Full magnetoelastic behavior of DP steel in biaxial mechanical loading condition -multiscale model

Advanced High Strength Steels (AHSS) raise a growing interest as weight saving solutions with high mechanical properties due to a complex (low scale and multiphased) microstructure. Adequate heat treatments of such alloys must be assessed in order to reach the targeted mechanical behavior. Online non-destructive magnetic monitoring is used to control the quality of steels. The control is done on moving laminated steel sheets which undergo variable multiaxial mechanical loads. Due to magneto-mechanical coupling, variable stress may have a strong effect on the magnetic behavior. Therefore miss-indication of the quality and false-positives can occur using such tests if stress influence on magnetic properties is not properly taken into account. It is necessary to understand how the material’s magnetic behavior can be modified by mechanical loading and especially by a multiaxial mechanical loading. Developing predictive models for such materials subjected to multiaxial loadings is another important issue. Models validation and/or identification of fitting parameters require experiments and magnetic measurements carried out under biaxial stress conditions in particular. In this study the biaxial set-up from [1] is enhanced. Results show a clear asymmetry of the magnetic behavior in tension and compression. A bitraction hardly changes the susceptibility while a bicompression divides it by two. A shear situation with negative stress along the rolling direction shows the lowest susceptibility values. A magneto-mechanical multiscale model from [2] is adapted to a dual-phase material. Domain fractions are calculated for each phase by minimising the energy at the domain scale. Due to the heterogeneous material localisation and homogenisation steps require a self-consistent scheme based on Eshelby inclusion model. Experimental and modelled evolutions of magnetic and magnetostrictive properties in the stress plane are then compared. If the order of magnitude lacks precision the trends are very similar. [1] J. L. Soudeer, O. Hubert, Full magnetoelastic behavior of dp steel in biaxial mechanical loading condition - equivalent stress for magnetostriction, Journal of Magnetism and Magnetic Materials, 628 (2025), 173058. doi:10.1016/j.jmmm.2025.173058 [2] L. Daniel, O. Hubert, N. Buiron, R. Billardon, Reversible magneto-elastic behavior: A multiscale approach, Journal of the Mechanics and Physics of Solids 56 (3) (2008) 1018–1042. doi:10.1016/j.jmps.2007.06.003.