Abstract
Usually, the stress corrosion crack (SCC) has a complex shape of non-zero conductivity. Its shape is very difficult to reconstruct accurately by using eddy current testing signals. At present, most defaults being dealt with are shallow cracks with a simple shape, which are not consistent with the actual cases. In order to detect the deep SCC in metal materials quantitatively, a new eddy current probe with capability of deep penetrating is proposed in the paper. Based on the research results of current literature, the conductivity model of deep SCC is established. ANSYS software is used to analyze the influence of crack inclination, branching position and branch number on eddy current signals to build the equivalent model of SCC. Simulation results show that the new probe is more sensitive to complex SCC than the conventional pancake probe, and can distinguish whether the SCC having branches or not and what the branching position is. The quantitative results of SCC obtained by using a calibration curve show that the detection signals picked up by the new probe can effectively be used to deduce the depth of branching SCC.
Introduction
Some key equipments of nuclear power plant, such as heat exchanger, cooler, pressure vessel, etc., are prone to stress corrosion cracking (SCC) in materials due to long-term stress and contact with corrosive media. This case may lead to serious disaster and cause great loss if there is no necessary measures to be taken. To avoid the unfortunate consequences, a rapid and comprehensive testing for the equipments is necessary. Comparing with other methods, eddy current testing method (ECT) has the characteristics of non-contact, fast and sensitive. It has been widely used to detect surface and near surface defects in various conductive materials [1–4]. Because SCC has a complex branching structure and unknown conductivity in the cracking area, it is very difficult to reconstruct its shape by using eddy current signals.
In order to improve the assessment accuracy of SCC quantitatively by using ECT, many scholars have carried out research works on SCC detection. Yusa [5] discussed the numerical modeling of fatigue and stress corrosion cracking. He found that a fatigue crack can be modeled as a non-conductive region without width needed to be considered, and the SCC needs to be modeled as a conductive region with a certain width. Wang Jing [6] studied the optimization of SCC model. Based on the analysis of the simulated and real crack experimental signals of the two models, it is found that it is more meaningful to study the equivalent resistance of SCC than to discuss the equivalent width and conductivity separately. Zhang Siquan and Geng Qiang [7,8] reconstructed the shape of SCC by using the neural network. This method has the advantages of sensitivity and accuracy, but it needs taking a lot of time to generate data and it is also difficult to reconstruct the crack conductivity.
Most of the SCC models studied in present literature have a simple structure, while the complex SCC with a branching structure in practice is seldom involved. In this paper, ANSYS is used to study the influence of the branch number, branching location of SCC on impedance signals, an equivalent conductivity model of SCC is proposed, which can effectively characterize the SCC branching shape. In order to improve the reconstruction accuracy, a new type of deep penetrating probe developed by us is used to pick up the disturbance signals induced mainly by SCC branches. The simulation results show that the new probe has better performance than the traditional one in detecting the complex SCC.
Modeling of SCC with branches
The SCC usually has a branching structure. As its structure and conductivity both have effects on impedance signals, it is necessary to take them into account to obtain better reconstruction results of crack shape. The quantitative target in this paper is set to reconstruct the crack branching range. This is realized by using an equivalent crack model with a constant conductivity and a simple shape. The model is built based on the consideration of the influence of crack branching and conductivity. Figure 1 shows the conductivity models (a) to (c) of the real SCC and the equivalent models (d) to (e). In order to simplify the modeling, their shape along the length direction is set as rectangles. The cross-section shape is modeled as one trunk with or without branches.
The crack is 15 mm long and 0.2 mm wide. Its total depth h is 15 mm. The crack trunk has a depth of h1 and the branching depth h2. The default value of crack inclination 𝛼 is set as 60 degrees. The SCC model is divided into 15 layers in depth direction. According to reference [9], the conductivity of SCC along the crack depth increases from 4.5% σ0 to 27% σ0 linearly [10], and that of the fifteenth layer is set as 40.5% σ0. σ0 is the conductivity of the base metal. The base metal is made of 304 SUS. Its size is 100 mm × 100 mm × 20 mm. Its conductivity and relative permeability are σ0 = 1.4 ×106 s ⋅ m−1 and μ r = 1 respectively.
To overcome the limitation of skin effect, a new type of eddy current probe based on phase-shifting field principle was proposed to inspect SCC in the paper. As shown in Fig. 2(a), the new probe uses two excitation coils e1 and e2 to inducing eddy currents. They are fed with AC of amplitude and phase adjusted to produce deep penetrating eddy currents at point O. The defect signals is detected by the coil p. As shown in Fig. 2(b), the penetrating depth of eddy currents can reach about 26 mm at 1 kHz. Because the eddy currents mainly concentrate on a point at the depth of 12 mm in the material, the new probe is more sensitive to the disturbance signals caused by the crack branching than the traditional one. For the excitation frequency of 1 kHz, the standard penetration depth of the eddy currents induced in the material by the new probe is about 2.3 times that by the traditional one. Figure 2(c) shows the comparison of detection signals between the new probe and the traditional one. It can be seen that the new probe is more sensitive to the change of crack depth than the traditional one.
The conductivity models of SCC and the equivalent models.
Principle of the new probe.
