E-Journal of Advanced Maintenance Vol.9-2 (2017) 78-83
Japan Society of Maintenology

Quantitative Evaluation of Stress Corrosion Cracking Based on Features ofEddy Current Testing Signals
Li WANG1,* and Zhenmao CHEN2
1

College of Science, Xi'an University of Posts and Telecommunications, Xi'an, 710121, China
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University,
Xi'an, 710049, China
2ABSTRACTStress corrosion cracking (SCC) occurs in several key structural components of nuclear power plants over time.
A sufficiently precise quantitative technique is necessary to guarantee the safety and efficient operation of thekey structural components when SCC occurs. Quantitative evaluation of SCC profiles using eddy current testing(ECT) signals often underestimates the crack depth due to the local conductive property and the ill-posedness of
the inverse problem. In this paper, a quantitative evaluation method based on features of ECT signals isproposed to improve the sizing accuracy of SCC profiles. The proposed strategy includes a numerical SCC
model based on the local conductivity distribution, a hybrid inverse strategy combined with the conjugate
gradient method and the particle swarm optimization algorithm, and a quantitative evaluation method using
features of ECT signals. Reconstruction is conducted with simulated ECT signals from conductive cracks, andthe results show that the proposed strategy is effective in improving the sizing precision of SCC profiles.
KEYWORDS

ARTICLE INFORMATION

eddy current testing, stress corrosion cracking, reconstruction, numericalmodel, optimization algorithm

Article history:
Received 7 Novemver 2016
Accepted 27 April 2017

1.

IntroductionStress corrosion cracking (SCC) is a failure phenomenon of materials used in nuclear power
plants, such as austenitic stainless steel and high-nickel alloys. SCC may cause sudden catastrophes
without obvious signs. Therefore, a sufficiently precise quantitative nondestructive testing technique
is necessary to enhance the safety and availability of nuclear power plants.
Given its superior detection ability for shallow surface cracks as well as serious effect of theanisotropy of the columnar crystal in the weld on ultrasonic signals, eddy current testing (ECT) is aviable complement to ultrasonic testing in the reconstruction of cracks, especially with regard torecognizing crack length and evaluating cross-sectional profiles [1-5]. However, the SCC depth isoften underestimated using ECT signals due to the local conductive property of cracks andill-posedness of the inverse problem [6]. In this paper, a quantitative evaluation method is proposed
based on feature analysis of ECT signals to improve the sizing accuracy of SCC profiles.
Reconstruction results from simulated ECT signals reveal that the proposed strategy is effective inimproving the sizing precision of SCC profiles.

2. A numerical SCC model based on feature analysis of ECT signals
The ECT inverse problem of crack reconstruction is usually defined as a minimum problem of
the mean square residual [7, 8]:min  (c,  )   Zn (c,  ) - Znmea

2(1)

n*

Corresponding author, E-mail: wl_3691@163.com

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

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L. Wang and Z. Chen/ Quantitative evaluation

where Z n (c,  ) and Z nmea are the simulated and measured ECT signals, respectively, at the nth scanningpoint; c and  is the crack shape and conductivity parameters, respectively. A model-based numericalmethod is usually applied to obtain the optimal solution by a series of iterative computations [9, 10].
In order to establish a numerical SCC model, we first investigate the relation between crack
shape parameters and features of ECT signal. In this section, a standard pancake coil (inner diameter
1.2 mm, outer diameter 3.2 mm and thickness 0.8 mm) and a plus-point coil (inner side length 4.5 mm,
outer side 5.5 mm and height 2.0 mm) are applied as the inspection probe. Cracks in a SUS304 platethat is 10 mm in thickness, 200 mm in length, 100 mm in width and 1.4 MS/m in conductivity aretaken as the detection object. The excitation frequency is 10 kHz for the pancake probe and 30 kHz
for the plus-point probe. The liftoff is 0.5 mm and 1.0 mm, respectively.
2.1. Crack length and ECT signal features
The crack length mainly influences the start and end positions of ECT signals and has little effecton the amplitude and phase for parallel scanning ECT signals above the crack plane as shown in Fig. 1.

