3.2. Characteristics Analysis of MBN and MIP
Figure 7 demonstrates the response of MBN characteristics to stress in the elastic strain range, from which it can be concluded that MBN characteristics change monotonically with the increase of stress. Applying tensile stresses in the rolling direction produces the effect of compressive stresses acting in the perpendicular rolling direction. With increasing tensile stress in the rolling direction, the MMAX, the MMEAN, and the MR in the vertical rolling direction in different samples show a monotonically decreasing trend; however, the HCM monotonically increases. The anisotropy of samples increases and the magnetic domains are more likely to move in the direction of the easy magnetization axis (rolling direction), and the external stress further decreases the exchange energy of the magnetic crystals in the rolling direction. In the perpendicular easy magnetization direction, it is more difficult for the domains to move, and the MBN signals are weakened.
Figure 8 demonstrates the relationship between MIP signal and stress in the elastic strain range for materials with different microstructures, from which it can be concluded that MIP characteristics change monotonically with the increase of stress. Similar to the variation pattern of MBN signal, with the increase of tensile stress in the vertical rolling direction, the UMAX, the UMMEAN and the UR in the rolling direction show a monotonically decreasing trend; however, the HCU monotonically increases.
The different microstructures have different lattice interaction forces, resulting in different material response to stress, and the resulting magnetic domain structure and domain motion properties are different, resulting in differences in magnetic properties [
34].
With both the reversible and irreversible motion of magnetic domains, the variability of sample 1 with external stress is greater compared to that of samples 2, 3, and 4. In terms of the slope of coercivity and width of butterfly curve change, sample 1 shows a significantly higher growth rate after 35 MPa than before 35 MPa.
For sample 1, in the elastic range, the micro-magnetic NDT signal can be divided into two stages. The microscopic residual stress interacts with the external stress and the internal stress has a greater effect on the magnetic domain motion than the external stress. The compressive stress applied in the magnetic field direction increases the domain wall exchange energy in the magnetic field direction, but does not change the domain structure, and it is more difficult for the domain to move in the magnetic field direction at the same magnetization strength, thus the peak value is reduced and the coercivity field is increased. However, when the external stress exceeds the internal stress limit, the external stress causes the ferrite to undergo elastic deformation (rolling direction). The ferrite elastic deformation leads to a longer path of domain motion in the rolling direction and a shorter path of domain motion in the magnetic field direction, which further increases the domain wall exchange energy and prevents the short path of domain motion from generating higher and more concentrated MBN pulses, resulting in a lower MMAX, higher HCM, and increased width of butterfly curve. However, unlike the irreversible motion, the reversible motion of the magnetic domains is less driven and therefore more sensitive to the resistance [
35]. In sample 1, the inflection point appears around 25 MPa, while in MBN, it is 35 MPa [
35].
Samples 2–4 show an increase in the content of ferrite (or martensite) and a decrease in grain size, which leads to a significant increase in dislocation density. At this point, external stresses (5–80 MPa) are not able to deform the microstructure. Therefore, samples 2–4 do not show the trend of sample 1.
3.3. Results of Magnetic Domain Observations
For sample 1, the height difference exists on the sample surface because the ferrite is easily corroded after corrosion and the carbon-rich phase (cementite Fe3C, pearlite, etc.) is not easily corroded (
Figure 9a). At the same time, the presence of carbon-rich phase makes the lattice defective, and dislocation density increases while lattice distortion energy increases, thus increasing the microscopic residual stress of the material. During the AFM inspection, the MFM probe encounters higher tissue and produces the black lines in the figure (
Figure 9b).
The domains in
Figure 9b are mainly ferrite domains (lamellar (3), dendritic (2), labyrinthine (1, 4 and 5)), while a few cementite domains surrounding the ferrite grain boundaries appear as small black beads. In
Figure 9b, it is concluded that the magnetic domains in all grains, except for grain 3, show the phenomenon of domain separation. A large amount of carburite is dispersed in grain 2, which leads to the phenomenon of domain separation. The magnetic lines of the carbon-rich phase (cementite) within the crystal are not closed [
15,
16], forming unclosed magnetic domains, which increases the demagnetization energy. To reduce the demagnetization energy, the ferrite domains are subdivided to increase the number of domains, which may be accompanied by the appearance of supplementary domains in the process to close the magnetic lines of force. Grains 1, 4, and 5 show the phenomenon of domain separation, which may be related to the crystal orientation. For ferrite (three easy magnetization axes), the direction of [100] is the easiest magnetization axis and requires the lowest energy. Therefore, there is generally no magnetic domain separation in the [100] direction. In contrast, the crystals are in the direction of the other easy magnetization axes, which require higher energy. The energy of the demagnetizing field is reduced by the magnetic domain subdomain.
