Application of Metal Magnetic Memory Testing Technology to the Detection of Stress Corrosion Defect

: The damage of equipment manufactured with ferromagnetic materials in service can be e ﬀ ectively detected by Metal Magnetic Memory Testing (MMMT) technology, which has received extensive attention in various industry ﬁelds. The e ﬀ ect of stress or strain on Magnetic Flux Leakage (MFL) signals of ferromagnetic materials has been researched by many scholars for assessing stress concentration and fatigue damage. However, there is still a lack of research on the detection of stress corrosion damage of ferromagnetic materials by MMMT technology. In this paper, the electrochemical corrosion system was designed for corrosion experiments, and three di ﬀ erent experiments were performed to study the e ﬀ ect of corrosion on MFL signals. The distribution of MFL signals on the surface of the specimen was investigated. The results indicated that both the normal component H n and tangential component H t of MFL signals presented di ﬀ erent signal characteristics when the specimen was subjected to di ﬀ erent working conditions. Finally, two characterization parameters, S n and S t , were deﬁned to evaluate the corrosion degree of the specimen, and S t is better. The direct dependence of corrosion depth on the parameter was developed and the average error rates between the predicted and measured values are 8.94% under the same working condition. Therefore, the expression can be used to evaluate the corrosion degree of the specimen quantitatively. The results are signiﬁcant for detecting and assessing the corrosion defect of ferromagnetic materials.


Introduction
Many types of equipment manufactured with ferromagnetic materials in service are working under the condition of stress corrosion. Most of this equipment is susceptible to corrosion defects. The effect of pitting corrosion on pipeline steel has been studied by many scholars [1][2][3][4]. Chen and Zhao reported the failure of oil and gas pipelines due to stress corrosion cracking [5,6]. It is necessary to conduct Non-Destructive Testing (NDT) for stress corrosion defects. The common NDT method for the quantitative evaluation of corroded defects, such as Electrochemical Noise Analysis (ENA), has been studied by many scholars [7][8][9]. It was used to investigate the corrosion behavior of mild steel (Q235) [10], and Wang reported that pitting corrosion of high strength steel is quantitatively evaluated by combining 3-D measurement and image-recognition-based statistical analysis [11]. However, the reliability for assessing the sizes of corrosion defects needs to be further discussed. The traditional magnetic testing technologies [12][13][14], such as magnetic particle testing [15,16], magnetic flux leakage testing [17][18][19], usually require a large external magnetic field [20][21][22], which is inconvenient to operate and even impractical under some conditions. Although the non-destructive testing of stress corrosion defects has been widely studied, the traditional NDT methods have some limitations. Therefore, it is necessary to develop a more simple and effective NDT technology.
The Metal Magnetic Memory Testing (MMMT) technology, which was first presented at the 50th International Welding Conference in 1997 by a Russian researcher, is an emerging testing method in the field of non-destructive testing technology [23,24]. It is a weak-field detecting method, which uses the geomagnetic field instead of an artificial magnetic field as the stimulus source. MMMT technology is used to diagnose the early damage by measuring the self-magnetized leakage field on the surface of ferromagnetic materials [25,26]. MMMT technology has the advantages of simple equipment, simple operation, and no treatment on the surface of the tested part. Nowadays, the MMMT technique has attracted the attention of scholars in many industry fields, such as machinery, pressure vessels, pipelines, etc. [27,28]. It is widely studied by many scholars for its advantages over other magnetic testing methods [29][30][31], and the stress-magnetism effect has also been widely studied [32][33][34]. The impact of stress or strain on Magnetic Flux Leakage (MFL) signals of ferromagnetic materials has been researched for assessing stress concentration [35,36] and fatigue damage [37][38][39]. The previous study [40] showed that the ambient stress conditions during corrosion defect formation would affect the MFL signals based on magnetic flux leakage testing. In recent years, MMMT was applied to the detection of rebar corrosion in concrete and the commonly used steel strand in structural engineering to locate the corrosion area and evaluated the corrosion degree [41,42]. However, there is still a lack of research on stress corrosion. Therefore, it is very promising to detect stress corrosion defects by MMMT technology.
In this paper, three experiments were performed to study the effect of corrosion on magnetic leakage signals. The electrochemical corrosion system was designed for corrosion experiments. The distribution regularity of MFL signals during the corrosion process was investigated. The feasibility of evaluating the degree of corrosion of ferromagnetic materials using the MFL signals was discussed.

Experimental Section
To study the effect of corrosion on MFL signals, three different experiments were performed. Experiment 1 is a static tensile experiment; experiment 2 and experiment 3 are corrosion experiments: Experiment 2 is a corrosion experiment without loading; experiment 3 is a corrosion experiment after loading. In addition, the Scanning Electron Microscope (SEM) and Energy Dispersive X-Ray Spectroscopy (EDX) were used to observe the surface of the specimen and analyze the corrosion layer, respectively.

Specimen Preparation
The specimens were made by 0.45% C steel in this study, which is medium-carbon structural steel and widely used in the structural engineering field. Composition of 0.45% C steel, % by weight is C (0.42-0.50%), Si (0.17-0.37%), Mn (0.50-0.80%), P (≤0.035%), S (≤0.035%). Its mechanical properties are listed in Table 1. Flat dog-bone specimens designed based on GB/T228-2002 were prepared without (used in corrosion experiments) and with a groove (used in the static tensile experiment). The rectangular groove (6.8 mm width and 2 mm depth) was carefully made by a linear cutting machine in the middle of the specimens. The specimen was designed to be a special shape (dog bone) to obtain a uniform distribution of stress in the corrosion area. The shape and size of the 6-mm-thick specimens used in the experiments were drawn in Figure 1. Five scanning lines with a length of 100 mm, denoted as Line 1, Line 2, Line 3, Line 4, and Line 5, were parallel to each other at intervals of 4.5 mm. Line 3 is the centerline of the specimen.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 18 The shape and size of the 6-mm-thick specimens used in the experiments were drawn in Figure  1. Five scanning lines with a length of 100 mm, denoted as Line 1, Line 2, Line 3, Line 4, and Line 5, were parallel to each other at intervals of 4.5 mm. Line 3 is the centerline of the specimen. Before experiments, all of the specimens were polished to grade P1000 grit, followed by rinsing with isopropyl alcohol, drying in warm air, and weighing with an electronic balance. The specimen was polished only to remove the corrosion on the specimen surface and measure the mass loss of the specimen more accurately. In addition, every specimen was demagnetized before it was loaded or corroded to eliminate the effect of mechanical processing on the magnetic field.

