E-Journal of Advanced Maintenance Vol.2 (2010/2011) 168-180
Japan Society of Maintenology

Electromagnetic modeling of stress corrosion cracks in Inconel welds
Haoyu HUANG1, Noritaka YUSA2,*, Kenzo MIYA1, Hidetoshi HASHIZUME2, Takehiko
SERA3, and Shinro HIRANO31

IIU Corp, 2-7-17-707, Ikenohata, Taito, Tokyo, 110-0008, Japan
Department of Quantum Science and Energy Engineering, Graduate School of Engineering, Tohoku
University, 6-6-01-2 Aramaki Aza Aoba, Aoba-Ku, Sendai, Miyagi, 980-8579, Japan
3
Kansai Electric Power, 13-8, Goichi, Mihama, Mikata, Fukui, 919-1141, Japan
2

ABSTRACTThis study evaluates suitable numerical modeling of stress corrosion cracks appearing in Inconel welds from theviewpoint of electromagnetic nondestructive evaluations. The stress corrosion cracks analyzed in this study are
five artificial ones introduced into welded flat plate, and three natural ones found in a pressurized nuclear power
plant. Numerical simulations model a crack as a planar region having a uniform conductivity inside and aconstant width, and evaluate the width and conductivity that reproduce the maximum eddy current signals
obtained by experiments. The results obtained validate the existence of the minimum value of the equivalent
resistance, which is defined by the width divided by conductivity. In contrast, the values of the width andconductivity themselves vary across a wide range. The results also lead to a discussion about (1) the effect ofprobe utilized on the numerical model, (2) the difference between artificial and natural stress corrosion cracks,and (3) the difference between stress corrosion cracks in base metals and those in Inconel welds in their models.
Electromagnetic characteristics of four different Inconel weld alloys are additionally evaluated using a
resistance tester and a vibrating sample magnetometer to support the validity of the numerical modeling and thegenerality of results obtained.
KEYWORDS

ARTICLE INFORMATION

electromagnetic nondestructive evaluation, eddy current testing, nuclear
power plant, nickel-based alloy, finite element method, numerical modeling,natural crack, inverse problem, Alloy 600

Article history:
Received 16 September 2010
Accepted 4 February 2011

1. Introduction
The emergence of stress corrosion cracks is one of the most important issues for the maintenanceactivity of aging nuclear power plants [1] [2] . The nondestructive evaluation of structures plays oneof the most important roles in dealing with the problems related to stress corrosion cracks, as well as
the development of technologies to prevent the initialization of such cracks. That is to say, taking asuitable maintenance action requires finding a stress corrosion crack in its initial state and evaluating
its profile precisely to discuss its effect on structural integrity.
Usually, ultrasonic inspections are used in the evaluation of cracks found in nuclear power plants.
However, the complexity and diversity of structures in nuclear power plants imply that it is preferable
not to depend only on ultrasonic-based techniques. Several studies such as [3] have discussed theapplication of non-ultrasonic tests to the sizing of cracks to which it is difficult to apply ultrasonictests. Eddy current testing is a promising nondestructive testing method from this point of view [4] .
In addition to a large number of studies dealing with ideal cracks [5] , recent studies have evenreported the success of sizing stress corrosion cracks from measured eddy current signals using
computational inversion techniques [6] [7] [8] .
In contrast, however, another recent study has pointed out that conventional techniques developed
to deal with ideal cracks are not always suitable for considering stress corrosion cracks [9] . One of themain reasons for this is that a numerical model suitable for dealing with a stress corrosion crack in*Corresponding author, E-mail: noritaka.yusa@qse.tohoku.ac.jp

ISSN-1883-9894/10/11 © 2010/2011 – JSM and the authors. All rights reserved.

