TELKOM
NIKA
, Vol.12, No
.3, Septembe
r 2014, pp. 5
23~630
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i3.96
623
Re
cei
v
ed Ma
rch 2
7
, 2014;
Re
vised July
8, 2014; Acce
pted Jul
y
21,
2014
Application Status of the Barkhausen Effect in
Nondestructive Testing
Yuan Huijuan
1
, Zhang Enjing
1
, Li Hongmei
2
, Fu Jian
1
, Yang Yin
g
1
, Zou Ying
1
, Hu Danda
n
1
1
T
he Higher E
ducati
o
n
a
l Ke
y Labor
ator
y
f
o
r Measuri
ng & C
ontrol
T
e
chn
o
l
o
g
y
and Instrum
entatio
ns of
Heil
on
gji
a
n
g
Provinc
e
, Harbi
n
Univers
i
t
y
of Scienc
e an
d
T
e
chno
log
y
No.52
Xu
efu R
oad N
a
n
gan
g District Ha
rbi
n
, 1500
80, Ch
ina
,
+
86-451-8
6
3
9
239
4
2
AVIC Harbin
Beari
ng Cor
por
ation LT
D
No.2 Na
nji
ng R
oad H
u
la
n Dist
r
ict Harbin, 1
5
0
025, Ch
in
a, +
8618
64
638
60
79
e-mail: h
u
ij
uan
y@
12
6.com
A
b
st
r
a
ct
Cha
nge of inte
rnal structure
or intern
al def
ec
t in ferroma
gnetic
mater
i
al
s can produc
e chan
ge i
n
Barkha
use
n
n
o
i
se, a
nd
by us
i
ng B
a
rkha
use
n
nois
e
si
gn
al
measur
e
m
ent, th
e q
ual
ity an
d i
n
ternal
defects
of
the materi
al ca
n be
jud
g
e
d
. T
he n
o
n
destruct
i
ve testin
g tec
hno
logy
is b
a
s
ed o
n
the B
a
r
k
haus
en
effect, it
gets the attenti
on bec
aus
e of
its advanta
ges,
such as rapi
d, non-d
e
st
ructiv
e, me
nsura
b
le,
mai
n
ly us
ed to
detect stress, hard
ness, grai
n si
z
e
,
grin
din
g
burn et
c.. T
he rese
arch s
t
atus of Barkhause
n
effect in
non
destructiv
e
testing
w
a
s r
e
view
ed. Its a
pplic
atio
n
situ
ation
w
a
s inv
e
stigated
that t
he
non
destruc
tive
testing tec
h
n
o
l
ogy
base
d
o
n
t
he B
a
rkha
use
n
effect on
stres
s
, hard
ness, gr
ain s
i
z
e
,
grin
di
ng
burn
det
ecti
on
etc., and the r
e
lati
onsh
i
p b
e
t
w
een the MBN
signa
ls a
nd
st
ress, hard
ness
,
grain si
z
e
,
gri
ndi
ng b
u
rn w
e
r
e
show
ed.
Ke
y
w
ords
: Ba
rkhaus
en n
o
ise
,
Barkhause
n
e
ffect, stress, hardness, gri
ndi
n
g
burn
1. Introduc
tion
Barkhau
se
n
effect wa
s fo
und fo
r the fi
st time
in 1
9
19, after yea
r
s of research
, today it
develop
ed in
to a nond
est
r
uctive te
stin
g tech
nology
. The non
de
stru
ctive testi
ng technolo
g
y
based o
n
Ba
rkha
usen effe
ct is
usi
ng th
e presen
ce
of
magn
etic
sig
nal cau
s
ed
b
y
the exce
ptions
or defe
c
ts of the intern
al st
ructure of mat
e
rial
s to determi
ne the dam
age de
gre
e
o
f
abnorm
a
litie
s
and defe
c
ts o
f
the structu
r
e. It being mainly us
ed fo
r evaluating th
e quality and
fatigue co
ndit
i
on
of the ferrom
agneti
c
mate
rials, h
a
ving the advanta
g
e
s of non
de
structive, qu
a
n
t
itative, reliable,
fast, throu
gh
the ele
c
tri
c
p
l
ating laye
r,
la
rge
area
d
e
tected,
environm
ental p
r
otection
and
no
harm
to h
u
m
an b
ody, the
tech
nolo
g
y
has si
gnifica
nt appli
c
atio
n
value i
n
fiel
ds th
at in
clu
d
ing
machi
n
e
r
y, metallurgy,
con
s
tru
c
tion, avi
a
tion an
d a
e
rosp
ace, nu
cl
ear
ene
rgy, transportatio
n
and
other i
ndu
stri
es, a
s
well a
s
the
geol
ogi
cal expl
orat
ion, safety testi
ng, materi
als scien
c
e
and
so
on. Th
us, th
e
non
de
stru
ctive testing
technolo
g
y
ba
se
d on
the B
a
rkha
usen
effect ha
s
be
co
me
hot spot of the resea
r
ch.