Fig. 1. ECT signal from a conductive crack model with different lengths using the pancake probe (left)
and plus point probe (right) (Crack parameters: width 0.2 mm, depth 3 mm, relative conductivity 5%)

2.2. Influence of crack depth and local conductivity on ECT signals
Figure 2 describes the ECT signals from a crack model with different local conductivity andshows that the variation in crack conductivity has obvious effect on amplitude and slight effect on phase.
Figure 3 shows that the change of crack depth influences both the amplitude and phase. In general, thecrack conductivity value and distribution in the depth direction affect the ECT signals in a manner that issimilar to the effect of the crack depth. Therefore, in model-based reconstruction of SCC profiles, thelocal conductivity of the crack zone should be considered to obtain accurate crack depth information.

Fig. 2. ECT signal from a crack model with different crack conductivity using the pancake probe (left)and plus point probe (right) (Crack parameters: length 16 mm, depth 3 mm, width 0.2 mm)

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Fig. 3. ECT signal from a conductive crack model with different depths using the pancake probe (left)
and plus point probe (right) (Crack parameters: length 16 mm, width 0.2 mm, relative conductivity 5%)

2.3. Crack width and ECT signal features
When crack length, depth, and local conductivity are fixed, the amplitude of the ECT signal
above the crack plane changes obviously and the phase changes only slightly with changes in crackwidth; this trend is similar to the effect of crack conductivity changes. Figure 4 depicts thecomparisons of ECT signals when the crack width ranged from 0.2 to 0.4 mm (length×depth: 16mm×3 mm), in which the relative increase of amplitude is far greater than that of phase. Accordingly,
variations in crack width can be considered to be just as influential as change in the crack conductivity[11, 12]. Therefore, if depth and length are kept constant and the error in the amplitude and phase ismaintained at low values, ECT signals of different crack widths can be approximated using a certain
width crack with its equivalent conductivity. For example, for crack length (16 mm) and depth (3 mm),the ECT signals of width (0.3 mm) and relative crack conductivity (5.0%) can be approximated using
the signals of width (0.2 mm) and relative crack conductivity (1.76%) or width (0.4 mm) and relative
crack conductivity (6.70%) without changing the crack length and depth.
Based on the results of numerical analysis and the measurement of the conductivity distribution
for an artificial SCC in the crack zone [13-15], a 2D numerical SCC model that considers the crack
conductivity distribution with multiple conductivity parameters in the crack depth direction isproposed, in which the width is fixed to a certain value and crack shape parameters comprise only thecrack length and depth.

Fig. 4. ECT signal from a conductive crack model with different widths using the pancake probe (left)
and plus point probe (right) (Crack parameters: length 16 mm; depth 3 mm; relative conductivity 5%)3.

A hybrid inverse strategy with the particle swarm optimization algorithm
Quantitative evaluation of SCC profiles is a multi-dimension optimization problem because the80

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crack shape and multiple conductivity parameters both need to be reconstructed. When the crack
conductivity and shape parameters are reconstructed simultaneously, the error on the crack shapeparameters often increases and the result may be not convergent because different kinds of crack
parameters have different modified scales. Therefore, we use a hybrid inverse strategy combined withthe conjugate gradient method and the particle swarm optimization algorithm to reconstruct
respectively the crack shape and conductivity parameters in order to solve the problem ofmulti-dimension and different modified scales. Specifically, for a set of given conductivity parameters,
the conjugate gradient method was used to optimize crack shape parameters and to obtain a minimalevaluation function corresponding to the given conductivity parameters. Then the particle swarm
optimization algorithm was utilized to guide the crack conductivity parameters to optimal solutions
according to the corresponding minimal evaluation function [16, 17]. Though the hybrid inverse
strategy needs more computational time than a single method, it is more stable and gives better results
for the inverse problem of SCC profiles reconstruction.

4.

