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Quantitatively related acoustic emission signal with stress corrosion crack growth rate of sensitized 304 stainless steel in high-temperature water
Corrosion Science 157 (2019) 79–86
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Corrosion Science journal homepage: www.elsevier.com/locate/corsci
Quantitatively related acoustic emission signal with stress corrosion crack growth rate of sensitized 304 stainless steel in high-temperature water Zhen Zhanga,b, Ziyu Zhanga, Jibo Tana, Xinqiang Wua,
T
⁎
a
CAS Key Laboratory of Nuclear Materials and Safety Assessment, Liaoning Key Laboratory for Safety and Assessment Technique of Nuclear Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, PR China b School of Materials Science and Engineering, University of Science and Technology of China, Hefei, 230026, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: A. Stainless steel B. SEM C. Stress corrosion C. High-temperature corrosion
Stress corrosion cracking (SCC) of sensitized 304 stainless steel in high-temperature water was in-situ monitored by coupling acoustic emission (AE) and direct current potential drop (DCPD) techniques. The AE signals were identified using novel recurrence quantification analysis (RQA) and k-mean cluster method. It was found that the RQA is feasible to identify the evolution of different AE waveforms generated by ligament tearing and plastic deformation of the crack tip. The AE cumulative hits rate was linear with the SCC crack growth rate, providing a possibility for applying the AE technique to quantitatively evaluate SCC in high-temperature water.
1. Introduction Austenitic stainless steels (SSs) such as 304 SS and 316 L SS have been used as primary pipe and reactor internal materials in nuclear power plants (NPPs). However, they are susceptible to stress corrosion cracking (SCC), and the SCC is a serious threat for structural components in NPPs due to its abrupt brittle failure prior to expected ultimate elongation [1–3]. Monitoring the SCC behavior of structural materials under actual service environments is important for ensuring the safe operation of NPPs. Acoustic emission (AE) measuring the spontaneous energy release within the material during the damage process is a promising monitoring technique and has been widely utilized to monitor the corrosion damages, in particular SCC [4–12]. Calabrese et al. investigated the SCC behavior of 17-7 pH SS in MgCl2 solution using AE technique and found that AE energy can separate different SCC stages including pre-activation phase, active damaging phase, long crack propagation phase and final catastrophic failure [8]. Delaunois et al. investigated the chlorideinduced SCC behavior of austenitic SS by AE [10]. It was found that different phases including initiation and propagation of pitting and cracking, fracture of the specimen can be separated by the AE amplitude. In the previous study, AE waveforms were related with SCC process of 304 SS in high-temperature water [12]. A discriminant factor calculated by the ratio of the burst signals and continuous signals and a discriminant model were proposed to auto-monitor the SCC. Though great achievements have been made in applying AE to monitor SCC
⁎
during the past several decades, most of the research was focused on qualitatively relating AE signals with SCC stages, and few studies were involved in the quantitative information between AE signals and stress corrosion crack propagation. Some attempts were made to establish the quantitative model between the AE signals and fatigue crack growth rate in air [13–15]. However, only mechanical fatigue crack propagation was treated, little attention was paid to SCC which is a synergistic result of stress and environmental factors. These factors including type and level of the stress, temperature, dissolved oxygen, ion species and concentration and so on make the SCC behavior quite complex [16–18], and there is a need to further investigate the possibility of AE quantitative evaluation of SCC. In order to apply AE technique to monitor the corrosion damages, another important task is how to deal with the AE signal. In general, the waves are directly detected by the AE sensor and are transformed into digital AE signals after the pre-amplification. Then some traditional parameters such as rise time, count, duration, amplitude, energy and so on can be extracted. Though these AE parameters have been widely used in most previous studies [4–10,19–21], there are still some drawbacks as mentioned by Chai et al. [22]. One of the serious problems is that the above parameters except for amplitude strongly depend on the selected threshold, which may hinder the correct reflection of the original AE waveform. So it is necessary to develop some advanced signal processing methods to analyze the AE signal. Marwan recently proposed a recurrence quantification analysis (RQA) method to characterize the digital time-series [23]. Savari et al. preliminarily
Corresponding author. E-mail address: [email protected] (X. Wu).
https://doi.org/10.1016/j.corsci.2019.05.030 Received 11 January 2019; Received in revised form 2 May 2019; Accepted 29 May 2019 Available online 30 May 2019 0010-938X/ © 2019 Elsevier Ltd. All rights reserved.
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analyzed the AE signal using the recurrence plot and RQA to monitor the hydrodynamic behavior of spouted beds, which proves that RQA is a powerful tool for monitoring this behavior [24]. In the present work, SCC of the sensitized 304 SS in high-temperature water was in-situ monitored by coupling AE and direct current potential drop (DCPD) techniques. An attempt was made to analyze the AE signal generated by SCC using the RQA method. A quantitative relation between the AE signal and SCC crack growth rate was established. The aim is to provide a novel AE signal processing method and explore the possibility for applying AE to quantitatively evaluate SCC crack growth rate in high-temperature water.
Matlab 2016a with cross recurrence plot toolbox developed by Norbert Marwan et al [23]. The RQA has been successfully applied in some fields such as finance, meteorology and psychology and so on to process the time-series [29–31]. There are also some applications in corrosion field to process the electrochemical oscillations signal [25]. However, to our knowledge, there is no work employing RQA to process the AE waves generated by corrosion damages. This is the first attempt to process the AE signals generated by corrosion damages using the RQA method.
