Effects of plastic strain and reloading stress on the magneto-mechanical behavior of electrical steels: Experiments and modeling

The properties of electro-mechanical systems are intimately linked to the mechanical state of the materials used for their design. Notably, the processing stages can lead to significant mechanical stresses, with a strong impact on the final magnetic behavior, through plasticity and residual stress effects. This work presents a thorough magneto-mechanical characterization, both hysteretic and anhysteretic, of an electrical steel (DC04) at different levels of plastic deformation and applied tension stress. The mechanical characterization of the material leads to the identification of two hardening stages: a first stage attributed to the development of long-range internal back stress, and a second stage dominated by intragranular stresses connected to the formation of dislocation structures. The magnetic characterization shows that, under no applied stress, plastic strain involves a significant degradation of the magnetic behavior. Mechanical reloading allows recovering part of the magnetic properties of the virgin material. A simplified multiscale modeling tool is proposed for the magneto-mechanical behavior, including the effects of internal stress and dislocation density. The model is notably used to predict the effect of a reloading stress on the magnetic behavior of a plasticized material, with a very satisfactory agreement. For the first time, a three-dimensional modeling approach is proposed for the magneto-mechanical behavior of materials including levels of plasticity up to necking. The very low computation cost of the modeling approach makes it suitable for the numerical study of magnetic devices under various mechanical states. In addition, this formulation opens a route for estimating the mechanical state of a plastically deformed material through the analysis of its magnetic behavior.