Magnetic Domain Theory Research Articles

Anisotropic piezomagnetic behavior of wire and arc additively manufactured low carbon steel

The objective of this study is to investigate the piezomagnetic behavior corresponding to the mechanical properties of a low-carbon steel fabricated by wire arc additive manufacturing (WAAM) under tensile stress. WAAM rectangular tubes with a nominal thickness of 4 mm were fabricated with ER70S-6 wires using a continuous path with single way stacking between layers. Tests were carried out on WAAM steel specimens with three different orientations relative to the deposition direction extracted from rectangular tubes, and the evolutions of magnetic field around the specimens were recorded. The variation characteristics of piezomagnetic response at different loading stages were analyzed, highlighting the anisotropic nature of the piezomagnetic field evolution. The internal correlation between piezomagnetic field and tensile stress was explored. It is found that the piezomagnetic behavior of WAAM steel during the tensile process corresponds to the mechanical response. The Villari reversal points can be used to predict the yield strength and tensile ultimate strength of WAAM steel, and the area of the magnetic field-stress curve may be a measure of the ductility of WAAM steel. The theory of microscopic magnetic domains and the constitutive relation of ferromagnetic materials considering magnetocrystalline anisotropy were used to explain the experimental results. This study provides new insights into the anisotropic piezomagnetic properties of WAAM steel, offering potential applications in non-destructive evaluation of mechanical performance.

Modelling Crystallographic Texture Evaluation and Non-Destructive Measurement of Magnetic Anisotropy using an Electromagnetic Sensor in Interstitial Free (If) Steels

Interstitial free (IF) steels are popular in the automotive industry for applications requiring good ductility (formability), strength and a superior surface quality. Magnetic anisotropy measurement can be used to gain information about the crystallographic texture, which is an important property controlling strength and especially the formability, for example rvalues. The crystallographic texture is generated during rolling and subsequent recrystallisation during the annealing heat treatment. A set of IF steel specimens, at different states of recrystallisation (cold rolled, partially recrystallised and fully recrystallised) and accordingly different texture components have been used to investigate measurement and prediction of magnetic anisotropy. A finite element microstructure model that considers crystallographic texture based on magnetic domain theory has been used for the evaluation of magnetic anisotropy in polycrystalline steels. In addition, a laboratory based electromagnetic (EM) U shaped sensor has been proposed to determine the magnetic anisotropy in IF samples by measuring at angles varying from 0° to 90°, in steps of 15°, with respect to the rolling direction. Kernel Average Misorientation (KAM) values from Electron Back Scattered Diffraction (EBSD) characterisation of the samples has been used to evaluate the recrystallisation fraction and correlate that to the texture.

Test and Analysis of High-Permeability Material's Microstructure in Magnetic Shielding Device.

The magnetic shielding device is used to provide an extreme weak magnetic field, which plays a key role in variety of fields. Since the high-permeability material constituting the magnetic shielding device determines the magnetic shielding performance, it is important to evaluate the property of the high-permeability material. In this paper, the relationship between the microstructure and the magnetic properties of the high-permeability material is analyzed using minimum free energy principle based on magnetic domain theory, and the test method of the material's microstructure including the material composition, the texture and the grain structure to reflect the magnetic properties is put forward. The test result shows that the grain structure is closely related to the initial permeability and the coercivity, which is highly consistent with the theory. As a result, it provides a more efficient way to evaluate the property of the high-permeability material. The test method proposed in the paper has important significance in the high efficiency sampling inspection of the high-permeability material.

The magneto-mechanic hysteresis model for giant magnetostrictive materials based on the magnetic domain theory

In the paper, a magneto-mechanic hysteresis model for giant magnetostrictive materials is suggested by considering the effect of the domain rotation and domain wall motion on the magnetization process under prestress and the applied magnetic field. The coercive force, which is magneto-mechanic dependent, is proposed instead of a pinning constant in the Jiles–Atherton model. The model can well predict the characteristics of a magnetization-applied field curve and magnetostrictive strain-applied field curve shown in the experiment, especially the “overturn phenomenon” under different compressive prestresses. Furthermore, the effect of the microstructure parameter, such as the ratio of the domain wall thickness to the internal stress wavelength, the amplitude of internal stress, the ratio of the domain wall thickness to the inclusion radius, and inclusion consistency, on coercive force under applied prestress can also be described by the model. The comparison between the results predicted by the model and experiment shows that the model is suited for a wide-ranging applied magnetic field.