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in Inconel welds

numerical simulations has not been established. Whereas a stress corrosion crack should be modeled not
as an insulating wall or nonconductive region but as a region with a certain conductivity inside [6] [10] ,more specific information such as the amount of conductivity to model a stress corrosion crack has notbeen obtained so far. Earlier studies by the authors have revealed that it is necessary to take not only
conductivity but also the width of a crack region explicitly into consideration to model a stress corrosion
crack [11] . In addition, they also report that whereas the values of conductivity and width to modelstress corrosion cracks vary across a wide range, it would be reasonable to assume the minimum valueof the equivalent resistance, which is defined as the width divided by the conductivity. The existence ofthe minimum value of the equivalent resistance enables one to impose a constraint on the numericalinversion to evaluate crack profiles from eddy current signals, and thus should enable the problem to beproperly considered. However, the earlier studies have considered only stress corrosion cracks in basemetals. Recent experiences show that stress corrosion cracks tend to appear especially in Inconel welds.
Thus discussions on the numerical modeling of stress corrosion cracks appearing in Inconel welds areindispensable from the viewpoint of the maintenance of nuclear power plants.
This study was conducted with the above background. The numerical models of five artificial
stress corrosion cracks are discussed on the basis of their eddy current signals and the true profiles of
the cracks revealed by destructive tests. This study also evaluates three natural stress corrosion cracks
found in actual nuclear power plants. The validity of the assumptions, as well as the difference
between the artificial and natural cracks, are discussed.

2. Evaluation of the electromagnetic characteristics of Inconel welds for the
discussion of numerical modeling
Since a variety of Inconel weld metals are utilized in actual nuclear power plants, this study firstevaluated the electromagnetic characteristics of four Inconel welds to discuss a suitable computationalmodel and also to support the generality of the results obtained through this study. The welds
evaluated and their AWS standard number are TR-52 (ERNiCrFe-7), NIC-70A (ENiCrFe-1), WEL
TIG S82 (ERNiCr-3), and TGS-70Ncb (ERNiCr-3).
Welded plate specimens were prepared to evaluate the electromagnetic characteristics of eachweld metal. The numbers of plate specimens to evaluate the electromagnetic characteristics of TR-52,
NIC-70A, WEL TIG S82, and TGS-70Ncb were three, unity, unity, and unity, respectively (sixwelded plates in total).
Columnar samples were cut from the plate specimens to measure the conductivity of the weld
metals. Each plate specimen provided two columnar samples with a diameter of 5 mm and a length of
90 mm. The resistance of the columnar samples was measured using a resistance tester (Resistance
HiTester 3541, HIOKI E.E. Corp.), and the conductivity of the weld metals was calculated from thedimension of the samples and the distance between the terminals of the measurements. Table 1
summarizes the results of the measurement of the conductivity. The table shows that the all the Inconel
welds are less conductive than Inconel 600 base metal[14], which agrees with other reports [15] [16] .
After measuring the conductivity, spherical samples were cut from the columnar samples tomeasure the relative permeability of the weld metals. Each columnar sample provided two sphericalsamples with a diameter of 4 mm. The B-H curves of the samples were measured using a vibrating
sample magnetometer (VSM5-15, Toei Industry Co., LTD.). Table 2 summarizes the relative
permeability of the weld metals calculated as (dB/dH)/μ0 at H=0, where μ0 denotes the permeabilityof vacuum. The table shows that the values of relative permeability of all the welds are almost unity.
In addition, all the samples did not show clear hysteresis or nonlinearity, as exampled in Fig. 1.
The experimental results confirm that the difference between the four weld metals in theirelectromagnetic characteristics is not significant from the viewpoint of electromagnetic
nondestructive evaluation. It is also reasonable to regard Inconel welds as a nonmagnetic material
with a uniform conductivity in numerical simulations. It should be noted, however, that theelectromagnetic characteristics evaluated here are rather macroscopic ones averaged over the samples.
This indicates that noise due to Inconel welds stems from non-uniform distribution of electromagnetic
characteristics, and thus the two conclusions above are valid only if signals are calibrated properly
and noise due to the weld is negligible.