2. Theory on RQA of AE signal
3.1. Specimen and experimental set-up
Generally AE waveform is a one-dimensional time-series and this time-series can be reconstructed using the time delay embedding to obtain the system trajectory of the AE waveform. In the present study, the embedding dimension of 5 determined by the false nearest neighbor method and the time delay of 4 determined by the mutual information method were used. Then recurrence plot (RP) of the AE signal can be calculated according to Eq. (1), where H is the Heaviside operator, ||…|| calculates the Euclidean norm between xi and xj, ε is the threshold value and is defined as standard deviation of the AE time-series in the present study.
The composition (wt. %) of sensitized 304 SS used in the present study is 0.03 C, 18.67 Cr, 9.25 Ni, 2.00 Mn, 0.64 Si, 0.98 Cu and Fe Balance. The sensitized treatment was performed at 650°C for 48 h and then followed by furnace cooling. 0.5 T compact tensile (CT) specimens were used. The dimensions of the specimen followed ASTM E399 with a thickness of 12.5 mm and a width of 30 mm. Specimens were ground to 2000 grit with silicon carbide paper and the two main surfaces were polished with 2.5 μm diamond paste. The specimens were firstly precracked in air with a maximum load of 4000 N under a sinusoidal wave at 20 Hz using a fatigue machine (EHF-EB10-20 L, Shimadzu, Japan), and the stress ratio is 0.2. Fig. 1 shows the SCC set-up in high-temperature water equipped with in-situ AE and DCPD monitoring system. Two AE wide band sensors provided by Physical Acoustics Co. were used, one as the experimental sensor was mounted on the load rod through the Vaseline to receive the AE waves generated by SCC, and the other mounted on the load device was regarded as guard sensor to eliminate the environmental noise. The AE waves were sent to the AE acquisition through a Type 2/4/6 preamplifier set at 40 dB and then were transferred to the digital signal. During the SCC tests in high-temperature water, the specimen was electrically isolated from the clamp with zirconia bushings and spacers. Pure nickel wires coated by heat-shrinkable polytetrafluoroethylene (PTFE) were spot-welded to the specimen and used to transmit the current and potential signals to the DCPD system. 3 A direct current (DC) was applied to the specimen by a DC power. Crack length was in-situ monitored by DCPD system continuously, and the crack growth rate is then determined by the slop of crack length vs. time curve.
Ri, j = H (ε -||x i − x j ||) i, j = 1, ⋯, N
3. Experimental
(1)
Ri,j is an N × N matrix consisting of 0 and 1. 0 is represented by a black point in RP, meaning this point can be recursive. Otherwise, 1 is represented by a white point. There are three patterns including single points, diagonal lines, vertical and horizontal lines in RP [25]. Some parameters can be extracted to quantitatively represent these patterns, and this process is called as the RQA method. Among these parameters, four parameters, namely, recurrence rate (R), determinism (D), Shannon entropy (E), average diagonal line length (Lmean) are commonly employed [26–28] and are also considered in the present investigation. (i) R represents the density of the recurrence points in RP and can be expressed as Eq. (2)
R=
N
1 N2
∑
R (i, j ) (2)
i, j = 1
• D represents the ratio of the recurrence points forming diagonal
3.2. Experimental process
lines of at least λmin length over all recurrence points and can be expressed as Eq. (3). λmin was chosen as 2 in the present study. P(λ) is the histogram of the diagonal lines of length.
The SCC tests were conducted in high-temperature (300 °C) and high-pressure (10 MPa) water, the flow rate was controlled to 3 L/h. The experimental system was maintained for 24 h at the target temperature and pressure to eliminate the most noise signals during the heating, and the amplitude threshold value was set at 35 dB. The specimen was pre-loaded to 1000 N to eliminate the gaps between the fixtures. Then, the SCC tests were started and continuously monitored by AE and DCPD. Two factors including load and dissolved oxygen concentration (DO) were considered to generate different AE signals and cracking behaviors. The detailed experimental parameters were listed in Table 1. The AE monitoring system was suspended at the moments when the loading was changed to avoid possible interference signals. The specimen was finally fractured by post-test fatigue in air to observe the fracture morphology using an FEIINSPECT F50 scanning electron microscope (SEM).
N
D=
∑λ = λmin λP (λ ) N
∑λ = 1 λP (λ )
(3)
•L
mean represents the average diagonal line length and can be expressed as Eq. (4)
N
L mean =
∑λ = λmin λP (λ ) N
∑λ = λmin P (λ )
• E is the Shannon entropy of the probability p(λ), p (λ) =
(4) P (λ ) ∑N λ=λ
min
P (λ )
.
