D.L. Atherton

Theory of ferromagnetic hysteresis

Abstract A mathematical model of the hysteresis mechanisms in ferromagnets is presented. This is based on existing ideas of domain wall motion including both bending and translation. The anhysteretic magnetization curve is derived using a mean field approach in which the magnetization of any domain is coupled to the magnetic field H and the bulk magnetization M . The anhysteretic emerges as the magnetization which would be achieved in the absence of domain wall pinning. Hysteresis is then included by considering the effects of pinning of magnetic domain walls on defect sites. This gives rise to a frictional force opposing the movement of domain walls. The impedance to motion is expressed via a single parameter k , leading to a simple model equation of state. This exhibits all of the main features of hysteresis such as the initial magnetization curve, saturation of magnetization, coercivity, remanence, and hysteresis loss.

Theory of ferromagnetic hysteresis (invited)

A mathematical theory of hysteresis in ferromagnetic materials is presented based on existing ideas of domain wall motion and domain rotation. Hysteresis is shown to occur as a result of impedances to changes of magnetization such as when domain walls are pinned, while the mutual interactions of the magnetic moments are shown to be of secondary importance in this respect. An equation for the anhysteretic or ideal magnetization curve is derived based on a mean field approximation and this is shown to be dependent on the mutual interactions of the moments but independent of impedances such as pinning. The introduction of a term which measures the impedance to changes in magnetization leads to a simple differential equation of state for a ferromagnet which exhibits all the features of hysteresis. Some modifications of the simple model are necessary in order to bring the solution closer to the real situation. Results are presented which show all the features of hysteresis such as initial magnetization curve, ...

Theory of the magnetisation process in ferromagnets and its application to the magnetomechanical effect

A theory of the magnetisation process in ferromagnets, based on existing ideas of domain rotation and domain wall motion is presented. This has been developed via a consideration of the various energy terms into a mathematical description of the process leading to an equation of state for a ferromagnet. The differential equation has been solved and a solution containing terms up to the second order presented, showing the essential features of ferromagnetic hysteresis. The theory has then been used to explain the effects of stress on magnetisation. It has been found that the magnetisation approaches the anhysteretic curve when a ferromagnet is subjected to stress and this is the underlying principle behind such changes in magnetisation. The change of magnetisation with stress can not be predicted solely on the basis of the magnetostriction coefficient except in special cases when the initial (zero stress) conditions of magnetisation lie on the anhysteretic. This condition is also approximately satisfied at higher fields.

Macroscopic models of magnetization

Four magnetization models, now considered as classical, are presented: the Stoner-Wolhfarth model, the Jiles-Atherton model, the Globus model, and the Preisach model. The paper describes the methods each model uses to simulate the magnetization mechanisms, reversible and irreversible processes, major and minor loops, and anhysteretic behavior. Improvements and changes are proposed to the Stoner-Wolhfarth and Globus models. The necessary simplifying assumptions define the limits of applicability of the models. The paper concludes with a table of the main characteristics of each model to help a potential user to make a suitable choice.

A mean field Stoner-Wohlfarth hysteresis model

A model of magnetic hysteresis is proposed. It is based on the Stoner-Wohlfarth coherent rotation model, but with a macroscopic mean field interaction (similar to Weisss molecular field theory), added to represent interaction between domains. Rotation of domain magnetization vectors gives both reversible and irreversible changes in bulk magnetization. A qualitative correlation is obtained between hysteresis curves calculated using this theoretical model and experimentally measured hysteresis curves of a ferrite permanent magnet. >

Measurement of residual stress in steel using the magnetic Barkhausen noise technique

Surface residual stresses on a structural beam steel sample were evaluated using a non-destructive technique based on the measurement of surface magnetic Barkhausen noise (MBN). MBN measurements were performed using a high resolution probe consisting of a small magnetic read head mounted between the poles of a ferrite U-core magnet. Applied stress magnitudes were correlated to MBN energy levels for calibration purposes. MBN energy measurements were done at various locations on the steel sample. The magnitude of the residual stress component along the sample beam axis was evaluated across the width of the beam using these calibration curves. The range of sensitivity of the MBN signal to stress as defined by the calibration curves was limited by the direction of easy magnetization. The effect of stress on the MBN signal was interpreted in terms of the active 180° domain wall population. The validity of the residual stress results was confirmed experimentally using conventional methods: cutting and sectioning and hole drilling. Possible sources of residual stresses and their distribution on the structural steel specimen are discussed.

