(
2
2
2
)
,
(
2
2
2
2
2
2
2
dx
d
E
E
r
r
r
dx
d
r
r
E
dx
d
E
r
r
r
dx
d
E
r
r
r
x
c
g
c
g
g
g
g
g
c
c
g
g
g
g
(4)
Due to the op
tical fiber an
d
the middle tier defo
r
m tog
e
ther, the strain ch
angin
g
rate is
similar [14]
dx
d
dx
d
c
g
(5)
And due to el
astic m
odulu
s
of the optical
and middle l
a
yer is la
rge
differen
c
e (ab
out
more than ten times
)
, so
)
ln(
)
1
(
1
)
ln(
2
2
2
2
g
m
g
c
g
g
m
g
g
c
r
r
r
E
E
r
r
E
r
G
k
(6)
while
)]
1
(
2
/[
c
c
E
G
，
is
she
a
r mod
u
lu
s of middle layer
}
)
ln(
1
)
ln(
1
{
2
2
1
1
2
2
n
i
g
c
i
i
i
g
g
m
r
r
G
r
r
G
E
r
k
(7)
while
，
m
k
is para
m
eter which is de
cide
d by thickne
ss of a
dhe
sive layer and sh
ear m
odulu
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Strain Tra
n
sf
er and T
e
st Rese
arch of Stic
k-up Fi
ber B
r
agg G
r
atin
g Senso
r
s (Wa
ng Bing)
591
2.2 Analysi
s
of influence p
a
ram
e
ters
Facto
r
affecti
ng the fibe
r g
r
ating
sen
s
o
r
s aver
age
strain tran
sfe
r
rate mainly in
clud
e the
length of the
fiber g
r
ating
sen
s
o
r
s
L
, the thickne
ss of the interl
ayer (
g
m
r
r
r
), ela
s
tic
modulu
s
of in
terlayer a
nd
Poisson'
s rati
o of interlayer.
Table1. Me
ch
anical pro
pert
i
es of the opti
c
al fiber
Material paramet
er
S
y
mbol
Number
range
Unit
Elastic modulus
of optical fiber
g
E
7.2*10
10
Pa
Elastic modulus
of middle tier
c
E
3-5*10
9
Pa
poisson's ratio the middle tie
0.25-0.35
--
Outer
diameter o
f
middle tier
m
r
400
m
Outer
diameter o
f
optical fiber
g
r
62.5
m
Sensor length
L
20-50
mm
2.2.1 Effect of elastic m
odulus of interl
a
y
er
Figure 1. The
average
strai
n
transf
e
r rate dist
rib
u
tion
along You
ng’
s modul
us of
interlaye
r
Figure1
sho
w
s
wh
en th
e middle thi
c
kne
ss i
s
0.
2 mm and
Poisson'
s ratio of the
interlaye
r
is 0.31, elasti
c modulu
s
of the middl
e lay
e
r influen
ce
on the avera
ge strai
n
tran
sfer
rate, L refe
rs to the length
of the sen
s
o
r
.
The great
e
r
the middl
e tier of the modul
us of ela
s
ticit
y
,
the greate
r
the avera
ge strain tran
sfer
rate,
the stro
nger
se
ction
combi
ne, the
more abu
nd
ant
the stre
ss tra
n
sfer. In the
range of m
o
d
u
lus of el
asti
city on middl
e tier, ela
s
tici
ty modulus
of the
averag
e st
rai
n
tran
sfer
rat
e
ha
s a g
r
e
a
t influen
ce.
In pra
c
tical
e
ngine
erin
g a
pplication
s
, can
approp
riate a
d
just th
e p
r
o
portion
of e
p
o
xy resi
n
co
mpone
nts; m
a
ke
the el
astic mod
u
lu
s
of
middle
tier
as large
as po
ssible.
The
lon
ger the
se
nso
r
, the
sm
aller
of the
avera
g
e
st
rain
tra
n
sf
er
rate on middl
e tier to elastic modulu
s
, the averag
e strain tran
sfe
r
rate variati
on amplitud
e
is
redu
ce
d. At the sa
me time
, the av
erage
strain tran
sfer rate incre
a
se
s with the in
crease of ela
s
tic
modulu
s
with
the mi
ddle
tier. Envisi
one
d when
the
modulu
s
of e
l
asticity mi
ddl
e laye
r rea
c
h
e
s
low-ca
rb
on
st
eel mo
dulu
s
of ela
s
ticity, even if
th
e laye
r
th
ic
kn
es
s is
6
mm
w
h
e
n
th
e a
v
er
ag
e
strain
tran
sfe
r
rate can
re
ach
0.997
18,
the st
rain
i
s
less tha
n
0.
