Va ia ion o eddy cu en densi y dis ibu ion and i s e ec on c ack signal
263
VARIATION OF EDDY CURRENT DENSITY DISTRIBUTION AND ITS EFFECT
ON CRACK SIGNAL IN EDDY CURRENT NON-DESTRUCTIVE TESTING
L. Janoušek
Depa men o Elec omagne ic and Biomedical Enginee ing, Facul y o Elec ical Enginee ing
Uni e si y o Zilina, Uni e zi na 1, 010 26 Zilina, Slo ak Republic
e-mail: [email p o ec ed].sk
Summa y
The pape deals wi h a ia ion o eddy cu en densi y dis ibu ion along ma e ial dep h and in es iga es an e ec
o he a ia ion on a c ack signal in eddy cu en non-des uc i e es ing. Fou coaxial ec angula angen ial coils a e used o
induce eddy cu en s in a es ed conduc i e objec . The exci ing coils a e d i en independen ly by phase-shi ed AC cu en s;
a a io o ampli udes o he exci ing cu en s is con inuously changed o a y he dis ibu ion o eddy cu en densi y along
ma e ial dep h unde a ci cula pick-up coil posi ioned in cen e be ween he exci ing coils. Dependences o a c ack signal
ampli ude and i s phase on he a io a e e alua ed and special ea u es a e ex ac ed. I is e ealed ha he dependences a e
s ongly in luenced by dep h o a c ack, and hus he ex ac ed ea u es can enhance e alua ion o a de ec ed c ack.
1. INTRODUCTION
Eddy cu en es ing (ECT) is a non-des uc i e
inspec ion me hod used o su ace es ing o
conduc i e ma e ials. P inciple o he me hod
unde lies in he in e ac ion o induced eddy cu en s
wi h a s uc u e o examined body [1]. Induc ance
coil d i en wi h AC cu en gene a es p ima y
al e na ing elec omagne ic ield. When he coil is
placed in p oximi y o a conduc i e body, he
elec omo i e o ce is induced in he body and eddy
cu en s low he e acco ding o he elec omo i e
o ce. Eddy cu en s gene a e seconda y
elec omagne ic ield which eac s o he p ima y
ield. When low o eddy cu en s is in luenced by
p esence o any discon inui y in he body, he mu ual
connec ion be ween he coil and he es ed objec is
al e ed esul ing in change o he coil impedance.
ECT is equen ly u ilized in many indus ial
ields due o indispu able ad an ages o he me hod
[2]. Howe e , i should be no ed ha ECT is mainly
applied o de ec ion while sizing o a de ec ed c ack
is done using some o he me hod, o example by
ul asonic es ing, because in e se p oblem o ECT
da a analysis is ill-posed. Thus, i is qui e di icul o
de e mine pa ame e s o a de ec ed c ack om a
sensed ECT signal. Special compu e in e se codes
a e used o ackle his ask i e a i ely based on
nume ical simula ions o o wa d p oblems. Se e al
nume ical echniques a e employed o ind global
minimum o a de ined unc ion. Howe e , he e is
possibili y ha a solu ion is apped in o some local
minimum o he unc ion. Mo eo e , du a ion o he
i e a ion p ocess is a iable depending on p oximi y
o ini ial and inal solu ions and on he unc ion
complexi y. I would be bene icial i he in e se
p oblem o ECT da a analysis can be sol ed di ec ly
using simple o mulae.
The pape p oposes o use a no el ECT p obe
wi h phase-shi ed exci a ion [3] o he pu pose. I
is possible o a y eddy cu en densi y dis ibu ion
along ma e ial dep h unde a pick-up coil using he
p obe. Changes in a c ack signal due o a ia ions in
he eddy cu en densi y dis ibu ion a e e alua ed
and wo ea u es a e ex ac ed om he gained
cha ac e is ics. I is shown ha he ea u es depend
on a c ack dep h and hus his app oach can be e y
help ul o di ec de e mina ion o i s alue.
