Analytical model of magnetic hysteresis loop in non-oriented silicon steel considering high-temperature induced phase transition

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In the heat treatment process of ferromagnetic materials, temperature serves as a critical influencing factor—this is particularly evident during the cooling stage after the material temperature exceeds the Curie temperature. Effective temperature regulation facilitates the control of the material’s microstructure and improves the mechanical properties. As an intrinsic characteristic of the material, the magnetic hysteresis loop is closely associated with its microstructural features. To better investigate the effect of temperature variations on the microstructure of ferromagnetic materials during heat treatment, it is particularly crucial to analyze the changes in the material’s magnetic characteristics throughout this process. This study proposes the establishment of analytical model based on the Jiles-Atherton (J-A) model that accounts for high-temperature induced phase transitions. By introducing the biphasic dose–response function, the phase transition process of the material can be effectively fitted. Then we develop the high-temperature Epstein frame system designed for detecting magnetic hysteresis loops for non-oriented silicon steel at high temperatures, capable of functioning effectively at temperatures up to 820°C. By integrating the double-wire parallel winding method and current feedback control strategy, the magnetic field intensity is increased to 3.3 times its original value, while ensuring consistent magnetic field intensity across the entire temperature range of interest. Based on the obtained experimental data, the variations in magnetic hysteresis loops during the heating and cooling procedure of non-oriented silicon steel were analyzed. Furthermore, on cooling stage, the fitted results derived from the model were compared with the experimental data and the quantitative analysis shows that the average error between the two is less than 0.06%. And a strong correlation exists between the fitted parameter p and temperature, which further confirms the rationality of the model in characterizing temperature-dependent magnetic behavior.