Description of Corrosion and Detection System
The schematic of the set-up for the corrosion system is shown in Figure 2a. The electrochemical method was used to accelerate the corrosion of the specimen. The working electrode is the specimen connected to the positive electrode of the direct current (DC) power source (UTP3303, produced by UNI-TREND Technology (China) CO. LTD). The copper sheet was served as a counter electrode connected to the negative electrode of the DC power source. There is no direct contact between the electrolyte and the specimen. The electrolyte contacts the surface of the specimen placed on a plastic block above the electrolyte level through a specially shaped sponge (Corrosion area = 175 mm 2 ). The electrolyte for the corrosion process was 3.5% (wt.%) NaCl solution. In corrosion experiments, the specimen is corroded by galvanostatic corrosion of 0.4 A.
(a) electrochemical corrosion system (b) 3D MFL detection system Before experiments, all of the specimens were polished to grade P1000 grit, followed by rinsing with isopropyl alcohol, drying in warm air, and weighing with an electronic balance. The specimen was polished only to remove the corrosion on the specimen surface and measure the mass loss of the specimen more accurately. In addition, every specimen was demagnetized before it was loaded or corroded to eliminate the effect of mechanical processing on the magnetic field.

Description of Corrosion and Detection System
The schematic of the set-up for the corrosion system is shown in Figure 2a. The electrochemical method was used to accelerate the corrosion of the specimen. The working electrode is the specimen connected to the positive electrode of the direct current (DC) power source (UTP3303, produced by UNI-TREND Technology (China) CO. LTD). The copper sheet was served as a counter electrode connected to the negative electrode of the DC power source. There is no direct contact between the electrolyte and the specimen. The electrolyte contacts the surface of the specimen placed on a plastic block above the electrolyte level through a specially shaped sponge (Corrosion area = 175 mm 2 ). The electrolyte for the corrosion process was 3.5% (wt.%) NaCl solution. In corrosion experiments, the specimen is corroded by galvanostatic corrosion of 0.4 A.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 18 The shape and size of the 6-mm-thick specimens used in the experiments were drawn in Figure  1. Five scanning lines with a length of 100 mm, denoted as Line 1, Line 2, Line 3, Line 4, and Line 5, were parallel to each other at intervals of 4.5 mm. Line 3 is the centerline of the specimen. Before experiments, all of the specimens were polished to grade P1000 grit, followed by rinsing with isopropyl alcohol, drying in warm air, and weighing with an electronic balance. The specimen was polished only to remove the corrosion on the specimen surface and measure the mass loss of the specimen more accurately. In addition, every specimen was demagnetized before it was loaded or corroded to eliminate the effect of mechanical processing on the magnetic field.

Description of Corrosion and Detection System
The schematic of the set-up for the corrosion system is shown in Figure 2a. The electrochemical method was used to accelerate the corrosion of the specimen. The working electrode is the specimen connected to the positive electrode of the direct current (DC) power source (UTP3303, produced by UNI-TREND Technology (China) CO. LTD). The copper sheet was served as a counter electrode connected to the negative electrode of the DC power source. There is no direct contact between the electrolyte and the specimen. The electrolyte contacts the surface of the specimen placed on a plastic block above the electrolyte level through a specially shaped sponge (Corrosion area = 175 mm 2 ). The electrolyte for the corrosion process was 3.5% (wt.%) NaCl solution. In corrosion experiments, the specimen is corroded by galvanostatic corrosion of 0.4 A.
(a) electrochemical corrosion system (b) 3D MFL detection system  Two Faraday's laws of electrolysis govern the mass of anodic material corroded or consumed when the current passes through the circuit.
Appl. Sci. 2020, 10, 7083 Hence, the mass of substance ( m, theoretical): where K is electrochemical equivalent; n is the valence of the substance; M is the atomic mass or the molecular weight of the substance; F is Faraday's constant, 96,494 C/mole; I is the current in the electrochemical reaction; t is time in hours.
The corrosion experiments were divided into four stages: Accelerated corrosion was performed by the galvanostatic corrosion method using 0.4 A current for 2 h in the first corrosion stage, and the corrosion products of specimens were rinsed off carefully. Then the specimens were dried in warm air and weighed with an electronic balance to calculate the mass loss m. The geometric dimensions (width and depth) of corrosion defects at every scanning line of specimens were measured to calculate the average value of them. After that, the specimens were corroded again for 2 h and repeated the above procedure until the specimens were corroded for 8 h.
Corrosion at different stages are given in Table 2. Photographs of the corroded specimen, at various corrosion stages during the experiment, and the schematic of corrosion defect are shown in Figure 3. Variations of mass loss of the specimen ( m, measured and m, theoretical) and defect feature (depth h) with corrosion time (t) are shown in Figure 4. It is found that the defect depth is associated with mass loss ( m, measured). With the increase of corrosion time, the defect depth and mass loss (measured and theoretical) have the same variation tendency. Hence, the mass of substance (△m, theoretical): where K is electrochemical equivalent; n is the valence of the substance; M is the atomic mass or the molecular weight of the substance; F is Faraday's constant, 96,494 C/mole; I is the current in the electrochemical reaction; t is time in hours.
The corrosion experiments were divided into four stages: Accelerated corrosion was performed by the galvanostatic corrosion method using 0.4 A current for 2 h in the first corrosion stage, and the corrosion products of specimens were rinsed off carefully. Then the specimens were dried in warm air and weighed with an electronic balance to calculate the mass loss △m. The geometric dimensions (width and depth) of corrosion defects at every scanning line of specimens were measured to calculate the average value of them. After that, the specimens were corroded again for 2 h and repeated the above procedure until the specimens were corroded for 8 h.
Corrosion at different stages are given in Table 2. Photographs of the corroded specimen, at various corrosion stages during the experiment, and the schematic of corrosion defect are shown in Figure 3. Variations of mass loss of the specimen (△m, measured and △m, theoretical) and defect feature (depth h) with corrosion time (t) are shown in Figure 4. It is found that the defect depth is associated with mass loss (△m, measured). With the increase of corrosion time, the defect depth and mass loss (measured and theoretical) have the same variation tendency.   The three-dimensional (3D) MFL detection system involves three main parts: a 3D scanning console system, a commercial EMS2003 metal magnetic memory testing apparatus, and a nonmagnetic scanning platform. A Hall probe with a resolution of 1 A/m is a part of the testing apparatus, which was fixed on a non-magnetic 3D scanning console system controlled by a computer moving automatically at a uniform detection speed (90 mm/min). The specimens were placed on the scanning platform along the south-north direction when the MFL signals were detected. The data were stored in the EMS2003 metal magnetic memory testing apparatus. The schematic of the 3D MFL detection system is shown in Figure 2b.

