Energy-based constitutive Model for Magnetostrictive Materials and its Application to Iron-Gallium Alloys
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Energy-based constitutive Model for Magnetostrictive Materials and its Application to Iron-Gallium Alloys Jayasimha Atulasimha and Alison B. Flatau, Department of Aerospace Engineering, University of Maryland, College Park, MD-20783, USA. ABSTRACT An energy-based constitutive model that can simulate the performance of magnetostrictive actuators and sensors along any of the crystallographic orientations was developed. This model was validated by comparing its predictions with experimental actuator characteristics (λ-H and B-H curves) along the and directions as well as sensor characteristics (B-σ curves) along the direction of single crystal FeGa samples with ~18-19 at. % Ga. These experimental characteristics were obtained using 1/4 inch diameter and 1 inch long, oriented single crystal rods grown using the Bridgman method by the DOE Ames Lab. INTRODUCTION Previous phenomenological 1-D models for actuators have employed both the Jiles-Atherton [1] and energy based methods [2, 3]. However, a comprehensive energy based approach that can model the 3-D actuator behavior over a wide range of compressive and tensile stresses as well as predict the 3-D sensing behavior of that material at various applied bias fields using model parameters estimated from the actuation behavior is lacking. Such a model will not only enable the prediction the behavior of single crystals along various crystallographic directions, but could also help better understand the behavior of textured polycrystalline samples. It is the objective of this work to both develop such a model and verify it with data obtained in house from experimental characterization of and oriented single-crystal FeGa samples using a magnetic transducer developed by Kellogg [4]. This 3-D model could, in the future, provide a basis for predicting the behavior of textured polycrystalline samples in terms of the behavior along individual crystallographic directions. A difficulty faced in applying this model to predicting sensing behavior is that the bias field through the sample varies on application of stress, despite maintaining a constant drive current, due to a magnetic coupling between the magnetic circuit and sample. Therefore, to improve the model prediction, the current model needs to be coupled with a simple lumped parameter model [5] of the magnetic circuit and sample. THEORY: MODEL FORMULATION The energy model is constructed to include the magneto crystalline, magneto elastic and magnetic field energy terms. Stray field energy can be accounted for by a demagnetization factor. For a given value of applied stress and magnetic field in any direction, the total corresponding to the magnetization vector being oriented along different directions is evaluated (Figure 1). The probability that a magnetic domain takes a particular orientation depends on the energy corresponding to that orientation, with orientations corresponding to lower energy being preferred. The magnetostriction and magnetization are calculated as the expected value
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