Estimation of the Effective Magnetic Properties of Two-Phase Steels

We investigate the predictive performance of specific analytical and numerical methods to determine the effective magnetic properties of two-phase steels at the macroscale. We utilize various mixture rules reported in the literature for the former, some of which correspond to rigorous bounds, e.g., Voigt (arithmetic) and Reuss (harmonic) averages. For the latter, we employ asymptotic homogenization together with the finite element method (FEM) and periodic boundary conditions (PBC). The voxel-based discretization of the representative volume element is conducted with digital image processing on the existing micrographs of DP600-grade steel. We show that unlike the considered isotropic mixture rules, which use only the phase volume fraction as the statistical microstructural descriptor, finite element method-based first-order asymptotic homogenization allows prediction of both phase content and directional dependence in the magnetic permeability by permitting an accurate consideration of the underlying phase geometry.