Static Tension Experiment
The tensile tests were performed with a universal testing machine named SANS-100kN, whose load error is within ±0.5%. Before loading, all specimens were demagnetized and put on the platform along the south-north direction to eliminate the influence of the sample orientation. The normal and tangential components of the demagnetization signals, namely Hn and Ht signals, were measured along the south-north direction using the 3D MFL detection system under the condition of room temperature. Tensile loads were applied at an increment of 5 kN. The specimens were measured offline to eliminate any possible effect of the machine, and the MFL signals of specimens were measured in the same way as the demagnetization signals. Then the specimens were loaded to a specific value, and the procedure was repeated until the specimen was loaded to 25 kN.

Corrosion Experiment without Loading
The experiment was divided into four stages. Before the experiment, the specimens were demagnetized and put on the platform along the south-north direction. The demagnetization signals of each scanning line were measured in the same way as the static tension experiment. Then the specimens were corroded for 2 h, and the corrosion products were rinsed off carefully. The specimens were dried in warm air and weighed. The geometric dimensions (width and depth) of corrosion defects were measured, and the MFL signals of every scanning line were measured in the same way as the demagnetization signals. After that, the specimens were corroded again for 2 h, and the procedures were repeated until the specimens were corroded for 8 h.

Corrosion Experiment after Loading
The measurement obtained yield stress of 50 kN for material before the experiment, so the specimens were loaded to a pre-determined value 25 kN. Before the experiment, the specimens were demagnetized and put on the platform along the south-north direction. The demagnetization signals of each scanning line were measured in the same way as the static tension experiment before load. Then the specimens were loaded on the machine, and the MFL signals of every scanning line were The three-dimensional (3D) MFL detection system involves three main parts: a 3D scanning console system, a commercial EMS2003 metal magnetic memory testing apparatus, and a non-magnetic scanning platform. A Hall probe with a resolution of 1 A/m is a part of the testing apparatus, which was fixed on a non-magnetic 3D scanning console system controlled by a computer moving automatically at a uniform detection speed (90 mm/min). The specimens were placed on the scanning platform along the south-north direction when the MFL signals were detected. The data were stored in the EMS2003 metal magnetic memory testing apparatus. The schematic of the 3D MFL detection system is shown in Figure 2b.

Static Tension Experiment
The tensile tests were performed with a universal testing machine named SANS-100kN, whose load error is within ±0.5%. Before loading, all specimens were demagnetized and put on the platform along the south-north direction to eliminate the influence of the sample orientation. The normal and tangential components of the demagnetization signals, namely H n and H t signals, were measured along the south-north direction using the 3D MFL detection system under the condition of room temperature. Tensile loads were applied at an increment of 5 kN. The specimens were measured offline to eliminate any possible effect of the machine, and the MFL signals of specimens were measured in the same way as the demagnetization signals. Then the specimens were loaded to a specific value, and the procedure was repeated until the specimen was loaded to 25 kN.

Corrosion Experiment without Loading
The experiment was divided into four stages. Before the experiment, the specimens were demagnetized and put on the platform along the south-north direction. The demagnetization signals of each scanning line were measured in the same way as the static tension experiment. Then the specimens were corroded for 2 h, and the corrosion products were rinsed off carefully. The specimens were dried in warm air and weighed. The geometric dimensions (width and depth) of corrosion defects were measured, and the MFL signals of every scanning line were measured in the same way as the demagnetization signals. After that, the specimens were corroded again for 2 h, and the procedures were repeated until the specimens were corroded for 8 h.

Corrosion Experiment after Loading
The measurement obtained yield stress of 50 kN for material before the experiment, so the specimens were loaded to a pre-determined value 25 kN. Before the experiment, the specimens were demagnetized and put on the platform along the south-north direction. The demagnetization signals of each scanning line were measured in the same way as the static tension experiment before load.
Then the specimens were loaded on the machine, and the MFL signals of every scanning line were measured offline in the same way as the demagnetization signals. After that, the specimens were corroded in the same way as experiment 2 (corrosion without loading).