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in Inconel welds
Table 1 Results of the measurement of conductivity of Inconel welds

Weld metal
TR-52

Welded Plate ID
1
2
3

NIC-70A

4

WEL TIG S82

5

TGS-70Ncb

6

Columnar Sample ID
1-1
1-2
2-1
2-2
3-1
3-2
4-1
4-2
5-1
5-2
6-1
6-2

Conductivity (MS/m)
0.90
0.90
0.90
0.90
0.90
0.90
0.94
0.94
0.89
0.89
0.88
0.88

Table 2 Results of the measurement of relative permeability of Inconel welds

Weld metal

Columnar Sample ID

TR-52

NIC-70A
WEL TIG S82
TGS-70Ncb

1-1
1-2
2-1
2-2
3-1
3-2
4-1
4-2
5-1
5-2
6-1
6-2

Relative permeability Relative permeabilityof spherical sample 1of spherical sample 2
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.01
1.01
1.01
1.01
1.00
1.01
1.00
1.00
1.00
1.00
1.00
1.00

3. Evaluation of the numerical model of stress corrosion cracks in Inconel
welds
3.1

Preparation of specimens

This study fabricated five welded plate specimens, whose dimensions are illustrated in Fig. 2, inorder to discuss numerical modeling of stress corrosion cracks in Inconel welds. The specimen was aflat plate made of type 304 and type 316L stainless steel plates butt welded using NIC-70A. The
surface of the weld was ground flat after welding. A stress corrosion crack was artificially introduced
by imposing tensile stress on the surface using a three-point bending jig and soaking in a polythionicacid solution. Table 3 presents the widths of the weld, which is denoted as w in Fig. 2.
3.2

Eddy current inspection

Eddy current inspections were carried out using a commercial eddy current instrument(aect2000s, ASWAN Co. Ltd.,) to gather eddy current signals due to the cracks. Four eddy current
probes were used: a differential type plus point probe for high frequencies, a differential type plus
point probe for lower frequencies, an absolute type pancake probe for higher frequencies, and an
absolute type pancake probe for lower frequencies. The square coils forming the plus point probes
measured 10 × 10 mm and 4.4 × 4.4 mm in outer and inner squares and 3.6 mm in width. The pancake170

H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds

probes had 5 and 1.6 mm in outer and inner diameters and were 2 mm in height. The probes for higher
frequencies were driven at 100, 200, and 400 kHz; those for lower frequencies were at 25, 50, and 100
kHz. The probes were positioned precisely by an automated XY stage and two-dimensionally scanned
the surface of the specimens. Signals gathered were recorded by a PC through an AD converter(NR-2000, Keyence Corporation).

Fig. 2. Plate specimen with artificial stresscorrosion cracks

Fig. 1. B-H curve of NIC-70A weld metal

Table 3 Widths of the weld lines of the specimens

Specimen ID
TP1
TP2
TP3
TP4
TP5

Width of weld line, w (mm)
35
35
45
45
45

Measured signals were calibrated using signals due to an artificial rectangular slit introduced intoa flat plate made from Inconel 600 base metal. The slit was 10 mm in long, 5 mm deep and 0.3 mm
wide. Then simple spatial filters to eliminate uniform noise were imposed on the measured signals as
V’(x,y)=V(x,y)-V(xs,y)-(V(xe,y)-V(xs,y))(x-xs)/(xe-xs), andV’’(x,y)=V’(x,y)-V’(x,ys)-(V’(x,ye)-V’(x,ys))(y-ys)/(ye-ys),

(1)
(2)

where V(x,y) is a two-dimensional vector consisting of the X- and Y-components of the measured
signals. Variables x and y indicate the probe position at which the signals were measured; x and y are
perpendicular and parallel to the weld line. Subscripts s and e denote the minimum and maximum
values of X and Y locations that the scan covers.
Figures 3 presents the distribution of eddy current signal amplitude obtained using the plus pointprobe for higher frequencies and the pancake probe for higher frequencies. The signals were obtained
at 100 kHz; the amplitudes of the signals were normalized so that the maximum signal amplitude dueto the slit was 10 V. The figure confirms that all the stress corrosion cracks provided clear signals.
Signals obtained using the plus point probe exhibited several peaks in most cases, although thoseusing the pancake probe provided only one peak approximately at the center of each crack. Since boththe probes had almost the same dimensions and thus there should not be such a significant difference
between their probes in their spatial resolutions, this implies that the stress corrosion cracks
introduced in this study had a large equivalent conductivity and a large equivalent width as indicatedin [17] . Signals obtained at other frequencies and other probes were qualitatively similar.

