Extension to the Jiles–Atherton Hysteresis Model Using Gaussian Distributed Parameters for Quenched and Tempered Engineering Steels

The Jiles-Atherton (J-A) model has seen extensive use for modelling the hysteresis behaviour of ferromagnetic materials due to its computational efficiency, simplicity of use, and small number of physically related parameters. However, in this work, the application of the J-A model to hysteresis curves obtained from experimental measurements for as-quenched and quenched-and-tempered engineering steels is considered. It has been demonstrated that the current form of the J-A model is not capable of representing certain observed features in the obtained hysteresis curves of these steels, in particular, the rapid narrowing of the loops seen for as-quenched steels and the sharp corners seen for quenched-and-tempered steels. This work has shown that a superior fit to the major loops for such steels can be obtained by applying Gaussian variations with respect to the applied magnetic field to the model parameters. The findings are supported by experimental results from engineering steels used in the oil and gas industry.