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

Abstract

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.

Multiscale magneto-elastic modeling of magnetic materials including isotropic second order stress effect

“…This Villari effect (so-called Villari reversal ) is well documented especially for pure iron and various steels [6,7,8,36,37]. Its modeling is generally possible when crystalline anisotropy and magnetization rotation are taken into account [38,39,37,26]. For stresses greater than 20 MPa, the sensitivity of the magnetization to stress is negative whatever the magnetic field level, including zero magnetic field as shown in figure 3b.…”

“…This concerns, for example, iron-silicon alloys constitutive of most of high and medium-range electrical machines and sometimes subjected to high operating stresses [5]. The non-monotonic effect may concern different iron-based ferromagnetic materials when they are subjected to plastic deformation and suffer the effect of high intensity multiaxial internal stresses [26]. Unlike the well-known Villari reversal, it may appear at the lowest magnetic field levels (e.g.…”

Multiscale Approach for the Modeling of Chemo-Magneto-Thermo-Mechanical Couplings – Reversible Framework

“…It is very well adapted to the description of many couplings involving a mechanical free deformation. The localization procedures from the RVE to the grain scale makes it possible to better account for demagnetizing fields and residual stresses effects [13]. Such a modeling requires physical parameters usually coming from literature and adjusting parameters identified using a differential scanning calorimetry measurement for the phase kinetic [16], a mechanical measurement for variant kinetic [15], and an anhysteretic magnetic measurement for the magnetic domain kinetic [8].…”

Multiscale Modeling of Magnetostrictive Materials

“…The gap between local and global quantities defines the demagnetising field and the residual stress. 9. More complex formulation can be proposed to take a possible phase transformation (ferromagnetic to ferromagnetic, or ferromagnetic to paramagnetic) or the existence of several variants into account.…”