Vector Preisach modeling of magnetic materials under stress

The Preisach formalism is used to model magnetic hysteresis loops in soft magnetic materials subject to tensile stress. The model uses the Stoner-Wohlfarth mechanism of coherent rotation and dispersion of easy axes to capture the vector response of the magnetization. The Preisach density is constructed as the weighed sum of normal probability density functions (pdf) for the regions of high and low induction. The model parameters reflect the effect of strain: increased pinning, modelled by the central pdf parameters; enhanced anisotropy dispersion modelled by the angular dispersion of easy axes. Upon removal of the tensile stress, compressive residual stresses give rise to effective demagnetizing fields leading to lower differential permeability with a two-peak profile. As deformation levels increase, the amplitude of and the relative distance between the two permeability peaks changes which is reflected in the side density parameters. Modelling results are in qualitative agreement with the experimental data. The potential and limitations of the model are discussed.