Evaluation of the Magnetocrystalline Anisotropy of Typical Materials Using MBN Technology

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Article Evaluation of the Magnetocrystalline Anisotropy of Typical Materials Using MBN Technology

Liting Wang, Cunfu He and Xiucheng Liu *

Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China; [email protected] (L.W.); [email protected] (C.H.) * Correspondence: [email protected]; Tel.: +86-010-6739-1720

Abstract: Magnetic Barkhausen noise (MBN) signals in the stage from saturation to remanence of the hysteresis loop are closely correlated with magnetocrystalline anisotropy energy. MBN events in this stage are related to the nucleation and growth of reverse domains, and mainly affected by the crystallographic textures of materials. This paper aims to explore the angle-dependent magnetocrystalline anisotropy energy. Based on the consideration of macroscopic magnetic anisotropy, with the concept of coordinate transformation, a model was ﬁrstly established to simulate the magnetocrystalline anisotropy energy (MCE) of a given material. Secondly, the MBN signals in different directions were tested with a constructed experimental system and the characteristic parameters extracted from the corresponding stage were used to evaluate the magnetic anisotropy of the material. Finally, the microstructures of 4 materials were observed with a metallographic microscope. The microtextures of local areas were measured with the electron backscatter diffraction (EBSD) technique. The MBN experimental results obtained under different detection parameters showed signiﬁcant differences. The optimal MBN detection parameters suitable for magnetic anisotropy research were determined and the experimental results were consistent with the results of MCE model. The study indicated Citation: Wang, L.; He, C.; Liu, X. that MBN technology was applicable to evaluate the MCE of pipeline steel and oriented silicon steel, Evaluation of the Magnetocrystalline especially pipeline steel. Anisotropy of Typical Materials Using MBN Technology. Sensors 2021, Keywords: magnetocrystalline anisotropy; magnetic Barkhausen noise; grain orientation; 21, 3330. https://doi.org/10.3390/ detection parameter s21103330

Academic Editor: Galina V. Kurlyandskaya 1. Introduction Received: 16 March 2021 Ferromagnetic materials such as pipeline steel and silicon steel are widely used in var- Accepted: 5 May 2021 ious industries due to their unique mechanical and magnetic properties [1,2]. The magnetic Published: 11 May 2021 anisotropy of the materials largely affects their overall performances. Ferromagnetic materials are mostly polycrystalline. As one kind of crystalline materials, they have a certain Publisher’s Note: MDPI stays neutral magnetocrystalline anisotropy. The continuous development of key detection technologies with regard to jurisdictional claims in such as magnetic Barkhausen noise (MBN) and Electron Backscatter Diffraction (EBSD) has published maps and institutional affil- laid a solid foundation for studying the magnetic anisotropy of ferromagnetic materials. iations. The Barkhausen effect refers to the discontinuous change in the magnetization intensity of a ferromagnetic material in a time-varying magnetic field. The sudden fluctuation of magnetization is caused by the discontinuous movement of the domain wall from one pin- ning site to the next site as well as the discontinuous rotation of the magnetic domain [3,4]. Copyright: © 2021 by the authors. In other words, MBN signals mainly come from irreversible domain wall motion and Licensee MDPI, Basel, Switzerland. irreversible domain rotation. The intensity of MBN jumps generated by the former is large This article is an open access article enough to overwhelm that generated by the latter [5]. Therefore, in previous studies on the distributed under the terms and magnetic anisotropy of MBN signals, the magnetization mechanism was ascribed to the conditions of the Creative Commons irreversible motion of 180◦ domain wall. In this case, the direction of the magnetic easy Attribution (CC BY) license (https:// axis was usually along the direction where the characteristic value of MBN signals was creativecommons.org/licenses/by/ the highest [6,7]. In recent years, some researchers [8–10] have focused on smaller MBN 4.0/).

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jumps caused by magnetic domain rotation. Espina-Hernández et al. [8] experimentally proved that the angular dependency of magnetocrystalline anisotropy energy (MCE) was closely correlated with multi-angle MBN signals in the saturation-to-remanence stage of the hysteresis loop in pipeline steels. Therefore, the magnetic anisotropy in the MBN signals with irreversible domain rotation has become a new research direction. In order to describe MBN signals, a large number of mathematical models have been developed. Existing MBN models, including the ABBM model [11–13], J-A hysteresis model [14,15] and multi-angle MBN energy model [16–18], were mainly focused on strong MBN jumps in the area around the coercive force point where domain wall motion dom- inated. However, existing theoretical models for the low-intensity MBN jumps related to the nucleation and growth of reverse domain in the saturation-to-remanence stage of the hysteresis loop cannot provide satisfactory simulation results. So far, only a Mexican team [9,19] has developed a model for MBN signals generated by the nucleation and growth of the reverse domain in this stage and interpreted the observed strong correlation between MBN signals and MCE. The intrinsic microstructures (grain boundaries, grain orientations and grain sizes) of various ferromagnetic materials are different, thus leading to the completely different magnetic properties of the materials. During the preparation of the material, a variety of methods can be used to adjust the microstructure and improve the magnetic properties of the material, such as crystallographic texture enhancement [20], controlling cooling speed [21], and adjustment with a strip steel casting process [22]. MBN is sensitive to microstructure parameters, including grain size [23], grain boundary [24], grain orientation [25] and carbon content [26], and also has high sensitivity to stress and residual stress [27]. The measurement and analysis of the MBN envelope provides relevant information about the magnetic properties of different materials and is affected by different magnetization mechanisms. However, in actual MBN tests, the MBN envelope is closely related to the measurement method and detection parameters [28]. Therefore, according to various experimental schemes based on MBN technology, the evaluation results of the magnetic anisotropy of the same material are often different. At present, the MBN signals affected by MCE have been seldom reported. Only a generalized model has been proposed to describe the randomness of MBN signals in the saturation-to-remanence stage. The magnetocrystalline anisotropy energy model or the influence of experimental parameters on model verification results has not been reported. Based on the generalized model, a theoretical model of angle-dependent MCE was firstly proposed in this study. Then, the microstructure parameters of the materials were measured with EBSD technology and introduced into the theoretical model. Through multi-angle MBN detection experiments under different detection parameters, the applicability and accuracy of the model were verified and the optimal MBN detection parameters suitable for magnetic anisotropy research were finally determined. The developed model and corresponding technical scheme can be used in the MBN evaluation of the magnetic anisotropy of ferromagnetic materials.

