International Journal of Applied Electromagnetics and Mechanics 23 (2006) 139–144 139 IOS Press Modelling of rearrangement yield surface under biaxial magnetic field in Ni-Mn-Ga shape memory alloys Nicolas Creton and Laurent Hirsinger Institut FEMTO-ST, Dpt de M´ ecanique Appliqu ´ ee, 24, Chemin de l’Epitaphe F-25000 Besanc ¸on, France Tel.: +33 381 666 024; Fax: +33 381 666 700; E-mail: laurent.hirsinger@univ-fcomte.fr Abstract. A predictive model of field-induced strain in Ni-Mn-Ga ferromagnetic shape memory alloys is proposed. The action of both biaxial magnetic field and mechanical stress on the martensitic rearrangement in a Ni-Mn-Ga single crystal are modelled. Yield surfaces of starting rearrangement are simulated. They show how applied mechanical stress helps or opposes to the applied magnetic field to make the rearrangement easier or harder. The results are fully compatible with the experiments of M¨ ullner et al. [8] describing the action of a rotating magnetic field. Keywords: Magneto-mechanical coupling, shape memory alloy, model 1. Introduction In the search of new active materials, ferromagnetic shape memory alloys (FSMA) such as Ni-Mn-Ga have a prominent position thanks to their capability to develop a strain more important than conventional active materials such as piezoelectric and magnetostrictive. Contrary to classical shape memory alloys, they are able to developthis strain very rapidly, under an applied magnetic field. This particular behaviour is in fact due to variant structure rearrangement of twinned martensite platelets: when a magnetic field is applied, this one tends to increase the volume fraction of the best oriented martensite between the two twinned ones. To describe and understand this mechanism of magnetic field-induced-strain, different models were proposed (Murray et al. [1], James et al. [2], Likhachev et al. [3] and M ¨ ullner et al. [4]). In this paper, the authors propose a magneto-mechanical model based on phenomenology, thermo- dynamics of irreversible processes and changing of scale. This model is written in order to predict the effect of biaxial magnetic field in a single crystal of 5 M or 7 M twinned martensite, with applied stress or not. For sake of simplicity, no demagnetizing field is considered. A Representative Elementary Volume is classically introduced with different microstructural parameters, i.e. volume fractions of martensitic bands, magnetization rotations, width ratios of two consecutive magnetic domains. It must be noticed that these variables are linked to physical phenomenon, for example, the movements of 180 ◦ magnetic domains corresponds to the evolution of width ratios. Contrary to what is done usually [5–7], the move- ments of magnetic domain walls into martensitic bands are dissociated. The driving force acting on twin boundaries is written. Some yield surfaces of rearrangement are deduced under applied biaxial magnetic field, showing the existence of directions (at ±45 ◦ with respect to c axis) in which the rearrangement under magnetic field is hard or impossible. 1383-5416/06/$17.00 © 2006 – IOS Press and the authors. All rights reserved