2. The Bar
k
h
a
usen e
f
fect
In 191
9, the
German
sci
entist
Dr. B
a
rk
hau
se
n fo
und th
at the
hysteresi
s
l
oop
of
ferrom
agn
etic material
s i
s
not pe
rfectl
y smoot
h
cu
rve in the
a
c
tion of o
u
tside alternatin
g
magneti
c
fiel
d, and
the
m
a
tte pa
rt is en
han
ced
in
a
step lea
p
way, it ca
n m
a
ke t
he
re
ceiving
coil
that placed
o
n
the
surfa
c
e
of the ferrom
agneti
c
ma
te
rials to
pro
d
u
c
e pul
se
sign
a
l
and
noise th
a
t
will ma
ke a
sou
nd after
being
amplifi
ed by lou
d
sp
eaker [1]. Th
is ph
enom
en
on is
call
ed
the
Barkhau
se
n
effect an
d th
e noi
se i
s
cal
l
ed MBN
(M
a
gnetic B
a
rkh
ausen n
o
ise) [2], as
sho
w
n in
Figure 1.
Along
with u
n
derstandi
ng
o
f
ferrom
agn
etic mate
ri
al
s,
peopl
e foun
d
that there
a
r
e
a lot of
magneti
c
do
mains segm
ented by
ma
gnetic
do
mai
n
wall in
sid
e
the fe
rroma
gnetic mate
ri
als,
becau
se of the intern
al magneti
c
doma
i
n sort in
ra
n
dom but the magneti
c
offsets ea
ch oth
e
r,
macro
s
copi
cally, the ferro
m
agneti
c
m
a
terials have
no ma
gneti
c
. The
magn
etic d
o
main
wo
uld
reo
r
de
r in the
directio
n the
external ma
gnetic
field
when the ferro
m
agneti
c
mat
e
rial
s pla
c
ed
in
magneti
c
fiel
d, at this ti
me, materi
al
s
will sho
w
magneti
c
to
the extern
al. Ferrom
agne
tic
material
s of
inside space,
defects
such as
di
slocat
ion and nonmetallic
slag com
p
licate t
h
e
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ISSN: 16
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930
TELKOM
NIKA
Vol. 12, No. 3, September 20
14: 62
3 – 630
624
magneti
c
do
main structu
r
e, and hin
der the moveme
nt of domain
wall. J. Pal’a
and othe
rs h
a
ve
desi
gne
d the experimenta
l
measu
r
em
e
n
t system
[3], as sho
w
n in Figure 2, the Barkhau
sen
noise ca
n be
observed
when ap
plying
parall
e
l
and
perp
endi
cul
a
r ma
gneti
c
field to the st
re
ss
dire
ction. Wit
h
the enh
an
cement
of external m
agn
etic field, 90
a
nd
180
dom
ain wall
(mai
nly
the 180
) a
r
e
going to h
a
p
pen irreve
rsi
b
le movement
in a jumpi
ng
way, namely
the Barkha
usen
Jump [4]. Du
e to the do
main wall i
r
reversi
b
le mo
vement, friction and extru
s
ion
will hap
pen
betwe
en the adja
c
ent mag
netic dom
ain
s
, and this wi
l
l
cause magn
eto-a
c
ou
stic
emission, so the
noise is
appearing, that is
Barkhaus
e
n noise. Be
c
a
us
e the magnetic
c
h
arac
teris
t
ics
is
dec
i
ded
by intern
al m
i
cro
s
tructu
re
of ferroma
g
n
e
tic m
a
terial
s, and
displa
cement
of the
dom
ain
wall
is
sen
s
itively inf
l
uen
ced
by
micro
st
ru
ctu
r
al
cha
nge
a
nd
surfa
c
e
st
ress dist
ributi
on of
materi
als,
Barkhau
se
n noise can reflect that interior micro
s
copi
c stru
ctu
r
e ch
ange an
d stress con
d
ition
s
of
metal materi
al. Since the
1960
s, re
se
arche
r
s
were
using the M
B
N nond
est
r
uctive testing
to
asse
ss the fe
rrom
agn
etic
material
s con
d
itions of
ma
cro
s
tructu
re,
stre
ss, grain
size, fatigue etc.