Investigation of the stress‐dependent magnetic easy axis in steel using magnetic Barkhausen noise

Angular‐dependent magnetic Barkhausen noise (MBN) measurements were performed on a pipeline steel sample for various values of applied uniaxial stress at three angles with respect to the sample’s zero stress magnetic easy axis direction. It was observed that the response of the MBN signal to stress was dependent upon the direction of the stress with respect to the zero stress easy axis. The stress response of the MBN signal was greatest for (i) tensile stresses oriented perpendicular to the zero stress easy axis direction and (ii) compressive stresses applied parallel to the easy axis direction. The modification of the MBN signal under an applied stress was attributed primarily to a change in the 180° domain wall population in the material investigated. Results were described by a model that considered regions of locally correlated domain behavior, termed ‘‘interaction regions,’’ that were typically the size of grains within the steel material. A basic result of the model was the stress required to modify...

CHARACTERIZATION OF THE MAGNETIC EASY AXIS IN PIPELINE STEEL USING MAGNETIC BARKHAUSEN NOISE

The angular dependence of magnetic Barkhausen noise (MBN) on eight surfaces through the thickness of a 2% Mn steel pipeline sample was investigated. The MBN signal was analyzed by integrating the square of the MBN voltage signal with respect to the time axis. The resulting value, referred to as the MBN energy signal, was modeled by considering the irreversible motion of 180° domain walls, under the influence of an oriented magnetic field. An expression for the angular dependence of the MBN energy signal was derived and was given by energy=α cos2 θ+β, where α and β are the fitting parameters and θ is the angle between the maximum MBN signal and the applied sweep field. The α parameter was associated with the irreversible motion of 180° walls that contributed to the net macroscopic easy axis near the surface of the sample, while the β parameter was associated with the isotropic background MBN signal. The energy equation could be used to fit the data for all sweep field amplitudes in which the MBN spectrum w...

The influence of pearlite on barkhausen noise generation in plain carbon steels

Abstract Barkhausen noise refers to the abrupt, discontinuous changes in magnetization which result from domain walls overcoming barriers to their movement. Barkhausen noise is sensitive to a number of parameters, notably stress level (for which it is being examined as a basis for non-destructive evaluation) and microstructure. The present study investigates the influence of pearlite content on the pulse height distribution of the magnetic Barkhausen noise signal in plain carbon steels. The responses of purely pearlitic and purely ferritic microstructures are determined to be quite different. Samples containing no pearlite display a narrow, symmetrical distribution of relatively small pulse heights. The behaviour of the pearlitic steel is quite different, however, exhibiting an asymmetrical pulse height distribution with a significant tail extending to comparatively large pulse heights (approximately four times that of the maximum for the ferrite signal). Steels containing both ferrite and pearlite produce signal distributions between the two extremes, but contain no significant tail and also appear to tend toward larger pulse heights than what would be expected for a purely “composite” distribution. Results are explained in terms of differences in domain wall pinning behaviour between the various microstructures.

Influence of uniaxial plastic deformation on magnetic Barkhausen noise in steel

Magnetic Barkhausen noise (MBN) measurements were made on hot-rolled mild steel samples uniaxially deformed to differing magnitudes of plastic strain, to study the dependence of MBN activity on plastic strain. The results indicated an initial increase in MBN energy with increasing plastic strain followed by a decrease at higher plastic deformations. At still higher plastic deformations, the MBN energy was found to be almost independent of plastic strain. The results are explained in terms of different mechanisms of interaction of domain walls with dislocations, with increasing plastic strain. The behavior of MBN energy with plastic strain was found to be anisotropic and the angular MBN measurements indicated that the deformation-induced easy axis of magnetization changed direction with increasing plastic strain. At higher deformations, the MBN activity was largely controlled by the deformation-induced anisotropy, due to residual stress.