3% loss,
whi
c
h in
dicates that
strain
steel
encap
sulate
d
FBG sen
s
o
r
mea
s
ur
em
ent error le
ss than 3%, the accuracy
o
f
measurement
in the experi
m
ent
al re
se
arch is a
b
le to meet the req
u
irem
ents.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 58
9 – 596
592
2.2.2 Effect of interlaye
r
thi
c
kne
s
s
To pa
ste the
light grating
sen
s
o
r
firml
y
and
stru
cture to
be te
sted, ne
ed t
o
have
a
certai
n thi
c
kn
ess of th
e pa
ste laye
r. If the p
a
ste
layer i
s
too
thin,
wh
en
stru
ct
ure
defo
r
m, it is
easy to fall
off the se
nsor,
deform
a
tion
of the fiber
B
r
agg
grating
sen
s
o
r
a
nd
matrix structu
r
e i
s
inco
nsi
s
tent to make the
sensor failu
re;
On the
contrary, if the middle pa
ste la
yer is too thick,
make
the
strain tra
n
sfe
r
coefficient i
s
too sma
ll, e
s
p
e
cially in
dyn
a
mic m
e
a
s
urement al
so m
i
ght
cau
s
e
strai
n
lag, make pro
duce very bi
g error
m
e
a
s
urem
ent
re
su
lt
s.
A
nd cr
os
s se
ct
ion
st
re
ss
con
c
e
n
tration
near the em
bedd
ed se
nsor dep
end
s largely on the
package lay
e
r thickne
s
s an
d
material p
r
o
pertie
s
, the smalle
r the
clad
ding
dia
m
eter, the smaller the
stress and
st
rain
c
o
nc
en
tr
a
t
io
n.
Figure 2. The
average
strai
n
transf
e
r rate dist
rib
u
tion
s alon
g the thickne
ss of int
e
rlaye
r
Figure 2 sho
w
s
whe
n
the
length is
0.2
mm and Po
i
s
son'
s
ratio of
the interlaye
r
is 0.31,
the avera
ge
strain
tran
sfe
r
rate
ch
ang
e
s
alo
ng
with the chan
ge of
thickne
ss
of interlaye
r
.
c
E
is
elasti
c modul
us of interlay
er, In gene
ra
l the aver
ag
e strain tran
sfer rate de
crea
se
s with the
increa
se of th
ickne
ss
of interlaye
r
, and it
s chan
ging
ra
te gra
dually d
e
crea
se
s, the
effect of st
rai
n
transfe
r
coeffi
cient is
more
and mo
re
sm
all by the th
ickne
s
s of inter layer; At the same time,
wi
th
the ela
s
tic
modulu
s
of i
n
terlaye
r
in
creases, th
e
a
v
erage
st
rain
tran
sfer rate in
cre
a
ses,
the
cha
ngin
g
am
plitude of av
erag
e strain
transfe
r rate
decrea
s
e
s
. T
he sm
aller t
he thickne
ss o
f
interlaye
r
, the smalle
r effect of elastic m
odulu
s
of
inte
rlayer o
n
the averag
e strai
n
transf
e
r rate.
2.2.3 Effect of interlaye
r
Poisson
Structu
r
e mai
n
ly passed
strain to fiber B
r
agg
g
r
atin
g sensor throug
h the interlay
er sh
ea
r
deform
a
tion. Middle laye
r she
a
r mo
dulu
s
ca
n refle
c
t throu
gh the P
o
isson'
s ratio
s
of interlaye
r
.
