The submission of a ferromagnetic material to a magnetic field causes a geometric distortion of the sample. This deformation is called the magnetostriction deformation. Conversely, the application of an external mechanical stress to a ferromagnetic material, initially magnetized even faintly, causes a significant change of magnetization. These observations reflect the same phenomenon called the piezomagnetic effect or Villari effect [1]. Indeed mechanical stress is one of the three major factors that can affect the magnetization in addition to the magnetic field and the temperature. The magnetic behavior is thus sensitive to any mechanical loading and its evolution will be different depending on the level of loading, its direction and its nature [2]. Since then, a lot of work has been done to understand, model and use this coupling effect in industrial applications such as on Nondestructive Testing (NDT) for example: magnetic particle inspection (MPI), eddy currents, Barkhausen noise... etc. The purpose of all these magnetic methods is to extract information about the metallurgical and mechanical states of a material by analyzing the electromagnetic signal [3].

Piezomagnetic control methods have undergone recent developments [4, 5] but still face modeling issues, especially when no controlled magnetic field is applied [6]. The development, the implementation and the generalization of such techniques involve, in one hand, the establishment of experiments to highlight the magnetoelastic coupling in a controlled framework, and on the other hand, the development of innovative modeling methods. Both aspects will be detailed in this communication. The measurements presented are related to the anhysteretic and cyclic piezomagnetic behavior [7] of a dual-phase steel obtained under different magnetic field and stress conditions. We then propose to model the piezomagnetic behavior of this material using a multiphase-multiscale model whose description of the hysteresis is inspired by [8].

Références

[1] E. Villari, “Change of magnetization by tension and by electric current” Ann. Phys. Chem., 126 (1865), 87-122.

[2] R. M. Bozorth, “Ferromagnetism”, New York: Ed. Van Nostrand, 1951.

[3] J. Dumont-Fillon, “Mesures – Analyses / Contrôle non destructif”, Techniques de l'ingénieur, 1996.

[4] L. Lollioz, S. Pattofatto and O. Hubert, "Application of piezo-magnetism for the measurement of stress during an impact", J. of Electrical Engineering, 57 8 (2006) 15-20.

[5] O. Hubert, K. J. Rizzo, “Anhysteretic and dynamic piezomagnetic behavior of a low carbon steel”. J. of Magnetism and Magnetic Materials, 320 20 (2008), 979-982.

[6] S. Bao, T. Erber, S.A. Guralnick, W.L. Jin, « Fatigue, Magnetic and Mechanical Hysteresis » Strain, 372-381, 2011.

[7]K.J. Rizzo, O. Hubert and L. Daniel, "A multiscale model for piezomagnetic behavior", European Journal of Electrical Engineering, 12 4 (2009) 525-540.

[8] H. Hauser. “Energetic model of ferromagnetic hysteresis: Isotropic magnetization”. Journal of Applied Physiscs, 96 5, (2004), 2753-2767.