E reflects the complexity of the RP with respect to the diagonal lines, and can be expressed as Eq. (5) N
E= −
∑ λ= λmin
4. Results and discussion
p(λ)lnp(λ) (5)
Fig. 2 shows the evolution of the crack length monitored by the DCPD and AE cumulative hits during the SCC tests of sensitized 304 SS
The RQA parameters mentioned above were calculated using 80
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Fig. 1. The set-up of SCC in high-temperature water equipped with in-situ AE and DCPD monitoring systems.
to have similar value for these AE signals (Fig. 4b). In comparison with the RQA parameters, the traditional parameters seem to be difficult to separate the AE signals (Fig. 4e-4 h). Only the rise time shows a certain ability (Fig. 4e), one type of signal has low rise time, the other type contains some signals with high rise time. Furthermore, k-mean cluster using the RQA parameters was employed to better cluster the AE signals. Fig. 5 shows the evolution of different AE clusters during the whole tests. It is clear that cluster 1 quickly increased from 0 h to around 5 h, and only several signals of this type can be detected within the subsequent test period. Otherwise, the cluster 2 became detectable after around 5 h and then dominated the AE behavior. Fig. 6 shows the typical AE waveforms and corresponding RPs of the two clusters. It is clear that the cluster 1 is a burst signal and cluster 2 is a continuous signal (Fig. 6a and b). According to the evolution of the crack length and different AE clusters, two phases can be identified. The first phase is 0 h to 5 h, the crack length keeps constant. The cluster 1, namely the burst signals, increased sharply. The second phase is 5 h to 150 h, the continuous signal became dominant and only several burst signals were randomly detected. At the first phase, the specimen was loaded to 4000 N through slow strain rate tension (SSRT) and no crack propagation occurred. The tested CT specimens had transgranular fatigue pre-crack, which inevitably leaves lots of ligaments. Once the specimen was re-loaded and pulled down, these residual ligaments were torn, which emitted AE signals. Therefore, it is inferred that the burst signals were generated by the residual ligaments tearing of fatigue pre-crack. At the second phase, the load was constant in each test. The crack began to propagate under the action of the stress and high-temperature water, and the crack growth rate mainly depended on the stress level and the water chemistry (Fig. 2a). In general, the crack propagation of SS under constant load was promoted by the plastic deformation of the crack tip, and the plastic deformation of the crack tip is believed to be an AE source, which can generate the continuous signals [32,33]. Another possible AE source during SCC crack propagation is the ligament tearing [32]. According to the previous results [12], the ratio of the burst and continuous signals can simply evaluate the SCC mode, the ratio for transgranular SCC (TGSCC) is around 1 and the ratio gradually decreases to around 0 with increasing the intergranular SCC (IGSCC)
Table 1 Detailed experimental parameters for SCC of sensitized 304 SS in high-temperature water. Number of tests
Duration
Load mode
DO
Test Test Test Test Test Test
0 – 5h 5 – 35 h 35 – 72 h 72 – 100 h 100 – 125 h 125 – 150 h
SSRT, v = 3 × 10−5 mm/s Constant load, F = 4000 N Constant load, F = 5000 N Constant load, F = 6000 N Constant load, F = 6000 N Constant load, F = 6000 N
8 ppm 8 ppm 8 ppm 8 ppm 5 ppb 3 ppm
1 2 3 4 5 6
in high-temperature water. Only a slight crack growth was observed from test 1 to test 3. After increasing the load to 6000 N in test 4, the crack length quickly increased to about 11.05 mm. A strong dependency of crack growth rate on DO was observed in the test 5 and 6. The crack growth rate decreased when DO was decreased below 5 ppb in test 5. High crack growth rate appeared again when increasing the DO to 3 ppm in test 6. However, it should be mentioned that the responses of the crack growth rate to the load and DO have a time delay. For example, there are two inflection points during the crack propagation of test 4. AE cumulative hits show a good agreement with the evolution of crack length except for test 1 (Fig. 2b). During the test 1, the AE signals quickly increased, while the crack length measured by DCPD seems to keep constant. To further understand the SCC behavior during test 1, another experiment was conducted and stopped at the stage of test 1. Fig. 3 shows the fracture morphology. Only two regions characterized by transgranular cracking can be observed, one is fatigue pre-crack region, the other is air post-crack region. Therefore, it was inferred that the crack did not propagate during test 1. The AE signals were analyzed by the RQA and traditional parameters such as rise time, count, amplitude and absolute energy. Firstly, all AE signals were labeled according to the order in which they were detected. Then four RQA parameters as mentioned in Section 2 were calculated and shown in Fig. 4a-4d, while the traditional AE parameters were shown in Fig. 4e-4 h. It seems that all AE signals can be divided into two clusters, one has a high value of R, Lmean and E, while the other has a low value of R, Lmean and E. Meanwhile, the value of D was found 81
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Fig. 2. The evolution of crack length and AE cumulative hits during SCC of sensitized 304 SS in high-temperature water, (a) crack length, (b) AE cumulative hits.
Fig. 3. The fracture morphology of sensitized 304 SS when the experiment was stopped at the stage of test 1.
cannot be recursive. With the burst peak fading away, the RP’s color gradually becomes black, indicating the points become recurrence. Otherwise, the RP of the continuous waveform is evenly black and white. Therefore, it can be concluded that the differences in the RQA parameters are due to the presence of the burst peaks on the AE waveform. In other words, the RQA parameters including R, Lmean and E can be used to effectively separate the burst signal and continuous signals. It should be noted that more kinds of AE waveforms generated by other corrosion damages should be analyzed by the RQA in future work to better illustrate the superiority of RQA in AE signals analysis field. To quantitatively relate the AE signals with the SCC process, the crack growth rate (da/dt) and the AE cumulative hits rate (dN/dt) were
proportion. The ratio for the mixture of TGSCC and IGSCC is probably expected to around 0.5. The value of this ratio between 5 h and 150 h is 0.032, indicating that IGSCC occurred during this test period. Fig. 7 shows the fracture morphology after SCC tested in high-temperature water, which was dominated by IGSCC with small amounts of TGSCC. The above illustration shows that the cluster results based on the RQA parameters are reasonably consistent with the SCC process, indicating that the RQA method is valid to separate the AE waveforms. The burst AE waveform has high R, Lmean and E, while the continuous AE signals have low R, Lmean and E. The RPs of different AE waveforms shown in Fig. 6c and d clearly reveal the difference. It can be found that RP of the burst waveform has white bands corresponding to the burst peaks in the time domain of the AE waveform, indicating these points 82
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Fig. 4. RQA parameters and traditional parameters of AE signals generated by SCC of sensitized 304 SS in high-temperature water, (a)-(d) RQA parameters: R, D, Lmean and E, (e)-(h) traditional parameters: rise time, count, amplitude and absolute energy.