2. Theoretical Analysis A model for the nucleation and growth of reverse domains was proposed [29]. The most possible origin of reverse domain nucleation are grain boundaries or lamellar precipi- tates. When the strength of the magnetic ﬁeld is low, the magnetization vectors of adjacent grains cannot rotate from their easy axis to the direction completely aligned with the magnetic ﬁeld. The magnetization vector component perpendicular to the grain boundary (GB) is generally discontinuous, so that magnetic free poles appear at the GBs. The nucleation of reverse domains is related to magnetic free poles at the GBs. The nucleation model of a reverse domain at a grain boundary is shown in Figure1. The magnetic free pole density ω* at the i-th grain boundary can be expressed as Equation (1):

∗ ωi = Js(cos θi1 − cos θi2) = Msµ0(cos θi1 − cos θi2) (1) Sensors 2021, 21, x FOR PEER REVIEW 3 of 19

nucleation model of a reverse domain at a grain boundary is shown in Figure 1. The magnetic free pole density ω* at the i-th grain boundary can be expressed as Equation (1): Sensors 2021, 21, 3330 3 of 18 ωθθ∗ =−=()()μ θθ − isJMcoscos i12 i s 012 coscos i i (1)

where Ms is the saturation magnetization of the single crystal, θ1 and θ2 are the angles where Ms is the saturation magnetization of the single crystal, θ1 and θ2 are the angles formed by the magnetization vectors of adjacent grains and the normal to GB; and μ0 is formed by the magnetization vectors of adjacent grains and the normal to GB; and µ0 is the thevacuum vacuum permeability. permeability.

D M2 − θ2 − − − M1

θ1 + + l r + +

Figure 1. NucleationNucleation model of a reverse domain at a grain boundary.

When the magnetic state of the material is changed from the saturated state to the remanence state, the magnetization direction of the grains on both sides of the GB rotates fromfrom thethe directiondirection ofof the the magnetic magnetic ﬁeld field to theto the direction direction of the of easythe easy axis. Dueaxis. toDue the to distri- the bution of misorientation between the grains, magnetic free poles appear at the GBs. Then, distribution of misorientation between the grains, magnetic free poles appear at the GBs. small reversed domains are nucleated at GBs in order to reduce the extra magnetostatic Then, small reversed domains are nucleated at GBs in order to reduce the extra energy generated by these magnetic free poles. The values of ω*i under the alternating magnetostatic energy generated by these magnetic free poles. The values of ω*i under the magnetic ﬁeld H of different angles are different, so the average magnetic free pole density alternating magnetic field H of different angles are different, so the average magnetic free in polycrystalline can be expressed as Equation (2) [19]: pole density in polycrystalline can be expressed as Equation (2) [19]: N GBNGB 1 1 ∗∗ ω ωηη Hη = = ω ωi η η Hη, gGB, θi θ1, θ θi2 (2) ()||,,,HHgηη∑ iGBii()12 (2) NGB i=1 NGB i=1

where Hη is the magnetic field value at each angular position η; gGB is the orientation of where Hη is the magnetic field value at each angular position η; gGB is the orientation of the GB; NGB is the number of GBs. the GB; NGB is the number of GBs. The MBN jumps are produced by the nucleation and growth of the reverse domains The MBN jumps are produced by the nucleation and growth of the reverse domains when the material goes from saturation to remanence. Based on the consideration of the when the material goes from saturation to remanence. Based on the consideration of the growth speed of the reverse domain from a nucleation point at GBs, grain size, and carbon growth speed of the reverse domain from a nucleation point at GBs, grain size, and carbon content, the MBN energy in this stage can be expressed as Equation (3) [9]: content, the MBN energy in this stage can be expressed as Equation (3) [9]: 2ρρχJsχd EMBN η Hη, p, dg ∝ 2 J sdH − Hn − Hg ω η Hη, p (3) EHpd()ηωη|,,ηη∝−−2 () HHHHp() |, MBN gdg µ2oμ n g (3) d go where ρ is the resistivity; χd isχ average differential magnetic susceptibility; dg is average wheregrain size; ρ isp isthe the resistivity; pearlite content; d is Haverageis the applied differential field; andmagneticHn and susceptibility;Hg are, respectively, dg is the critical magnetic field strength for generating the reverse domain and the threshold average grain size; p is the pearlite content; H is the applied field; and Hn and Hg are, respectively,magnetic field the required critical magnetic for moving field the strength domain for wall generating after nucleation. the reverse domain and the thresholdMCE magnetic is closely field related required to the for orientation moving the ofthe domain magnetization wall after vectornucleation. relative to the crystalMCE axis. is MCEclosely has related a direct to relationship the orientation with of the the crystallographic magnetization texture vector ofrelative the material. to the The density of magnetic free poles is determined by the grain-to-grain misorientation crystal axis. MCE has a direct relationship with the crystallographic texture of the defined by the crystallographic texture, so the density of magnetic free poles is proportional material. The density of magnetic free poles is determined by the grain-to-grain to MCE [30]. Based on Equation (3) where EMBN is proportional to ω, the following relationship can be obtained: EMBN ∝ ω ∝ MCE (4)

Equation (4) shows that a higher number of average magnetic free poles in the polycrystalline corresponds to a larger number of reverse domains and stronger MBN signals. Sensors 2021, 21, x FOR PEER REVIEW 4 of 19

misorientation defined by the crystallographic texture, so the density of magnetic free poles is proportional to MCE [30]. Based on Equation (3) where EMBN is proportional to , the following relationship can be obtained: ∝∝ω EMBN MCE (4)

Sensors 2021, 21, 3330 Equation (4) shows that a higher number of average magnetic free poles in4 ofthe 18 polycrystalline corresponds to a larger number of reverse domains and stronger MBN signals. In other words, the MBN events generated in this stage are mainly affected by the grain orientation distribution of the material. In other words, the MBN events generated in this stage are mainly affected by the grain 3.orientation Magnetocrystalline distribution Anisotropy of the material. Energy Model 3. MagnetocrystallineIn this study, based Anisotropy on the concept Energy Modelof coordinate transformation, the material macroscopic reference coordinate system is combined with the microscopic grain In this study, based on the concept of coordinate transformation, the material macro- orientationscopic reference and coordinatea model is system then isestablishe combinedd withto simulate the microscopic the MCE grain of orientationa given grain and orientation.a model is then established to simulate the MCE of a given grain orientation. AsAs shown shown in in Figure Figure 22,, the rolling direction of the material is set as the reference direction and the angle between the applied magnetic field HH and the reference direction direction and the angle between theϕ applied magnetic ﬁeld and the reference direction isis η.η The. The magnetization magnetization direction direction inϕ thein the material material varies varies with with the applied the applied magnetic magnetic field strength.ﬁeld strength.

