Investigation of the magnetostrictive effect in a terfenol-D plate under a non-uniform magnetic field by atomic force microscopy Slim Naifar a,b, ⁎, Sonia Bradai a,b , Christian Viehweger a , Olfa Kanoun a , Slim Choura b a Measurement and Sensor Technology, Technische Universität Chemnitz, Reichenhainer Straße 70, 09126 Chemnitz, Germany b Laboratory of Electromechanical Systems, National Engineering School of Sfax, University of Sfax, Route de Soukra km 4, 3038 Sfax, Tunisia abstract article info Article history: Received 12 November 2015 Received in revised form 2 February 2016 Accepted 16 February 2016 Available online 21 February 2016 We present a novel high resolution approach for the characterization of the evolution of magnetic domain struc- tures and magnetostrictive shifts in a Terfenol-D plate under different magnetic fields distribution using atomic force microscopy (AFM). Investigations are made to examine the magnetostrictive effect in the material under similar conditions as it is used in magnetoelectric vibration energy converters. The surface topography of the sample was imaged as it changes with induced magnetization for different relative height positions between the magnets and the plate. The magnetic field distribution was analyzed based on finite element analysis while both longitudinal and transversal magnetostrictive strains were determined based on cross sections analysis performed on the AFM topography images. In addition, AFM amplitude images are presented to visualize the evolution of magnetic domain structures. Results demonstrate that the maximum longitudinal elongation of the plate is 266 ppm when it is placed just above the magnets. On the other hand, magnetostriction close to zero are observed when the sample was placed in the farthest measured position from the magnets which confirm the validity of the proposed approach. © 2016 Elsevier Ltd. All rights reserved. Keywords: Magnetostriction Terfenol-D plate Atomic force microscopy Energy harvesting Vibration converter 1. Introduction The magnetostrictive effect can be defined as the deformation of a material during the magnetization process and conversely change of magnetization in response to applied stress. The phenomenon of mag- netostriction depends on the crystal symmetry and in atomic scale on spin-orbit interaction [1,2]. Additionally, it depends on texture and material composition [3]. Giant magnetostrictive material Terfenol-D (Tb 1 - x Dy x Fe 2 , 0.70 b x b 0.73) exhibits large displacements up to 2000 ppm and has an an- isotropy compensation temperature approximately at room tempera- ture [4–6]. For these reasons, this material has been used in different advanced applications such as automotive and medical [7,8]. Further- more, in vibration energy harvesting, promising concepts use laminated composites of piezoelectric and of Terfenol-D plates [9]. In these config- urations, during operation the giant magnetostrictive material will un- dergo a non-uniform time dependent magnetic field which makes the prediction of magnetostriction not evident (Fig. 1). Investigation is im- portant in order to examine the magnetomechanical coupling between the magnets and the giant magnetostrictive material and to predict the optimal initial position of the transducer. Investigation of the domain structure and local magnetic properties of magnetostrictive materials has been extensively performed by differ- ent techniques including X-ray topography [10] Lorentz transmission electron microscopy [11], scanning probe microscopy [12] and magnetic force microscopy [13]. However, most of these investigations focused on the domain structures exhibited by the material in the absence of ap- plied magnetic field. Recently, several approaches have been proposed to study the evolution of magnetic domains and to measure magneto- strictive strains in Terfenol-D under an external magnetic field [14,15]. In [14] a laser displacement sensor to measure the magnetostric- tive strain of Terfenol-D. Investigations were performed on two dif- ferent material compositions of Terfenol-D. It is reported that deformations of 622 ppm and 725 ppm were obtained respectively for Tb x Dy 1 - x Fe 2y and Tb 0.27 Dy 0.73 Fe 2 under an external magnetic field in- tensity of 3000 Oe. Nevertheless, the investigation method was proposed for large cylindrical samples (100 mm long and 20 mm in diameter) because the magnetic field was generated by a solenoid-power supply system. In addition, the overall accuracy is limited to 1 μm. In [15], defor- mations and local magnetic domain structures in Tb 0.27 Dy 0.73 Fe 2 disc of 10 mm diameter and 0.7 mm thickness, polished down to 0.05 μm dia- mond finish, were investigated simultaneously using strain gauges and atomic force microscope [10]. The applied magnetic field was generated by variable field module (VFM) able to apply in-plane magnetic field up to 2000 Oe and the resulting magnetostrictive strains were measured using strain gauges boned to the surface of the disc. Positive deformation was observed parallel to the applied magnetic field in the range of Materials and Design 97 (2016) 147–154 ⁎ Corresponding author at: Measurement and Sensor Technology, Technische Universität Chemnitz, Reichenhainer Straße 70, 09126 Chemnitz, Germany. E-mail address: slim.naifar@etit.tu-chemnitz.de (S. Naifar). URL: http://tu-chemnitz.de/etit/messtech/ (S. Naifar). http://dx.doi.org/10.1016/j.matdes.2016.02.065 0264-1275/© 2016 Elsevier Ltd. All rights reserved. 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