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signals still can be detected. It is consistent with the meaning of the critical stress intensity factor (Kscc). Only the stress intensity factor (K) exceeds the Kscc, the crack begins to propagate. If the K is less than the critical value, only plastic deformation occurs, which can also generate the detectable AE signals. Therefore, the intercept can be related to the Kscc. It is critical to assess the SCC crack growth rate for life prediction of structural components in NPPs, and some possible crack monitoring techniques have been studied [34,35]. The DCPD is a widely accepted method in laboratory. However, a DC must be applied to monitor the crack length by DCPD, and the value of DC is related to the size of the specimen. For a large component, it is rather difficult to apply a large DC and it is unknown whether the large DC has an effect on the crack propagation behavior. Obviously, it is questionable to use the current DCPD technique in industry. AE as a non-destructive technique just passively receives the signals generated by crack propagation. Therefore, AE has the potential for industrial applications. Rabiei proposed a quantitative model relating the AE count rate with the fatigue crack growth rate in air [14]. Chai established a similar model using the AE entropy parameter [15]. However, only the fatigue crack propagation was concerned. As mentioned by Rabiei and Chai, the uncertainty of the AE quantitative model mainly generated by the measurements of crack length and AE data [15]. There is a certain difference between the air fatigue cracking and the SCC in high-temperature water. Therefore, it is still unclear whether AE can be quantitatively applied in high-temperature water. In the present study, through coupled AE and DCPD in high-temperature water environment, in-situ AE signals were quantitatively related with the SCC crack growth rate, indicating the AE has a possibility to quantitatively evaluate SCC crack growth rate in NPPs. It should be noted that the present empirical formula is only suitable for the SCC behavior of sensitized 304 SS in high-temperature water. More materials served in NPPs such as 316 L SS, Alloy 690 and so on need to be further studied to obtain the corresponding empirical formulas and clarify the physical meaning of the empirical formula.
Fig. 5. k-mean cluster result using RQA parameters of AE signals generated by SCC of sensitized 304 SS in high-temperature water.
fitting within the different test periods. As analyzed above, no crack propagation occurred and the AE signals were generated by the ligament tearing of fatigue pre-crack during test 1. Therefore only the following tests were considered. Fig. 8 shows the relationship between the crack growth rate (da/dt, mm/h) and the AE cumulative hits rate (dN/dt, /h). It should be noted that the da/dt and dN/dt in the present work is an average value within a certain test period because the responses of the crack growth rates to the load and DO has a time delay as mentioned above. It can be found that there is a good linear relationship between the da/dt and the dN/dt, and this linear relationship can be represented using the following empirical formula. According to Eq. (6), it is possible to assess y = 3.51 × 10−3 x – 4.98082 × 10-4
(6)
the SCC crack growth rate of sensitized 304 SS in high-temperature water using AE. During actual application, the AE signals can be monitored within a certain period and the AE cumulative hits rate can be obtained. Then the crack growth rate can be predicted using the empirical formula. In addition, the value of the intercept in the Eq. (6) is negative, meaning that when the crack growth rate is zero, some AE
5. Conclusions In this study, a set-up of SCC in high-temperature water equipped with AE and DCPD was established and the SCC behavior of sensitized
Fig. 6. Typical AE waveforms and corresponding RPs of the two clusters, (a) and (c) Cluster 1, (b) and (d) Cluster 2. 84
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Fig. 7. The fracture morphology of sensitized 304 SS in high-temperature water after the tests, (a) typical morphology of IGSCC (b) morphology containing some transgranular cracking characteristic.
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Fig. 8. The relationship between the SCC crack growth rate and the AE cumulative hits rate within different test periods.
304 SS in high-temperature water was in-situ monitored. An attempt was made to process the AE signals using RQA method. Some conclusions are drawn as follows. 1 Compared with traditional AE parameters, RQA can better reflect the AE waveform. It can separate the burst signals and continuous signals generated by ligaments tearing and plastic deformation of crack tip respectively. The burst signals have high R, Lmean and E, while the continuous signals have low R, Lmean and E. 2 The present set-up equipped AE and DCPD can achieve the quantitative AE study during SCC in high-temperature water. There is a linear relationship between the SCC crack growth rate of the sensitized 304 SS in high-temperature water and the AE cumulative hits rate, which proves the AE has an application potential to quantitatively evaluate SCC crack growth rate in NPPs. More materials served in NPPs need to be further studied to obtain the corresponding empirical formulas and clarify the physical meaning of the empirical formula.