Figure 3. The
average
strai
n
transf
e
r rate dist
rib
u
tion
along the Poi
s
son ratio of i
n
terlaye
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Strain Tra
n
sf
er and T
e
st Rese
arch of Stic
k-up Fi
ber B
r
agg G
r
atin
g Senso
r
s (Wa
ng Bing)
593
Adopting i
n
terlaye
r
thickness
r=0.2m
m,
Elastic modulu
s
of
interlaye
r
GPa
E
c
4
,
length of fibe
r Brag
g grati
ng se
nsor i
s
40mm, Fi
gu
re 3 sho
w
s th
e averag
e strain se
nsi
ng rate
decrea
s
e
s
wi
th Poisson'
s
ratio of interl
a
y
er in
cre
a
se,
whi
c
h b
e
com
e
s a
linea
r
ch
ange. But from
the averag
e
strain tran
sfe
r
rate value,
the infl
uen
ce
of Poisso
n's ratio of the interlaye
r
on the
averag
e strai
n
tran
sfer rate is very sm
a
ll. Due to
the
Poisson'
s ratio of interlaye
r
material
s ra
n
g
e
is not big, so
can b
e
igno
re
d.
Con
s
id
erin
g t
he p
a
ra
meters influ
e
n
c
ing t
he ave
r
ag
e
strain t
r
an
sfer rate, the thi
c
kness
of
interlaye
r
do
minate, the smalle
r the t
h
ickne
s
s
of interlaye
r
, the greate
r
the
averag
e strain
transfe
r
rate,
the influ
e
n
c
e of oth
e
r p
a
ram
e
ters
o
n
the
avera
ge
strain
tra
n
sfer rate al
so
corre
s
p
ondin
g
ly redu
ce
d, the influen
ce of the el
a
s
ticity mod
u
lus of inte
rla
y
er is
small,
th
e
averag
e strai
n
tra
n
sfe
r
rat
e
in
cre
a
ses with
th
e
inte
rlayer el
asti
c
modulu
s
i
n
creasi
ng,
whe
n
the
elasti
c modul
us of interlay
er rea
c
h
e
s el
astic mo
dul
u
s
of low-ca
rb
on iron, strai
n
transfe
r rati
o is
clo
s
e to
1, it i
s
fea
s
ibl
e
by
steel
pipe
di
rect
ly en
ca
psulated
FBG
sensor; T
h
e
Poisson'
s ratio
on
the averag
e strain tran
sfer
rate is not ob
vious.
3. The strain
trans
f
er an
a
l
y
s
is of fiber Bragg gr
ati
ng senso
r under non
-axi
al force
Figure 4. Dist
ribution of no
rmal strai
n
tra
n
sfer
rate in fiber alo
ng the
length with dif
f
erent angl
e
As can b
e
se
en from
Figu
re 4, u
nde
r t
he an
gl
e of
e
a
ch
se
nsor,
strain
tran
sfe
r
ratio
is
bigge
st in the
cente
r
of the
sen
s
o
r
on b
o
th side
s to redu
ce g
r
ad
u
a
lly, and the more
clo
s
e to
the
end, the
gre
a
ter the
rate
of strain tra
n
sfer rate.
refers to the
degree
between the
ba
si
c
stru
cture of the prin
cipal
stress and t
he fi
ber g
r
ating
se
nso
r
s
(unit, d
egre
e
).
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Figure 5. The
average
strai
n
transf
e
r rate dist
rib
u
tion
along the a
n
g
l
e of fiber Bra
gg se
nsor
As can be se
en
fro
m
Fig
u
re
5,
fibe
r
g
r
at
ing sen
s
o
r
s,
t
he smalle
r of
the
a
ngle
be
twee
n
the prin
cipal
stre
ss axis a
nd matrix, the greate
r
the averag
e strai
n
transfe
r rat
e
. With the angle
increa
se
s, th
e average
strain tra
n
sfe
r
rate de
cr
ea
se
s, the
rate of
ch
ange
of th
e average
strain
transfe
r
rate
i
n
crea
sed
g
r
a
dually. When
optical fibe
r
s
e
ns
or
is
ver
t
ic
a
l
w
i
th
the
ma
tr
ix pr
in
c
i
pa
l
stre
ss, the av
erag
e
strain
tran
sfer rate
i
s
zero,
the fib
e
r Bragg
grating
strain
sen
s
or can’t d
e
te
ct
st
ru
ct
ur
e st
r
a
i
n
.