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds

TP1

TP2

TP3

TP4

TP5
Fig. 3. Eddy current signals measured using the plus point probe (left) and pancake probe (right).
The origin of the XY plane corresponds to the center of the specimen.

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3.3

Destructive tests

After the eddy current tests, the specimens were destroyed to reveal the true profiles of the stresscorrosion cracks. The destructive tests observed the cross-sectional profiles of the cracks at planes
perpendicular to the weld lines. The distance between two neighboring planes was 2 mm.
Figures 4 and 5 show the cross-sectional profiles of the cracks observed at the center of thespecimens and the boundary profiles of the cracks evaluated on the basis of the maximum depths ofthe cracks on each planes, respectively. The destructive tests revealed that the profiles of theintroduced stress corrosion cracks are categorized into three types. That is,1) TP1 and TP2 had planar cracks propagating mainly in depth direction. The cracks
showed clearer crack openings than other specimens. TP2 contained one relatively long
crack and a few shorter cracks running in parallel, and the maximum distance between
them was about 1.3 mm.
2) TP3 contained quite a few small cracks running parallel to each other. The maximum
distance between the cracks was as much as 10 mm.
3) TP4 and TP5 had single but quite volumetric cracks. Each specimen contained a single
crack; the cracks propagated not only to the depth direction but also the horizontal
direction of the specimen. Several cross-sectional planes, including the ones shown in Fig.
4, showed crack openings that were not connected to the surface of the specimen. This
indicates that the cracks propagated inside the weld metal in a complicated fashion.
3.4

Numerical evaluation of the crack parameters and comparison with natural stresscorrosion cracks found in Inconel welds of nuclear power plants

Finite element simulations were carried out to evaluate numerical models of the stress corrosion
cracks. The computational model adopted in the simulations is illustrated in Fig. 6. A crack wasmodeled as an assembly of columnar regions embedded inside a flat plate with uniform
electromagnetic characteristics of a conductivity of 0.94 MS/m and a relative permeability of 1. The
depths of the columnar regions corresponded to the boundary profiles of the cracks revealed by thedestructive tests; the columnar regions had a constant width, w, and uniform conductivity σ’. The
number of columnar regions in crack width direction was unity and thus a crack was modeled as aplanar region with a width of w.
The simulations were carried out using a finite element method-boundary element method eddy
current simulator based on a time-harmonic A-φ formulation [18] . The maximum signal obtained by
the numerical simulations was compared with that obtained by the experiments, and evaluated theequivalent width, w, and the equivalent conductivity, σ’, of a crack. Specifically, the numericalsimulations were carried out using the parameters shown in Table 4, and signals at an arbitrary
conductivity were calculated by interpolating the results of the numerical simulations. Then, w and σ’satisfying|V’’-Vsimu(w, σ’) |/|V’’|≤ ε(3)were regarded as suitable parameters termed as equivalent width and equivalent conductivity,
respectively in this study. Two-dimensional vectors V’’ and Vsimu were measured and simulated eddy
current signals, and were calibrated using the signals due to the slit so that they were quantitatively
comparable to each other. The threshold, ε, was set to 0.05 because of the presence of noise due to theweld. The evaluation took consideration of not only the maximum amplitude of signals but also its
qualitative spatial distribution. That is, evaluation of the signals due to the plus point probes imposedsuch a constraint that whether a crack provided a single signal peak directly above the crack or two
signal peaks appearing in the proximity of the crack, whereas the locations of the two peaks were notexplicitly taken into consideration. It should be noted that the simulations considered only one crack
although the destructive tests revealed some of the specimens contained multiple cracks.

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds

TP1

TP2

TP3

TP4

TP5

Fig. 4. Cross-sectional profiles of the cracks, observed at Y=0.