Acknowledgements This work was jointly supported by the National Natural Science Foundation of China (51671201, 51371174), the National Science and Technology Major Project (2017ZX06002003-004-002), the Key Programs of the Chinese Academy of Sciences (Research on the Development of Nuclear Power Materials and Service Security Technology, ZDRW-CN-2017-1), and the Innovation Fund of Institute of Metal Research, Chinese Academy of Sciences (SCJJ-2013-ZD-02). 85
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Quantitatively related acoustic emission signal with stress corrosion crack growth rate of sensitized 304 stainless steel in high-temperature water Zhen Zhanga,b, Ziyu Zhanga, Jibo Tana, Xinqiang Wua,
T
⁎
a
CAS Key Laboratory of Nuclear Materials and Safety Assessment, Liaoning Key Laboratory for Safety and Assessment Technique of Nuclear Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, PR China b School of Materials Science and Engineering, University of Science and Technology of China, Hefei, 230026, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: A. Stainless steel B. SEM C. Stress corrosion C. High-temperature corrosion
Stress corrosion cracking (SCC) of sensitized 304 stainless steel in high-temperature water was in-situ monitored by coupling acoustic emission (AE) and direct current potential drop (DCPD) techniques. The AE signals were identified using novel recurrence quantification analysis (RQA) and k-mean cluster method. It was found that the RQA is feasible to identify the evolution of different AE waveforms generated by ligament tearing and plastic deformation of the crack tip. The AE cumulative hits rate was linear with the SCC crack growth rate, providing a possibility for applying the AE technique to quantitatively evaluate SCC in high-temperature water.
1. Introduction Austenitic stainless steels (SSs) such as 304 SS and 316 L SS have been used as primary pipe and reactor internal materials in nuclear power plants (NPPs). However, they are susceptible to stress corrosion cracking (SCC), and the SCC is a serious threat for structural components in NPPs due to its abrupt brittle failure prior to expected ultimate elongation [1–3]. Monitoring the SCC behavior of structural materials under actual service environments is important for ensuring the safe operation of NPPs. Acoustic emission (AE) measuring the spontaneous energy release within the material during the damage process is a promising monitoring technique and has been widely utilized to monitor the corrosion damages, in particular SCC [4–12]. Calabrese et al. investigated the SCC behavior of 17-7 pH SS in MgCl2 solution using AE technique and found that AE energy can separate different SCC stages including pre-activation phase, active damaging phase, long crack propagation phase and final catastrophic failure [8]. Delaunois et al. investigated the chlorideinduced SCC behavior of austenitic SS by AE [10]. It was found that different phases including initiation and propagation of pitting and cracking, fracture of the specimen can be separated by the AE amplitude. In the previous study, AE waveforms were related with SCC process of 304 SS in high-temperature water [12]. A discriminant factor calculated by the ratio of the burst signals and continuous signals and a discriminant model were proposed to auto-monitor the SCC. Though great achievements have been made in applying AE to monitor SCC
⁎
during the past several decades, most of the research was focused on qualitatively relating AE signals with SCC stages, and few studies were involved in the quantitative information between AE signals and stress corrosion crack propagation. Some attempts were made to establish the quantitative model between the AE signals and fatigue crack growth rate in air [13–15]. However, only mechanical fatigue crack propagation was treated, little attention was paid to SCC which is a synergistic result of stress and environmental factors. These factors including type and level of the stress, temperature, dissolved oxygen, ion species and concentration and so on make the SCC behavior quite complex [16–18], and there is a need to further investigate the possibility of AE quantitative evaluation of SCC. In order to apply AE technique to monitor the corrosion damages, another important task is how to deal with the AE signal. In general, the waves are directly detected by the AE sensor and are transformed into digital AE signals after the pre-amplification. Then some traditional parameters such as rise time, count, duration, amplitude, energy and so on can be extracted. Though these AE parameters have been widely used in most previous studies [4–10,19–21], there are still some drawbacks as mentioned by Chai et al. [22]. One of the serious problems is that the above parameters except for amplitude strongly depend on the selected threshold, which may hinder the correct reflection of the original AE waveform. So it is necessary to develop some advanced signal processing methods to analyze the AE signal. Marwan recently proposed a recurrence quantification analysis (RQA) method to characterize the digital time-series [23]. Savari et al. preliminarily
Corresponding author. E-mail address: [email protected] (X. Wu).
https://doi.org/10.1016/j.corsci.2019.05.030 Received 11 January 2019; Received in revised form 2 May 2019; Accepted 29 May 2019 Available online 30 May 2019 0010-938X/ © 2019 Elsevier Ltd. All rights reserved.
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analyzed the AE signal using the recurrence plot and RQA to monitor the hydrodynamic behavior of spouted beds, which proves that RQA is a powerful tool for monitoring this behavior [24]. In the present work, SCC of the sensitized 304 SS in high-temperature water was in-situ monitored by coupling AE and direct current potential drop (DCPD) techniques. An attempt was made to analyze the AE signal generated by SCC using the RQA method. A quantitative relation between the AE signal and SCC crack growth rate was established. The aim is to provide a novel AE signal processing method and explore the possibility for applying AE to quantitatively evaluate SCC crack growth rate in high-temperature water.
Matlab 2016a with cross recurrence plot toolbox developed by Norbert Marwan et al [23]. The RQA has been successfully applied in some fields such as finance, meteorology and psychology and so on to process the time-series [29–31]. There are also some applications in corrosion field to process the electrochemical oscillations signal [25]. However, to our knowledge, there is no work employing RQA to process the AE waves generated by corrosion damages. This is the first attempt to process the AE signals generated by corrosion damages using the RQA method.
