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

Abstract

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.

Modelling Shape-Memory Effects in Ferromagnetic Alloys

“…[13,14,22,[38][39][40][41][42]). Most of them include explicitly dissipation terms occurring in twin reorientation to account for hysteresis in strainmagnetic field loops and deal with magnetostatic effects by means of approximate calculations of demagnetizing factors.…”

“…The model allows to take into account the effect of multi-axial stresses and rotating magnetic fields. The model reported by LaMaster et al [42] is formulated with only three adjustable parameters, and allows for 2-dimensional magnetic and stress fields.…”

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape-memory alloy sample—III: Magneto-mechanical behaviors

“…The response of MSMA specimens under more general magneto-mechanical loading conditions [13,15] will be studied in our future works.…”

“…In the experiments, the magneto-mechanical response of MSMA specimens has been investigated systematically [3][4][5][6][7][8][9][10][11][12][13][14][15]. Two typical loading patterns are usually adopted in the experiments.…”

“…Besides these two typical loading patterns, the response of MSMA specimens subject to some other kinds of magnetic and mechanical loading conditions has also been investigated. For example, Chen et al [13,14] studied the twin boundary motion in NiMnGa single crystals under biaxial compressions, and LaMaster et al [15] measured the response of a NiMnGa specimen subject to the magnetic fields with different orientations. In Chmielus et al [12], the influence of end constraints on the magneto-mechanical properties of MSMA samples was studied.…”