M. J. Sablik

Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis

It is demonstrated that hysteresis in the magnetostriction k is coupled to hysteresis in the magnetization M because of the dependence of the magnetostriction on the magnetization. At the same time, when stress is present, the magnetization is in turn coupled to the behavior of the part of the magnetostriction associated with domain moment rotation. An expression for the magnetostriction is formulated, and numerical modeling results for magnetostriction hysteresis are compared to experimental results. Although some features of the magnetostriction in iron and steel still need additional explanation, the main features of the magnetostriction are accounted for. These include liftoff (failure of the magnetostriction to return to its value in the demagnetized state as the hysteresis loop is cycled) and a magnetostriction increase after flux density B reaches its maximum and starts to decrease. A macromagnetic, multidomain formulation that yields zero magnetostriction in the demagnetized specimen is used. >

A model for the effect of stress on the low‐frequency harmonic content of the magnetic induction in ferromagnetic materials

A simple model used previously by the authors to explain stress variation of magnetic hysteresis is now employed to explain the effect of stress on the amplitudes of the first‐ and third‐order harmonics of the magnetic induction signal resulting from application of an ac magnetic field of low frequency to a steel specimen. An improved expression for the effective field contribution Hσ due to stress has been derived from thermodynamic considerations.

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.

A model for hysteretic magnetic properties under the application of noncoaxial stress and field

Although descriptions of the effect of stress on spontaneous magnetization within a single domain already exist, there remains no adequate mathematical model for the effects of noncoaxial magnetic field and stress on bulk magnetization in a multidomained specimen. This article addresses the problem and provides a phenomenological theory that applies to the case of bulk isotropic materials. The magnetomechanical hysteresis model of Sablik and Jiles is thus extended to treat magnetic properties in the case of noncoaxial stress and magnetic field in an isotropic, polycrystalline medium. In the modeling, noncollinearity between magnetization and magnetic field is taken into account. The effect of roll‐axis anisotropy is also considered. Both magnetic and magnetostrictive hysteresis are describable by the extended model. Emphasis in this article is on describing properties like coercivity, remanence, hysteresis loss, maximum flux density, and maximum differential permeability as a function of stress for variou...

Modeling the effect of grain size and dislocation density on hysteretic magnetic properties in steels

In this article, the Jiles–Atherton model is modified to elucidate the variation of magnetic properties with grain size and dislocation density. The modified model predicts generally that coercive field increases with increasing dislocation density and inverse grain size and that remanent flux density and permeability at the coercive field decrease with increasing dislocation density and inverse grain size. Using the same model, it should be possible to model the effects of grain size and dislocation density on other magnetic measurements such as nonlinear harmonics of the flux density or Barkhausen noise.

The effect of mechanical stress on a Barkhausen noise signal integrated across a cycle of ramped magnetic field

Experimental Barkhausen data are presented for XC10 French steel at various stress levels. The experimental data show an apparent almost linear correlation with stress of WH (hysteresis loss) and WBN (Barkhausen noise amplitude integrated over H). A model previously suggested by Sablik for Barkhausen noise stress and field dependence is used for analysis of the experimental data. With slight modifications of the previous model, it has been possible to produce semiquantitative fits to the Barkhausen peaks as a function of H while at the same time obtaining the apparent linear correlation between WH and WBN and stress. The model suggests however that the apparent linear correlation may only apply to certain types of materials. In addition, the fit to experiment suggests that additional refinements to the model may yet be necessary.

Modeling the effects of torsional stress on hysteretic magnetization

Opposite torques applied axially to a polycrystalline ferromagnetic rod result in tensile and compressive stresses acting perpendicularly at the rod surface at 45/spl deg/ to the rod axis. These stresses affect the magnetization of the rod when a magnetic field is applied parallel to the rod axis. It is shown how one can formulate the magnetomechanical hysteresis model so as to treat this special case of biaxial stress and take into account the effect of opposite torques on the magnetic properties of the rod. Variation of hysteresis parameters such as coercive field, remanent flux density, differential permeability at the coercive field, and hysteresis loss as a function of applied torque are determined from the model. In the model, the torque is applied first and then the field is cycled to give hysteresis loops. It is found that the torque dependence of the magnetic properties is different, depending on what is chosen for H/sub max/, the maximum value of the applied magnetic field H. The best parameter to use for tracking the torque is found to be H/sub c/ at saturation or near saturation, since that parameter shows an almost linear decrease with the applied torque.

A model for hysteresis in magnetostriction

The domain wall pinning model used previously by the authors to explain magnetic hysteresis and stress effects on magnetic hysteresis is used in conjunction with the Callen and Callen expression for magnetostriction λ to qualitatively explain magnetostriction hysteresis both with respect to magnetic intensity H and flux density B. The Callen and Callen form for the magnetostriction is used because it depends functionally on effective field He rather than M, and this produces hysteresis in λ vs B whereas λ=λ(M) does not. To our knowledge, this is the first time that magnetic hysteresis and magnetostriction hysteresis have been modeled simultaneously.

Micromagnetic model for biaxial stress effects on magnetic properties

Abstract A micromagnetic formulation has been developed for modeling the effect of biaxial stress on magnetoelastic processes in polycrystalline steels. The formulation uses a modified version of the Kashiwaya model for the effect of biaxial stress on magnetic properties and combines it with the Schneider-Cannell-Watts model for magnetoelastic processes in steels. In particular, the model involves use of an effective stress equal to one of the deviatoric (i.e. distortional) normal stress components, depending on whether the field is parallel to a tensile or compressive axis or to the third axis perpendicular to the plane of biaxial stress. Computer results are compared to experimental results on the effects of biaxial stress on magnetic properties in mild steel and in SAE-4130 steel. Good qualitative agreement is found in almost all cases, in that in going from one biaxial stress case to the next, the same kinds of changes are seen magnetically.

A model for asymmetry in magnetic property behavior under tensile and compressive stress in steel

Presents a way to relate two standard models for magnetomechanical hysteresis-the Sablik-Jiles-Atherton model and the Schneider-Cannell-Watts model-while at the same time presenting physical models for the asymmetry in magnetic property behavior under tensile and compressive stress in steel, including, for /spl sigma/H processes, the presence of an extremum in the dependence of magnetic properties on tensile stress, an effect which is sometimes known as the Villari effect.