2. Theory on RQA of AE signal
3.1. Specimen and experimental set-up
Generally AE waveform is a one-dimensional time-series and this time-series can be reconstructed using the time delay embedding to obtain the system trajectory of the AE waveform. In the present study, the embedding dimension of 5 determined by the false nearest neighbor method and the time delay of 4 determined by the mutual information method were used. Then recurrence plot (RP) of the AE signal can be calculated according to Eq. (1), where H is the Heaviside operator, ||…|| calculates the Euclidean norm between xi and xj, ε is the threshold value and is defined as standard deviation of the AE time-series in the present study.
The composition (wt. %) of sensitized 304 SS used in the present study is 0.03 C, 18.67 Cr, 9.25 Ni, 2.00 Mn, 0.64 Si, 0.98 Cu and Fe Balance. The sensitized treatment was performed at 650°C for 48 h and then followed by furnace cooling. 0.5 T compact tensile (CT) specimens were used. The dimensions of the specimen followed ASTM E399 with a thickness of 12.5 mm and a width of 30 mm. Specimens were ground to 2000 grit with silicon carbide paper and the two main surfaces were polished with 2.5 μm diamond paste. The specimens were firstly precracked in air with a maximum load of 4000 N under a sinusoidal wave at 20 Hz using a fatigue machine (EHF-EB10-20 L, Shimadzu, Japan), and the stress ratio is 0.2. Fig. 1 shows the SCC set-up in high-temperature water equipped with in-situ AE and DCPD monitoring system. Two AE wide band sensors provided by Physical Acoustics Co. were used, one as the experimental sensor was mounted on the load rod through the Vaseline to receive the AE waves generated by SCC, and the other mounted on the load device was regarded as guard sensor to eliminate the environmental noise. The AE waves were sent to the AE acquisition through a Type 2/4/6 preamplifier set at 40 dB and then were transferred to the digital signal. During the SCC tests in high-temperature water, the specimen was electrically isolated from the clamp with zirconia bushings and spacers. Pure nickel wires coated by heat-shrinkable polytetrafluoroethylene (PTFE) were spot-welded to the specimen and used to transmit the current and potential signals to the DCPD system. 3 A direct current (DC) was applied to the specimen by a DC power. Crack length was in-situ monitored by DCPD system continuously, and the crack growth rate is then determined by the slop of crack length vs. time curve.
Ri, j = H (ε -||x i − x j ||) i, j = 1, ⋯, N
3. Experimental
(1)
Ri,j is an N × N matrix consisting of 0 and 1. 0 is represented by a black point in RP, meaning this point can be recursive. Otherwise, 1 is represented by a white point. There are three patterns including single points, diagonal lines, vertical and horizontal lines in RP [25]. Some parameters can be extracted to quantitatively represent these patterns, and this process is called as the RQA method. Among these parameters, four parameters, namely, recurrence rate (R), determinism (D), Shannon entropy (E), average diagonal line length (Lmean) are commonly employed [26–28] and are also considered in the present investigation. (i) R represents the density of the recurrence points in RP and can be expressed as Eq. (2)
R=
N
1 N2
∑
R (i, j ) (2)
i, j = 1
• D represents the ratio of the recurrence points forming diagonal
3.2. Experimental process
lines of at least λmin length over all recurrence points and can be expressed as Eq. (3). λmin was chosen as 2 in the present study. P(λ) is the histogram of the diagonal lines of length.
The SCC tests were conducted in high-temperature (300 °C) and high-pressure (10 MPa) water, the flow rate was controlled to 3 L/h. The experimental system was maintained for 24 h at the target temperature and pressure to eliminate the most noise signals during the heating, and the amplitude threshold value was set at 35 dB. The specimen was pre-loaded to 1000 N to eliminate the gaps between the fixtures. Then, the SCC tests were started and continuously monitored by AE and DCPD. Two factors including load and dissolved oxygen concentration (DO) were considered to generate different AE signals and cracking behaviors. The detailed experimental parameters were listed in Table 1. The AE monitoring system was suspended at the moments when the loading was changed to avoid possible interference signals. The specimen was finally fractured by post-test fatigue in air to observe the fracture morphology using an FEIINSPECT F50 scanning electron microscope (SEM).
N
D=
∑λ = λmin λP (λ ) N
∑λ = 1 λP (λ )
(3)
•L
mean represents the average diagonal line length and can be expressed as Eq. (4)
N
L mean =
∑λ = λmin λP (λ ) N
∑λ = λmin P (λ )
• E is the Shannon entropy of the probability p(λ), p (λ) =
(4) P (λ ) ∑N λ=λ
min
P (λ )
.
E reflects the complexity of the RP with respect to the diagonal lines, and can be expressed as Eq. (5) N
E= −
∑ λ= λmin
4. Results and discussion
p(λ)lnp(λ) (5)
Fig. 2 shows the evolution of the crack length monitored by the DCPD and AE cumulative hits during the SCC tests of sensitized 304 SS
The RQA parameters mentioned above were calculated using 80
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Fig. 1. The set-up of SCC in high-temperature water equipped with in-situ AE and DCPD monitoring systems.