2. VARIATION OF EDDY CURRENT
DENSITY DISRIBUTION ALONG
MATERIAL DEPTH
A no el ECT p obe o iginally p oposed by he
au ho o non-des uc i e inspec ion o nea -side
deep c acks in hick conduc i e s uc u es [4] is
shown in Fig. 1.
on iew
50
exci e s
de ec o
1
side iew
op iew
1
3
inne
ou e
10 10 10 10
30
28
30
28
Fig. 1. A angemen and dimensions o he no el eddy
cu en es ing p obe
The p obe consis s o ou coaxial ec angula
angen ial exci ing coils di ided in o wo de ached
se s sepa a ed by a space o 50 mm. The inne
exci ing coils and he ou e ones o he se s a e
connec ed in se ies, espec i ely, and hey a e d i en
independen ly by phase-shi ed cu en s o 180°. The
signal is picked-up by a no mal ci cula coil placed
in cen e be ween he wo se s o he exci ing coils.
A pla e specimen shown in Fig. 2 is inspec ed in
his s udy. I is made o s ainless s eel SUS316L
which is equen ly used as a base ma e ial o
Ad ances in Elec ical and Elec onic Enginee ing
264
design o s uc u al componen s in nuclea powe
plan s; ECT is employed o non-des uc i e
inspec ion o hose componen s. Thickness o he
specimen is 25 mm and elec omagne ic
cha ac e is ics o he ma e ial a e: conduc i i y o
 = 1.4 MS/m and ela i e pe meabili y o 
= 1.
40
dc
0.5
σ= 1.4 MS/m
µ = 1
SUS316L
25
Fig. 2. Tes -piece
An elec o-discha ge machined (EDM) no ch –
c ack wi h a leng h o 40 mm, a wid h o 0.5 mm is
in oduced in o nea -side o he specimen, Fig. 2. A
dep h o he no ch is changed om 0 o 100% o he
ma e ial hickness.
A h ee dimensional ini e elemen code is used
o calcula e dis ibu ion o he magne ic ec o
po en ial and o eddy cu en s in a conside ed
olume. The ol age induced in he pick-up coil is
hen calcula ed.
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25
absolu e alue o eddy cu en densi y [mA/m2]
ma e ial dep h [mm]
ou e
inne
Fig. 3. Dependence o absolu e alue o eddy cu en
densi y on ma e ial dep h o he ou e exci ing coils and
o he inne exci ing coils, espec i ely
Dis ance be ween he exci ing coil and he pick-
up coil in luences he dis ibu ion o eddy cu en
densi y unde he pick-up coil. The si ua ion is
shown in Fig. 3 o wo cases: 1) only ou e exci ing
coils o he no el p obe a e d i en; 2) only inne
exci ing coils o he no el p obe a e d i en. As i can
be seen, he e is a di e ence be ween he
cha ac e is ics due o di e en posi ions o he
exci ing coils conce ning a posi ion o he pick-up
coil. Those di e ences can be also obse ed in he
calcula ed c ack signals; only one pai o he
exci ing coils, i.e. a pai o he inne coils o a pai o
he ou e coils, is u ilized o d i e eddy cu en s,
Fig. 4, 5.