FigureFigure 2. 2. MagnetizationMagnetization direction direction under under a agiven given applied applied magnetic magnetic field field strength. strength. The total magnetic energy in the system is expressed as Equation (5): The total magnetic energy in the system is expressed as Equation (5): 2 2 E(η, ϕ) = K1 sin 22ϕ cos ϕ − µ0 Ms H cos(ϕ − η) (5) EK()ηϕ,sincoscos=−− ϕ ϕ μ MH ( ϕ η ) (5) 10s where K1 is the magnetocrystalline anisotropy constant. whereAccording K1 is the magnetocrystalline to the principle ofthermodynamic anisotropy constant. balance, ϕ is determined by minimizing ϕ the totalAccording magnetic to energythe principle on both sidesof thermodynamic of the GB. For each balance, angular position is determinedη and a given by minimizingvalue of H, the a corresponding total magnetic value energy of onϕ can both be sides obtained of the and GB. its For steady each stateangular condition position is ηexpressed and a given as: value of H, a corresponding value of ϕ can be obtained and its steady state  dE(η,ϕ) condition is expressed as:  dϕ = 0 d2E(η,ϕ) (6) dE ()ηϕ,2 > 0 d(ϕ) = 0  ϕ According to the magnetic properties d of iron single crystal, parameters are set as 4 4  3 2 6 (6) H = 5 × 10 (A/m), K1 = 4.8 × 10 (J/mdE), and()ηϕ,Ms = 1.71 × 10 (A/m). Through changing  > the angle η of the applied magnetic field with the0 step size of 5◦, Equation (6) can be  d ()ϕ 2 solved to obtain the magnetization direction ϕ (star point) corresponding to each angular position η, as shown in Figure3. The point intersecting the straight line in the figure According to the magnetic properties of iron single crystal, parameters are set as H = represents the magnetization direction, which is the same as the magnetic field direction. 5 × 104 (A/m), K1 = 4.8 × 104 (J/m3), and Ms = 1.71 × 106 (A/m). Through changing the angle However, at the remaining angular positions, the δ value represents the angle between the η of the applied magnetic field with the step size of 5°, Equation (6) can be solved to obtain magnetization direction and the magnetic field direction. The smaller the δ value is, the closer the magnetization direction is to the magnetic field direction.

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the magnetization direction ϕ (star point) corresponding to each angular position η, as Sensors 2021, 21, x FOR PEER REVIEWshown in Figure 3. The point intersecting the straight line in the figure represents the 5 of 19

magnetization direction, which is the same as the magnetic field direction. However, at the remaining angular positions, the δ value represents the angle between the magnetization direction and the magnetic field direction. The smaller the δ value is, the the magnetization direction ϕ (star point) corresponding to each angular position η, as closer the magnetization direction is to the magnetic field direction. shown in Figure 3. The point intersecting the straight line in the figure represents the magnetization direction, which is the same as the magnetic field direction. However, at 90 the remaining angular positions, the δ value represents the angle between the δ Sensors 2021, 21, 3330 magnetization360 direction and the magnetic field direction. The smaller5 of 18 the δ value is, the

closer) the magnetization45 direction is to the magnetic field direction. °

( 45 C 90

φ 270 90 180 δ 360

90 ) Magnetization 45 °

( 45 C 90

φ 2700 0 90 180 270 360 180 Applied magnetic field η (°)

Figure90 3. Magnetization direction under the applied magnetic field with different angular positionsMagnetization η. 0 As shown0 in90 Figure 1804, there is270 a macroscopic 360 reference coordinate system O-XYZ and a cubic crystal coordinate system O′-x′ y′ z′ in the space. Based on the concept of coordinate Applied magnetic field η (°) transformation, the crystal coordinate system in the initial orientation is rotated in the ϕ ϕ ϕ ϕ Figureorder 3.of Magnetization1 (0 ≤ 1 direction≤ 2π), underΦ (0 the≤ Φ applied ≤ π) magneticand 2 ﬁeld (0 ≤ with 2 different ≤ 2π) angularto obtain any grain Figure 3. Magnetization direction under the applied magnetic field with different angular positionsorientationη. in space (ϕ , Φ, ϕ ). These three independent angles are called Euler angles. positions η. 1 2 The Asgrain shown orientation in Figure4, g there after is abeing macroscopic rotated reference by the coordinate Euler angle system is expressedO-XYZ and as Equation (7) 0 0 0 0 a[31]: cubic crystal coordinate system O -x y z in the space. Based on the concept of coordinate transformation,As shown the in crystal Figure coordinate 4, there system is a inmacroscopic the initial orientation reference is rotated coordinate in the order system O-XYZ and ϕϕof ϕ (0 ≤ ϕ ≤ 2π), Φ (0 ≤ Φ ≤ π) and ϕ (0 ϕϕ≤ ϕ ≤ 2π) to obtain any grain orientation cos22a cubic sin1 crystal1010 coordinate 0system  cos O2 ′-x 11′ y′2 z sin′ in the 0space. Based on the concept of coordinate in space (ϕ , Φ, ϕ ). These three independent angles are called Euler angles. The grain g =−sinϕϕtransformation, cos1 0 02 the cos crystal φφ sin coordinate  − sin ϕϕ system cos in 0 the initial orientation is rotated in the 22orientationϕg after beingϕ rotated by the Euler angle 11 is expressedϕ as Equationϕ (7) [31]: order of 1 (0 ≤ − 1 ≤φφ 2π), Φ (0 ≤ Φ ≤ π) and 2 (0 ≤ 2 ≤ 2π) to obtain any grain  0010 sincos  00 1  cos ϕ2 orientationsin ϕ2 0 in space1 (ϕ0 , Φ, ϕ 0). These costhreeϕ1 independentsin ϕ1 0 angles are called Euler(7) angles. g = − sin ϕ ϕϕcos ϕ −+0 ϕφϕ0 cos1 φ sin ϕϕ2 φ − sin ϕφϕϕ cos ϕ 0 φϕ  cos2 12 cos2 sin 1 cos sin 2 sin 12 cos cos 11 cos sin 1 2sin sin 2 0 The0 grain1 orientation0 − gsin afterφ beingcos φ rotated0 by the Euler0 angle1 is expressed as Equation (7)  =− cosϕϕ sin − sin ϕ cos φϕ cos − sin ϕsinϕϕφϕϕφ+ cos cos cos cos sin (7) cosϕ1 cos ϕ[31]:212− sin ϕ1 cos φ sin 1ϕ2 sin 2ϕ1 cos ϕ2 1+ cos ϕ211 cos φ sin ϕ2 sin φ 22sin ϕ2 =  − cosϕ1 sinϕφϕ2 − sin ϕ1 cos φ cos ϕ2 − sin ϕ−1 sin ϕϕφ2 + cos ϕ1 cos φ cos ϕ2 cos ϕ2 sin φ φ sin1 sin cos1 sin cos ϕϕsin ϕ1 sin φ − cos ϕ1 sin ϕϕφ cos φ cos22 sin010 0  cos 11 sin 0 g =−sinϕϕ cos 0 0 cos φφ sin  − sin ϕϕ cos 0 22  11 − φφ 0010 sincos  00 1 ϕϕ−+ ϕφϕ ϕϕ ϕφϕ φϕ (7) cos12 cos sin 1 cos sin 2 sin 12 cos cos 1 cos sin 2sin sin 2 =− cosϕϕ sin − sin ϕ cos φϕ cos − sin ϕsinϕϕφϕϕφ+ cos cos cos cos sin 12 1 2 121 22 sinϕφ sin −cosϕφ sin cos φ 1 1