An evaluation strategy of SCC based on features of ECT signals

Crack length is easily identified using the start and end positions of parallel scanning ECT
signals above the crack plane in the detection process and it is rarely affected by other crack
parameters. Accordingly, this section mainly considers the crack depth and conductivity parameters tosimplify the problem of the quantitative evaluation of SCC profiles.
Numerical experiments show overall similarities with certain differences in the effect of the ECT
signal features with the change of crack depth and local conductivity as shown in Fig. 2 and Fig. 3. In
general, the real and imaginary parts of ECT signals vary differently with changes in the crack depthand local conductivity. In reconstructing crack profiles, if the conductivity parameters are set as
smaller than the real values, the reconstructed crack depth is often smaller than the actual values inaccordance with the minimum principle of the mean square error. This difference usually causes theabsolute value of the real part of the ECT signals to be larger while the absolute value of theimaginary part to be smaller than the true values. In contrast, if a larger crack conductivity value is set,
then the reconstructed depth will often be larger, the absolute value of the real part of the ECT signals
will usually be smaller than the true values. Consequently, the reconstruction precision of crack
profiles is expected to be improved by setting a proper crack conductivity value when using theminimal mean square residual of the real and imaginary parts of the ECT signals. Therefore, weproposed a strategy to reconstruct SCC profiles using features of ECT signals to reduce theill-posedness of SCC profiles reconstruction.

5.

Numerical results

To validate the strategy, an example of SCC reconstruction is performed by taking numericalsimulation ECT signals as target signals. The simulation signals are from a conductive elliptical crackmodel of 14 mm length, 3 mm depth and 0.4 mm width. The excitation frequency is 30 kHz andlift-off is 1.0 mm. The inspection probe is taken as the above-mentioned plus-point coil. For the fast
forward solver [18], databases of unflawed potentials were established for a search region of 18 mmin length, 5.5 mm in depth and 0.4 mm in width. The search region was subdivided into 198 (18 111) cells. The crack relative conductivity is expressed as 3 parameters, that is, 2%, 5% and 8%
from the surface to the bottom layers of the inspection specimen. Each conductivity parametercorresponds to 1 mm thickness of the inspection specimen.
Take the crack conductivity, depth and length as reconstructed parameters. 7 times reconstruction
was performed with different initial values using the proposed strategy. On condition that the relative
error of mean square of ECT signals is less than 4.5 107 , the reconstructed crack depth is from 2.96
mm to 3.12 mm, and the average depth is 3.04 mm. The reconstructed crack length is from 13.84 mm
to 14.00 mm. By comparing with the true crack profiles, all of 7 times reconstruction results converge
to the true values with high accuracy. The results corresponding to the reconstructed maximum depth(3.12 mm) and the minimum depth (2.96 mm) from the repeat processes are shown in Fig. 5(a).
Comparison of ECT signals is shown in Fig. 5(b). Since the reconstruction results of crack81

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conductivity distribution are equivalent values, there may be some errors between the reconstructedvalues and the true ones as shown in Tab. 1. Nevertheless, as SCC complicated conductive property isdescribed using multiple conductivity parameters and the effect between the crack depth andconductivity is distinguished using features of ECT signals, reconstruction precision of crack depth isimproved.

(a) Comparison of crack profiles(b) Comparison of ECT signals
Fig. 5. Comparison of reconstruction results from a conductive elliptical crack model
Table 1 Reconstructed crack conductivity distribution using 3 conductivity parameters

Figure 6 depicts a reconstruction result from simulated ECT signals with 5% white noise. 6 times
reconstruction process are implemented using the proposed strategy with different initial values. On
condition that the relative error of mean square of ECT signals is less than 5.85 105 , the reconstructedaverage depth of crack is 3.09 mm and the average length is 13.96 mm. Good predictions on the crack
profiles are obtained even for the signals with 5% white noise. Reconstructions of several other crackmodels are also conducted. All the results reveal that the scheme is efficient for reconstruction of SCC
profiles.

(a) Comparison of crack profiles(b) Comparison of ECT signals
Fig. 6. Reconstruction results from ECT signals with 5% white noise from a conductive crack model82

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6. Conclusion
In this paper, a quantitative evaluation method based on features of ECT signals is proposed toimprove the sizing accuracy of SCC profiles. The method includes a 2D numerical SCC model
considering crack conductivity distribution, a hybrid inverse strategy combined with the conjugate
gradient method and the particle swarm optimization algorithm, and a quantitative evaluation method
using feature analysis of ECT signals. Reconstruction results from simulated ECT signals due toconductive cracks reveal that the proposed strategy is effective for the sizing of SCC profiles.

Acknowledgement
This work is supported in part by the National Magnetic Confinement Fusion Program of China(2013GB113005), Natural Science Foundation of China (51277139 and 11321062) and the Scientific
Research Scheme of Education Department of Shaanxi Province, China (15JK1677).

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