Formulation of a Mechanical Stress Dependent Macroscopic Magnetic Model for Incremental Permeability Simulation

Electromagnetic based systems receive ever-growing interest for on-line assessment of steel strip properties for major manufacturers, especially when Advanced High Strength Steel (AHSS) products for automotive purposes are considered. Manufacturing AHSS need optimal control of the thermo-mechanical processing using in-line sensors for real time monitoring. IMPOC, 3MA and PropertyMon are some of the well-known electromagnetic sensors. Identification of a mechanical or metallurgical state from a magnetic signal is of great interest, requiring however sophisticated models to mimic the real behaviour and its sensitivity to many influencing parameters. Our paper presents a proposition to add the dependency of mechanical stress to the Jiles-Atherton hysteresis model. Experimental data consist of B(H) curves of carbon steels strips subjected to different levels of mechanical stress applied along the magnetic measurement direction. The Jiles-Atherton model has then been used to find out a set of stress-dependent coefficients. The variation of coefficients with stress is in close relationship with the variations of coercive field, remanent induction and permeability with stress. A coupled magneto-mechanical approach allows physics-based functions to be proposed to describe the evolution of Jiles-Atherton coefficients with stress. In this paper, experimental working conditions will be described, as well as the stressdependent Jiles-Atherton model. The model is finally implemented in FEM software, allowing more complex magneto-mechanical situations to be modelled. After matching with measurement, the new model is applied on 3MA modelling where magnetic transient analysis and magnetic AC steady state analysis are linked through incremental permeability.