In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed. The standard square (SS) constitutive model is developed by means of truncating the polynomial expansion of the Gibbs free energy. The hyperbolic tangent (HT) constitutive equations, which involve a hyperbolic tangent magnetic-field dependence, are proposed to model the magnetic-field-induced strain saturation of magnetostrictive materials in the region of intense magnetic fields. A new model based on density of domain switching (DDS) is established in terms of the basic truth that magnetic domain switching underlies magnetostrictive deformation. In this model, it is assumed that the relation between density of domain switching, defined by the quantity of magnetic domains switched by per unit magnetic field and magnetic field can be described by a density function with normal distribution. The moduli in these constitutive models can be determined by a material function that is proposed to describe the dependence of the peak piezomagnetic coefficient on the compressive pre-stress for one-dimensional cases based on the experimental results published. The accuracy of the non-linear constitutive relations is evaluated by comparing the theoretical values with experimental results of a Terfenol-D rod operated under both compressive pre-stress and bias magnetic field. Results indicate that the SS constitutive equations can accurately predict the experimental results under a low or moderate magnetic field while the HT model can, to some extent, reflect the trend of saturation of magnetostrictive strain under a high magnetic field. The model based on DDS, which is more effective in simulating the experimental curves, can capture the main characteristics of the mechanism of magnetoelastic coupling deformation of a Terfenol-D rod, such as the notable dependence of magnetoelastic response on external stress and the saturation of magnetostrictive strain under intense magnetic fields. In addition, the SS constitutive relation for a general three-dimensional problem is discussed and an approach to characterize the modulus tensors is proposed.

Non-linear constitutive relations for magnetostrictive materials

This paper reviews recent developments in highly magnetostrictive terbium-dysprosium-iron alloys. This includes discussion of domain structure, the magnetization process, microstructure, sample preparation, magnetostriction, effects of different chemical compositions on magnetic properties of the alloys, and possible applications of these materials. It has been found over recent years that there has been a steady improvement in material properties, both in terms of increased strain amplitude and reduction in variability from sample to sample. The material is now finding applications in magnetostrictive transducers, actuators and adaptive vibration control systems.

http://iopscience.iop.org/article/10.1088/0022-3727/27/1/001/pdf

The development of highly magnetostrictive rare earth-iron alloys

We present a new approach to magnetostriction that is formulated to describe materials with large magnetostriction. The main idea of the theory is to derive precisely from lattice considerations the potential wells of the anisotropy energy. The theory exhibits frustration in the sense explored by the authors in the rigid case, with fine domains modelled by minimizing sequences. It is applied to the material Tbx Dy1-xFe2 and predicts accurately the domain structures observed by Lord in growth twinned crystals, and suggests a mechanism of magnetostriction involving a switch from a coarse domain structure to a different finer domain structure.

Theory of magnetostriction with applications to TbxDy1-xFe2

The present analysis provides Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) magnetization and magnetostriction states during applied magnetic field and stress processes by minimizing the total magnetic free energy in the presence of a parameter selected inverse exponential magnetic free energy distribution. A comparison between experimental and model results shows that the model provides a qualitatively accurate description of the magnetostriction and magnetization in Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) during applied magnetic field processes for a range of constant uniaxial applied stresses. Therefore, the model appears to be a useful tool for the analysis of Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) applications with constant stress or strain dependent stress states. Furthermore, the good qualitative agreement between model and experiment supports the contention that the magnetostriction and magnetization response of Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) is influenced by a defect induced defocusing of local magne...

Magnetization and magnetostriction processes in Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0)

One of the most frequent applications of magnetostrictive actuator technology is the active structural vibration control (AVC). Magnetostrictive actuators (MAs) can deliver high-output forces and can be driven at high frequencies. These characteristics make them suitable for a variety of vibration control applications. The use of this technology, however, requires an accurate knowledge of the dynamics of such actuators. Several models are available in the literature. However, their use in control applications, characterized by high dynamics, is often limited by nonlinearities and complexity of the model. To overcome this difficulty, the paper introduces a linear model of magnetostrictive actuators that is valid in a range of frequencies below 2 kHz. The assumptions supporting the linearity of the system are discussed and the theoretical model is presented. Finally the model is validated through experimental tests carried out on two different magnetostrictive actuators.

A model of magnetostrictive actuators for active vibration control

The magnetostrictive properties of single crystal Tb .27 Dy .73 Fe 2 was examined under compressive loads up to 48 MP a. Magnetostrictions > 1.8 × 10-3were observed for stresses greater than 20 MPa. Magnetization and magnetostriction were calculated for the magnetization rotation model, which was extended to include cubic anisotropy and compressive loading along the [111] axis. The effect of a distribution of magnetic moment directions is discussed.

Effect of stress on the magnetostriction and magnetization of single crystal Tb .27 Dy .73 Fe 2

The magnetostrictions and magnetizations of highly magnetostrictive rare earth-Fe 1.95 alloys have been measured under compressive stress up to 48 MPa. The shape of the magnetostriction and magnetization curves depend upon the relative concentrations of Tb, Dy, and Ho and the degree of crystallite orientation.

Effect of stress on the magnetostriction and magnetization of rare earth-Re 1.95 alloys

We have measured large scale strain as a function of field and external stress in two rare-earth iron alloys. From this data we calculate the external work and find it modified by various defects. The defects are characterized by a single parameter, T o . A large scale figure-of-merit is found that exceeds that of hydraulics or electric motors.

Strain-field relationships in rare-earth iron alloys

Melt-spun amorphous Fe-based ribbons containing B and Si, when heat treated near the Curie temperature, possess extremely high magnetomechanical coupling factors: 0.90 k = (1 + M 4 s /9E M λ 2 χM 2 ) −1 2 . EM denotes Young's modulus at constant magnetization. The large magnetomechanical coupling is reflected in a huge magnetic field dependence of elastic modulus (ΔE effect) as well as a large stress dependence of the permeability (Δμ effect). Refinements of the model, such as the inclusion of a residual stress, account for details in the shape of the magnetization curve and its dependence on stress [2].

M. Spano

Papers

Effect of stress on the magnetostriction and magnetization of single crystal Tb .27 Dy .73 Fe 2

Effect of stress on the magnetostriction and magnetization of rare earth-Re 1.95 alloys

Strain-field relationships in rare-earth iron alloys

Magnetomechanical properties of amorphous Fe-B-Si alloys