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20 25
c ack signal ampli ude [mV]
c ack dep h [mm]
ou e
inne
Fig. 4. Dependence o he c ack signal ampli ude on he
c ack dep h gained wi h he no el p obe when only ou e
exci ing coils o he inne exci ing coils a e d i en
105
110
115
120
125
130
135
0 5 10 15 20 25
c ack signal phase [deg ee]
c ack dep h [mm]
ou e
inne
Fig. 5. Dependence o he c ack signal phase on he c ack
dep h gained wi h he no el p obe when only ou e
exci ing coils o he inne exci ing coils a e d i en
When he inne and he ou e exci ing coils o
he wo se s a e d i en a he same ime
independen ly om each o he by phase-shi ed
cu en s o 180 , he dis ibu ion o eddy cu en
densi y unde he pick-up coil depends on a a io o
densi ies o hose exci ing cu en s. I means ha he
dis ibu ion o eddy cu en densi y can be changed
by changing he a io. An example is shown in
Fig. 6. The eddy cu en densi y dis ibu ion unde
Va ia ion o eddy cu en densi y dis ibu ion and i s e ec on c ack signal
265
he pick-up coil along he ma e ial dep h is plo ed
o he a io o he inne and he ou e exci ing
cu en s densi ies o J
i
/J
o
= 6.4/10. As i can be seen,
wi h p ope adjus men o he exci ing cu en s
densi ies i is e en possible o supp ess eddy cu en
densi y on he su ace o ma e ial o ze o.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 5 10 15 20 25
absolu e alue o eddy cu en densi y [mA/m2]
ma e ial dep h [mm]
Fig. 6. Dependence o absolu e alue o eddy cu en
densi y on ma e ial dep h, he inne and he ou e exci ing
coils a e d i en a he same ime wi h cu en s shi ed by
180°, he a io o exci ing cu en s is
J
i
/J
o
= 6.4/10
I has been ound ou ha he dis ibu ion o
eddy cu en densi y along ma e ial dep h unde he
pick-up coil in luences ampli ude, phase as well as
shape o a c ack signal. The e o e, by changing he
a io i is possible o o a e he c ack signal and o
a y i s ampli ude. The nex sec ion in es iga es
hese dependences.
3. INFLUENCE OF THE EDDY CURRENT
DISTRIBUTION ON CRACK SIGNAL
ECT signal o he c ack wi h a leng h o
l
c
= 40 mm, a wid h o w
c
= 0.5 mm, and a dep h o
d
c
= 0 – 100% o he ma e ial hickness (Fig. 2), is
calcula ed o di e en alues o he a io J
i
/J
o
.
In luence o he a io on he c ack signal beha iou
is in es iga ed by means o nume ical simula ions.
Fi e signals o he c ack wi h a dep h o
d
c
= 10 mm o i e di e en alues o he a io J
i
/J
o
plo ed in he complex plane a e shown in Fig. 7. I
is e iden ha he c ack signal o a es clockwise
wi h inc easing o he a io while i s ampli ude
dec eases up o a ce ain alue o he a io and hen
inc eases again. This dependence can be mo e
clea ly obse ed in Fig. 8. Al hough he a io was
changed in a wide ange, he dependences o he
c ack signal ampli ude and i s phase on he a io a e
shown jus up o J
i
/J
o
= 3 as his ange is su icien
o explo e conside ed changes in he c ack signal.
-1
-0.5
0
0.5
1
-1 -0.5 0 0.5 1
imagina y [mV]
eal [mV]
Ji/Jo=0.0/1.0
Ji/Jo=0.5/1.0
Ji/Jo=1.0/1.0
Ji/Jo=1.0/0.5
Ji/Jo=1.0/0.0
Fig. 7. Signals o he c ack wi h a dep h o dc = 10 mm o
di e en alues o he a io
J
i
/J
o
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5 3
-50
0
50
100
ampli ude [mV]
phase [deg ee]
a io Ji/Jo [-]
ampli ude
phase
Fig. 8. Dependences o he c ack signal ampli ude and i s
phase on he a io
J
i
/J
o
o he c ack wi h a dep h o
dc = 10 mm
Simila dependences o he c ack wi h dep hs
o 5, 10, 15 and 20 mm a e shown in Fig. 9, 10. The
ampli udes a e plo ed in uni e alues e e ed o a
maximum ampli ude o he signal o whole ange o
he a io and o each dep h o he c ack. The change
o he c ack signal phase is e e ed o a alue o he
phase when only ou e coils a e d i en (J
i
/J
o
= 0). I
can be seen ha dep h o he c ack de e mines a
alue o he a io when he c ack signal ampli ude
eaches i s minimum (Fig. 9). Ro a ion o he c ack
signal wi h inc easing alue o he a io also depends
on he c ack dep h (Fig. 10). Thus, wo ea u es can
be ex ac ed om hese cha ac e is ics o he c ack
wi h a ce ain dep h: 1) alue o he a io when
ampli ude o he c ack signal eaches i s minimum;
2) alue o he a io when he c ack signal o a es o
an angle de ined as a hal alue o he o al c ack
signal o a ion.