Surface Characterization
A sample was prepared for SEM to observe the surface of the uncorroded sample. The dimensions of this sample after being cut were 10 × 5 × 3 mm. The surface of the sample was wet ground through successive grades of SiC papers from P180 to P2000 and then polished until there were no scratches. Finally, the sample was immersed in etching reagent, 4mL HNO3 + 96 mL ethanol, for 5-10 s. The surface of the specimen was observed by LEO-1450 SEM equipped with KEVEX-Superdry EDX.
After the corrosion experiment, the dimensions of corrosion sections being cut were 10 × 5 × 3 mm to observe the surface of the sample by SEM. In addition, the cross-section of the sample was found to analyze the thickness and composition of the corrosion layer. To prevent the corrosion layer on the surface of the sample from being damaged artificially during grinding and polishing, the sample was cast into epoxy resin. Then the cross-section of the sample was wet ground and polished by the above treatment method. SEM and EDX observed the cross-section of the sample.

Results and Discussion
It should be noted that three specimens in each experiment (experiment 1, 2 and 3) were tested. MFL signals on all testing lines are the same. Thus, the MFL signals on Line 3 are shown here.

Experimental Results
The distributions of MFL signals (H n and H t ) during experiment 1 (static tension) under different loads were plotted in Figure 5. It is found that the normal component H n and the tangential component H t presented different signal characteristics at the defect during the load process from Figure 5. As can be seen in Figure 5, the demagnetization signals at the defect presented prominent distortion characteristics. H n presented a "trough-peak" shape, while H t presented a "peak" shape. Compared with the demagnetization signals, the MFL signals at the defect occurred significant changes after loading. The normal component H n changed from "trough-peak" to "peak-trough," while the tangential component H t changed from "peak" to "trough"; and the baseline amplitude value of H n and H t besides the defect increased dramatically. In addition, with the increase of the applied load, the abnormal peak amplitude of H n and H t increased. The theory of the magnetic charge can explain the change of MFL signals during the load process [39,41].

Surface Characterization
A sample was prepared for SEM to observe the surface of the uncorroded sample. The dimensions of this sample after being cut were 10 × 5 × 3 mm. The surface of the sample was wet ground through successive grades of SiC papers from P180 to P2000 and then polished until there were no scratches. Finally, the sample was immersed in etching reagent, 4mL HNO3 + 96 mL ethanol, for 5-10 s. The surface of the specimen was observed by LEO-1450 SEM equipped with KEVEX-Superdry EDX.
After the corrosion experiment, the dimensions of corrosion sections being cut were 10 × 5 × 3 mm to observe the surface of the sample by SEM. In addition, the cross-section of the sample was found to analyze the thickness and composition of the corrosion layer. To prevent the corrosion layer on the surface of the sample from being damaged artificially during grinding and polishing, the sample was cast into epoxy resin. Then the cross-section of the sample was wet ground and polished by the above treatment method. SEM and EDX observed the cross-section of the sample.

Results and Discussion
It should be noted that three specimens in each experiment (experiment 1, 2 and 3) were tested. MFL signals on all testing lines are the same. Thus, the MFL signals on Line 3 are shown here.