to have similar value for these AE signals (Fig. 4b). In comparison with the RQA parameters, the traditional parameters seem to be difficult to separate the AE signals (Fig. 4e-4 h). Only the rise time shows a certain ability (Fig. 4e), one type of signal has low rise time, the other type contains some signals with high rise time. Furthermore, k-mean cluster using the RQA parameters was employed to better cluster the AE signals. Fig. 5 shows the evolution of different AE clusters during the whole tests. It is clear that cluster 1 quickly increased from 0 h to around 5 h, and only several signals of this type can be detected within the subsequent test period. Otherwise, the cluster 2 became detectable after around 5 h and then dominated the AE behavior. Fig. 6 shows the typical AE waveforms and corresponding RPs of the two clusters. It is clear that the cluster 1 is a burst signal and cluster 2 is a continuous signal (Fig. 6a and b). According to the evolution of the crack length and different AE clusters, two phases can be identified. The first phase is 0 h to 5 h, the crack length keeps constant. The cluster 1, namely the burst signals, increased sharply. The second phase is 5 h to 150 h, the continuous signal became dominant and only several burst signals were randomly detected. At the first phase, the specimen was loaded to 4000 N through slow strain rate tension (SSRT) and no crack propagation occurred. The tested CT specimens had transgranular fatigue pre-crack, which inevitably leaves lots of ligaments. Once the specimen was re-loaded and pulled down, these residual ligaments were torn, which emitted AE signals. Therefore, it is inferred that the burst signals were generated by the residual ligaments tearing of fatigue pre-crack. At the second phase, the load was constant in each test. The crack began to propagate under the action of the stress and high-temperature water, and the crack growth rate mainly depended on the stress level and the water chemistry (Fig. 2a). In general, the crack propagation of SS under constant load was promoted by the plastic deformation of the crack tip, and the plastic deformation of the crack tip is believed to be an AE source, which can generate the continuous signals [32,33]. Another possible AE source during SCC crack propagation is the ligament tearing [32]. According to the previous results [12], the ratio of the burst and continuous signals can simply evaluate the SCC mode, the ratio for transgranular SCC (TGSCC) is around 1 and the ratio gradually decreases to around 0 with increasing the intergranular SCC (IGSCC)
Table 1 Detailed experimental parameters for SCC of sensitized 304 SS in high-temperature water. Number of tests
Duration
Load mode
DO
Test Test Test Test Test Test
0 – 5h 5 – 35 h 35 – 72 h 72 – 100 h 100 – 125 h 125 – 150 h
SSRT, v = 3 × 10−5 mm/s Constant load, F = 4000 N Constant load, F = 5000 N Constant load, F = 6000 N Constant load, F = 6000 N Constant load, F = 6000 N
8 ppm 8 ppm 8 ppm 8 ppm 5 ppb 3 ppm
1 2 3 4 5 6
in high-temperature water. Only a slight crack growth was observed from test 1 to test 3. After increasing the load to 6000 N in test 4, the crack length quickly increased to about 11.05 mm. A strong dependency of crack growth rate on DO was observed in the test 5 and 6. The crack growth rate decreased when DO was decreased below 5 ppb in test 5. High crack growth rate appeared again when increasing the DO to 3 ppm in test 6. However, it should be mentioned that the responses of the crack growth rate to the load and DO have a time delay. For example, there are two inflection points during the crack propagation of test 4. AE cumulative hits show a good agreement with the evolution of crack length except for test 1 (Fig. 2b). During the test 1, the AE signals quickly increased, while the crack length measured by DCPD seems to keep constant. To further understand the SCC behavior during test 1, another experiment was conducted and stopped at the stage of test 1. Fig. 3 shows the fracture morphology. Only two regions characterized by transgranular cracking can be observed, one is fatigue pre-crack region, the other is air post-crack region. Therefore, it was inferred that the crack did not propagate during test 1. The AE signals were analyzed by the RQA and traditional parameters such as rise time, count, amplitude and absolute energy. Firstly, all AE signals were labeled according to the order in which they were detected. Then four RQA parameters as mentioned in Section 2 were calculated and shown in Fig. 4a-4d, while the traditional AE parameters were shown in Fig. 4e-4 h. It seems that all AE signals can be divided into two clusters, one has a high value of R, Lmean and E, while the other has a low value of R, Lmean and E. Meanwhile, the value of D was found 81
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Fig. 2. The evolution of crack length and AE cumulative hits during SCC of sensitized 304 SS in high-temperature water, (a) crack length, (b) AE cumulative hits.
Fig. 3. The fracture morphology of sensitized 304 SS when the experiment was stopped at the stage of test 1.
cannot be recursive. With the burst peak fading away, the RP’s color gradually becomes black, indicating the points become recurrence. Otherwise, the RP of the continuous waveform is evenly black and white. Therefore, it can be concluded that the differences in the RQA parameters are due to the presence of the burst peaks on the AE waveform. In other words, the RQA parameters including R, Lmean and E can be used to effectively separate the burst signal and continuous signals. It should be noted that more kinds of AE waveforms generated by other corrosion damages should be analyzed by the RQA in future work to better illustrate the superiority of RQA in AE signals analysis field. To quantitatively relate the AE signals with the SCC process, the crack growth rate (da/dt) and the AE cumulative hits rate (dN/dt) were
proportion. The ratio for the mixture of TGSCC and IGSCC is probably expected to around 0.5. The value of this ratio between 5 h and 150 h is 0.032, indicating that IGSCC occurred during this test period. Fig. 7 shows the fracture morphology after SCC tested in high-temperature water, which was dominated by IGSCC with small amounts of TGSCC. The above illustration shows that the cluster results based on the RQA parameters are reasonably consistent with the SCC process, indicating that the RQA method is valid to separate the AE waveforms. The burst AE waveform has high R, Lmean and E, while the continuous AE signals have low R, Lmean and E. The RPs of different AE waveforms shown in Fig. 6c and d clearly reveal the difference. It can be found that RP of the burst waveform has white bands corresponding to the burst peaks in the time domain of the AE waveform, indicating these points 82
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Fig. 4. RQA parameters and traditional parameters of AE signals generated by SCC of sensitized 304 SS in high-temperature water, (a)-(d) RQA parameters: R, D, Lmean and E, (e)-(h) traditional parameters: rise time, count, amplitude and absolute energy.
