Jiles-Atherton Theory Research Articles

Phenomenological modelling of first order phase transitions in magnetic systems

First order phase transitions may occur in several magnetic systems, with two structural phases having different magnetic properties each and a structural transition between them. Here, a novel physics based phenomenological model of such systems is proposed, in which magnetization is represented by the volumetric amounts of ferromagnetism (described by extended Jiles-Atherton theory) and paramagnetism (described by the Curie-Weiss law) in respective phases. An identification procedure to extract material parameters from experimental data is proposed. The proposed phenomenological approach was successfully applied to magnetocaloric Gd5(SixGe1−x)4 system and also has the potential to describe the behavior of Griffiths phase magnetic systems.

Modeling of two-phase magnetic materials based on Jiles–Atherton theory of hysteresis

The Jiles–Atherton (JA) theory of hysteresis has been extended in the present paper to model hysteresis in two-phase magnetic materials. Two-phase materials are those that exhibit two magnetic phases in one hysteresis cycle: one at lower fields and the other at higher fields. In magnetic hysteresis, the transition from one phase to the other i.e. low field phase to high field phase depends mainly on the exchange field. Hence, the material-dependent microstructural parameters of JA theory: spontaneous magnetization, MS, pinning factor, k, domain density, a, domain coupling, α, and reversibility factor, c, are represented as functions of the exchange field. Several cases based on this model have been discussed and compared with the measured data from existing literature. The shapes of the calculated and measured hysteresis loops are in excellent agreement.

Theoretical Model of Temperature Dependence of Hysteresis Based on Mean Field Theory

The magnetization processes in ferromagnetic materials are dependent on temperature. In order to understand thoroughly the behavior of magnetization processes in ferromagnetic materials at different temperatures, a temperature dependent hysteresis model is necessary. In the present study, a physical model based on Jiles-Atherton (JA) theory was developed to study the effects of temperature on magnetic hysteresis. This was achieved through the introduction of temperature dependent hysteresis parameters of the existing model. The material dependent parameters such as Curie temperature and critical exponent have also been added as additional variables to the existing model. The temperature dependent extension of the JA model was validated against measurements made on cation substituted cobalt ferrite material and the results show good agreement between theory and experiment.

Generalized form of anhysteretic magnetization function for Jiles–Atherton theory of hysteresis

A generalized form of anhysteretic magnetization function to extend Jiles–Atherton theory to different forms of anisotropy has been derived. The general equation for the function has been compared with those of calculations made on the basis of known equations for specific cases: axially anisotropic (one-dimensional), planar anisotropic (two-dimensional), and isotropic (three-dimensional). The Jiles–Atherton model using the proposed functional form of generalized anhysteretic magnetization function for anisotropy dependence has been validated and the necessary equations derived. It has been shown in this work that this functional form of anhysteretic magnetization with necessary boundary conditions can be reduced to the familiar specific model equations in the particular cases.

Modeling the Temperature Dependence of Hysteresis Based on Jiles–Atherton Theory

A temperature-dependent model is necessary in order to understand the behavior of magnetization processes in ferromagnetic materials at different temperatures. In the present study, a physical model based on Jiles-Atherton (JA) theory was developed to study the effects of temperature on magnetic hysteresis. The thermal effects were incorporated through temperature-dependent hysteresis parameters of the existing model, adding critical exponent and Curie temperature as additional parameters. The temperature-dependent JA model was validated against measurements made on substituted cobalt ferrite material, and the results were in good agreement.

A transformer model based on the Jiles-Atherton theory of ferromagnetic hysteresis

This paper presents a transformer model that is useful for lowfrequency applications. To describe the iron-core magnetic behavior, the Jiles Atherton hysteresis model is used, which is able to generate minor asymmetric loops and remanent flux. The obtained results are compared with those measured in the laboratory on a commercial resistance welding transformer.