Experimental Results
The distributions of MFL signals (Hn and Ht) during experiment 1 (static tension) under different loads were plotted in Figure 5. It is found that the normal component Hn and the tangential component Ht presented different signal characteristics at the defect during the load process from Figure 5. As can be seen in Figure 5, the demagnetization signals at the defect presented prominent distortion characteristics. Hn presented a "trough-peak" shape, while Ht presented a "peak" shape. Compared with the demagnetization signals, the MFL signals at the defect occurred significant changes after loading. The normal component Hn changed from "trough-peak" to "peak-trough," while the tangential component Ht changed from "peak" to "trough"; and the baseline amplitude value of Hn and Ht besides the defect increased dramatically. In addition, with the increase of the applied load, the abnormal peak amplitude of Hn and Ht increased. The theory of the magnetic charge can explain the change of MFL signals during the load process [39,41].  The distributions of MFL signals (Hn and Ht) during experiment 2 (corrosion without loading) at different corrosion degrees were plotted in Figure 6. It is found that Hn and Ht of the demagnetization signal presented other characteristics. Hn showed an approximately linear change along Line 3 with a shallow gradient, while Ht kept a nearly constant value. As can be seen in Figure 6, Hn and Ht presented different distortion characteristics at the defect during the corrosion process. Hn presented The distributions of MFL signals (H n and H t ) during experiment 2 (corrosion without loading) at different corrosion degrees were plotted in Figure 6. It is found that H n and H t of the demagnetization Appl. Sci. 2020, 10, 7083 7 of 18 signal presented other characteristics. H n showed an approximately linear change along Line 3 with a shallow gradient, while H t kept a nearly constant value. As can be seen in Figure 6, H n and H t presented different distortion characteristics at the defect during the corrosion process. H n presented a "trough-peak" shape, while H t presented an apparent "peak" shape. With the increase of corrosion degree, the abnormal peak amplitude of H n and H t increased. The results indicated that both H n and H t presented abnormal peak features during the corrosion process, showing the location of corrosion defect accurately. different corrosion degrees were plotted in Figure 7. It is found that Hn and Ht of the demagnetization signal also presented different characteristics. Hn showed an approximately linear change along Line 3 with a shallow gradient, while Ht kept an almost constant value. After the specimen was loaded, the gradient and amplitude of Hn increased significantly, while changes only in amplitude could be found for Ht, still almost horizontal linear distribution. Such a phenomenon is due to the piezomagnetic effect [43]. It is known that applied stress can lead to the reorientation of magnetic domains along the tensile direction [44]. As can be seen in Figure 7, Hn and Ht presented different distortion characteristics at the defect during the corrosion process. Hn presented a visible "troughpeak" shape, while Ht presented an apparent "peak" shape. With the increase of corrosion degree, the abnormal peak amplitude of Hn and Ht increased significantly. At the same time, the gradient of Hn and the baseline amplitude value of Hn and Ht decreased. The results of experiment 3 (corrosion after loading) indicated that both Hn and Ht presented abnormal signal characteristics during the corrosion process, showing the location of the corrosion defect accurately.  The distributions of MFL signals (H n and H t ) during experiment 3 (corrosion after loading) at different corrosion degrees were plotted in Figure 7. It is found that H n and H t of the demagnetization signal also presented different characteristics. H n showed an approximately linear change along Line 3 with a shallow gradient, while H t kept an almost constant value. After the specimen was loaded, the gradient and amplitude of H n increased significantly, while changes only in amplitude could be found for H t , still almost horizontal linear distribution. Such a phenomenon is due to the piezomagnetic effect [43]. It is known that applied stress can lead to the reorientation of magnetic domains along the tensile direction [44]. As can be seen in Figure 7, H n and H t presented different distortion characteristics at the defect during the corrosion process. H n presented a visible "trough-peak" shape, while H t presented an apparent "peak" shape. With the increase of corrosion degree, the abnormal peak amplitude of H n and H t increased significantly. At the same time, the gradient of H n and the baseline amplitude value of H n and H t decreased. The results of experiment 3 (corrosion after loading) indicated that both H n and H t presented abnormal signal characteristics during the corrosion process, showing the location of the corrosion defect accurately.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 18 a "trough-peak" shape, while Ht presented an apparent "peak" shape. With the increase of corrosion degree, the abnormal peak amplitude of Hn and Ht increased. The results indicated that both Hn and Ht presented abnormal peak features during the corrosion process, showing the location of corrosion defect accurately. The distributions of MFL signals (Hn and Ht) during experiment 3 (corrosion after loading) at different corrosion degrees were plotted in Figure 7. It is found that Hn and Ht of the demagnetization signal also presented different characteristics. Hn showed an approximately linear change along Line 3 with a shallow gradient, while Ht kept an almost constant value. After the specimen was loaded, the gradient and amplitude of Hn increased significantly, while changes only in amplitude could be found for Ht, still almost horizontal linear distribution. Such a phenomenon is due to the piezomagnetic effect [43]. It is known that applied stress can lead to the reorientation of magnetic domains along the tensile direction [44]. As can be seen in Figure 7, Hn and Ht presented different distortion characteristics at the defect during the corrosion process. Hn presented a visible "troughpeak" shape, while Ht presented an apparent "peak" shape. With the increase of corrosion degree, the abnormal peak amplitude of Hn and Ht increased significantly. At the same time, the gradient of Hn and the baseline amplitude value of Hn and Ht decreased. The results of experiment 3 (corrosion after loading) indicated that both Hn and Ht presented abnormal signal characteristics during the corrosion process, showing the location of the corrosion defect accurately.

Comparison of Experimental Results
The normal components H n and the tangential component H t of MFL signals in the last stage in three experiments were selected to compare the characteristics of signals under different working conditions. The surface and contour maps of signals in the chosen stage were drawn in Figure 8. As can be seen in Figure 8a, H n and H t of experiment 1 at the defect showed apparent "peak-trough" shape and "trough" shape, respectively. As can be seen in Figure 8b,c, H n and H t at the defect presented a "trough-peak" shape, and "peak" shape, respectively. Figure 9a shows the comparison of unprocessed H n in three experiments. For the convenience of comparison, H n and H t were further processed. H n subtracts the baseline amplitude, and the baseline amplitude of H t returns to zero. Figure 9b shows the comparison of H n subtracting the baseline amplitude value in three experiments. Figure 9c shows the comparison of H t where the baseline amplitude returns to zero in three experiments. It is found that H n and H t presented different signal characteristics under different working conditions: When the specimen was subjected to tensile load and corrosion, respectively, H n and H t both exhibited opposite signal characteristics. When the specimen was corroded without and after loading, H n and H t both showed the same signal characteristics, and a more substantial amplitude value could be found in corrosion experiment after loading.

Comparison of Experimental Results
The normal components Hn and the tangential component Ht of MFL signals in the last stage in three experiments were selected to compare the characteristics of signals under different working conditions. The surface and contour maps of signals in the chosen stage were drawn in Figure 8. As can be seen in Figure 8a, Hn and Ht of experiment 1 at the defect showed apparent "peak-trough" shape and "trough" shape, respectively. As can be seen in Figure 8b,c, Hn and Ht at the defect presented a "trough-peak" shape, and "peak" shape, respectively. Figure 9a shows the comparison of unprocessed Hn in three experiments. For the convenience of comparison, Hn and Ht were further processed. Hn subtracts the baseline amplitude, and the baseline amplitude of Ht returns to zero. Figure 9b shows the comparison of Hn subtracting the baseline amplitude value in three experiments. Figure 9c shows the comparison of Ht where the baseline amplitude returns to zero in three experiments. It is found that Hn and Ht presented different signal characteristics under different working conditions: When the specimen was subjected to tensile load and corrosion, respectively, Hn and Ht both exhibited opposite signal characteristics. When the specimen was corroded without and after loading, Hn and Ht both showed the same signal characteristics, and a more substantial amplitude value could be found in corrosion experiment after loading.