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds

TP1

TP2

TP3

TP4

TP5
Fig. 5. The boundary profiles of the cracks. Black solid circles indicate the maximum depths of the cracks
observed at each plane. The origin of the horizontal axis corresponds to the center of the specimen.

Fig. 6. Numerical modeling of the stress corrosion cracks. The conductivity of base material is denoted as σ0.

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
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Table 4 Parameters utilized in the numerical simulations

Parameter
width, w (mm)conductivity, σ’ (%)*

Value
0.01, 0.03, 0.05, 0.1, 0.3, 0.5, 1, 1.5, 2.0, 3.0, 4.0, 5.00, 0.1, 0.3, 0.5, 1, 2, 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99* conductivity with respect to those of outside crack (σ0)

Figures 7 and 8 summarize the results of the simulations to analyze signals obtained using the
pancake probes and the plus point probes, respectively. The figures exclude cases that did not satisfy
eqn. (3). That is, for example, Fig. 7 (a) excludes signals measured at 100 kHz using the low
frequency pancake probe as well as those at 200 kHz using the high frequency pancake because thesignals measured at these frequencies were not reproduced by the numerical simulation. In addition,
signals due to TP2 measured by the pancake probes did not satisfy eqn. (3) at all the frequencies. The
equivalent resistance of a crack, denoted as R in the figure, is defined as equivalent width divided by
the equivalent conductivity [12] . The figures indicate that the equivalent width and equivalentconductivity of stress corrosion cracks vary significantly and therefore it would not be reasonable toassume their minimum and maximum values in modeling stress corrosion cracks. In contrast, thefigures imply the validity of assuming the minimum equivalent resistance of stress corrosion cracks,
which agrees well with the finding of an earlier study by the authors considering stress corrosion
cracks in base metal. The results obtained by analyzing the signals obtained using the plus pointprobes are rather complicated. This is because the equivalent width of a crack has a significant effecton the characteristics of signals [17] [22] . Comparing the two figures indicates that the probe utilized
had less effect on equivalent resistance of a crack than equivalent width and conductivity themselves.

(a) TP1(b) TP3(c) TP4(d) TP5

Fig. 7. Results of the numerical simulations to evaluate suitable model of the artificial stress corrosion
cracks, when signals are measured by the pancake probes.

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds(a) TP1(b) TP2(c) TP4(d) TP5

Fig. 8. Results of the numerical simulations to evaluate suitable model of the artificial stress corrosion
cracks, when signals are measured by the plus point probe.

Figure 9 presents the results of the same analysis on three natural stress corrosion cracks found inInconel welds of nuclear power plants, together with the maximum depth and length of each crack.
Eddy current signals were obtained using a plus point probe; each crack was sufficiently separate
from the others, and two-dimensional distribution of the measured signals showed only a single peakdirectly above the crack. This implies that the natural stress corrosion cracks were not volumetric likethe artificial ones. Actually, the results presented in Fig. 9 indicate that the natural stress corrosion
cracks should be modeled as a relatively thin region. The equivalent resistances of the natural stresscorrosion cracks are somewhat smaller than those of the artificial ones.
Figure 10 shows the results of the earlier study analyzing stress corrosion cracks in base metals[13]. There is not such a significant difference between stress corrosion cracks in base metals andthose in Inconel welds from the viewpoint of their equivalent resistance, whereas the results obtainedin this study imply that stress corrosion cracks appearing in Inconel welds tend to have less equivalent
resistance. It should be noted that the figure summarizes the results obtained by various eddy current
probes, and parameters to model a stress corrosion crack depend on the probe utilized. Therefore
systematically obtained data are needed for further quantitative discussion.

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds(a) SCC1 (20.3 mm deep, 15 mm long)(b) SCC2 (11 mm deep, 3.5 mm long)(c) SCC3 (3mm deep, 4 mm long)
Fig. 9. Results of the numerical simulations to evaluate suitable model of the natural stress corrosion
cracks.

Fig. 10. Numerical models of stress corrosion cracks in base materials (originally presented in [13] , usedin this paper with a permission of copyright).