Figure 1. Time seq
uen
ce
s
of Barkh
a
u
s
e
n
noise mea
s
ured in a p
o
lycry
s
talline Fe
Si 7.8 % wt.
ribbo
n (left) a
nd an amo
r
p
hou
s Fe21
Co
64B15 un
de
r mode
rate ten
s
ile stress (ri
ght). The lab
e
ls
indicate the freque
ncy of the applie
d field [2]
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TELKOM
NIKA
ISSN:
1693-6
930
Applicatio
n Status of the Barkhau
se
n Effect
in Non
d
e
s
tru
c
tive Test
ing (Yua
n Hui
j
uan)
625
Figure 2. Ske
t
ch of the me
asu
r
ing
syste
m
[3]
3. The applic
ation statu
s
of Bar
k
ha
us
en effec
t
in nondes
t
ru
cti
v
e
testing
3.1. Stress testing
The resea
r
ch
on that no
nd
estru
c
tive te
sting tech
nolo
g
y for dete
c
ti
ng st
re
ss
dist
ribution
and th
e
size
of the
re
sid
ual
stre
ss ba
sed
on
Barkhau
sen
effect has be
en i
n
-de
p
th. In 1
987,
Kirsti Tiitto etc. used th
e Barkha
use
n
effect
to
measure re
si
dual
st
re
ss i
n
ferromag
n
e
tic
material
s, a
n
d
obtain
ed
g
ood
con
s
i
s
te
ncy by
com
p
aring
with
hol
e-d
r
illing
stre
ss metho
d
a
nd X
ray methods
[5]. It was al
so proved the
feasibilit
y of MBN measuri
ng the residual stress. C. G.
Stefanita etc.
had
analy
z
e
d
the p
r
in
cipl
e of MBN testing technolo
g
y setting
out
from the
micro
theory, and rese
arche
d
after mate
rial be
nding the
rela
tionshi
p between mate
rial
stre
ss co
ndition
of pla
s
tic
def
ormatio
n
an
d
ela
s
tic d
e
formation a
nd
MBN
sign
al. As sho
w
n i
n
Figure 5, it’
s
the
relation
shi
p
b
e
twee
n st
re
ss conditio
n
of
the pl
a
s
tic
d
e
formatio
n a
nd MBN sig
n
al, the two
cu
rves
in the figure
are
respe
c
tively measurin
g re
sult
of de
tection he
ad t
hat parallel a
nd pe
rpe
ndi
cular
to the directio
n of stre
ss [6]
.
Duri
n G etc.
found that there i
s
ce
rta
i
n
relation b
e
twee
n noise
and stre
ss (strain),
namely n
o
ise
increa
se
s
wi
th the in
crea
se
of stra
in,
r
edu
ce
s wit
h
t
he in
cr
ea
se
of
st
re
s
s
,
si
n
c
e
they combin
e
d
with the po
wer
spe
c
trum
analysi
s
and
statistical ana
lysis, from th
e perspe
c
tive
o
f
sign
al an
alysi
s
an
d p
r
o
c
e
s
sing [7]. S. Desvaux et
c. h
a
ve the MB
N testing te
ch
n
o
logy ap
plied
to
the M50
steel
stre
ss testin
g [8], t
hey found that di
strib
u
tion an
d si
ze
in
surfa
c
e
resid
ual
stre
ss of
the annul
ar
M50 ste
e
l ha
ve certai
n lin
ear relation
sh
ip with MBN
sign
al sp
ect
r
um, and com
pare
d
to
th
e
me
as
ur
in
g r
e
s
u
lt
o
f
th
e
X
r
a
y in d
i
ffr
ac
tio
n
,
bo
th
h
a
v
e g
ood
co
ns
is
ten
cy, a
s
s
h
ow
n
in
Figure 6.