Accurate calculation of global hysteresis properties of grain-oriented silicon steel based on an improved J-A model with variable parameters

Based on the consideration of the magnetic domain motion under different magnetization levels, an improved J-A model with variable parameters is proposed to solve the problem of significant errors in the process of calculating the inner symmetric small loops. The proposed method introduces a variable scale parameter v(B) to correct the irreversible magnetization component of the J-A model. Meanwhile, based on the magnetic domain theory, a method with variable pinning parameter k(B) and a variable domain wall bending parameter c(B) is proposed. By comparing the measured data of B30P105 Grain-Oriented (GO) silicon steel, the calculation error for each magnetization level of the model is within 7%, which means that the global hysteresis properties of GO silicon steel can be well reproduced.

Magnetic properties and coercivity mechanism of high Ce-content CeNdFeB film with Tb diffusion

Magnetic properties and coercivity mechanism of an anisotropic Ce–Nd–Fe–B film with a high Ce content (70 at. % Nd is replaced by Ce) have been investigated. After grain boundary diffusion with Tb layers, an enhancement of coercivity from 4150 to 9250 Oe is observed. Combining the initial magnetization curves, micromagnetic theory, and in-siut observation of magnetic domains in the demagnetization process, it is confirmed that the coercivity mechanism for the high-Ce-content magnets is the mixed type dominated by the pinning mechanism. Moreover, as the thickness of the Tb diffusion layer increases, the pinning center of domain walls changes from narrow planar inhomogeneities to wide planar inhomogeneities. A growing role of pinning plays in determining the coercivity of samples with increasing the thickness of Tb layer due to the increase in magnetocrystalline anisotropy after Tb substitution in the RE2Fe14B phase. In addition, the CeFe2 intergranular phase leads to the enhancement of coercivity due to decoupling the hard magnetic phase grains. Our results provide an insight into the coercivity mechanism of high-Ce-concentration Ce–Nd–Fe–B magnetic materials and promote the comprehension of the effect of Tb diffusion in the magnetization reversal process.

Research on Microstructure Characteristics of Welded Joint by Magneto-Optical Imaging Method

This paper proposes an approach for analyzing the microstructure evolution of laser welding seam by magneto-optical imaging (MOI). The Faraday magneto-optical effect and magnetic domain theory are used to account for the MOI mechanism. The influence of laser welding on the welded joint was inspected by the analysis of color, grayscale and brightness of magneto-optical images. The relation between the brightness of magneto-optical image and grain size of microstructure is discussed as well, and the characteristics of magneto-optical images of weld microstructure were compared with those of scanning electron microscope (SEM) images. Experimental results show that three regions, including the weld zone (WZ), the heat-affected zone (HAZ), and the base metal (BM) are distributed in the magneto-optical image of the welded joint. The MOI method can investigate the microstructure evolution of welded joints and provide a theory and experimental basis for detecting weld defects.

A Novel Dynamic Hysteresis Model for Grain-Oriented Electrical Steels Based on Magnetic Domain Theory

A novel approach is adopted to model the hysteresis phenomenon of grain-oriented electrical steels (GOESs), by incorporating a variation of the domain patterns associated with ferromagnetic materials during magnetization and demagnetization. The ensuing model treats the anisotropic and isotropic components separately, together with the coupling effect of the excitation field. Its ability to replicate experimentally obtained dynamic hysteresis loops (DHLs) for Epstein size laminations of GO 3% SiFe electrical steels, for different magnetizing frequencies and peak flux densities, and facilitate the straightforward evaluation of the energy loss in GOESs is demonstrated for the case of controlled sinusoidal magnetic induction. Close agreement is found to exist between the predicted energy loss and corresponding bulk measurements, with the maximum difference being less than 2%.

