The piezo-magnetic parameters of Terfenol-D: An experimental viewpoint
Introduction
The magnetostrictive materials have the unique feature to couple mechanical variables with magnetic variables. They can store high energy densities and convert mechanical energy into electric one or viceversa. For these and other reasons, they have experienced in the last decades a growing technological interest and they have been proposed as key element in innovative sensors and actuators both for bulk and MEMS devices. More recently, magnetostrictive materials have been proposed for energy harvesting applications by exploiting the so-called Villari effect [1]. On the other hand, their external behavior is rather complicated and the accurate modeling of magnetostrictive devices is still under development.
Indeed, the constitutive relationships of magnetostrictive materials, like Terfenol-D, show nonlinear and rate-independent memory effect (hysteresis) and the mechanical and magnetic variables (H, B) are cross-coupled [1]. The cross-coupling terms are usually named piezo-magnetic coefficients and, in the energy harvesting framework, a deep knowledge of them is crucial because they are related to the material ability to convert energy [1]. For example, the accurate knowledge or modeling of their behavior, with respect to the magnetic field and prestress biases, can be useful to choose the working point that guarantees the best performance in an energy harvesting device [8] or in a sensor.
Now, in the case of characteristics without hysteresis, the piezo-magnetic parameters have to satisfy a thermodynamic constraint, that iswhich highlights the strict dependence of both magnetostrictive and magnetic characteristic and , respectively) [2]. In other words, if Eq. (1) holds, they cannot be assigned independently.
Then, it is worth to investigate at what extent the above constraint (i.e. the link between mechanical and magnetic characteristics) can be generalized when hysteresis phenomena taking place in the material are considered. Answering to this question would also help the definition of new hysteresis models with a thermodynamic consistency.
Several papers have tackled the experimental problem of measuring the piezo-magnetic coefficients of magnetostrictive material, as well other parameters as mechanical compliance, Young modulus, etc. This study is mandatory to explore the performance of new magnetostrictive compounds [3], [4], [5]. Nevertheless, the accent in those paper is more on the relation of those parameters with the material chemical and crystallographic properties. In an early paper, the problem of hysteresis of those coefficients started to be considered [6].
Also the variability of the piezo-magnetic parameter with the applied prestress has been considered [7], leading to the conclusion that magnetic and mechanical bias must be chosen with attention in order to get the best performance. This result have been confirmed by a later paper on nonlinear modeling [8].
Aim of this paper is to present and to comment a full set of measurements on a commercial Terfenol-D rod under controlled conditions for the magnetic field and the mechanical stress. The set of measurements allows to obtain the piezo-magnetic coefficients and to put in evidence relevant properties.
Section snippets
Experimental
The magnetostriction and the magnetic characteristics have been measured in different stress and magnetic field conditions in order to explore the previous conjecture. Let us recall that the magnetostrictive and magnetic characteristics can be written as:where H is the applied magnetic field, is the compressive stress, is the strain and B is the magnetic induction. The relationships are nonlinear with non-local memory [1]. In order to measure those characteristics, a
Discussion
The magnetostrictive and magnetic characteristics under variable magnetic field and constant stress are shown in Fig. 2, Fig. 3, respectively. The magnetostrictive characteristics include the elastic effect, i.e. the mechanical strain induced by the constant stress. As expected, the curves are symmetric with respect to the magnetic field and are narrower for lower stress (self-similarity).
As expected, the magnetic characteristic in Fig. 3 shows that the material becomes magnetically harder
Conclusions
In this paper a complete set of measurements on a Terfenol-D rod has been presented. The piezo-magnetic parameters of the material have been measured at different stress and field conditions and, even if they are in the same orders of magnitude, they are not equal, reflecting the internal loss mechanism, i.e. the hysteresis, of the material. The obtained data can be used as a starting point to develop more accurate fully coupled models of magnetostriction.
The measured data can also have
Acknowledgment
The authors thank Dr. P. Krejí for the useful discussions on the characteristics behavior.
This work has been supported by the Italian Ministry of Foreign Affairs, in the framework of a project Italy–Egypt.
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