An Extension of the Vector-Play Model to the Case of Magneto-Elastic Loadings

Abstract

The influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach, and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.INDEX TERMS Hysteresis model, magneto-elastic behavior, multiscale modeling, electrical steel.

Corrections to “An Extension of the Vector-Play Model to the Case of Magneto-Elastic Loadings”

“…α 11 . Although the expression given for ϵ µ(2) α 11 by ( 14) in [1] is correct, the 11 component is not the only non-null component of ϵ µ(2) α . The general expression of ϵ µ(2) α is given by equation (1) below:…”

“…There is an error in the above article [1] when the components of the second order magnetostriction strain tensor ϵ µ(2) α are introduced in section II.B, just before equation ( 14). It is stated that, in the case of a uniaxial stress tensor applied parallel to the magnetic field (direction 1), the only non-null component of ϵ…”

Measurement Criteria for the Magnetic Characterization of Magnetic Materials

“…Such a problem can be split into two categories: (a) uniaxial (the applied uniaxial stress is in the direction of the applied magnetic field) and (b) multiaxial (multiaxial stress is applied or the uniaxial stress is not in the direction of the applied magnetic field). The uniaxial problem does not generally suffer from stress non-uniformity and was the subject of numerous works [23][24][25][26][27][28][29][30][31][32][33][34][35]. The sample shapes can be parallelepipedal [23], [27], [28], [32], [35] or cylindrical [31].…”

“…The uniaxial problem does not generally suffer from stress non-uniformity and was the subject of numerous works [23][24][25][26][27][28][29][30][31][32][33][34][35]. The sample shapes can be parallelepipedal [23], [27], [28], [32], [35] or cylindrical [31]. 𝑩 is measured using a B-coil wound around the sample cross-section, and 𝑯, using an H-coil [27], a Hall sensor [28], or a magnetic incremental permeability sensor [30].…”

“…The excitation coil can be wound around the sample [24] or the yokes [28]. Both isotropic [26] and anisotropic [24] materials were studied in the elastic [35] and plastic [25], [30], [35] regimes for low [32] and high [31] frequencies. In contrast, far fewer works treat the multiaxial problem, and they deal mainly with in-plane biaxial loading.…”