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H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds

4. Conclusion
This study evaluated numerical modeling of stress corrosion cracks in Inconel welds. The study
dealt with five artificial stress corrosion cracks introduced into Inconel welds, NIC-70A, and anotherthree natural ones found in Inconel welds of actual power plants. A crack was modeled as a region
having a constant width and uniform conductivity inside, and numerical simulations were carried out
to evaluate the values of the width and conductivity. These simulations provided reasonableagreement between measured and simulated signals in their maximum signals.
(1) When a stress corrosion crack is modeled as above, the width and conductivity of themodeled crack depend significantly on the probe and excitation frequency. However theequivalent resistance, which was defined as width divided by conductivity, depends much les
on these factors.
(2) The artificial stress corrosion cracks prepared in this study were more volumetric than natural
ones. This is confirmed not only the results of destructive tests revealing their cross-sectional
profiles; actually in the numerical model the artificial cracks were regions with relatively
large width and large conductivity. However, there was no significant difference between
their equivalent resistances.
(3) The stress corrosion cracks in Inconel welds considered in this study tended to have lessequivalent resistance than those in base metals.
Additional experiments were carried out to evaluate the electromagnetic characteristics of four
Inconel weld metals. The experiments confirmed their differences were negligible from the viewpointof eddy current testing, which supports the generality of the results obtained in this study. It should be
noted that in this study Inconel welds were modeled as a non-magnetic region having a uniform
conductivity. However, actually, the electromagnetic characteristics measured were averaged over a
volume. It is quite likely that from a more microscopic point of view the weld has more distributed
electromagnetic characteristics, which would be one of the reasons why the agreement between theexperiments and simulations were not satisfactory in several cases.
Although earlier studies by the authors demonstrated that a crack model with a uniform
conductivity inside provides good agreement when the maximum signals due to stress corrosion
cracks in a base metal are considered [12] [13] , this study sometimes failed to reproduce signals by
numerical simulations using the model. The most plausible reason for this is that this study consideredcracks in welds and signal processing adopted could not eliminate noise due to the weld sufficiently
or modified signals due to the crack. It would be likely that more complicated crack modeling such as
anisotropic conductivity [23] and three-dimensional modeling [24] would be necessary to deal withstress corrosion cracks in a general sense.

References
[1]
[2]
[3]
[4]
[5]
[6]
[7]

S. Suzuki, K. Takamori, K. Kumagai, A. Sakashita, N. Yamashita, C, Shitara, and Y. Okamura, Stresscorrosion cracking in low carbon stainless steel components in BWRs, E-Journal of Advanced
Maintenance 1 (2009), 1-29
H. Tanaka, Industry’s efforts toward technology development related to aging management of PWR
plants, E-Journal of Advanced Maintenance 1 (2010), GA10,.
I. Komura, T. Hirasawa, S. Nagai, J. Takabayashi, and K. Naruse, Crack detection and sizing technique
by ultrasonic and electromagnetic method, Nuclear Engineering and Design 206 (2001), 351-362.
D. Horn and W.R. Mayo, NDE reliability gains from combining eddy-current and ultrasonic testing,
NDT&E International 33 (2000), 351-362.
B.A. Auld and J.C. Moulder, Review of advances in quantitative eddy current nondestructive evaluation,
Journal of Nondestructive Evaluation 18 (1999), 3-36.
N. Yusa, Z. Chen, K. Miya, T. Uchimoto, and T. Takagi, Large-scale parallel computation for thereconstruction of natural stress corrosion cracks from eddy current testing signals, NDT&E International
36 (2003), 449-459.
H. Huang and T. Takagi, Inverse analyses for natural and multicracks using signals from a differential
transmit-receive ECT coil, IEEE Transactions on Magnetics 38 (2002), 1009-1012.

