Two phase modeling of the influence of plastic strain on the magnetic and magnetostrictive behaviors of ferromagnetic materials

A growing interest of automotive industry in the use of high performance steels is observed. These materials are obtained thanks to complex manufacturing processes whose parameters fluctuations lead to strong variations of microstructure and mechanical properties. The on-line magnetic non-destructive monitoring is a relevant response to this problem but it requires fast models sensitive to different parameters of the forming process. The plastic deformation is one of these important parameters. Indeed, ferromagnetic materials are known to be sensitive to stress application and especially to plastic strains. In this paper, a macroscopic approach using the kinematic hardening is proposed to model this behavior, considering a plastic strained material as a two phase system. Relationship between kinematic hardening and residual stress is defined in this framework. Since stress fields are multiaxial, an uniaxial equivalent stress is calculated and introduced inside the so-called magneto-mechanical multidomain modeling to represent the effect of plastic strain. The modeling approach is complemented by many experiments involving magnetic and magnetostrictive measurements. They are carried out with or without applied stress, using a dual-phase steel deformed at different levels. The main interest of this material is that the mechanically hard phase, soft phase and the kinematic hardening can be clearly identified thanks to simple experiments. It is shown how this model can be extended to single phase materials.