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

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

Search for NDE Methods to Characterize Thermal History and Mechanical Properties of Al-Li Alloys

Aluminum-lithium alloys have attracted the interest of the aerospace industry for some time now since the use of such alloys would reduce the weight of an airframe by roughly ten percent. The production of these alloys, however, requires precise thermal and/or thermomechanical treatments to insure required material properties, such as the yield strength and ductility. On-line monitoring of the state of the material thus seems to be desirable for quality control of these materials. This paper presents results of an investigation of fieldable NDE methods capable of providing information on the state of the material. Eddy current measurements were found to be particularly sensitive to Li in solid solution. Furthermore, it appears that hardness measurements are sensitive to the volume fractions, and probably the morphology, of the various precipitates formed. The results obtained so far (see also [1]) as well as by other authors on different aluminum alloys [2–4], this work will continue with additional results to be reported in future publications

Detection of Expended Fatigue Life of AISI 4140 Steels from Magnetic Measurements

The objective of this study was to determine how magnetic properties such as coercivity, hysteresis loss and initial susceptibility of AISI 4140 steels depended on the expended fatigue life. If one or more of these magnetic properties was found to be sensitive to fatigue cycling, then it should be possible to devise a magnetic NDE technique based on these results, for monitoring of in-service components subjected to fatigue cycling

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

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, M S , 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 M S and the effective coercivityk, 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

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