4. Chara
c
te
ristic te
st o
f
FBG se
nsor
In ord
e
r to
e
liminate the i
n
fluen
ce of t
e
mpe
r
ature, the
tempe
r
at
ure com
pen
sation
of
fiber grating
sen
s
o
r
is adopted
which i
s
a
hollo
w cylin
drical struct
ure. Tem
perature
comp
en
satio
n
sen
s
o
r
i
s
a
c
tually a
pa
st
e type
st
rai
n
se
nsor, th
e
measured
structural m
a
terial
paste
it in
the
sa
me
materi
al supp
ort, its sp
ecif
i
c
stru
cture
g
uarant
ee the
temp
e
r
ature
sen
s
o
r
is
not su
bje
c
t to stress, whe
n
used
with t
he st
rain
se
n
s
ors at
the same
temp
era
t
ure
field. Wh
en
the temperature
chan
ge
s, the sam
e
wa
velength
s
of
two ki
nd
s of sensor cau
s
ed
by temperat
ure
cha
nge, so temperature
co
mpen
sation
can be u
s
ed.
4.1 Fatigue T
e
st
In orde
r to i
n
vestigatio
n of the fiber
Bragg g
r
atin
g strai
n
sen
s
or
and a
n
ti-fatigue
prop
ertie
s
of i
n
stallatio
n
p
r
oce
s
s, ad
opt
ed a
meth
o
d
of accel
e
rate
d fatigue
exp
e
rime
nt re
se
arch
of sen
s
o
r
. Use figure fatig
ue test
with t
e
mpe
r
at
ure
compen
satio
n
of FBG sen
s
or. Strain
se
n
s
or
positio
n pa
st
e in the mid
d
l
e
of the ste
e
l
rule,
an
d in th
e steel
rule
a
nd on th
e correspon
ding
F
B
G
sen
s
o
r
p
o
siti
on is hig
h
p
r
eci
s
ion
re
si
stance st
rain
g
age
s. Steel rule fixed in th
e loadi
ng
dev
ice,
throug
h step
ping moto
r d
r
iven load d
e
v
ice add, unl
oadin
g
. Steps by controlli
ng the motor to
control the
si
ze of the
ste
e
l rule
form v
a
riabl
e, the
maximum
stroke i
s
1
000
0
step
s, ea
ch
500
step
s re
co
rd
a wavel
ength
data. In a te
st, loadin
g
an
d unlo
ading
cycles, a total
of 1000
0 times,
three d
r
a
w
n at rando
m during the te
st (one month
early, middle
and late) da
ta. Fatigue dat
a
displ
a
ys wavelength m
a
ximum drift is
4.95 nm. Th
rough 1
000
0 times fatigu
e test, the se
nsor i
s
in goo
d
con
d
i
tion; In different pe
riod
s
unde
r the
sa
me loa
d
, the
maximum l
o
ad
wavelen
g
th
deviation is 8
8
PM, the largest unin
s
tall
wave
length
deviation is 1
25 PM. Maximum wavele
ngth
deviation i
s
resp
ectively of
1.7% and
2.5% of fu
ll scale. Uni
n
stall
error i
s
bi
gg
er
whi
c
h may
be
asso
ciated
with the p
r
e
c
i
s
ion
of the
step
motor
drive. Illustrate that
the
sensors
fo
r strain
measurement
ca
n m
eet t
he
req
u
irem
ents
of fati
gu
e
for
a lo
ng
time
, an
d w
i
th ve
r
y
go
o
d
repeatability.
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TELKOM
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930
Strain Tra
n
sf
er and T
e
st Rese
arch of Stic
k-up Fi
ber B
r
agg G
r
atin
g Senso
r
s (Wa
ng Bing)
595
4.2 Con
s
i
s
ten
cy a
nd calibration
Adopting a
stand
ard
eq
ual strength
beam
a
s
experim
ent device, carry
throug
h
con
s
i
s
ten
c
y testing
an
d
calibratio
n
. B
unch fou
r
different ce
nter
wavel
ength
strain se
nsors
together, p
a
ste on the eq
u
a
l stre
ngth b
eam axis
of
each point, a
t
the same ti
me, paste
a high
pre
c
isi
on resi
stan
ce st
rain
gage
s an
d ad
apt the
re
sist
ance strain g
auge m
easured strain valu
es
as a
stand
ard, throug
h weight loadi
ng
durin
g t
he te
st, the wavel
ength de
mod
u
lation with
F
i
ber
Bragg G
r
atin
g demod
ulati
on instrume
nt FBGIS (F
ibe
r
Bragg G
r
ati
ng Interrogati
on System). The
wavele
ngth
o
f
the devi
c
e
resolution
is
1 PM,
scanni
ng
rang
e i
s
1285
nm
- 1
285
nm,
swe
e
p
freque
ncy i
s
50 Hz. Wi
th gene
ral
optical fib
e
r sen
s
o
r
s ad
opt FC/APC jump
stitch
es.