Applying tensile stress in the direction of the easy magnetization axis changes the microscopic residual state (no elastic deformation of the microstructure) and reduces the exchange energy of the easy magnetization axis, causing the MBN and MIP signals in the perpendicular easy magnetization axis direction to decrease. After a certain threshold is exceeded, the ferrite elongates in the direction of the easy magnetization axis, which decreases the magnetic domain motion path in the vertical direction (at this point, the external stress has a greater effect on the magnetic domain motion than the microstructure). Therefore, the MBN and MIP signals weaken. Stresses exceeding the elastic limit cause plastic deformation of the ferrite, which causes lattice rupture and a further increase of dislocation density [
36], and MBN and MIP are weakened again. However, there is a difference in the physical principles of these two cases.
Figure 10 shows the domain structure of sample 2. For sample 2, granular pearlite and ferrite dominate, and the structure of the granular pearlite magnetic domains can be clearly seen in the figure. Before magnetization, it can be noticed that the domains are divided in grain 1 (ferrite organization) and that multiple granular pearlite magnetic domains in region 2 (white area,
Figure 10b) are black and white. After applying a magnetic field of 200 Oe, the magnetic domains in grain 1 are deflected to the same direction, and multiple granular pearlite magnetic domains in region 2 appear to have a laminar structure. It can be concluded that the ferrite domains in the granular pearlite are deflected, and the motion is different from that of the domains in grain 1 due to the presence of the cementite domains, implying that the magnetic domains within the pearlite require higher energy for their motion than the ferrite domains.
The crystal structure affects not only the magnetic domain structure and motion properties, but also the mechanical properties. Compared with ferrite, granular pearlite has a different crystal structure and is harder, less plastic, and more difficult to deform [
34]. Under stresses of 5–80 MPa, ferrite in sample 2 was not deformed, so it showed more consistent variation.
The microstructure of samples 3 and 4 is dominated by ferrite and martensite (
Figure 11 and
Figure 12). The martensitic magnetic domains (
Figure 11b and
Figure 12b, white area) hardly move at a magnetic field strength of 200 Oe (
Figure 11d and
Figure 12d). Essentially, martensite is also a mixture of cementite and pearlite chemicals, but is more complex than pearlite and with a higher dislocation density. The martensite domain is also an unclosed domain similar to the cementite domain, and in samples 3 and 4, the ferrite domain is more affected by martensite due to the absence of grain boundaries. White areas similar to martensitic domains appear in the ferrite domains (1 and 2,
Figure 12) and the morphology of the domains does not change at a magnetization intensity of 200 Oe. As shown in
Figure 11b, 1 and 2, the ferrite domains both show domain splitting. At a magnetization intensity of 200 Oe, the magnetic domains in grain 2 in
Figure 11b show stripes, which are called striped magnetic domains. It shows that the ferrite magnetic domains are more difficult to move under the same magnetic field excitation in the duplex steel with ferrite and martensite than in the duplex steel with pearlite and ferrite (
Figure 10d,
Figure 11d and
Figure 12d).
Compared with pearlite, martensite is characterized by higher hardness (374 HV) dislocation density, but lower toughness and less deformation. Under the stress condition of 0~80 MPa, the microscopic residual stress equilibrium state of samples 3 and 4 is less affected, i.e., the deformation is smaller in the perpendicular rolling direction, and the magnetic domain motion path changes less, so the magnetic domains are less affected by the compressive stress under the excitation of the external magnetic field; therefore, the micro-magnetic characteristics, such as UR and HCU, are basically stabilized in a horizontal line. The MBN and MIP signals of samples 3 and 4 are lower than those of sample 2, indicating that there is an inflection point in the influence of microstructure on the reversible and irreversible motions of magnetic domains. The martensitic dislocation density is greater than that of pearlite, and the pearlite dislocation density is greater than that of ferrite. Within the sample, the impedance of the reversible and irreversible motions of the magnetic domains increases sequentially, and the MBN and MIP signals weaken above a certain threshold.
The mechanism by which the micro-magnetic signal is altered by stress is shown in
Figure 13. The external stresses change the micro-magnetic signal by affecting the deformation of the microstructure, which, in turn, affects the magnetic domain structure or the path of motion. Dislocations are a manifestation of microscopic stresses (caused by crystal defects) in materials, and their vector sum with crystal deformation, etc., is the microscopic residual stress.
In the study, at low stress levels, the external stress first changes the dislocation equilibrium state and thus affects the microscopic residual stress (MBN and MIP signals change in sample 1). when the external stress increases to a certain degree, the external stress changes the crystal shape, causing the crystal to undergo elastic deformation, and then the magnetic domain motion path changes, resulting in the micro-magnetic signals changing accordingly. When the external stress continues to increase, the crystal undergoes plastic deformation, which leads to lattice breakage (increased defects) and thus increased dislocation density (increased microscopic residual stress) [
36]. Meanwhile, the magnetic domain structure, motion path, and motion characteristics are changed, and the micro-magnetic signal is also changed.
In different microstructures, the lattice interaction forces and dislocation densities are different even without the influence of external stresses. Therefore, the effects of different microstructures on the structure and motion characteristics of magnetic domains are also different, while the micro-magnetic signals are also different. Due to the different lattice interaction forces and dislocation densities in different microstructures, the microscopic residual stress equilibrium state and the organizational deformation state are different under the same stress. As a result, the trends of the micro-magnetic signals are also different.