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signals still can be detected. It is consistent with the meaning of the critical stress intensity factor (Kscc). Only the stress intensity factor (K) exceeds the Kscc, the crack begins to propagate. If the K is less than the critical value, only plastic deformation occurs, which can also generate the detectable AE signals. Therefore, the intercept can be related to the Kscc. It is critical to assess the SCC crack growth rate for life prediction of structural components in NPPs, and some possible crack monitoring techniques have been studied [34,35]. The DCPD is a widely accepted method in laboratory. However, a DC must be applied to monitor the crack length by DCPD, and the value of DC is related to the size of the specimen. For a large component, it is rather difficult to apply a large DC and it is unknown whether the large DC has an effect on the crack propagation behavior. Obviously, it is questionable to use the current DCPD technique in industry. AE as a non-destructive technique just passively receives the signals generated by crack propagation. Therefore, AE has the potential for industrial applications. Rabiei proposed a quantitative model relating the AE count rate with the fatigue crack growth rate in air [14]. Chai established a similar model using the AE entropy parameter [15]. However, only the fatigue crack propagation was concerned. As mentioned by Rabiei and Chai, the uncertainty of the AE quantitative model mainly generated by the measurements of crack length and AE data [15]. There is a certain difference between the air fatigue cracking and the SCC in high-temperature water. Therefore, it is still unclear whether AE can be quantitatively applied in high-temperature water. In the present study, through coupled AE and DCPD in high-temperature water environment, in-situ AE signals were quantitatively related with the SCC crack growth rate, indicating the AE has a possibility to quantitatively evaluate SCC crack growth rate in NPPs. It should be noted that the present empirical formula is only suitable for the SCC behavior of sensitized 304 SS in high-temperature water. More materials served in NPPs such as 316 L SS, Alloy 690 and so on need to be further studied to obtain the corresponding empirical formulas and clarify the physical meaning of the empirical formula.
Fig. 5. k-mean cluster result using RQA parameters of AE signals generated by SCC of sensitized 304 SS in high-temperature water.
fitting within the different test periods. As analyzed above, no crack propagation occurred and the AE signals were generated by the ligament tearing of fatigue pre-crack during test 1. Therefore only the following tests were considered. Fig. 8 shows the relationship between the crack growth rate (da/dt, mm/h) and the AE cumulative hits rate (dN/dt, /h). It should be noted that the da/dt and dN/dt in the present work is an average value within a certain test period because the responses of the crack growth rates to the load and DO has a time delay as mentioned above. It can be found that there is a good linear relationship between the da/dt and the dN/dt, and this linear relationship can be represented using the following empirical formula. According to Eq. (6), it is possible to assess y = 3.51 × 10−3 x – 4.98082 × 10-4
(6)
the SCC crack growth rate of sensitized 304 SS in high-temperature water using AE. During actual application, the AE signals can be monitored within a certain period and the AE cumulative hits rate can be obtained. Then the crack growth rate can be predicted using the empirical formula. In addition, the value of the intercept in the Eq. (6) is negative, meaning that when the crack growth rate is zero, some AE
5. Conclusions In this study, a set-up of SCC in high-temperature water equipped with AE and DCPD was established and the SCC behavior of sensitized
Fig. 6. Typical AE waveforms and corresponding RPs of the two clusters, (a) and (c) Cluster 1, (b) and (d) Cluster 2. 84
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Fig. 7. The fracture morphology of sensitized 304 SS in high-temperature water after the tests, (a) typical morphology of IGSCC (b) morphology containing some transgranular cracking characteristic.
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Fig. 8. The relationship between the SCC crack growth rate and the AE cumulative hits rate within different test periods.
304 SS in high-temperature water was in-situ monitored. An attempt was made to process the AE signals using RQA method. Some conclusions are drawn as follows. 1 Compared with traditional AE parameters, RQA can better reflect the AE waveform. It can separate the burst signals and continuous signals generated by ligaments tearing and plastic deformation of crack tip respectively. The burst signals have high R, Lmean and E, while the continuous signals have low R, Lmean and E. 2 The present set-up equipped AE and DCPD can achieve the quantitative AE study during SCC in high-temperature water. There is a linear relationship between the SCC crack growth rate of the sensitized 304 SS in high-temperature water and the AE cumulative hits rate, which proves the AE has an application potential to quantitatively evaluate SCC crack growth rate in NPPs. More materials served in NPPs need to be further studied to obtain the corresponding empirical formulas and clarify the physical meaning of the empirical formula.
Acknowledgements This work was jointly supported by the National Natural Science Foundation of China (51671201, 51371174), the National Science and Technology Major Project (2017ZX06002003-004-002), the Key Programs of the Chinese Academy of Sciences (Research on the Development of Nuclear Power Materials and Service Security Technology, ZDRW-CN-2017-1), and the Innovation Fund of Institute of Metal Research, Chinese Academy of Sciences (SCJJ-2013-ZD-02). 85
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