179

H. HUANG et al./ Electromagnetic modeling of stress corrosion cracks
in Inconel welds
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]

F. Kojima, N. Kubota, F. Kobayashi, and T. Takagi, Shape recovery of natural crack using evolutionary
programming related to eddy current testing, International Journal of Applied Electromagnetics andMechanics 15 (2001/2002), 243-247.
N. Yusa, L. Janousek, M. Rebican, Z. Chen, K. Miya, N. Dohi, N. Chigusa, and Y. Matsumoto, Caution
when applying eddy current inversion to stress corrosion cracking, Nuclear Engineering and Design 236(2006), 211-221.
Z. Badics, Y. Matsumoto, K. Aoki, F. Nakayasu, and A. Kurokawa, Finite element models of stresscorrosion cracks (SCC) in 3-D eddy current NDE problems, in: Nondestructive Testing of Materials, R.
Collins, W.D. Dover, J.R. Bowler, and K. Miya eds., IOS Press, Amsterdam, 1995, pp. 21-29.
N. Yusa, S. Perrin, K. Mizuno, and K. Miya, Numerical modeling of general cracks from the viewpointof eddy current testing, NDT&E International 40 (2007), 577-583.
N. Yusa and K. Miya, Discussion on the equivalent conductivity and resistance of stress corrosion cracks
in eddy current simulations, NDT&E International 42 (2009), 9-15.
N. Yusa and H. Hashizume, Evaluation of stress corrosion cracking as a function of its resistance to eddy
currents, Nuclear Engineering and Design 239 (2009), 2713-2718.
T. Takagi and H. Fukutomi, Benchmark activities of eddy current testing for steam generator tubes, in:Electromagnetic Nondestructive Evaluation (IV), S.S. Udpa, T. Takagi, J. Pavo, and R. Albanese, eds.,
IOS Press, Amsterdam, 2000, pp. 235-252.
L. Janousek, N. Yusa, Z. Chen, and K. Miya, Recognition of INCONEL weld conductivity variation bymeans of eddy current testing, in: Electromagnetic Nondestructive Evaluation (VIII), T. Sollier, D.
Premel, and D. Lesselier eds., IOS Press, Amsterdam, 2004, pp. 286-293.
W. Cheng, I. Komura, M. Shiwa, and S. Kanemoto, Eddy current examination of fatigue cracks in
Inconel welds, Journal of Pressure Vessel Technology 129 (2007), 169-174.
Z. Chen, L. Janousek, N. Yusa, and K. Miya, A nondestructive strategy for distinction of natural fatigue
and stress corrosion cracks based on signals of the eddy current testing, Journal of Pressure Vessel
Technology 129 (2007), 719-728.
F. Matsuoka and A. Kameari, Calculation of three dimensional eddy current by FEM-BEM coupling
method, IEEE Transactions on Magnetics 24 (1998), 182-185.
W. Cheng, S. Kanemoto, I. Komura, and M. Shiwa, Sizing of partial-contact stress corrosion cracks from
ECT signals, NDT&E International 39 (2006), 374-383.
H. Endo, T. Uchimoto, T. Takagi, A. Nishimizu, M. Koike, and T. Matsui, Natural crack sizing based on
eddy current image and electromagnetic field analyses, Review of Progress in Quantitative
Nondestructive Evaluation 25 (2006), 720-727.
N. Yusa, Z. Chen, and K. Miya, Sizing of stress corrosion cracking on austenitic stainless piping in a
nuclear power plant from eddy current NDT signals, Nondestructive Testing and Evaluation 20 (2005),
103-114.
S. Perrin, N. Yusa, and K. Miya, Automatic discrimination of stress corrosion and fatigue cracks using
eddy current testing, in: Electromagnetic Nondestructive Evaluation (V), S. Takahashi and H. Kikuchi,
eds., IOS Press, Amsterdam, 2007, 91-98.
M. Tanaka, H. Tsuboi, Finite element model of natural crack in eddy current testing problem, IEEE
Transactions on Magnetics 37 (2001), 3125-3128.
Y. Li, L. Udpa, and S. Udpa, Three-dimensional defect reconstruction from eddy-current NDE signals
using a genetic local search algorithm, IEEE Transactions on Magnetics 40 (2004), 410-417.

180