Frequency dependence of hysteresis curves in conducting magnetic materials

An extension of the hysteresis model has been developed that takes into account the effects on the hysteresis curves of eddycurrents in electrically conducting media. In the derivation presented it is assumed that the frequency of the applied field is low enough (or the thickness of the material medium small enough) that the skin effect can be ignored so that the magnetic field penetrates uniformly throughout the material. In this case, the dc hysteresis equation is extended by the addition of a classical eddy‐current‐loss term depending on (i) the rate of change of magnetization with time, (ii) the resistivity of the material, and (iii) the shape of the specimen; and on an anomalous (or excess) eddy‐current‐loss term which depends on (dB/dt)3/2. In the limit, as the frequency of the magnetic field tends to zero, the frequency‐dependent hysteresis curve approaches the dc curve

Estimation of fatigue exposure from magnetic coercivity

An investigation of the effects of fatigue on A533B steel under constant load amplitude is reported in this paper. It was found that the plastic strain of the sample accumulated logarithmically with the number of stress cycles after initial fatigue softening. Based on the fact that plastic strain is often linearly related to the coercivity of material, at least for small changes of H c , a phenomenological relationship has been developed and tested to correlate the number of stress cycles to this magnetic parameter. This result represents the first successful attempt to relate the fatigue exposure directly to a magnetic parameter

Modeling of micromagnetic Barkhausen activity using a stochastic process extension to the theory of hysteresis

Recent work by Bertotti [IEEE Trans. Magn. MAG‐24, 621 (1988)] and others has shown that it is possible to model the micromagnetic Barkhausen discontinuities at the coercive point using a two‐parameter stochastic model. However, the present formulation of the model is restricted to limited regions of the hysteresis curve over which dM/dH is approximately constant and whendH/dt is held at a constant rate. A natural extension of this model is to take the basic result, in which the level of Barkhausen activity in one time period is related to the activity in the previous time period, and increment it by a small amount which is dependent on the differential permeability. The extension of the model proposed here uses the theory of ferromagnetichysteresis to determine the differential permeability at any point of the hysteresis loop. The Barkhausen activity is then assumed to vary in proportion to the differential permeability. The resulting model allows the Barkhausen sum of discontinuous changes in magnetization to be modelled around the entire hysteresis loop, leading to an important generalization of the basic model

Generalization of hysteresis modeling to anisotropic materials

An extension to the model of hysteresis has been presented earlier which included the effect of anisotropy in the modeling of the anhysteretic magnetization curves of uniaxially anisotropic single crystalline materials. Further exploration of this extension shown here considers different kinds of crystal anisotropy in materials. Theory considers that the differential susceptibility at any given field is determined by the displacement of the prevailing magnetization from the anhysteretic magnetization. Thus, it has been shown that the effect of anisotropy on magnetic hysteresis in materials can be incorporated into the model of hysteresis through the anisotropic anhysteretic. This extension is likely to be particularly useful in the case of hard magnetic materials which exhibit high anisotropy

Modeling of the magnetomechanical effect: Application of the Rayleigh law to the stress domain

Stress is one of the principal external factors affecting the magnetization of materials. The magnetomechanical effect, that is, the change of magnetization of a magnetic material resulting from the application of stress, has attracted attention because of its scientific complexity. An improved model equation for interpreting the magnetomechanical effect has been developed based on extension of the previous equation to include the Rayleigh law. According to the previous theory of the magnetomechanical effect, which is based on the “law of approach,” application of stress induces changes in magnetization toward anhysteretic magnetization which itself is stress dependent, and the rate of change of magnetization with the input elastic energy is dependent on the displacement of the prevailing magnetization from the anhysteretic magnetization. The theory has been refined by including a linear term in the model equation in addition to the well-known quadratic term. It was found that the modified theory provides a much better description of the magnetization changes under stress, particularly at small applied stress amplitudes and when the stress changes sign

Examination of the relationship between the parameters of Barkhausen effect model and microstructure of magnetic materials

A relationship between the parameters of a hysteretic-stochastic process model of the Barkhausen effect (BE) and the microstructural features of a series of ferritic/pearlitic steel samples has been identified. The root-mean-square values and pulse height distributions of the experimental and modeled BE signals showed similar dependence on the pearlite content. The correlation length parameter ξ of the model, which represents the range of interaction of domain walls with pinning sites, was found to obey ξ=AVfDf+BVpDp where Vf(Vp)and Df(Dp) are the volume fraction and grain size of ferrite (pearlite)

Effects of surface condition on Barkhausen emissions from steel

Temperature changes during mechanical processing such as grinding of steel parts can cause phase changes in the microstructure. Thermal shock during the process can give rise to localized surface residual stress. The net result can be reduced wear resistance and fatigue life leading to early failure during service. Effective methods for the detection of such damage are necessary. Barkhausen emissions, which arise from discontinuous motion of domain walls, are sensitive to microstructual changes that affect domain dynamics. Detected Barkhausen signals are predominantly from a surface layer about 200 μm thick, those from deeper being attenuated due to eddy currents. An analysis of the detected signals can provide an indication of the surface condition of the material.Barkhausen signals from parts ground under controlled conditions were found to be dependent on the grinding process conditions. The signal changes were consistent with residual stress measured by x‐ray diffraction and with hardness measurements that are indicative of changes in microstructure

Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons

Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynamical systems, is inherently suited to support multistability. We derive the bifurcation structure and parametric trends leading to multistability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure

Measurements of magnetic circuit characteristics for comprehension of intrinsic magnetic properties of materials from surface inspection

A transfer function is presented for calculating magnetic field and flux density inside a test material as a result of surface measurement. By considering flux leakage, we introduce a parameter η, called the leakage coefficient, which can be experimentally determined. It is introduced into the equations to make the transfer function more practical. The distribution of field inside a test material is then discussed in accordance with a surfacemagnetic charge model

Superparamagnetic magnetization equation in two dimensions

An equation for the dependence of magnetization on magnetic field in the case of two-dimensional (base plane) anisotropy has been derived. The resulting equation is expressed as an infinite series of modified Bessel functions, unlike the elementary function expressions that are applicable to the one-dimensional (axially anisotropic) and three-dimensional (isotropic) cases. Nevertheless, in the low-field limit, the series can be effectively truncated to give an approximate solution, while, in the high-field limit, an alternative expression has been derived which represents the limiting function as the field strength tends to infinity. The resulting expressions can be used to describe the superparamagnetic magnetization and susceptibility as a function of magnetic field in situations where the magnetic moments are constrained to lie in a plane, with no preferred direction within the plane. This can therefore be applied to two-dimensional structures, such as magnetic thin films, where magnetostatic energy confines the moments to the plane of the film, or to three-dimensional structures with planar magnetocrystalline anisotropy