Sheet thickness dependence of magnetization properties based on domains and walls within the non-linear diffusion-like equation for Grain-Oriented Electrical Steels

International audienceThe definition and development of a dynamic or transient magnetic formulation compatible with the Finite Element Method, able to take the dynamic hysteresis and classical and extra losses into account (not a posteriori but a priori), and using the most adapted state variable that makes the problem well defined and easily convergent requires the knowledge of dynamic behavioral properties of soft magnetic materials whatever the thickness and the working conditions. The dynamic hysteresis of soft magnetic materials corresponds to excess iron losses, due to dynamic magnetization reversal processes within magnetic domains and especially to microscopic eddy currents around the magnetic walls in motion and inside rotating domains. The model properties used are the internal quasi-static permeability mu and the dynamic magnetization property Lambda that lumps the magnetization mechanisms (domain walls displacement, bowing, fusion, nucleation and multiplication). The latter are involved in the magnetic field damping due to microscopic eddy currents within the field diffusion that renders the magnetic behavior geometry dependent. This model does not separate the field diffusion process from the magnetization reversal mechanisms. In this paper, the sheet thickness dependence of the dynamic magnetization property for a Grain Oriented Electrical Steel (GOES: steel made of 3% Silicon and Iron: SiFe) is analyzed in the Rolling Direction (RD). To this extend, it is proposed to carry out and interpret magnetic measurements on GOES samples with the Epstein frame for four different thicknesses (0.23, 0.27, 0.30 and 0.35 mm), but with similar metallurgical and crystallographic properties for the whole specimens. Magnetic properties are first identified at low induction with linear assumptions and at higher induction with non-linearities. It makes it possible to re-compute the dynamic hysteresis loops of the material and to predict the losses whatever the working conditions with frequencies from 50 to 800 Hz. It is found that mu does not depend significantly on the sheet thickness whereas Lambda depends on it significantly. Microscopic observation of the magnetic domains width are then performed thanks to the MOIF (Magneto-Optical Indicator Film) technique. It helps us discriminate between three simultaneous origins for the dependence of iron losses to the sheet thickness: a skin-like effect, a domains’ refinement and changes on the walls’ mobility. Results are discussed taking the dipolar magnetic effects, closure domains, the grains and texture and the manufacturing and coating residual stress on the metal surface into account