Nanoheterogeneity response in large-magnetostriction Fe-Ga alloys: An in-situ magnetic small-angle neutron scattering study

The underlying mechanism of large magnetostriction in Fe-Ga alloys is obviously beyond the conventional domain rotation and twin boundary motion, but has been attributed to the nanoscale magnetic heterogeneities. However, the nanoheterogeneity response as well as the interaction with matrix during magnetization process is still an open question. Through in-situ magnetic small-angle neutron scattering (SANS) study on a Fe81Ga19 alloy, the present work clearly reveals that the reorientation of nanodomains relevant to face-centered-tetragonal L60 nanoprecipitates occurs at relatively lower fields than that of the magnetic domains. These nanoheterogeneities show a larger magnetic correlation length than their size, ensuring the exchange coupling between nanoprecipitates and matrix as well as the flipping of their magnetizations. This process contributes to the low-field-triggered large magnetostriction, unlike that induced by non-180° domain switches in the homogeneous magnetostrictive materials (such as Terfenol-D). Further study reveals that the correlation length can be effectively tuned by simple heat-treatment, which in turn significantly enhances the magnetostriction without enlarging the triggering field. Consequently, this work contributes to uncover the physical mechanism of the large heterogeneous magnetostriction besides the typical magnetic domain theory, and may also provide a general guideline for achieving tunable magnetostriction in heterogeneous ferromagnets.

Zigzag domain boundaries in magnetostrictive Fe-Ga alloys

A recent development in magnetic materials research on a non-Joulian magnetostriction phenomenon [H. D. Chopra and M. Wuttig, Nature 521, 340 (2015)] highlights peculiar cellular magnetic domains with zigzag boundaries in Fe-Ga alloys. The cause of zigzag boundaries of cellular domains is attributed to hypothetical charge density waves beyond classical magnetic domain theory. In this paper, we report observations in Fe-Ga alloys of zigzag boundaries that form conventional stripe domains. The responses of stripe domains to external magnetic fields are observed, and the behaviors of zigzag boundaries are examined, which are further compared with those in cellular domains. It shows that both cellular and stripe domains and the constituent zigzag boundaries in magnetostrictive Fe-Ga alloys can be explained well by classical magnetic domain theory, without resorting to theory based on hypothetical charge density waves. In particular, our findings provide convincing evidence that zigzag boundaries in Fe-Ga alloys are conventional V lines commonly observed in cubic magnetic crystals like Fe-Si alloys. The intricate cellular domain structure is shown to correlate with the simple stripe domain structure in terms of zigzag V lines and flux-closure surface domains.

Tensorial permeability microstructure model considering crystallographic texture and grain size for evaluation of magnetic anisotropy in polycrystalline steels

ABSTRACT A finite element microstructure model with permeability tensors that considers crystallographic texture and grain size based on magnetic domain theory has been developed for the evaluation of magnetic anisotropy in polycrystalline steels. The model has proved capable of capturing the crystallographic texture, the grain size and the vector induction effects on the effective permeability behaviours for typical textures in steels. The predicted magnetic properties as a function of the magnetic field direction enables a quantitative characterisation of the magnetic anisotropy. The predicted effective permeability maps can serve as a visual indication of the crystallographic texture from magnetic values. These features have been experimentally validated against a commercial grain oriented electrical steel featuring strong texture and magnetic anisotropy.

Variations in the cellular magnetic domain structure in Fe–Ga alloys

The so-called cellular magnetic domain structure has been widely observed in Fe–Ga alloys of different compositions and heat treatment. It has attracted attention for producing desirable magnetic properties and also for arousing controversy over its cause and identity. Two existing models, one based on novel charge density waves and the other based on traditional V-lines from the classical magnetic domain theory, give contradictory interpretations of the cellular domains in Fe–Ga alloys, which remain to be clarified. The cellular domains observed in Fe–Ga alloys so far are highly periodic, consisting of parallel chains of rectangular cells. This paper reports on the presence of various deviations in the cellular domains from the previously known ideal periodic cellular structure in Fe–Ga alloys and explores the implications of those variations. The variations include changes in the cell shape, spacing, branching, and nesting. It is shown that the observed variations in the cellular domains can be explained well by the V-line model where the competition between elastic and wall energy drives the pattern formation process. In comparison, the disagreements of the charge density wave model with the experimental observations are addressed. Similar cellular domain variations observed previously in Fe–Si alloys are also discussed, confirming the generic aspects of the cellular domains and their variations in cubic magnetostrictive materials. The findings provide insights into the magnetic domain phenomena in Fe–Ga alloys.