Figure 4. 4.Schematic Schematic diagram diagram of general of general grain orientation grain orientation inside polycrystalline inside polycrystalline materials. materials. When many grains in polycrystalline are oriented in one or some orientation positions, this situationWhen ismany called thegrains texture. in Forpolycrystalline example, grains inare oriented oriented silicon in steel one with or Goss some orientation texturepositions, are mostly this situation arranged inis thecalled vicinity the of texture. the rolling For direction. example, In the grains production in oriented and silicon steel processing of ferromagnetic materials, after cold and hot rolling, the crystal structure of the materials show the texture phenomenon to different degrees, which cause anisotropy in the structure and performances of materials. In this study, individual grain orientation in the selected area was analyzed with EBSD technology.

Figure 4. Schematic diagram of general grain orientation inside polycrystalline materials.

When many grains in polycrystalline are oriented in one or some orientation positions, this situation is called the texture. For example, grains in oriented silicon steel

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◦ ◦ ◦ Taking a given grain orientation g1 = (ϕ1, Φ, ϕ2) = (0 , 0 , 45 ) as an example, the components of the magnetization vector in the reference coordinate system and the crystal 0 0 0 coordinate system are respectively x, y, z and x , y , z and the matrix g1 is expressed as Equation (8):   cos ϕ2 sin ϕ2 0 g1 =  − sin ϕ2 cos ϕ2 0  (8) 0 0 1 Then the components of the magnetization vector in the crystal coordinate system are expressed as Equation (9):

 0 = +  x cos ϕ2x sin ϕ2y 0 y = − sin ϕ2x + cos ϕ2y (9)  z0 = z

Based on the macroscopic magnetization direction obtained by Equation (6), the components of the magnetization vector in the reference coordinate system at any given angular position η can be expressed as Equation (10):  →  x = Ms cos ϕ   → (10) y = Ms sin ϕ    z = 0

By substituting Equation (10) into Equation (9), the components of the magnetization vector in the crystal coordinate system can be determined as Equation (11):

 → → → 0  x = Ms cos ϕ cos ϕ + Ms sin ϕ sin ϕ = Ms cos(ϕ − ϕ)  2 2 2  → → → 0 (11) y = − Ms sin ϕ cos ϕ + Ms cos ϕ sin ϕ = − Ms sin(ϕ − ϕ)  2 2 2   z0 = 0

The magnetocrystalline anisotropy energy of a single crystal is expressed as Equation (12) [30]:

2 2 2 2 2 2 2 2 2 Fk = K0 + K1 α1α2 + α2α3 + α1α3 + K2α1α2α3 (12)

where K1 and K2 are magnetocrystalline anisotropy constants; K0 is an angle-independent constant representing the isotropic component; α1, α2 and α3 are the direction cosines of Ms with respect to the three crystal axes. According to Equation (11), the following relationship can be obtained as Equation (13):

 = −  α1 cos(ϕ2 ϕ) α2 = − sin(ϕ2 − ϕ) (13)  α3 = 0

Finally, the MCE of cubic crystal with Euler angle g1 can be expressed as Equation (14): h 2 2 i Fk1 = K0 + K1 cos (ϕ2 − ϕ) sin (ϕ − ϕ2) (14) With Matlab software, the MCE at any angular position η can be obtained, as shown in Figure5. SensorsSensors 20212021,, 2121,, xx FORFOR PEERPEER REVIEWREVIEW 77 ofof 1919

Finally,Finally, thethe MCEMCE ofof cubiccubic crystalcrystal withwith EulerEuler angleangle gg11 cancan bebe expressedexpressed asas EquationEquation (14):(14): 22 FKK=+=+cos22()()()()ϕϕϕϕ − − sin ϕϕ ϕϕ − − (14) FKKkk101101cos 2 2 sin 2 2 (14)  Sensors 2021, 21, 3330 7 of 18 WithWith MatlabMatlab software,software, thethe MCEMCE atat anyany angularangular positionposition ηη cancan bebe obtained,obtained, asas shownshown inin FigureFigure 5.5.

1 FigureFigure 5. 5. SimulationSimulation results results of of MCE MCE ( (gg11).).).

In order to verify the applicability of the model, taking another grain orientation InIn orderorder toto verifyverify thethe applicabilityapplicability ofof thethe model,model, takingtaking anotheranother graingrain orientationorientation gg22 == gϕ= (ϕ ,ϕΦ, ϕ ) = (0◦, 45◦, 0◦) as an example, the MCE can be expressed as Equation (15), ((ϕ2 1,, ΦΦ,, 1 ϕ 2)) == 2 (0°,(0°, 45°,45°, 0°)0°) asas anan example,example, thethe MCEMCE cancan bebe expressedexpressed asas EquationEquation (15),(15), asas as1 shown2 in Figure6a. shownshown inin FigureFigure 6a.6a. h 2 222 2 2242 4 i FKKFk2 =+==+K0 + K1 coscos22ϕϕϕϕϕsin sinϕ + + +cos cosφ 224sin φφϕ φφϕ sinφ sin sinϕ (15)(15) FKKkk201201cos sin cos sin sin (15) 

2 1 2 FigureFigureFigure 6. 6.6. Simulation SimulationSimulation results resultsresults of ofof MCE: MCE:MCE: ( (a(aa))) grain graingrain orientation orientationorientation g gg22;(;; ((bb))) graingraingrain orientationorientationorientation 60%60%60%ggg11 ++ 40% 40%gg22...