3.4. Definition and Quantification of Magnetic Domain Characteristics
The MBN and MIP signals mainly originate from the motion of ferrite magnetic domains, while the magnetic domains of other phases directly affect the structure and motion properties of the ferrite magnetic domains. The magnetic domains of other phases (cementite domains in sample 1, pearlite domains in sample 2, and martensite domains in samples 3 and 4) in the MFM image at zero magnetic field strength are identified as magnetic domain features using image processing techniques. This not only reflects the influence of crystal structure and dislocation density on magnetic domains, but also reflects the influence of external stress on the structure and motion characteristics of magnetic domains to some extent.
The phase of cementite in sample 1, pearlite in sample 2, and martensite in samples 3 and 4 is special compared to that of ferrite, and the dislocation density is higher than that of ferrite, both of which results in a higher demagnetization energy than that of ferrite. Magnetic domains in ferrite crystals are split into small-sized domains (domain division phenomenon), which surround the other phase domains to close the unclosed magnetic lines of force. Thus, the magnetic domains are subdivided to reduce the energy of the demagnetizing field. Meanwhile, the magnetic domains of these tissues are not only difficult to be magnetized, but also affect the motion of the surrounding ferrite magnetic domains. Magnetic domains are characterized as the percentage of domain area that is difficult to magnetize in an external magnetic field of less than 200 Oe. In addition, the magnetic domain characteristics defined in this investigation not only characterize the effect of dislocation density on the magnetic domains, but also provide feedback on the effect of external stress on the magnetic domains.
Image gray level layering technique based on Python was used for magnetic domain feature extraction [
34]. First, the image is binarized by choosing a suitable threshold value, and then the area share of the target pixels is extracted as the area share of the difficult-to-magnetize magnetic domains (
Figure 14) [
34] The quantitative results are shown in
Table 3.
By comparing
Table 2 and
Table 3, it can be seen that the characteristic microstructure (α) has a strong consistency with the magnetic domain characteristics (
Figure 15), and the relationship is almost linear. The fitting relationship is as follows:
y = 1.2048
x − 0.4066.
As can be seen from
Table 4, the largest error in the three sets of validation data is 0.26%, and the smallest error is 0.01%. It is concluded that this fitting relationship can more accurately characterize the microstructure characteristics and magnetic domain characteristics of the trend.
3.5. Pattern Recognition Results
In the process of data processing, it is found that under 5 MPa stress gradients, the accuracy of pattern recognition results (the degree of agreement between the predicted label and the actual label) is only 12.7%. Therefore, the micro-magnetic characteristic data at stresses such as 5 MPa, 15 MPa, …, 75 MPa, etc. are removed from the sample set to extend the stress gradient. Finally, the filtered sample set (micro-magnetic data and corresponding microstructure and stress data) has a total of 7700 pieces.
According to the previous section, microstructure (pearlite content, martensite content, grain size, etc.) and external stresses have a direct influence on micro-magnetic NDT. A set of microstructures and stress states has a set of corresponding micro-magnetic characteristics. In theory, the corresponding microstructure features and stress states can be quickly determined based on the micro-magnetic features. On the one hand, the microstructure features and stresses are coupled, and on the other hand, there are countless combinations of microstructure and stress states. In order to describe the microstructure and stress state in a simple and uniform way, the set of microstructure features and stress states is defined as a pattern (a label), which is the patterned representation of microstructure features and stress states. Then, the dataset is composed of micro-magnetic features and labels. According to different microstructures and stress gradients, the samples were divided into 32 categories (
Table 5).
The two-hidden-layer (25, 25) MLP model was adopted. The hidden layer function is ‘tansig’, the output layer function is ‘purelin’, and the network training function is ‘trainlm’. Based on experience, the maximum number of iterations of the MLP model is 1000. The learning efficiency is 0.1 and the target error is 0.00001.
The sample set is divided into a training set and a test set, and the number of training set samples is 5200. The test set is prepared using sample data of the same steel grade as sample 1 and sample 3 but belonging to different batches. The number of samples is 2500.
As shown in
Figure 16a, the prediction accuracy of the MLP model without adding magnetic domain features is 80%. By taking the magnetic domain features together with the micro-magnetic features as input for pattern recognition, the prediction accuracy of the MLP model is 97.39% (
Figure 16b), which is 17.39% higher than that of micro-magnetic features alone.
In addition, as shown in
Figure 16a, part of the pattern recognition result is label 15, while the actual label is 23. After querying the original data, it is found that the micro-magnetic features corresponding to the actual labels of 15 and 23 are cross-interfering, which leads to the wrong result of pattern recognition. However, the labels 15 and 23 can be distinguished, after adding the magnetic domain feature.
The experimental results show that the pattern recognition accuracy of the magnetic domain feature and the micro-magnetic feature together as input is higher than that of the micro-magnetic feature as the input alone. The pattern recognition method proposed in this investigation takes the effects of microstructure and stress on micro-magnetic signals into account, which realizes the quantitative characterization of microstructure features and stress states.