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

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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A Memory Variable Approach to Modeling the Magneto-Mechanical Behavior of Magnetic Shape Memory Alloys

Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation and Control of Adaptive Systems; Integrated System Design and Implementation ◽

10.1115/smasis2013-3036 ◽

2013 ◽

Cited By ~ 2

Author(s):

Doug LaMaster ◽

Heidi Feigenbaum ◽

Isaac Nelson ◽

Constantin Ciocanel

Keyword(s):

Magnetic Field ◽

Shape Memory Alloys ◽

Shape Memory ◽

Mechanical Strain ◽

Magnetization Vector ◽

Unit Cell ◽

Magnetic Shape Memory ◽

Magnetic Shape Memory Alloys ◽

Short Side ◽

Recoverable Strain

Magnetic shape memory alloys (MSMAs) have attracted interest because of their considerable recoverable strain (up to 10%) and fast response time (1 kilohertz or higher). MSMAs are comprised of martensitic variants that have tetragonal unit cells and a magnetization vector that is innately aligned with the short side of the unit cell. These variants rotate 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 builds upon the work of Kiefer and Lagoudas [4,5] as well as improvements proposed by LaMaster et al. [1] to present a thermodynamic based model to predict the response of an MSMA to axial mechanical loading and transverse magnetic loading. This work is unique, however, in its use of a memory variable, which references the last stable configuration. This is similar to the approach used by Saint-Sulpice [2] in modeling SMA wires. The resulting model has zero driving force for reorientation of variants at the beginning of any load and again when the load is removed. Thus the model predicts what is seen physically, that the material is stable when no magneto-mechanical load is present. Furthermore, this model is more physical and less empirical than others in the literature, having only 2 material parameters associated with the stress-strain or stress-field response. 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 and predictions are compared with both the more established Keifer and Lagoudas model as well as experimental data. Results show decent correlation with experiments. The model can be further improved by calibrating the demagnetization factor to experimentally measured changes in magnetic field.

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A Constitutive Model for Magnetic Shape Memory Alloys That Includes a Tilted Magnetic Easy Axis

Volume 2: Mechanics and Behavior of Active Materials; Integrated System Design and Implementation; Bioinspired Smart Materials and Systems; Energy Harvesting ◽

10.1115/smasis2014-7660 ◽

2014 ◽

Author(s):

Jason L. Dikes ◽

Heidi P. Feigenbaum ◽

Constantin Ciocanel ◽

Isaac D. Nelson

Keyword(s):

Shape Memory Alloys ◽

Shape Memory ◽

Easy Axis ◽

Unit Cell ◽

Short Axis ◽

Magnetic Shape Memory ◽

Magnetic Shape Memory Alloys ◽

Short Side ◽

Power Harvesting ◽

Magnetic Easy Axis

Magnetic shape memory alloys (MSMAs) are materials commonly used for actuation, sensing, and/or power harvesting applications. While the actuation response of MSMAs can be fairly accurately predicted by currently available constitutive models, the power harvesting and/or sensing performance is not predicted as well. This suggests that current models lack features related to the change in magnetization. One such feature that is known to exist, but is not present in any current model, is the natural offset of the magnetic easy axis from the short axis of the tetragonal martensitic unit cell of MSMAs. Experimentally, Scheerbaum et al. [1] observed that this offset angle is in the range of 2° to 6°. While this is a relatively small angle, it is expected to make a dramatic difference in the evaluation of the power harvesting output, as it creates favorable domains even when the field is applied perpendicular to the short axis of the unit cell. Therefore, to facilitate the design of MSMA based sensing and power harvesting devices, a continuum model for the magneto-mechanical response of MSMAs, that accounts for the magnetic easy axis offset from the short side of the unit cell is derived from thermodynamic requirements and evaluated in this work.

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Model predictions of strain and magnetization responses under magneto-thermo-mechanical loading paths in magnetic shape memory alloys

10.1117/12.885035 ◽

2011 ◽

Author(s):

Krishnendu Haldar ◽

Dimitris C. Lagoudas

Keyword(s):

Shape Memory Alloys ◽

Shape Memory ◽

Mechanical Loading ◽

Magnetic Shape Memory ◽

Magnetic Shape Memory Alloys ◽

Loading Paths ◽

Model Predictions

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Constitutive Modeling of Magneto-Thermo-Mechanical Response of Field-Induced Phase Transformations in NiMnCoIn Magnetic Shape Memory Alloys

ASME 2010 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Volume 1 ◽

10.1115/smasis2010-3733 ◽

2010 ◽

Author(s):

Krishnendu Haldar ◽

Dimitris C. Lagoudas ◽

Burak Basaran ◽

Ibrahim Karaman

Keyword(s):

Shape Memory Alloys ◽

Shape Memory ◽

Constitutive Modeling ◽

Mechanical Response ◽

Temperature Phase ◽

Magnetic Shape Memory ◽

Magnetic Shape Memory Alloys ◽

Model Predictions ◽

Working Principle ◽

The Magnetic Field

In this work we model the magnetic field induced phase transformation (FIPT) of magnetic shape memory alloys (MS-MAs). The working principle of such materials is described by the cross coupling of mechanical, thermal and magnetic fields. The Thermo-magneto-mechanical constitutive equations are derived in a thermodynamic consistent way. A 3-D stress-field-temperature phase diagram is constructed using the model. The model is calibrated from the experimental data and the model predictions are compared with experimental results.

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