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Research Papers

A Full Two-Dimensional Thermodynamic-Based Model for Magnetic Shape Memory Alloys

[+] Author and Article Information
Douglas H. LaMaster

Graduate Research Assistant
Student Member of ASME
Department of Mechanical Engineering,
Northern Arizona University,
Flagstaff, AZ 86011
e-mail: dl294@nau.edu

Heidi P. Feigenbaum

Assistant Professor
Member of ASME
Department of Mechanical Engineering,
Northern Arizona University,
Flagstaff, AZ 86011
e-mail: Heidi.Feigenbaum@nau.edu

Isaac D. Nelson

Graduate Research Assistant
Student Member of ASME
Department of Mechanical Engineering,
Northern Arizona University,
Flagstaff, AZ 86011
e-mail: idn2@nau.edu

Constantin Ciocanel

Associate Professor
Member of ASME
Department of Mechanical Engineering,
Northern Arizona University,
Flagstaff, AZ 86011
e-mail: Constantin.Ciocanel@nau.edu

1Corresponding author.

Manuscript received November 6, 2013; final manuscript received January 10, 2014; accepted manuscript posted January 15, 2014; published online February 3, 2014. Assoc. Editor: Daining Fang.

J. Appl. Mech 81(6), 061003 (Feb 03, 2014) (12 pages) Paper No: JAM-13-1457; doi: 10.1115/1.4026483 History: Received November 06, 2013; Revised January 10, 2014; Accepted January 15, 2014

Magnetic shape memory alloys (MSMAs) are interesting materials because they exhibit considerable recoverable strain (up to 10%) and fast response time (higher than 1 kHz). MSMAs are comprised of martensitic variants with tetragonal unit cells and a magnetization vector that is innately aligned approximately to the short side of the unit cell. These variants reorient either to align the magnetization vector with an applied magnetic field or to align the short side of the unit cell with an applied compressive stress. This reorientation leads to a mechanical strain and an overall change in the material's magnetization, allowing MSMAs to be used as actuators, sensors, and power harvesters. This paper presents a phenomenological thermodynamic-based model able to predict the response of an MSMA to any two-dimensional (2D) magneto-mechanical loading. The model presented here is more physical and less empirical than other models in the literature, requiring only three model parameters to be calibrated from experimental results. In addition, this model includes evolution rules for the magnetic domain volume fractions and the angle of rotation of the magnetization vectors based on thermodynamic requirements. The resulting model is calibrated using a single, relatively simple experiment. Model predictions are compared with experimental data from a wide variety of 2D magneto-mechanical load cases. Overall, model predictions correlate well with experimental results. Additionally, methods for calibrating demagnetization factors from empirical data are discussed, and results indicate that using calibrated demagnetization factors can improve model predictions compared with the same model using closed-form demagnetization factors.

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Figures

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Fig. 1

Assumed microstructure of variants and magnetic domains

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Fig. 2

Overall view of the experimental setup

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Fig. 3

Stress versus strain curve of an MSMA specimen under no applied field. Includes points used to calibrate model and subsequent model predictions.

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Fig. 4

Calibration of demagnetization factors using experimental data

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Fig. 5

Experimental and predicted results for constant stress and constant field loading cases using closed form and calibrated D22 with magnetic field applied transversely

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Fig. 6

Experimental and predicted results for constant stress and constant field loading cases using closed form and calibrated demagnetization factors with magnet rotated 4 deg from transverse direction

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Fig. 7

Experimental and predicted results for constant stress and constant field loading cases using closed form and calibrated demagnetization factors with magnet rotated 8 deg from transverse direction

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Fig. 8

Experimental and predicted results for complex loading with field and stress varied simultaneously using closed form and calibrated D22 with magnetic field applied transversely. Inset shows the loading.

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Fig. 9

Experimental and predicted results for complex loading with field and stress varied simultaneously using closed form and calibrated demagnetization factors with magnet rotated 4 deg from transverse direction. Inset shows the loading.

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Fig. 10

Experimental and predicted results for complex loading with field and stress varied simultaneously using closed form and calibrated demagnetization factors with magnet rotated 8 deg from transverse direction. Inset shows the loading.

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Fig. 11

Theoretical results for changing magnetization under constant stress and constant field cases with magnetic field applied transversely, (a) and (b), and magnetic field applied 8 deg from the transverse direction, (c) and (d). Uses both closed form and calibrated demagnetization factors.

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