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ISSN: 16
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930
TELKOM
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Vol. 12, No. 3, September 20
14: 62
3 – 630
626
Figure 5. Rel
a
tionship bet
wee
n
stress
con
d
ition of the pla
s
tic d
e
f
ormation a
n
d MBN
s
i
gnal [6]
Figure 6. The
measu
r
e
d
su
rface
re
sidu
al
stre
ss
of the
annul
ar M5
0 steel by X-ray
diffraction
versu
s
surfa
c
e resi
dual
stress estimate
d of the annul
ar M50
steel
by Barkh
a
u
s
e
n
noise [8]
Aki Sorsa
etc. used th
e ch
ara
c
teri
stic v
a
l
ue of the
M
B
N si
gnal
(h
alf pea
k wi
dth, pea
k
positio
n, cre
s
t factor, coe
r
cive force,
re
mained
mag
netic) to buil
d
the math
e
m
atical m
ode
l of
forecast mat
e
rial ha
rdne
ss
a
nd stre
ss [9].
T.
Inagu
ma etc.
used
MBN te
ch
no
logy to evalu
a
te
steel stress
con
d
ition in different ca
rbon c
ontent,
also gave the cu
rve ab
out relation
ship
betwe
en
stre
ss of the
mil
d
ste
e
l
with
Carbon
conte
n
t 0.1% - 0.5
%
and th
e B
a
rkhau
se
n n
o
ise
[10]. O. Kypri
s
et
c. u
s
ed
M
B
N technol
og
y to eval
uate the
stress un
der differe
nt depth
[1
1],
they
had stress
ca
lculatio
n method of differe
nt
depth by stress pie
z
o
e
le
ctri
c ch
ecking
.
To evalu
a
ting
stre
ss
con
d
ition u
s
ing
MB
N fo
r ste
e
l pi
ece
s
of the
plane
wa
s p
r
o
p
ose
d
by
Ma xianyao
who
ha
s
given the
relation
sh
ip
b
e
twee
n MB
N extrem
er and
stre
ss [12].
Multifunction
magneti
c
el
asticity in
stru
ment wa
s d
e
velope
d
to detect re
sidu
al
stress
by Mu
Xiangrong
et
c. [13].
Weld
resi
dual
st
re
ss d
e
tect
o
r
ba
sed
on
MBN techn
o
logy was develo
ped
by
Qi xin etc., whi
c
h
can
preci
s
ely dete
c
t the stre
ss
distrib
u
tion o
f
weld
s an
d
the value of
the
resi
dual
st
re
ss, an
d the
M
B
N
signal
ca
libration
curv
e was drawn
[
14]-[16]. The
y
obtaine
d th
e
result that th
e
dist
ribution
o
f
the weld
re
sidual
stre
ss
i
s
app
roximate
with symmetry
and gave
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Applicatio
n Status of the Barkhau
se
n Effect
in Non
d
e
s
tru
c
tive Test
ing (Yua
n Hui
j
uan)
627
mathemati
c
al
model of Barkh
a
u
s
en n
o
i
s
e. Ju
an Ch
e
n
made the Barkhau
se
n detectio
n
sen
s
or
that wa
s u
s
e
d
to dete
c
t th
e internal
stress of fe
rro
m
agneti
c
mate
rials [17]. Yu
Shishe
ng
an
d Qi
xin etc. have been committed to the rail longitudi
nal temperature
stress re
sea
r
ch, developed ra
il
longitudin
a
l tempe
r
ature stress dete
c
to
r, and
carr
ie
d on the te
st at the scen
e of the rail
an
d
insp
ecte
d the
health of th
e rail [18]
-[2
2
]. Chen
Li
g
ong et
c. stud
ied ste
e
l welding p
a
rt in t
he
cha
nge
s of MBN noise before h
eat treatme
nt
or after [23]-[24
]. They have analyzed p
o
w
er
spe
c
tru
m
for the MBN
n
o
ise
sig
nal,
and fou
nd th
at before or
after he
at tre
a
tment, with
the
decrea
s
in
g of
wel
d
resi
dual
stre
ss that th
e MBN
si
gnal
level i
s
on
th
e de
cline.