Using TACS Functions Within EMTP to Set Up Current-Transformer Model Based on the Jiles–Atherton Theory of Ferromagnetic Hysteresis

The subject of this paper is to construct a current- transformer (CT) model based on the Jiles-Atherton (J-A) theory of ferromagnetic hysteresis using transient analysis of control systems (TACS) functions within the electromagnetic transients program (EMTP) in a closed-loop manner. The J-A theory of ferromagnetic hysteresis is presented by the nonlinear first-order ordinary differential equations and inclusive of five parameters that can be found by measurements of hysteresis characteristic. We can use TACS functions within EMTP to describe the J-A theory of ferromagnetic hysteresis. The powerful advantage of this way is the interaction between the electrical network and TACS in EMTP. Compared with the CT model based on the type 96 nonlinear hysteresis inductor, the simulated result of the CT model based on the J-A theory of ferromagnetic hysteresis is almost the same in steady-state situations, but apparently different in a fault transient situation. The analysis and simulation of the actual measured fault profiles in the Taiwan power system is an example of the validation of this proposed model. Therefore, this proposed CT model based on the J-A theory of ferromagnetic hysteresis has the analysis capability of the transient response. The flexibility of TACS makes the simulation of any other situation easier and is another advantage.

A 3-D hybrid Jiles-Atherton/Stoner-Wohlfarth magnetic hysteresis model for inductive sensors and actuators

The Jiles-Atherton (JA) theory of hysteresis is currently used in the majority of commercial CAD tools, mainly due to its implementation simplicity in fast and stable algorithms. The JA model provides precise results in the case of isotropic, polycrystalline, multidomain magnetic devices, where flux-reversal is governed by pinning mechanisms. Dynamic response of such devices, including Eddy-current loss and magnetic resonance, can also be accurately modeled. However, JA theory is not applied for three-dimensional (3-D) magnetization simulations and does not account for anisotropy that affects severely hysteresis curves of single-domain, thin-film devices, which are usually incorporated in miniature inductive sensors and actuators. In that case, the Stoner-Wohlfarth (SW) theory can be applied, which, however, does not account for dynamic response and incremental energy loss. In this work, we employ a virtual 3-D anisotropy-field vector calculated with SW theory that introduces magnetic feedback to the classical equation of Paramagnetism, in order to derive a proper 3-D "input" for the JA algorithm. This way, a hybrid 3-D JA/SW model is developed, which incorporates both models into one single formulation, capable of modeling simultaneously: 1) temperature effects, 2) pinning and Eddy-current loss, 3) magnetic resonance, and 4) uniaxial anisotropy, the orientation of which can be simulated to vary with time. The model that owns a solid physical basis has been implemented in a computation-efficient, stable algorithm capable of functioning with arbitrary excitation-field input. The algorithm has been successfully applied to model the behavior of a series of miniature Fluxgate magnetometers based on the Matteucci effect of thin glass-covered magnetic wires

An Improved Low-Frequency Transformer Model for Use in GIC Studies

A hysteresis model based on the Jiles-Atherton theory is incorporated into a power transformer model in an electromagnetic transient program (EMTP)-type program. The eddy current effects are also included in the same model. Comparisons are made between recorded and simulated waveforms using a single-phase distribution transformer. A good agreement is achieved between recorded and simulated data.

Discussion of "A current transformer model based on the Jiles-Atherton theory of ferromagnetic hysteresis" [Closure to discussion

W.C. Kotheimer comments on the paper by U.D. Annakkage et al. (see ibid., vol.15, no.1, p.57-61, 2000). The author points out that the original authors have identified an apparent limitation of the Jiles-Atherton algorithm using the Langevin function when used to model the core of a current transformer subjected to high fault currents in the presence of a significant amount of remanence. The original authors reply to the comments.

A current transformer model based on the Jiles-Atherton theory of ferromagnetic hysteresis

The hysteresis loop of the core material in a test current transformer is simulated using the Jiles-Atherton theory. Comparisons are made between recorded and simulated waveforms and it is found necessary to replace the modified Langevin function used by Jiles and Atherton. Using an alternative function described in the paper, good agreement is achieved between test and simulated waveforms.

Stress dependence of ferromagnetic hysteresis loops for two grades of steel

Residual stress is an essential input into calculations of the remaining life of operational plant. However, many life predictions are inherently conservative because measurements of the absolute stress are unavailable. The magnetic properties of material are sensitive to stress, and in this paper, the magnetic properties (at maximum magnetisation, at remnance, and at the coercive field) of two grades of steel (Durehete 1055 and AS1548-7-46OR) under uni-axial stress are presented. The magnetic parameters are more sensitive to compressive stress than to tensile stress. A mathematical model using the Jiles–Atherton theory for ferromagnetic hysteresis is used to explain the trends in the experimental data. The ability of magnetic techniques to measure stress is demonstrated.

