Modelling of rearrangement yield surface under biaxial magnetic field in Ni-Mn-Ga shape memory alloys

Abstract

Abstract. A predictive model of field-induced strain in Ni-Mn-Ga ferromagnetic shape memory alloys is proposed. Theaction of both biaxial magnetic field and mechanical stress on the martensitic rearrangement in a Ni-Mn-Ga single crystal aremodelled. Yield surfaces of starting rearrangement are simulated. They show how applied mechanical stress helps or opposesto the applied magnetic field to make the rearrangement easier or harder. The results are fully compatible with the experimentsof Mullner 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-Gahave a prominent position thanks to their capability to developa strain more important than conventionalactive materials such as piezoelectric and magnetostrictive. Contrary to classical shape memory alloys,theyareabletodevelopthisstrainveryrapidly,underanappliedmagneticfield. Thisparticularbehaviouris in fact due to variant structure rearrangement of twinned martensite platelets: when a magnetic fieldis applied, this one tends to increase the volume fraction of the best oriented martensite between the twotwinned ones. To describe and understand this mechanism of magnetic field-induced-strain, differentmodels were proposed (Murray et al. [1], James et al. [2], Likhachev et al. [3] and Mullner 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 theeffect of biaxial magneticfieldin asingle crystalof 5 M or 7 M twinnedmartensite, with appliedstressornot. For sake of simplicity, no demagnetizing field is considered. A Representative Elementary Volumeis classically introduced with different microstructural parameters, i.e. volume fractions of martensiticbands, magnetization rotations, width ratios of two consecutive magnetic domains. It must be noticedthat these variables are linked to physical phenomenon, for example, the movements of 180