Characterization of the Corrosion Layer
The SEM micrographs of the surface of the samples are shown in Figure 10. As can be seen in Figure 10a, the microstructure of the uncorroded sample was composed of lamellar pearlite and white ferrite. As can be seen in Figure 10b, the surface of the sample was covered with relatively uniform corrosion products after 8 h of corrosion. Figure 11 shows the cross-section SEM image, analytical line, and corresponding X-ray maps of Fe and O for the sample corroded for 8 h. The thickness of the

Characterization of the Corrosion Layer
The SEM micrographs of the surface of the samples are shown in Figure 10. As can be seen in Figure 10a, the microstructure of the uncorroded sample was composed of lamellar pearlite and white ferrite. As can be seen in Figure 10b, the surface of the sample was covered with relatively uniform corrosion products after 8 h of corrosion. Figure 11 shows the cross-section SEM image, analytical line, and corresponding X-ray maps of Fe and O for the sample corroded for 8 h. The thickness of the

Characterization of the Corrosion Layer
The SEM micrographs of the surface of the samples are shown in Figure 10. As can be seen in Figure 10a, the microstructure of the uncorroded sample was composed of lamellar pearlite and white ferrite. As can be seen in Figure 10b, the surface of the sample was covered with relatively uniform corrosion products after 8 h of corrosion. Figure 11 shows the cross-section SEM image, analytical line, and corresponding X-ray maps of Fe and O for the sample corroded for 8 h. The thickness of the corrosion layer is relatively uniform, approximately 16 µm. As can be seen in X-ray maps, the corrosion layer mainly contained oxygen and iron elements. Compared with the iron matrix, the content of the oxygen element in the corrosion layer increased obviously. In contrast, the content of iron decreased obviously, indicating that the corrosion layer was mainly constituted of iron oxides. Therefore, the permeability of the corrosion layer is much less than iron [45], and the corrosion layer reduced the permeability of the sample.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 18 corrosion layer is relatively uniform, approximately 16 μm. As can be seen in X-ray maps, the corrosion layer mainly contained oxygen and iron elements. Compared with the iron matrix, the content of the oxygen element in the corrosion layer increased obviously. In contrast, the content of iron decreased obviously, indicating that the corrosion layer was mainly constituted of iron oxides. Therefore, the permeability of the corrosion layer is much less than iron [45], and the corrosion layer reduced the permeability of the sample. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 18 corrosion layer is relatively uniform, approximately 16 μm. As can be seen in X-ray maps, the corrosion layer mainly contained oxygen and iron elements. Compared with the iron matrix, the content of the oxygen element in the corrosion layer increased obviously. In contrast, the content of iron decreased obviously, indicating that the corrosion layer was mainly constituted of iron oxides. Therefore, the permeability of the corrosion layer is much less than iron [45], and the corrosion layer reduced the permeability of the sample.

Analysis and Discussion
The magnetic charge is an equivalent model, which has been developed to interpret the magnetic field leakage of ferromagnetic materials. For a ferromagnet, its external magnetic field would be considered to originate from the magnetic charge [41]. For the convenience of discussion, it is assumed that the magnetic flux leakage was caused by the equivalent magnetic charge on the two interfaces of the defect zone. Then, the MFL H at the measuring point caused by equivalent magnetic charge q is given as = 4π (4) where is the permeability of air, r is the position vector from equivalent magnetic charge to measuring point.
The schematic diagram of MFL signals in experiment 1 (static tensile) is shown in Figure 12a. The initial leakage magnetic field Hi is formed by the magnetic polarity generated due to the accumulation of a small number of magnetic charges at both sides of the defect after the specimen was demagnetized [39,41,46], which coincides with the initial magnetic field He. The demagnetization signals are the vector sum of He and Hi. Thus, Hn presents a "trough-peak" shape, and Ht gives a "peak" shape at the defect. After being loaded, the magnetization of the specimen changes under the combined action of the geomagnetic field and stress [43,44], results in the formation of leakage magnetic field HL. The accumulation of more magnetic charges at both sides of the defect due to the stress concentration at the defect after the specimen was loaded, resulting in a strong leakage magnetic field Hm, which is opposite to the leakage magnetic field Hi. In addition, the leakage magnetic field Hm is stronger than Hi, causing the reversal of MFL signals at the defect. Under such conditions, the MFL signals are the vector sum of the initial magnetic field He, leakage magnetic field HL, Hm, and Hi. Thus, the normal component Hn of MFL signals at the defect presents a "peak-trough" shape, and the tangential component Ht shows a "trough" shape. With the increase of the load, the stress concentration on both sides of the defect increases, increasing the number of magnetic charges, which leads to the strengthening of leakage magnetic field Hm, causing the increase of the MFL signals at the defect (see Figure 5).