Modeling of permanent magnets: Interpretation of parameters obtained from the Jiles–Atherton hysteresis model

The Jiles–Atherton theory is based on considerations of the dependence of energy dissipation within a magnetic material resulting from changes in its magnetization. The algorithm based on the theory yields five computed model parameters, MS, a, α, k, and c, which represent the saturation magnetization, the effective domain density, the mean exchange coupling between the effective domains, the flexibility of domain walls and energy-dissipative features in the microstructure, respectively. Model parameters were calculated from the algorithm and linked with the physical attributes of a set of three related melt-quenched permanent magnets based on the Nd2Fe14B composition. Measured magnetic parameters were used as inputs into the model to reproduce the experimental hysteresis curves. The results show that two of the calculated parameters, the saturation magnetization MS and the effective coercivity k, agree well with their directly determined analogs. The calculated a and α parameters provide support for the concept of increased intergranular exchange coupling upon die upsetting, and decreased intergranular exchange coupling with the addition of gallium.

Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis

The authors describe how the various model parameters needed to describe hysteresis on the basis of the Jiles-Atherton theory can be calculated from experimental measurements of the coercivity, remanence, saturation magnetization, initial anhysteretic susceptibility, initial normal susceptibility, and maximum differential susceptibility. The determination of hysteresis parameters based on this limited set of magnetic properties is of the most practical use since these are the properties of magnetic materials that are most likely to be available.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A differential equation approach to minor loops in the Jiles-Atherton hysteresis model

The reason for the failure of the differential equations to yield physical minor loops involved in the magnetization in ferromagnetic materials is explained. A modified solution for minor loops is presented which retains the features of D.C. Jiles and D.L. Atherton's (1983) original motor loops, but only requires knowledge of the initial point on each portion of the loop to obtain the solution. This yields a general differential equation formulation for the Jiles-Atherton theory that can be used with circuit simulations having arbitrary excitations and initial conditions for ferromagnetic components. >

The influence of stress on ferromagnetic hysteresis

It is argued that attempts to describe the stress magnetization behavior of ferromagnetic materials have, in general, relied upon unsubstantiated assumptions regarding the distribution of domains and the relative motion of domain walls under the combined influences of applied field and mechanical stress. An empirical description of stress-induced magnetization is presented as a practical extension of the Jiles-Atherton model of ferromagnetic hysteresis. It permits a semiquantitative description of the stress magnetization characteristics of ferromagnetic materials and highlights the profound influence of previous magnetic history. It is concluded that measuring the B/H characteristics of a material as a function of stress and invoking the Jiles-Atherton theory of ferromagnetism could provide a computational basis for predicting the magnetic behavior of complex structures under mechanical stress.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Pneumatic stressing mechanism for magnetomechanical studies

A low-pressure pneumatically controlled stressing mechanism for investigating the effects of uniaxial stress on the magnetostrictive and magnetomechanical behavior of 2% Mn pipeline steel is described. The apparatus uses microcomputer control and data logging. It has been developed to allow convenient stress cycling so that reversible and irreversible changes can be separated. Irreversible stress-induced changes in magnetization are toward the anhysteretic, in accordance with Jiles–Atherton theory. Reversible magnetomechanical effects may be correlated with reversible magnetostrictive effects.

Effect of order of stress and field application on the measured flux density in 1% Mn pipeline steel

Experiments involving different orders of field and stress application on the measured flux density in 1% Mn pipeline steel samples were performed in order to examine the validity of LeChatelier’s principle. In the low-field regions the flux density in the sample was found to be strongly dependent on the order of applied stress and field, as stated by Bozorth. The results obtained for stress-induced magnetization changes were in accordance with the Jiles–Atherton theory.

Model for the effect of tensile and compressive stress on ferromagnetic hysteresis

A model is presented for the stress-dependent effective field, which when used in conjunction with the Jiles–Atherton theory, qualitatively accounts for (1) the change in slope and shape of the hysteresis curves with uniaxial stress and (2) the convexity of the curves depicting remanent and peak magnetization as a function of stress. Also, the model can produce the Villari reversal if parameters are selected appropriately.