Wavele
ngth-strain rel
a
tion
curv
e i
s
sh
own in Figure 6.
Figure 6. Fiber bragg g
r
ati
ng strai
n
se
n
s
or
cha
r
a
c
teri
stic curve
Acco
rdi
ng to Figure 6, the result is sh
own
(1)
Good lin
ea
rity: linear rel
a
tionshi
p by a
fiber
Brag
g
grating
se
nsor an
d re
si
stance strain
gaug
e mea
s
urem
ent exp
e
rime
nt data
is the fi
tting equation, th
e linea
r fitting is re
aching
more tha
n
0.99;
(2)
High
se
nsitivi
t
y: the slope
of the fitting
l
i
ne. re
sp
ectiv
e
ly 1.05 PM/
m
u ep
silo
n,
1.03 PM/mu
epsil
on, 1.08
PM/mu epsi
l
on, 1.11 PM/mu epsilo
n zero, with a
mean of 1.068 PM/mu
epsil
on, max
i
mum erro
r i
s
7.5%, ba
sic con
s
is
te
nt, explain fou
r
grating
strain sen
s
or
con
s
i
s
ten
c
y is goo
d, sho
w
s that rea
s
on
able de
sign
a
nd pa
ckagin
g
.
5. Conclusio
n
Based
on
the
com
m
on
sh
ear l
ag
meth
od's ba
si
c p
r
i
n
cipl
e, ado
pts a
serie
s
of
reali
s
tic
assumptio
n
s,
or direct b
u
ri
ed pipe
en
ca
psul
ati
on is
e
s
tabli
s
he
d when the axial
force
und
er t
he
action
of fibe
r Bra
gg
grating
sen
s
o
r
in
ea
ch
poi
nt
of the relatio
n
shi
p
b
e
twee
n the
strai
n
an
d
matrix structu
r
e of th
e a
c
tu
al strain, thu
s
the sen
s
o
r
l
ength i
s
o
b
tai
ned at va
rio
u
s p
o
ints
withi
n
the scope
of the strai
n
tra
n
sfer
ratio a
n
d
overall
le
ng
th is within th
e scope
of the avera
ge st
rain
transfe
r
rate,
fiber
grating
se
nsors a
r
e
also di
scu
s
sed a
nd th
e
matrix st
ruct
ure i
s
th
e a
n
g
le
betwe
en th
e
prin
cipal
st
re
ss to th
e effe
cts
of th
e
av
erag
e
strai
n
t
r
an
sfer rate.
And axial
force
unde
r the acti
on of strain transfe
r mod
e
l were co
mpa
r
ed and tra
n
sf
erred corre
s
p
ondin
g
ly.
Finally discu
s
sed the em
b
edde
d fiber
Bragg
g
r
ating
angula
r
devi
a
tion for the averag
e
strain tran
sfer rate and the i
m
pac
t of the
measurement
result
s, t
he rese
arch resul
t
s sho
w
that:
(1)
No matte
r what angle
se
nso
r
in the
strain tr
a
n
sfe
r
ratio from th
e
sen
s
o
r
end t
o
the ce
nter
point increa
ses gradu
ally, reached the
maximu
m in the center,
make the g
r
eatest st
ress
trans
fer.
(2)
The bigg
er of
the angle in the fiber Brag
g
grating
sen
s
or a
nd the
matrix maximum prin
cipa
l
stre
ss, the smaller the av
erag
e strai
n
transfe
r rate.
With the decre
ase of the angle, the
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Vol. 12, No. 3, September 20
14: 58
9 – 596
596
averag
e st
rai
n
tran
sfer
rat
e
increa
se
s
grad
ua
lly, the
cha
nge of th
e avera
ge
strain tran
sfe
r
rate de
crea
se
s. Therefor
e, unde
r the pre
m
ise of the a
c
tual
situ
ation
shoul
d try to redu
ce the
fiber Bra
gg g
r
ating
sen
s
o
r
in the axial and t
he a
ngl
e betwe
en th
e prin
cip
a
l st
ress m
a
trix
st
ru
ct
ur
es.