A nonlinear magneto-mechanical coupling model for magnetization and magnetostriction of ferromagnetic materials

A new magneto-mechanical coupling model was proposed for ferromagnetic materials under applied stress and in magnetic fields. The proposed model is based on the thermodynamic theory of ferromagnetic materials and Jiles–Atherton–Sablic (J–A–S) theory with respect to the effective magnetic field. Compared with the existing models for ferromagnetic materials, the prediction results of this model are more consistent with the existing experimental results, and the prediction accuracy has been significantly improved. This model can more accurately predict the nonlinear changes in the magnetization and magnetostriction under the applied stress and magnetic field. In addition, the effects of applied stress and magnetic field on magnetization and magnetostriction of ferromagnetic materials are analyzed on the basis of magnetic domain theory. In conclusion, the proposed model can fully describe the effect of applied stress on magnetization, magnetic permeability, and magnetostrictive strain, and the effects of applied stress and magnetic field on total magnetostrictive strain (i.e., the ΔE effect); furthermore, it sufficiently reflect the nonlinear coupling properties of the magnetic field, magnetization, and magnetostriction for ferromagnetic materials under applied stress and in magnetic fields.

Residual Flux Density Measurement Method for Transformer Core Considering Relative Differential Permeability

The residual flux measurement is one of the difficulties in the transformer research field. This article presents a residual flux density (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ) measurement method considering the relative differential permeability (μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sub> ) of the core material. First, the basic relationship between μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sub> and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is analyzed on the basis of the magnetic domain theory. Then, combining the experimentally measured relationship between B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sub> , using μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sub> as an intermediate variable, the relationship between B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> and time constant is derived. Furthermore, a square iron core model is established by the finite-element method, and the empirical formula for calculating B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is was fit. Finally, the feasibility of this method and the accuracy of the proposed empirical formula are verified through experiments.

The Barkhausen effect revisited using LEDs

It has now been over 100 years since Heinrich Barkhausen published his description of a crackling sound heard when a piece of iron is magnetized inside of a coil wired to a set of headphones, and this phenomenon provided evidence for the theory of magnetic domains. Traditionally, this effect is performed as a demonstration by connecting the coil to an audio amplifier, such as one used for electric guitars.

Applied Problems of Magnetism

The saturation magnetization of single-crystalline garnet ferrite films of different compositions is calculated on the basis of the familiar relations of the Neel model on the sublattice structure of ferrimagnetic compounds. Other parameters of the films are calculated using the theory of strip domains and the stability theory of cylindrical magnetic domains. The presented material is educational and intended for use in practical exercises in the study of magnetism. The problem is given to students of specialties 22.03.01, Materials Science and Materials Technology (when studying the discipline of Physics of Magnetic Materials); 03.03.02, Physics (when studying the disciplines of General Physics, in the section on Electricity and Magnetism and the disciplines of the Magnetic Properties of Matter); and to students of specialty 13.03.02, Electric Power Engineering and Electrical Engineering (when studying the discipline of Magnetic Measurements) at Astrakhan State University.

A mechanism study on influence of strong external magnetic field on fracture properties of a ferromagnetic steel

For some ferromagnetic metallic materials, measurable influence of strong external magnetic field on their fracture properties has been observed experimentally, i.e., an external magnetic field of large intensity can promote the propagation of the crack. In order to clarify the mechanism of this phenomenon, a fracture model is put forward in this paper based on reversal magnetic domain theory and minimum free energy algorithm and verified through observations of magnetic domains structure. Compact tensile (CT) specimens which were stretched in strong magnetic field are adopted to observe their magnetic domains structure with the powder grain method in practice. It is found that the crack in the CT specimen propagated mainly along the magnetic domain wall rather than passing through the domain body. Together with the experimental results, the fracture model for the rupture and propagation mechanism under strong magnetic field was discussed.