EvenEven inin strongstrong texturetexture materialsmaterials suchsuch asas ororientediented siliconsilicon steel,steel, therethere isis moremore thanthan oneone graingrain orientation.orientation. ItIt isis assumedassumed thatthat 60%60% anandd 40%40% ofof grainsgrains are,are, respectively,respectively, inin thethe orientationorientation gg11 andand orientationorientation gg22 insideinside thethe material.material. ByBy solvingsolving thethe weightedweighted averageaverage ofof thethe MCEMCE ofof eacheach grain,grain, thethe MCEMCE ofof thethe popolycrystallycrystal cancan bebe obtainedobtained (Figure(Figure 6b).6b).

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Even in strong texture materials such as oriented silicon steel, there is more than one grain orientation. It is assumed that 60% and 40% of grains are, respectively, in the orientationWheng 1Hand is orientation set as 10g2 ×inside 104 the(A/m), material. with By solvingthe increase the weighted in the average strength of of the applied the MCE of each grain, the MCE of the polycrystal can be obtainedϕ (Figure6b). magneticWhen field,H is set the as 10 magnetization× 104 (A/m), with direction the increase in corresponding the strength of the appliedto each angular position canmagnetic be obtained ﬁeld, the magnetization(Figure 7). direction ϕ corresponding to each angular position can be obtained (Figure7).

90 δ 360

45 (°) 270 45 C 90 φ

180

90 Magnetization

0 0 90 180 270 360 Applied magnetic field η (°)

Figure 7. Magnetization direction at each angular position with the increase in the applied magnetic Figurefield strength. 7. Magnetization direction at each angular position with the increase in the applied magnetic field strength. The comparison results of Figures3 and7 are summarized below. At the angular positions of 0◦, 45◦, 90◦, 135◦, 180◦, 225◦, 270◦, 315◦ and 360◦, the magnetization direction rotatesThe to thecomparison same direction results as the magnetic of Figures field. However, 3 and 7 at theare other summarized angular positions, below. At the angular positionsincreasing theof applied0°, 45°, magnetic 90°, 135°, field strength180°, 225°, reduces 270°, the δ 315°value, and indicating 360°, that the the magnetization driv- direction ing force of the external magnetic field is stronger at this time and makes the magnetization rotatesdirection to closer the to thesame direction direction of the magnetic as the field. magnetic field. However, at the other angular positions,Similarly, increasing taking the the grain applied orientations maggnetic1, g2, and field 60% strengthg1 + 40% greduces2 as examples, the δ value, indicating thatthe simulationthe driving results force of MCE of the are external shown in Figuremagnetic8. It can field be seen is stronger from Figure at8 thisthat time and makes the increasing the magnetic field strength does not change the positions of the magnetic hard magnetizationaxis and magnetic direction easy axis determined closer to by th thee direction crystal structure, of the namely, magnetic the positions field. of the shortSimilarly, and long taking axes in the MCE grain pole orientations diagram. At 9 g special1, g2, angularand 60% positions, g1 + 40% since g2 as examples, the simulationthe magnetization results direction of MCE has not are changed, shown the MCEin Figure value has 8. not It changed.can be Atseen other from Figure 8 that angular positions, the magnetization direction is closer to the magnetic field direction, thus increasingchanging the the MCE magnetic value. field strength does not change the positions of the magnetic hard axis and magnetic easy axis determined by the crystal structure, namely, the positions of the short and long axes in the MCE pole diagram. At 9 special angular positions, since the magnetization direction has not changed, the MCE value has not changed. At other angular positions, the magnetization direction is closer to the magnetic field direction, thus changing the MCE value.

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Figure 8. Simulation results of MCE under the condition of the increasing magnetic ﬁeldfield strength: (a) grain orientation g1;; ((b)) graingrain orientationorientation gg22;;( (c) grain orientation 60% g1 + 40% 40% gg22. .

4. Experimental Experimental Measurement Method 4.1. MBN MBN Test The experimental experimental setup setup shown shown in in Figure Figure 99 wawass used used to to test test MBN MBN signals. signals. The The entire en- experimentaltire experimental system system was was controlled controlled by bythe the LabVIEW LabVIEW program program installed installed on on the the host computer. Sine wave signals we werere generated with an excitation board and output to the KEPCO BOP100-4ML bipolar power amplifier. amplifier. After the amplification, amplification, the signals entered the excitation coil wound on the top of the U-shaped electromagnet. A detection coil was arranged on the central axis of the U-shaped magnetic circuit to receive the MBN signals. arranged on the central axis of the U-shaped magnetic circuit to receive the MBN signals. The detection coil was made of 2000 turns of varnished wire with a wire diameter of The detection coil was made of 2000 turns of varnished wire with a wire diameter of 0.05 0.05 mm, an outside diameter of 5.4 mm, an inner diameter of 2 mm, and a height of 10 mm mm, an outside diameter of 5.4 mm, an inner diameter of 2 mm, and a height of 10 mm and filled with ferrite cores of the same height. The output voltage signals of the detection and filled with ferrite cores of the same height. The output voltage signals of the detection coil were collected by the NI-PXIe-6376 multi-channel acquisition card. coil were collected by the NI-PXIe-6376 multi-channel acquisition card.

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Power Amplifier Signal Generator Host Computer

Excitation Coil A D Data Acquisition Card

Yoke B C

Hall Element Detection Coil

(a) 30SQG120 Excitation coil Reference direction

200mm Detection coil 底 Base Rolling direction

200mm (b) (c)

FigureFigure 9. 9.ExperimentalExperimental setup: setup: (a) flow (a) chart ﬂow chartof the ofexperimental the experimental system, system,(b) sensors, (b) sensors,and (c) and (c) detectiondetection diagram. diagram.

ThreeThree types types of of electromagnets electromagnets were were desi designed,gned, and and all all the the electromagnets electromagnets had had a aU- U- shapedshaped ferrite ferrite core core with with an an excitation excitation coil coil wo woundund on on the the top. top. The The inner inner span span C Cof of the the three three U-shapedU-shaped ferrite ferrite cores cores was was different. different. The The size size parameters parameters are are shown shown in in Table Table 1.1.