Analysis and Discussion
The magnetic charge is an equivalent model, which has been developed to interpret the magnetic field leakage of ferromagnetic materials. For a ferromagnet, its external magnetic field would be considered to originate from the magnetic charge [41]. For the convenience of discussion, it is assumed that the magnetic flux leakage was caused by the equivalent magnetic charge on the two interfaces of the defect zone. Then, the MFL H at the measuring point caused by equivalent magnetic charge q is given as where µ 0 is the permeability of air, r is the position vector from equivalent magnetic charge to measuring point. The schematic diagram of MFL signals in experiment 1 (static tensile) is shown in Figure 12a. The initial leakage magnetic field H i is formed by the magnetic polarity generated due to the accumulation of a small number of magnetic charges at both sides of the defect after the specimen was demagnetized [39,41,46], which coincides with the initial magnetic field H e . The demagnetization signals are the vector sum of H e and H i . Thus, H n presents a "trough-peak" shape, and H t gives a "peak" shape at the defect. After being loaded, the magnetization of the specimen changes under the combined action of the geomagnetic field and stress [43,44], results in the formation of leakage magnetic field H L . The accumulation of more magnetic charges at both sides of the defect due to the stress concentration at the defect after the specimen was loaded, resulting in a strong leakage magnetic field H m , which is opposite to the leakage magnetic field H i . In addition, the leakage magnetic field H m is stronger than H i , causing the reversal of MFL signals at the defect. Under such conditions, the MFL signals are the vector sum of the initial magnetic field H e , leakage magnetic field H L , H m, and H i . Thus, the normal component H n of MFL signals at the defect presents a "peak-trough" shape, and the tangential component H t shows a "trough" shape. With the increase of the load, the stress concentration on both sides of the defect increases, increasing the number of magnetic charges, which leads to the strengthening of leakage magnetic field H m , causing the increase of the MFL signals at the defect (see Figure 5). The schematic diagram of MFL signals in experiment 2 (corrosion without loading) is shown in Figure 12b. The defect formed on the surface of the specimen due to corrosion, results in the formation of an initial leakage magnetic field Hi. In addition, magnetic charges accumulated at both sides of the defect due to the effect of corrosion, result in the formation of leakage magnetic field Hc, which is opposite to the initial magnetic field Hi. Under such conditions, the MFL signals are the vector sum of the initial magnetic field He, leakage magnetic field Hc and Hi. Thus, the normal component Hn of MFL signals presents a "trough-peak" shape, and the tangential component Ht presents a "peak" shape. With the increase of corrosion degree, the leakage magnetic field Hc is gradually enhanced, causing the MFL signals increasing at the defect (see Figure 6).
The schematic diagram of MFL signals in experiment 3 (corrosion after loading) is shown in Figure 12c. Different from experiment 2, the specimen in experiment 3 was corroded after having been loaded, so a strong leakage magnetic field Hc was generated at the defect after the specimen was corroded, which is stronger than the leakage magnetic field Hm and Hi. Under such conditions, the MFL signals are the vector sum of the initial magnetic field He, leakage magnetic field HL, Hc, Hm, and Hi. Thus, the normal component Hn of MFL signals presents a "trough-peak" shape, and the tangential component Ht presents a "peak" shape. With the increase of corrosion degree, the vector sum of leakage magnetic field Hc, Hm, and Hi increases, causing the MFL signals at the defect gradually increasing (see Figure 7).

Quantitative Evaluation Parameters
To further analyze the relationship between the MFL signals and corrosion degree, two characteristic magnetic parameters Sn and St were defined. The parameters Sn and St were extracted from the MFL signals of representative scanning line (Line 3) in experiment 3 (corrosion after loading), and the calculation methods of magnetic characteristic parameters are shown in Figure 13. For the normal component presented in Figure 13a, the parameter Sn can be obtained directly. The The schematic diagram of MFL signals in experiment 2 (corrosion without loading) is shown in Figure 12b. The defect formed on the surface of the specimen due to corrosion, results in the formation of an initial leakage magnetic field H i . In addition, magnetic charges accumulated at both sides of the defect due to the effect of corrosion, result in the formation of leakage magnetic field H c , which is opposite to the initial magnetic field H i . Under such conditions, the MFL signals are the vector sum of the initial magnetic field H e , leakage magnetic field H c and H i . Thus, the normal component H n of MFL signals presents a "trough-peak" shape, and the tangential component H t presents a "peak" shape. With the increase of corrosion degree, the leakage magnetic field H c is gradually enhanced, causing the MFL signals increasing at the defect (see Figure 6).
The schematic diagram of MFL signals in experiment 3 (corrosion after loading) is shown in Figure 12c. Different from experiment 2, the specimen in experiment 3 was corroded after having been loaded, so a strong leakage magnetic field H c was generated at the defect after the specimen was corroded, which is stronger than the leakage magnetic field H m and H i . Under such conditions, the MFL signals are the vector sum of the initial magnetic field H e , leakage magnetic field H L , H c , Hm, and H i . Thus, the normal component H n of MFL signals presents a "trough-peak" shape, and the tangential component H t presents a "peak" shape. With the increase of corrosion degree, the vector sum of leakage magnetic field H c , H m , and H i increases, causing the MFL signals at the defect gradually increasing (see Figure 7).