(3)
Whe
n
the
r
e
i
s
d
e
viation t
he e
m
bed
din
g
an
gle
se
nsor,
strain
me
asu
r
em
ent e
r
ror a
s
the
embed
ding a
ngle in
cre
a
se
s, the rate also incr
ea
sed,
whi
c
h und
er t
he sam
e
devi
a
tion angle,
the greate
r
th
e embed
ding
angle of mea
s
ureme
n
t error.
Ref
e
ren
c
e
[1]
Z
hang Bo-m
in
g, Leng Ji
n-so
ng, Du Sha
n
-
y
i. Compat
i
b
il
it
y stud
y
of optic
fiber and mat
r
ix i
n
smart
compos
ite material.
Jo
urna
l o
f
F
unctional M
a
teria
l
s
. 199
8; 29: 240-
24
5.
[2]
Pak YE. Lo
ngit
udi
nal s
h
e
a
r transfer i
n
fib
e
r
optic se
nsors.
Smart
mat
e
ria
l
s and struct
ure
s
. 1992;
1:
57-6
2
.
[3]
Betz DC.,
T
hursb
y
G, Culsh
a
w
B. Advn
ac
es la
yo
ut of a fiber bragg gr
ating strai
n
ga
uge ros
e
tte.
Journ
a
l of lig
ht
w
a
ve techno
lo
gy
. 2006; 2
4
:1
019-
102
6.
[4]
Nan
n
i A,
Yan
g
CC, P
a
n
K. F
i
ber-o
ptic se
ns
or for c
oncr
e
te
strain/stress
measur
ement.
ACI Materials
jour
nal.
19
92;
88: 257-
26
4.
[5]
Ansari F
,
Yua
n
LB. Mecha
n
ic
s of bon
d an
d i
n
te
rface sh
ear
transfer in o
p
ti
cal fiber s
ens
or
s.
Journa
l of
eng
ine
e
ri
ng mecha
n
ics.
19
98
; 4: 385-39
4.
[6]
Li QB, Li G, W
ang G. Elasto-
p
lastic
bon
di
ng
of embe
dde
d
optica
l
fiber s
e
nsors in c
oncr
e
te.
Journ
a
l
of engi
ne
erin
g mec
h
a
n
ics
. 20
02a; 12
8: 471-
478.
[7]
Li DS, Li HN. Strain transferring
an
al
ysis
of fiber Bra
gg
gra
t
ing se
nsors.
Optical e
n
g
i
ne
erin
g.
20
06
b
;
45:27-
34.
[8]
Yuan
LB, Z
h
o
u
L. Sens
itivit
y
coefficie
n
t ev
a
l
uatio
n of
an
e
m
bed
ded
fib
e
r-optica
l
se
nsors
.
Journ
a
l of
eng
ine
e
ri
ng mecha
n
ics.
19
98
; 128: 471-
478.
[9]
Ren L, Li H
N
, Z
hou J. Applic
ations of tub
e
-pa
cka
ge
d F
B
G strain sensor
in vibrati
on e
x
perime
n
t o
f
submari
ne p
i
p
e
lin
e mod
e
l.
C
h
in
a oce
an en
gin
eeri
ng.
20
0
6
; 20:15
5-16
4.
[10]
Prabh
ug
oud M
,
Gill A and Pe
ters K.
Modifie
d
transfer matri
x
mod
e
l for Bragg gr
atin
g strain se
nsors
.
Smart structures an
d mater
i
a
l
s: Smart sens
or te
chn
o
l
o
g
y
and m
eas
urem
ent s
y
stems, Procee
din
g
s o
f
SPIE, SanDie
g
o
. 2004: 5
384-
24.
[11]
Lin
g
HY, lau K
T
, Cheng L. Embed
ded fibr
e
Bragg gr
ati
ng
sensors for no
n-un
iform strain sensi
ng i
n
compos
ite structures.
Measur
ement scie
n
ce
and tech
no
logy
.
2005; 16: 24
1
5
-24
24.
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