Ad ances in Elec ical and Elec onic Enginee ing
266
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3
ela i e signal ampli ude [-]
a io Ji/Jo [-]
dc=5mm
dc=10mm
dc=15mm
dc=20mm
Fig. 9. Dependences o he c ack signal ela i e ampli ude
on he a io
J
i
/J
o
o he c ack wi h dep hs o dc = 5, 10,
15 and 20 mm
0
20
40
60
80
100
120
140
160
180
0 0.5 1 1.5 2 2.5 3
phase change [deg ee]
a io Ji/Jo [-]
dc=5mm
dc=10mm
dc=15mm
dc=20mm
Fig. 10. Dependences o he c ack signal phase change on
he a io
J
i
/J
o
o he c ack wi h dep hs o dc = 5, 10, 15
and 20 mm
Dependences o he a io J
i
/J
o
on he c ack
dep h o he wo ex ac ed ea u es a e shown in
Fig. 11. As i can be seen, he dependences o bo h
he ex ac ed ea u es a e nea ly he same and hey
a e almos linea . I can be concluded ha o each
dep h o he c ack he e is a unique alue o he a io
whe e he c ack signal ampli ude eaches a
minimum alue and he signal o a es in a de ined
angle. The e o e, when a de ec ed c ack is inspec ed
using he no el p obe wi h di e en adjus men s o
he a io, i is possible o ind a alue o he a io o
he wo ex ac ed ea u es and hus o di ec ly
es ima e a dep h o he c ack.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 5 10 15 20 25
a io Ji/Jo [-]
c ack dep h [mm]
ampli ude
phase
Fig. 11. Dependences o he a io
J
i
/J
o
on he c ack dep h
dc o he wo ex ac ed ea u es
4. CONCLUSION
The pape deal wi h he in es iga ion on how
dis ibu ion o induced eddy cu en s in luences he
signal o a de ec ed c ack in non-des uc i e eddy
cu en es ing. A no el eddy cu en es ing p obe
u ilizing phase-shi ed exci a ion was used o d i e
eddy cu en s o a ious dis ibu ions con olled by
changing he a io o he exci ing cu en s densi ies.
I was shown ha ampli ude and phase o he c ack
signal depend on he dis ibu ion o eddy cu en s
and hus on he a io. Signals o conside ed c ack
we e calcula ed o wide ange o he a io by means
o nume ical simula ions. Two ea u es we e
ex ac ed om he ob ained complex c ack signal
cha ac e is ics; i s one o he signal ampli ude and
he second one o he signal phase. I has been
p o ed ha he ex ac ed ea u es can be e y
help ul in di ec es ima ion o a c ack dep h.
Fu he nume ical in es iga ions and expe imen al
e i ica ions will be ca ied ou o e eal e iciency
o he newly p oposed app oach o di ec e alua ion
o a c ack dep h in eddy cu en non-des uc i e
es ing.
REFERENCES
[1] Janousek, L., Ma ek, T., Gomba ska, D.: J.
Communica ions (2006) in p ess.
[2] Auld, B. A., Moulde , J. C.: J. Nondes uc.
E al. 18 (1999) 3.
[3] Janousek, L., Chen, Z., Yusa, N., Miya, K.: J.
NDT&E In . 38 (2005) 508.
[4] Janousek, L., Chen, Z., Yusa, N., Miya, K.:
P oc. 3
d
Wo kshop NDT in P og ess, P ague
(2005), 125.