An anisotropic magneto-mechanical model of ferromagnetic materials for the magnetic memory testing method

The metal magnetic memory (MMM) method shows great potential in the early damage evaluation of ferromagnetic materials. The MMM signal is affected by the environmental magnetic field because of the magneto-mechanical coupling effect. For instance, the effect of the environmental magnetic field is connected with the angle between the environmental magnetic field and the detected structure, which is referred to as the angle effect. This paper aims to explore the angle effect on the MMM method under the weak magnetic field. An anisotropic nonlinear magneto-mechanical constitutive relationship is proposed based on the magnetic domain theory and the approach law. Compared to the existing model, the present constitutive relationship in this paper can predict the stress-magnetization curve of ferromagnetic materials under the combined action of the loading stress and the environmental magnetic field with different directions. Based on the present constitutive relationship, an anisotropic nonlinear magneto-mechanical model of the MMM method is established, and then the angle effect is discussed in detail. The prediction of the anisotropic nonlinear magneto-mechanical model shows a good agreement with experimental data. The proposed model can clarify the reasons for some complex phenomena of the MMM signal, and thus help in the practical application of the MMM method.

Presence of mixed magnetic phase in mechanically milled nanosized Co0.5Zn0.5Fe2O4: A study on structural, magnetic and hyperfine properties

Abstract In this paper, we have presented a detailed study on the effects of mechanical activation caused by high energy ball milling on the structural, magnetic and hyperfine properties of nanosized Co0.5Zn0.5Fe2O4 having three different particle sizes 63 (M1), 25 (M2) and 17 nm (M3) synthesized by chemical coprecipitation method. Characterization techniques like powder x-ray diffraction, high resolution transmission electron microscopy, dc magnetic measurements and Mossbauer spectroscopic techniques have been employed to examine M1, M2 and M3 thoroughly. All the three samples are cubic spinel ferrites with Fd 3 - m symmetry. The lattice parameters of M1, M2 and M3 are 8.395, 8.391 and 8.375 A, respectively. The particles constituting all the three samples possess both superparamagnetic and ferrimagnetic phases at room temperature. The values of blocking temperature of M1, M2 and M3 are 204, 210 and 220 K, respectively. The values of saturation magnetization of M1, M2 and M3 at 300 and 10 K are 56.8, 55.3, 51.5 emu g−1 and 115.68, 113.84, 109.65 emu g−1, respectively. The values of coercivity for M1, M2 and M3 at 10 K are 1395, 2190 and 1950 Oe, respectively. The theory of magnetic domains has been exploited to explicate the trend in coercivity. The cation distribution of M2 is (Zn2+0.48Fe3+0.52)A[Co2+0.5Zn2+0.02Fe3+1.48]BO4. The effects of mechanical activation on cation redistribution and magnetic property of M2 have been investigated by infield Mossbauer spectroscopic measurements and verified by theoretical analysis of experimental results of Rietveld refinement of powder x-ray diffraction data in conjugation with dc magnetic study. The sample M2 is basically ferrimagnetic in nature possessing a slightly canted core surrounded by a disordered shell. It exhibits excellent memory effect in its dc magnetization measurement. The sample is capable of encoding, preserving and recalling binary numbers through magnetic field change. This property of the sample may be used to design magnetic coding and sensing devices.

Modeling for detecting weld defects based on magneto-optical imaging.

A magneto-optical (MO) imaging nondestructive testing (NDT) method for ferromagnetic weldments has been proposed. The mechanism of MO imaging was analyzed by the Faraday MO effect, magnetic domain theory, and magnetic hysteresis loops. Then, the relation between MO images and their corresponding excitation voltages was investigated. To explain the MO imaging system, magnetic domain distribution models of various welding states were established. These models are excited by two kinds of magnetic fields. One is the external magnetic field (Hex), and the other is a weldment remanence field (Mr) after Hex is removed. Relations of magnetic field excitation voltages, thickness of the spacer plate, and the corresponding MO images were also researched, which indicates the proposed NDT method can be used to detect incomplete penetration defect. Then, an experiment that uses MO imaging to detect the defects of high-strength steel (HSS) weldment was performed. Experimental results proved this method can detect crack, sag, and incomplete penetration of weldment effectively. Finally, a series of welded joint MO images of the HSS weldment were captured, which are used as the input data of the defect classification model established by using principal component analysis and an error backpropagation neural network, and the accuracy of this classification model can achieve 92.8%.