TableTable 1. 1.SizeSize parameters parameters of of the the U-shaped U-shaped cores. cores.

ParametersParameters (mm) (mm) ElectromagnetElectromagnet Numbers Numbers A ABCDB C D CX-1CX-1 120 12080 80 60 60 30 30 CX-2CX-2 60 6035 35 30 30 15 15 CX-3CX-3 30 3035 35 10 10 10 10

InIn order order to to measure measure MBN MBN signals signals in in different different directions, directions, the the sensor sensor base base shown shown in in FigureFigure 9b9b was was produced produced by by 3D 3D printing printing and and had had card card slots slots distributed distributed at at equal equal angular angular ◦ intervalsintervals of of 10°. 10 By. By manually manually rotating rotating the the MBN MBN detection detection sensor sensor and and placing placing it itin in the the correspondingcorresponding card slot,slot, the the MBN MBN signal signal detection detection in different in directionsdifferent wasdirections implemented. was implemented.Four steel plates of different materials were tested. The length and width of 30SQG120 orientedFour siliconsteel plates steel, B50A470of different non-oriented materials silicon were steel,tested. and The X60 length and X70 and pipeline width steels of × 30SQG120are the same oriented (200 mm silicon200 steel, mm) B50A470 and their non-oriented heights are 0.3 silicon mm, 0.5steel, mm, and 2 mm,X60 andand 2X70 mm, pipelinerespectively. steels Forare the a given same material, (200 mm the × 200 results mm) of and the their magnetic heights anisotropy are 0.3 mm, tested 0.5 based mm, on2 MBN signals were affected by a variety of testing parameters. In this study, the magnetic mm, and 2 mm, respectively. For a given material, the results of the magnetic anisotropy circuit span, excitation frequency and excitation ﬁeld amplitude were selected as the three tested based on MBN signals were affected by a variety of testing parameters. In this main inﬂuencing factors. A total of 12 sets of testing parameters were designed (Table2). study, the magnetic circuit span, excitation frequency and excitation field amplitude were

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Table 2. Detection parameters.

Detection Parameters Electromagnet Numbers Excitation Frequency/Hz Excitation Field Amplitude/V Group 1 CX-1 20 4 Group 2 CX-2 20 4 Group 3 CX-3 20 4 Group 4 CX-1 20 1 Group 5 CX-1 20 2 Group 6 CX-1 20 3 Group 7 CX-1 20 5 Group 8 CX-1 20 6 Group 9 CX-1 1 4 Group 10 CX-1 10 4 Group 11 CX-1 50 4 Group 12 CX-1 100 4

The first group of detection parameters were taken as an example to illustrate the signal processing and feature parameter extraction methods. The output voltage signals of the MBN detection coil were band-pass filtered (10~50 kHz) with the 4th-order Butterworth digital filter and the MBN signals were smoothed to obtain the MBN envelope curve with the moving average method. After the background noise threshold point of MBN signals was set to be 0.1 mV, the starting point A of the MBN envelope curve was determined. Then the first intersection point of the 75% envelope peak and the MBN envelope curve was selected as the cutoff point B. Then root mean square RMS in the section from point A to point B was extracted as the characteristic parameter. In the test, the rolling direction of steel plates was set as the reference direction and the angle of the excitation field H relative to the reference direction was gradually changed with a step of 10◦ (Figure9c). A total of 5 repeated MBN detection experiments were performed at each angle θ and the characteristic parameters obtained in all the experiments were averaged to analyze the magnetic anisotropy of the materials. With the third-order Fourier series expansion, the characteristic parameter RMS is fitted as Equation (16):

3 RMS = a0 + ∑ [an cos(nωη) + bn sin(nωη)] (16) n=1

Sensors 2021, 21, x FOR PEER REVIEWwhere a, b, and ω are undetermined coefﬁcients and η is the angle of the excitation ﬁeld12 of 19H relative to the reference direction. Finally, the results of the anisotropy are obtained in the form of the MBN characteristic parameter pole diagram, as shown in Figure 10.

FigureFigure 10. 10. MagneticMagnetic anisotropy anisotropy measured measured in in X60 X60 pipeline pipeline steel. steel.

4.2. Microstructure After the MBN test was completed, the 4 materials were cut into the samples with a size of 30 × 30 mm. Metallographic samples were prepared according to standard procedures. The microstructures are shown in Figure 11.

(a) (b)

Figure 11. Optical micrographs of the microstructures of 4 materials: (a) 30SQG120, (b) B50A470, (c) X60, and (d) X70.

The microstructures of B50A470 non-oriented silicon steel, X60 and X70 pipeline steel showed a random distribution pattern (Figure 11), indicating that the microstructures of these three materials did not affect their anisotropy. However, in 30SQG120 oriented silicon steel, the grains were elongated obviously along the rolling direction to form a

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Sensors 2021, 21, 3330 12 of 18 Figure 10. Magnetic anisotropy measured in X60 pipeline steel.

4.2. Microstructure After the MBN test was was completed, completed, the the 4 4 materials materials were were cut cut into into the the samples samples with with a asize size of of 30 30 ×× 3030 mm. mm. Metallographic Metallographic samples samples were were prepared prepared according to standardstandard procedures. The microstructures areare shownshown inin FigureFigure 1111..

(a) (b)

Figure 11.11. Optical micrographs ofof thethe microstructuresmicrostructures ofof 44 materials:materials: ((aa)) 30SQG120,30SQG120, ((bb)) B50A470,B50A470, ((cc)) X60,X60, andand ((dd)) X70.X70. The microstructures of B50A470 non-oriented silicon steel, X60 and X70 pipeline steel The microstructures of B50A470 non-oriented silicon steel, X60 and X70 pipeline steel showed a random distribution pattern (Figure 11), indicating that the microstructures showed a random distribution pattern (Figure 11), indicating that the microstructures of of these three materials did not affect their anisotropy. However, in 30SQG120 oriented these three materials did not affect their anisotropy. However, in 30SQG120 oriented silicon steel, the grains were elongated obviously along the rolling direction to form a silicon steel, the grains were elongated obviously along the rolling direction to form a typical ﬁbrous structure, indicating that the anisotropy of 30SQG120 oriented silicon steel was strong.