Effect of crack inclination angle
In order to improve the reconstruction accuracy of SCC with branches by using eddy current signals, it is necessary to study the sensitivity of the eddy current probe to crack branching, that is, the influence of crack inclination, crack branching position and branch number on detection signals. As shown in Figs 1(a) and (b), the variation of impedance signals for the non-branching crack with angle 𝛼 of 90, 75 and 60 degrees was investigated, as well as that for the two-branching crack with angle 𝛼 of 75 and 60 degrees in this section. The total depth for the crack without or with branching is 15 mm. The crack with two branches has the trunk length of 5 mm and branching length of 10 mm. In order to avoid the influence of crack conductivity on impedance signals, here the crack conductivity is taken as 0.
Figure 3 is the comparison of impedance signals for the angle 𝛼 of different value by using the new probe. From the results of the figure, it can be seen that the change in crack inclination and branching angle will cause the change in impedance signals. Position of the impedance peak will shift to the inclined direction of the crack. Figure 3(b) shows that the larger the angle 𝛼, the wider the peak value of the impedance signals. Other results show that the impedance signals of the crack obtained by the new probe is larger than that of the traditional one. And the former is more sensitive to the inclination and branching angle of the crack.
Impedance signals for cracks at different inclination angle.
In this section, the influence of branching position and branch number of SCC on impedance signals is analyzed. The research object includes a vertical non-branching crack, a two-branch crack and a three-branch crack. The trunk size of SCC with two or three branches is 15 mm × 0.2 mm × 5 mm. The total crack depth h for them is 15 mm. The branching occurs at depth of h1 = 5 mm. For the two-branch crack, the branch width and the angle 𝛼 between the branches are w1 = 0.1 mm and 60 degrees respectively. While for the three-branch crack, they are 0.07 mm and 30 degrees respectively.
The impedance signals for the crack with different number of branches by using the new probe are compared and shown in Fig. 4(a). It can be seen that whether with branches or not the crack can be identified through the detection signals obtained by the new probe, but the number of branches is difficult to distinguish.
Figure 4(b) is the comparison of impedance signals for the crack branching at different position. It shows that there is an obvious difference in impedance magnitude between the signals obtained by the new probe due to the crack branching at different position. Other results show that for the signals picked up by the traditional probe, it is difficult to know whether the crack has branches, where is the branching position or what is the number of branches from signals. These results indicate that the new probe is more sensitive to crack branching than the traditional one, and is more suitable for quantitative detection of SCC with branches.
Impedance signals for the cracks with branches.
The conductivity of SCC is not zero. This would affect the detection signals and then the reconstruction accuracy of the crack shape if it is not taken into account. To improve the reconstruction accuracy, it is necessary to obtain the conductivity distribution of SCC in advance. However, the detailed distribution is difficult to obtain because it is not only related to material properties, but also to crack size and shape. At present, there are only a few works about the conductivity distribution of SCC region in the stainless steel material having been done.
To overcome the difficulty in measurement of conductivity, equivalent models of conductivity are tried to build for reconstruction of SCC with branches. The models have a simple shape with constant conductivity. There are two equivalent models of conductivity considered here. Model 1 has two branches. Its shape is the same as that of the real SCC (Fig. 1d). Because the number of branches has little effect on impedance signals, the model with two branches can be used to represent the three-branch SCC. Model 2 has a rectangular shape surrounding whole or part of the SCC branching region to characterize the branching range (Fig. 1e).
The testing signals of the models are used as the input of inverse problem for quantifying the shape or branching range of SCC. Therefore, the testing signals should be same as that of the real SCC. To find the appropriate conductivity to achieve the goal, the impedance signals of Model 1 with the crack of different conductivity value are calculated and shown in Fig. 5(a). The result shows that when the conductivity of the crack is set as about 9% σ0, the signal peak is close to that of the SCC.
Figure 5(b) is a comparison of the impedance signals between the SCC and Model 2. It shows that only the width of the rectangular region is set as 0.4 mm and the area with conductivity of 18% σ0, the detection signal is similar to that of the SCC. Conversely, if the rectangular region is much wider than the width of the crack trunk, the signals of the model and SCC differ greatly, regardless of the value of conductivity. It indicates that compared with Model 1, Model 2 can only used to describe the range of the crack trunk, not including the branching zone. Therefore, Model 1 is selected for reconstruction of SCC shape in the paper.
Comparison of impedance signals between the models and SCC.
In order to verify the applicability of Model 1 to SCC reconstruction, a calibration curve for inspection of SCC depth is built by using the impedance peak of Model 1. Firstly, the conductivity of the crack zone is set as 9% σ0 and the crack depth is changed to calculate the corresponding impedance signals. The impedance peak and the corresponding crack depth is extracted to form the relationship curve. Then, the impedance peak of the SCC is also obtained and used as the input of the interpolation method or the curve fitting method to deduce the SCC depth. The deduction results show that for the SCC with total depth of 15 mm, the depth obtained by the calibration curve is 14.45 mm. The relative error between the deduction result and the true value is 3.65%.
Conclusion
In this paper, the influence of crack branching on impedance signals is studied by using the ANSYS software. Based on the detection signal obtained by using a new eddy current probe with capability of deep penetrating, an equivalent model of conductivity is built. Using the model, the SCC shape can be reconstructed accurately without considering the actual distribution of conductivity in the crack area. The simulation results show that the relative error of deduction by using the equivalent model for quantifying SCC branching length is about 3.65%.
Footnotes
Acknowledgements
This work was supported in part by National Natural Science Foundation of China (Grant No. 51667001), Key Scientific Research Projects of North Minzu University (Grant No. 2019KJ36) and General research projects of Key Laboratory of Chemical Engineering and Technology Foundation of State Ethnic Affairs Commission (Grant No. 2017HG06).