Ta
ng
Ded
ong
etc.
resea
r
ched the tempe
r
at
ure influe
nce
mecha
n
ism
of the flexible cabl
e force
sen
s
o
r
and
desi
gne
d a di
fferential stru
cture to r
eali
z
e temperature comp
en
sati
on [25].
3.2. Testing
of hardn
ess
and grain size
Ranj
an, R et
c. have used
the Barkh
a
u
s
en effe
ct to deci
de the g
r
ain si
ze of ni
ckel and
decarb
u
ri
zed
steel [26]. They had obta
i
ned the re
lat
i
on between
grain
si
ze an
d both a
c
ou
stic
Barkhau
se
n sign
al(AB) a
nd magn
etic Barkhau
se
n sign
al(MB
)
by designin
g
the mea
s
ure
m
ent
device of MB
N grai
n si
ze,
namely in nickel, bot
h AB and MB sig
nal de
cre
a
se
with increa
si
ng
grain
si
ze, i
n
de
carbu
r
ize
d
ste
e
l,ho
we
ver, AB and
MB sig
nal
s i
n
crea
se
with
increa
sin
g
g
r
ain
size. P. Ze
ro
vnik et
c. was used th
e Ba
rkh
a
u
s
en
effect to
mea
s
u
r
ing th
e
size
of steel
an
d t
h
e
result sho
w
in
g that the noise incre
a
ses
with the
incre
a
se of hardn
ess [27
]. Cha
r
les
H. etc. used
the Barkha
usen testin
g me
thod to dete
c
t
the micro
s
tr
u
c
ture
of nu
cle
a
r rea
c
tor fe
rroalloys
(HT-9
)
for three diffe
rent p
r
o
c
e
s
s
of heat treat
ment [28].
Th
is p
r
oved th
at the main
loo
p
co
ercive fo
rce
and remna
n
t magneti
z
atio
n are
pro
porti
onal to the h
a
rdn
e
ss, an
d
MSN sig
nal i
s
propo
rtional
to
the hardne
ss. P. Zerovnik etc. evaluat
ed micr
o
s
tru
c
ture, hardne
ss and su
rfa
c
e stre
ss
of the
material
su
rfa
c
e ha
rd
ening
layer by usi
n
g the Barkha
use
n
noi
se [2
9]. It was fou
nd that ch
ang
es
of energy in
put in the specim
en surf
ace laye
r affected the
microstructu
re variation
and,
con
s
e
que
ntly, microh
ard
n
e
ss a
nd the re
sidu
al stre
ss.
Li Qiang etc. designe
d the magn
eto
elasti
c sen
s
or and testin
g system ba
sed on
Barkhau
se
n
effect to me
a
s
ure the
grai
n si
ze
of
the f
e
rromag
netic material
s, th
ey found th
at the
Barkhau
se
n noisy si
gnal
increa
se
s
wit
h
the increa
se of avera
g
e
grain di
am
eter [30]. Tian
Jianl
ong etc.
design
ed th
e magneto el
astic sen
s
o
r
and testing
system based
on Barkh
a
u
s
en
effect for det
ecting
45
#ste
el on
line [3
1
], the re
sult
sho
w
e
d
that
the Barkh
a
u
s
en n
o
isy
sign
al
increa
se
s wit
h
the increa
se of hardn
ess.
3.3. Quantita
tiv
e
anal
y
s
is of grinding burn
Grindi
ng bu
rn is the re
sult of energy
bei
ng co
nverted to heat
in the prod
uction of
workpi
ece. T
h
is
heat
is co
nce
n
trated
in
the
su
rf
ace l
a
yers a
nd
m
a
y ca
use
del
eteriou
s
effects if
not
prope
rly manag
ed. Ce
urter. Jeffrey S
etc.
put
up
usi
ng Ba
rkh
ausen effe
ct
to evaluate t
he
degree
of gri
nding
bu
rns
of gea
r an
d t
he a
c
id
co
rr
o
s
ion
actin
g
a
s
a
refe
ren
c
e
,
they set u
p
a
relation
cu
rve
about ma
gn
etic pa
ramet
e
rs
MP
value
and de
gree
of grindi
ng b
u
rn fo
r one
g
ear
type on a motorcy
c
le tra
n
smi
ssi
on ge
ar sy
stem [32], as sho
w
n
in Figure 7.