4.3. EBSD Testing In global texture measurements, all the grains in a polycrystalline are analyzed as a whole, whereas microtexture measurements can provide speciﬁc information such as grain orientation, grain size and misorientation between adjacent grains in the polycrystalline. The rapid developed EBSD technology has become the main means of micro-texture detection. In this study, JSM-7900F thermal ﬁeld emission scanning electron microscope equipped with EBSD analysis software was used to perform the orientation imaging analysis on the local area of the materials. Taking the point O shown in Figure9c as the center point, a sample with the size of 10 × 10 mm was cut from 4 materials by a wire cutting method for microtexture measurements. In order to accurately estimate the MCE of the tested sample with the obtained texture data, it is necessary to adjust the scan step length to determine the appropriate number of grains in the observation area. Table3 provides the number of grains determined by EBSD microtexture measurements. Sensors 2021, 21, 3330 13 of 18

Table 3. Number of grains determined by EBSD microtexture measurement.

Material Numbers of Measuring Points Numbers of Grains 30SQG120 34,700 2 B50A470 216,250 1447 X60 216,750 3016 X70 216,250 1887

Figure 12 shows the orientation imaging of four materials. The grain orientation of 30SQG120 oriented silicon steel had a preference phenomenon. The lattice orientation of each grain was mostly the same, indicating that there was a strong texture inside the material. The grain orientation of B50A470 non-oriented silicon steel seemed to be Sensors 2021, 21, x FOR PEER REVIEWrandomly distributed and its texture phenomenon was not obvious. The orientation14 of 19

diagrams of X60 and X70 pipeline steels were respectively green and blue, displaying the texture phenomenon to a certain degree.

Figure 12.12. Orientation maps of 4 materials: (a) 30SQG120, ((b)) B50A470,B50A470, ((cc)) X60,X60, andand ((dd)) X70.X70.

According toto thethe methodmethod described described above, above, with with the the orientation orientation of eachof each grain grain rep- resentedrepresented by by different different colors colors in in Figure Figure 12 12,, the the MCE MCE model model was was obtained. obtained. ByBy averagingaveraging the contribution contribution of of individual individual grains grains with with a adirect direct method, method, the the MCE MCE results results based based on the on theconsideration consideration of the of direction the direction of the of external the external magnetic magnetic field were ﬁeld finally were obtained ﬁnally obtained (Figure (Figure13). 13).

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FigureFigure 13.13. SimulationSimulation resultsresults ofof MCEMCE inin 44 materials:materials: ((aa)) 30SQG120,30SQG120, ((bb)) B50A470,B50A470, ((cc)) X60,X60, andand ((dd)) X70.X70.

5.5. Analysis and Discussion TheThe MBNMBN envelopeenvelope curve curve is is closely closely related related to theto detectionthe detection parameters, parameters, so the so mag- the neticmagnetic anisotropy anisotropy results results obtained obtained under differentunder different detection detection parameters parameters are not completely are not thecompletely same. Inthe order same. to In ensure order to that ensure the MBN that the test MBN results test are results consistent are consistent with the with model the results,model results, it is necessary it is necessary to determine to determine the optimal the optimal detection detection parameters parameters for exploring for exploring the magneticthe magnetic anisotropy. anisotropy. 5.1. Influences of Detection Parameters on Experimental Results 5.1. Influences of Detection Parameters on Experimental Results In order to eliminate the influences of the parameter dimension on the image compari- In order to eliminate the influences of the parameter dimension on the image son, the results of the MCE model and the MBN results obtained from the experiment were comparison, the results of the MCE model and the MBN results obtained from the normalized. Figure 14 shows a qualitative comparison between the experimental results experiment were normalized. Figure 14 shows a qualitative comparison between the obtained under different detection parameters and the results of the MCE model. The experimental results obtained under different detection parameters and the results of the experimental results obtained under different detection parameters showed significant dif- MCE model. The experimental results obtained under different detection parameters ferences and the obtained main characteristics of magnetic anisotropy also showed angular showed significant differences and the obtained main characteristics of magnetic deviations. In X60 pipeline steel, X70 pipeline steel and 30SQG120 oriented silicon steel, the anisotropy also showed angular deviations. In X60 pipeline steel, X70 pipeline steel and experimental results corresponding to the 10th, 4th and 3rd groups of test parameters were 30SQG120 oriented silicon steel, the experimental results corresponding to the 10th, 4th largely consistent with the results of the MCE model. In order to quantitatively describe and 3rd groups of test parameters were largely consistent with the results of the MCE the correlation between the two methods, the angles θy and θn between the reference directionmodel. In and order the to long quantitatively and short axes describe in the the pole correlation diagram werebetween extracted the two to representmethods, thethe angles θy and θn between the reference direction and the long and short axes in the pole diagram were extracted to represent the direction cosine of the magnetic easy and hard

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directionaxes. Table cosine 4 summarizes of the magnetic the easycharacteristic and hard parameters axes. Table4 θsummarizesy and θn related the characteristic to magnetic parametersanisotropy θextractedy and θn fromrelated Figure to magnetic 14. anisotropy extracted from Figure 14.

FigureFigure 14.14. NormalizedNormalized comparisoncomparison betweenbetween experimentalexperimental resultsresults underunder differentdifferent detectiondetection parametersparameters andand simulationsimulation results:results: ((aa)) 30SQG120,30SQG120, ((bb)) B50A470,B50A470, ( c(c)) X60, X60, and and ( d(d)) X70. X70.

TableTable 4. 4.Characteristic Characteristic parametersparameters of ofmagnetic magnetic anisotropy anisotropy obtained obtained by by two two methods. methods.

