Characterization of the evolution of recrystallization by fluctuation and fractal analyses of the magnetic hysteresis loop in a cold rolled non-oriented electric steel

Silicon steels with non-oriented grains are widely used in the fabrication of electrical motor nucleus where a low magnetic loss is an important point. The performance of these motors is affected by the level of recrystallization of these steels which can come from the steel plant in a semi-processed condition. In this condition, they have a partially deformed structure and are submitted to an adequate annealing heat treatment, after reaching the end shape, to get an appropriate magnetic property. In this study, samples of an electric steel, cold rolled 50% in thickness, were withdrawn during the industrial heat treatment at temperatures of 575, 580, 600, 620 and 730 °C with the objective of evaluating the evolution of recrystallization with temperature. Magnetic properties were measured at room temperature in a vibrating sample magnetometer and the changes in magnetic hysteresis loop with temperature have been identified by using two pattern classification techniques, principal-component analysis and Karhunen-Loève (KL) expansion, associated with statistical fluctuations and fractal analyses. The fluctuation and fractal analyses were used as preprocessing tools of the series which are built from each hysteresis loop, properly renormalized, whose values correspond to the amplitudes of the loop at given equally spaced values of the renormalized field interpolated between the experimental data. The samples have been classified in four sets corresponding to different temperatures, and to samples without annealing heat treatment and recrystallized ones. The classification of the different microstructures have been obtained by applying the two pattern classification techniques to the vectors obtained from the preprocessing, and in particular a 100% success rate has been reached by using KL expansion.