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.

中文翻译：

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基于修正瑞利模型的软铁磁钢迟滞数学分析

对马氏体时效 400 钢的溶解和时效样品的小环进行了测量和数学分析。为这种软铁磁材料获得的磁滞曲线的下降和上升部分与不同程度的多项式拟合。拟合成功并且获得的多项式系数表明对称运算（S2）将上升部分转换为下降部分（反之亦然）。基于多项式之间的特定数学关系，获得了作为特定最大外加场的函数的小环面积的解析表达式。每个老化样品的小环面积与最大施加场的曲线显示为累积分布函数 (CDF) 的典型曲线。使用希尔方程的互补函数拟合实验曲线。拟合 Hill 参数揭示了对样品老化条件的系统依赖性。