Figure 7
a
is a
correl
ation fo
r the maximu
m MP values measure
d
o
n
all scan
s of a gear, whil
e Figure 7b i
s
a
correl
ation fo
r the differen
c
e bet
wee
n
maximum an
d minimum
MP values
measured on
all
scan
s of a ge
ar.
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ISSN: 16
93-6
930
TELKOM
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Vol. 12, No. 3, September 20
14: 62
3 – 630
628
Figure 7. (a)
Maximum MP correlatio
n with nital etch. (b) Diffe
ren
c
e (Maximum
Minimum
)
MP correlation
with nital etch
[32]
Kendri
s
h S.J.
and Siiriai
n
e
n
J. etc. u
s
ed
magneti
c
Ba
rkh
a
u
s
en
Noi
s
e Analy
s
is(B
NA) to
evaluate change in mi
crostructura
l properties [33],[34]. They go
t the qualitative results that
correl
ate BNA test values to acid etch
pattern
s/
col
o
rs fo
r the detection of retempe
r
ing b
u
rn
defect
s
. Vaid
hianath
a
sam
y
M. etc. hav
e mad
e
the
MBN me
asurements on
M
a
rine
Ge
ars
made
with ca
se
-ca
r
bu
rised En3
6
steel u
s
in
g three
different meth
od
s, namely,
High F
r
eq
ue
ncy,
Medium F
r
eq
uen
cy and Lo
w Fre
que
ncy
MBN mea
s
u
r
ements [35].
They found that the grindi
ng
damag
e in
dif
f
erent d
eep
l
a
yers can
be
detecte
d u
s
in
g differe
nt fre
quen
cy MB
N
measurement
s,
and th
e the
m
al da
mage
caused
by g
r
i
nding
brun
is cle
a
rly
revea
l
ed by th
e
sh
ifting of the
L
o
w
freque
ncy M
B
N perk tolo
wer ma
gneti
c
field. Su
vi
Santa-a
ho a
nd A. Sorsa
et al. produced
calib
ration
sa
mples fo
r th
e Barkha
use
n
noi
se met
hod
s with la
ser
processi
ng an
d opti
m
ized
para
m
eters for the laser
p
r
ocessin
g
[36
],[37].
4. Conclusio
n
MBN a
pplied
in en
gine
eri
ng i
s
the i
n
e
v
itable tren
d
of future
dev
elopme
n
t, while the
developm
ent
of testing
eq
u
i
pment i
s
th
e
ultimate
wa
y
to re
alize
ind
u
strial
ap
plication, thu
s
M
B
N
sen
s
o
r
s a
nd
the whol
e eq
uipment rese
arch and d
e
velopme
n
t will
also be the
focu
s of future
resea
r
ch and
developm
ent.
Above all, the following
con
c
lu
sion
s are dre
w
:
(1)
MBN si
gnal i
n
crea
se
s wit
h
the in
cre
a
se of
tensil
e stress, de
crea
se
s with th
e
increa
se of
comp
re
s
s
iv
e st
re
s
s
.
(2)
MB
N sig
nal i
n
cr
ea
se
s wit
h
incre
a
si
ng h
a
rdn
e
s
s
.
(3)
MBN sig
nal i
n
crea
se
s with
incre
a
si
ng of
burn de
gree.
(4)
MBN sig
nal
begin
s
to in
crea
se
with the in
crea
se of
the material
that being t
e
sted
ca
rbo
n
conte
n
t, wh
e
n
in
crea
se to
a
ce
rtain
extent, MB
N si
g
nal d
e
crea
se
s
with th
e in
crea
se
of the
material
that being
te
sted carbon conte
n
t.
(5)
MBN sig
nal a
ttenuation de
gree
will incre
a
se
with the increa
se of the detectio
n
d
epth.
So the stre
ss, hard
n
e
ss,
grain
size, grinding bu
rn o
f
ferromag
net
ic materi
als
can b
e
detecte
d by using MB
N sig
nal.
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H.
T
w
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h
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w
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u
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etis
m a
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07
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TELKOM
NIKA
ISSN:
1693-6
930
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