Quantitative Evaluation Parameters
To further analyze the relationship between the MFL signals and corrosion degree, two characteristic magnetic parameters S n and S t were defined. The parameters S n and S t were extracted from the MFL signals of representative scanning line (Line 3) in experiment 3 (corrosion after loading), and the calculation methods of magnetic characteristic parameters are shown in Figure 13. For the normal component presented in Figure 13a, the parameter S n can be obtained directly. The parameter S n is calculated by taking the signal difference between the peak and trough of the H n . However, the tangential component H t presented in Figure 13b and the parameter S t cannot be obtained straightforwardly. Figure 13c shows the gradient of H t , the position of the peak and trough of the gradient, A and B, can be obtained directly. Therefore, the parameter S t can be calculated by taking the distance from the peak position of H t to line AB.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 18 parameter Sn is calculated by taking the signal difference between the peak and trough of the Hn. However, the tangential component Ht presented in Figure 13b and the parameter St cannot be obtained straightforwardly. Figure 13c shows the gradient of Ht, the position of the peak and trough of the gradient, A and B, can be obtained directly. Therefore, the parameter St can be calculated by taking the distance from the peak position of Ht to line AB. Variations of characteristic magnetic parameters (Sn and St), mass loss of the specimen (△m, measured and △m, theoretical), and defect feature (corrosion depth h) with corrosion time (t) are shown in Figure 14. It is found that magnetic characteristic parameters, mass loss, and corrosion depth have the same variation tendency. St is considered to be the best parameter for quantitatively evaluating the degree of the corrosion among the four characterization parameters. Variations of characteristic magnetic parameters (S n and S t ), mass loss of the specimen ( m, measured and m, theoretical), and defect feature (corrosion depth h) with corrosion time (t) are shown in Figure 14. It is found that magnetic characteristic parameters, mass loss, and corrosion depth have the same variation tendency. S t is considered to be the best parameter for quantitatively evaluating the degree of the corrosion among the four characterization parameters. The direct dependence of mass loss (△m, theoretical) on the parameter St was obtained by Equations (3) and (5) where is the density of the specimen. The direct dependence of corrosion depth (h, theoretical) on the parameter St, ℎ, theoretical = ( ), was obtained by Equations (6) and (7) as follows: ℎ, theoretical = 3600( + 0.0476) 1.3047 (8) The relationship between the parameter S t and the corrosion time t is shown in Figure 15. It is found that the parameter S t and the corrosion time t have established a good linear relationship. After linear fitting, the equation defining the dependence of S t on t was found, and the correlation coefficient R 2 = 0.999: Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 18 The direct dependence of mass loss (△m, theoretical) on the parameter St was obtained by Equations (3) and (5) where is the density of the specimen. The direct dependence of corrosion depth (h, theoretical) on the parameter St, ℎ, theoretical = ( ), was obtained by Equations (6) and (7) as follows: ℎ, theoretical = 3600( + 0.0476) 1.3047 (8) Figure 15. The relationship between the parameter S t and the corrosion time t.
The direct dependence of mass loss ( m, theoretical) on the parameter S t was obtained by Equations (3) and (5) as follows: At the same time, the width change of the corrosion defect is small in the corrosion test, so the area of the corrosion area S is considered unchanged. The corrosion depth h, theoretical can be calculated from the mass loss m, theoretical: where ρ is the density of the specimen. The direct dependence of corrosion depth (h, theoretical) on the parameter S t , h, theoretical = f (S t ), was obtained by Equations (6) and (7) as follows: h, theoretical = 3600(S t + 0.0476) 1.3047nFρS MI In order to verify the reliability of the expression, the comparison between corrosion depth h, theoretical obtained by parameter S t and h, measured in experiment 3 (corrosion after loading) is shown in Figure 16. Meanwhile, corrosion depth h, measured in experiment 2 (corrosion without loading), is also shown in Figure 16. The average error rates of experiment 2 and experiment 3 were calculated to be 15.65% and 8.94%, respectively. It is found that the expression can predict the corrosion depth well and has a smaller error under the same working condition.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 18 In order to verify the reliability of the expression, the comparison between corrosion depth h, theoretical obtained by parameter St and h, measured in experiment 3 (corrosion after loading) is shown in Figure 16. Meanwhile, corrosion depth h, measured in experiment 2 (corrosion without loading), is also shown in Figure 16. The average error rates of experiment 2 and experiment 3 were calculated to be 15.65% and 8.94%, respectively. It is found that the expression can predict the corrosion depth well and has a smaller error under the same working condition.

Conclusions
In this paper, static tensile experiments, corrosion experiments without and after loading were performed to study the effect of corrosion on MFL signals. The normal and tangential components of the MFL signals, namely Hn and Ht, were measured using the 3D MFL detection system, and the distribution regularity of them during the corrosion process was investigated. The following conclusions are obtained: (1) The normal and tangential components of the MFL signals in corrosion experiments without and after loading presented a "trough-peak", and "peak" shape, respectively. It is known from experimental results that when the specimen was corroded without and after loading, the normal and tangential components both showed the same signal characteristics, and a more substantial amplitude value could be found in the corrosion experiment after loading. (2) The normal and tangential components of the MFL signals in the static tensile experiment presented a "peak-trough", and "trough" shape, respectively. It is found that the normal and tangential components showed different signal characteristics under different working conditions: When the specimen was subjected to tensile load and corroded, respectively, the normal and tangential components both exhibited opposite signal characteristics. According to the analysis, the critical reason for different signal characteristics is that the leakage magnetic field Hc generated at the defect after the specimen has been corroded is opposite to the leakage magnetic field Hm caused by force.

Conclusions
In this paper, static tensile experiments, corrosion experiments without and after loading were performed to study the effect of corrosion on MFL signals. The normal and tangential components of the MFL signals, namely H n and H t , were measured using the 3D MFL detection system, and the distribution regularity of them during the corrosion process was investigated. The following conclusions are obtained: (1) The normal and tangential components of the MFL signals in corrosion experiments without and after loading presented a "trough-peak", and "peak" shape, respectively. It is known from experimental results that when the specimen was corroded without and after loading, the normal and tangential components both showed the same signal characteristics, and a more substantial amplitude value could be found in the corrosion experiment after loading. (2) The normal and tangential components of the MFL signals in the static tensile experiment presented a "peak-trough", and "trough" shape, respectively. It is found that the normal and tangential components showed different signal characteristics under different working conditions: When the specimen was subjected to tensile load and corroded, respectively, the normal and tangential components both exhibited opposite signal characteristics. According to the analysis, the critical reason for different signal characteristics is that the leakage magnetic field H c generated at the defect after the specimen has been corroded is opposite to the leakage magnetic field H m caused by force. (3) The characterization parameters of MFL signals, S n and S t , are capable of evaluating the corrosion degree of the specimen, and S t is better. The characterization parameter of the tangential component of the MFL signals is more sensitive to the corrosion, which is different from the traditional research results on the MFL signals caused by stress where the characterization parameter of the normal component of the MFL signals is more sensitive to the force. The direct dependence of corrosion depth (h, theoretical) on the parameter S t , h, theoretical = f (S t ) was developed and the average error rates between the predicted and measured values are 8.94% under the same working condition. Therefore, the expression can be used to evaluate the corrosion degree of the specimen quantitatively.