Mathematical analysis for the hystereses of a soft ferromagnetic steel by a modified Rayleigh model

Minor loops of solubilized and aged samples of maraging-400 steel were measured and mathematically analyzed. The descending and ascending parts of the hysteresis curves obtained for this soft ferromagnetic material were fit with polynomials of varying degree. The fits were successful and the obtained polynomial coefficients revealed that a symmetry operation (S2) transforms the ascending part into the descending part (or vice versa). Based on the particular mathematical relation between the polynomials, an analytical expression for the minor loop area was obtained as a function of the specific maximum applied field. The curves of the minor loop area versus the maximum applied field for every aged sample were shown to be typical for a cumulative distribution function (CDF). The experimental curves were fit using the complementary function of the Hill equation. The fit Hill parameters revealed a systematic dependence on the sample aging conditions.