ParametersParameters MethodMethod 30SQG120 30SQG120 X60 X60 X70 X70 Simulation 37 136 101 134 45 Simulation 37 136 101 134 45 θθy//°◦ y ExperimentExperiment 24.5924.59 146.15146.15 99.2 99.2 120.32 120.32 57.3057.30 SimulationSimulation 8282 151 151 0 0 θθn//°◦ n ExperimentExperiment 92.2992.29 1.15 1.15 0.72 0.72

AccordingAccording toto thethe analysisanalysis resultsresults inin TableTable4 ,4, the the maximum maximum deviation deviation of of the the direction direction cosinecosine ofof thethe magneticmagnetic hardhard axisaxis obtainedobtained byby thethe twotwo methodsmethods isis 14 14°.◦. SinceSince thethe FourierFourier seriesseries methodmethod waswas usedused toto smoothsmooth thethe resultsresults ofof MBNMBN experiments,experiments, thisthis smallsmall discrepancydiscrepancy waswas acceptable.acceptable. InIn B50A470B50A470 non-orientednon-oriented siliconsilicon steel,steel, itit waswas difficultdifficult toto findfind aa groupgroup ofof detectiondetection parametersparameters whichwhich werewere consistentconsistent withwith thethe simulatedsimulated values.values. Non-orientedNon-oriented siliconsilicon steelsteel hashas aa nearlynearly isotropicisotropic crystalcrystal texture,texture, andand therethere isis residualresidual stressstress insideinside thethe material.material. TheThe measuredmeasured MBNMBN anisotropyanisotropy isis thethe consequenceconsequence ofof stress-inducedstress-induced magneticmagnetic anisotropyanisotropy andand magnetocrystallinemagnetocrystalline anisotropy.anisotropy. TheThe MCEMCE modelmodel cancan onlyonly reflectreflect thethe magnetocrystallinemagnetocrystalline anisotropyanisotropy ofof thethe material.material. Therefore,Therefore, itit isis difficultdifficult toto evaluateevaluate thethe MCEMCE ofof non-orientednon-oriented siliconsilicon steelsteel withwith MBNMBN technology.technology. OrientedOriented siliconsilicon steelsteel isis aa strongstrong texturetexture materialmaterial andand thethe directiondirection of of the the magnetic magnetic easy easy axis axis produced produced by the by two the mechanisms two mechanisms in oriented in oriented silicon steelsilicon are steel similar. are Therefore, similar. comparedTherefore, withcomp non-orientedared with siliconnon-orient steel,ed MBN silicon technology steel, MBN can stilltechnology be used can to evaluate still be used MCE. to evaluate MCE.

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5.2. Evaluation Evaluation of MCE with MBN Technology Under differentdifferent testing testing parameters, parameters, the the valid va magneticlid magnetic field field strength strength and testing and testing depth depthin a material in a material are different. are different. Therefore, Therefore, it is necessaryit is necessary to compare to compare the the absolute absolute values values of ofMCE MCE of theof fourthe four materials materials obtained obtained with thewith two the methods two methods under a under group ofa group fixed detection of fixed detectionparameters parameters (Figure 15 (Figure). The optimal 15). The detection optimal detection parameters parameters of each material of each arematerial different. are different.The set of The parameters set of parameters selected in Figureselected 15 in were Figure suitable 15 were for evaluating suitable for the evaluating pipeline steel the pipelinematerial steel and thereforematerial theand differences therefore the in thediff twoerences results in the of the two 30SQG120 results of oriented the 30SQG120 silicon orientedsteel could silicon be understood. steel could be As understood. for non-oriented As for siliconnon-oriented steel (B50A470), silicon steel although (B50A470), the althoughpattern obtained the pattern by the obtained two methods by the exhibitedtwo methods four-petal exhibited butterfly four-petal type, butterfly the resulting type, hard the resultingaxes (short hard axis) axes were (short approximately axis) were approx perpendicularimately perpendicular to each other. to If theeach model other. results If the modelwere rotated results 90were degrees rotated clockwise, 90 degrees the clockwis resultse, obtained the results by obtained the two methods by the two had methods strong hadcorrelation. strong Exceptingcorrelation. B50A470 Excepting non-oriented B50A470 siliconnon-oriented steel, the silicon other threesteel, materials the other showed three materialsthe consistent showed relative the values consistent of MCE relative when values the two of methods MCE when were respectivelythe two methods used. Basedwere respectivelyon the aforementioned used. Based qualitative on the aforemention comparison results,ed qualitative it was confirmedcomparison that results, MBN signalsit was confirmedextracted inthat the MBN section signals from extracted point A in to the point section B could from be point used A to point evaluate B could the MCEbe used of tooriented evaluate silicon the MCE steel of and oriented pipeline silicon steel. steel The MBNand pipeline signals steel. in this The stage MBN were signals also closelyin this stagecorrelated were withalso closely the crystallographic correlated with structure. the crystallographic This conclusion structure. was This consistent conclusion with was the consistentprevious results with the [32 previous]. results [32].

Figure 15.15. Comparison of experimental results and simulationsimulation results underunder ﬁxedfixed detectiondetection parameters:parameters: (a)) simulationsimulation results andand ((b)) experimentalexperimental results.results.

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The magnetic anisotropy of a material is mainly affected by three mechanisms: average magnetocrystalline anisotropy, processing (texture, dislocation packing, etc.) and stress-induced magnetic anisotropy. Inside the silicon steel material produced by cold rolling, crystals are severely deformed and elongated in the rolling direction, thus making the texture direction close to the rolling direction. In addition, residual stress is generated during the deformation of grains and the residual stress in the rolling direction is significantly larger than that perpendicular to the rolling direction. The experimental results of silicon steel materials included the effect of residual stress on magnetic anisotropy. Therefore, the MCE evaluation method based on MBN technology was more suitable for pipeline steel materials than silicon steel.

6. Conclusions In this study, a theoretical model of angle-dependent MCE was firstly proposed and then the applicability and accuracy of the model were verified through EBSD technology and MBN test experiments. In addition, the optimal MBN detection parameters suitable for magnetic anisotropy research were obtained. The main conclusions are drawn as follows: (1) Based on the concept of coordinate transformation, the material macroscopic reference coordinate system was combined with the microscopic grain orientation. The EBSD technology was used to measure the micro-texture of the local area, and a model was established to simulate the magnetocrystalline anisotropy of given materials. (2) With MBN technology, the magnetic anisotropy of materials was evaluated. The obtained experimental results were in good agreement with the results of the MCE model, indicating that the MBN technology could be used to evaluate the MCE of pipeline steel and oriented silicon steel. (3) The MBN experimental results obtained under different detection parameters were significantly different, so it is necessary to determine the optimal detection parameters for exploring magnetic anisotropy. (4) Non-oriented silicon steel has a nearly isotropic crystallographic texture and it is difficult to predict its MCE with MBN technology. Due to the residual stress in silicon steel materials, the MCE evaluation method based on MBN technology was more suitable for pipeline steel than silicon steel.

Author Contributions: Conceptualization, C.H. and X.L.; methodology, L.W. and X.L.; experimental set-up, L.W.; validation, L.W.; writing—original draft preparation, L.W.; writing—review and editing, C.H. and X.L. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by National Natural Science Foundation of China (Project No. 11527801 and 11872081) and National Key Research and Development Program (2018YFF01012300). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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