Magnetic Field Within a Magnetic Shape Memory Alloy and an Equivalent Uniform Applied Magnetic Field for Model Input

2017 ◽  
Author(s):  
J. Lance Eberle ◽  
Heidi P. Feigenbaum ◽  
Constantin Ciocanel
Keyword(s):  
Magnetic Field ◽  
Shape Memory ◽  
Applied Field ◽  
Volume Fraction ◽  
Unit Cell ◽  
Uniform Field ◽  
Magnetic Shape Memory ◽  
Twin Boundaries ◽  
Short Side ◽  
3 Dimensional

Magnetic shape memory alloys (MSMAs) exhibit recoverable strains of up to 10% due to reorientation of their martensitic tetragonal unit cell. A stress or magnetic field applied to the material will cause the short side of the unit cell (which is approximately aligned with the magnetic easy axis) to align with the input to the material, resulting in an apparent plastic strain. This strain can be fully recovered by an applied stress or magnetic field in a perpendicular direction. When the martensitic variants reorient, twin boundaries, which separate the different variants, form and move throughout the specimen. A number of models have been proposed for MSMAs and many of these models are homogenized, i.e. the models do not account for twin boundaries, but rather account for the volume fraction of material in each variant. These types of models often assume that the MSMA is subject to a uniform field so that there is no appreciable difference in the volume fraction of variants in each location. In this work, we address the issue of how these models can be used when the field is not uniform. In particular, we look at the experiments from Feigenbaum et al., in which a MSMA trained to accommodate three variants, was subject to 3-dimensional magneto-mechanical loading. Due to experimental constraints, the field applied to the MSMA was not uniform. In this work, to understand the actual field distribution during experiments, we performed a high-resolution 3-dimensional finite element analysis (FEA) of the magnetic field experienced by the MSMA sample. The FEA allowed us to determine how non-uniform the experimentally applied field was and the differences between the applied field and the field experienced by the MSMA. Furthermore, we use the FEA to determine the average field experienced by the MSMA, and identify an equivalent uniform applied field that could serve as input for the model. For the latter, we seek a uniform magnetic field which gives similar magnetic field within the MSMA specimen as the true experimental conditions.

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

2013 ◽  
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.

Magnetic Shape Memory Effect in Ni-Mn-Ga Single Crystal

2016 ◽  
Vol 879 ◽  
pp. 738-743
Author(s):  
Oleg Heczko ◽  
Vít Kopecký ◽  
Jan Drahokoupil ◽  
Marek Vronka ◽  
Oleksiy Perevertov ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
High Mobility ◽  
Type I ◽  
X Ray Diffraction ◽  
Magnetic Shape Memory ◽  
Twin Boundaries ◽  
Induced Structure

Magnetic shape memory effect is general name for several effects in which the most visible feature is huge strain induced by magnetic field. Magnetic field-induced structure reorientation (MIR) occurs due to motion of twin boundaries in single phase. As the magnetic field is a relatively weak force compared with mechanical stress, very high mobility of twin boundaries is crucial. Here we study the properties of martensite relevant for this effect using X-ray diffraction, optical and electron microscopy, magnetic observation and mechanical testing. In 10M modulated martensite, two types of mobile twin boundary (type I and type II) are observed with complex layered microstructures consisting of a hierarchy of twinning systems. We search for analogue with non-magnetic Cu-Ni-Al shape memory alloy.

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

2014 ◽  
Vol 81 (6) ◽  
Author(s):  
Douglas H. LaMaster ◽  
Heidi P. Feigenbaum ◽  
Isaac D. Nelson ◽  
Constantin Ciocanel
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Magnetization Vector ◽  
Unit Cell ◽  
Experimental Results ◽  
Two Dimensional ◽  
Magnetic Shape Memory ◽  
Magnetic Shape Memory Alloys ◽  
Short Side ◽  
Model Predictions

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.

Microstructure of Magnetic Shape-Memory Alloys: Between Magnetoelasticity and Magnetoplasticity

2008 ◽  
Vol 583 ◽  
pp. 43-65 ◽  
Author(s):  
Peter Müllner ◽  
G. Kostorz
Keyword(s):  
Magnetic Field ◽  
Martensitic Transformation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Mutual Orientation ◽  
Magnetic Shape Memory ◽  
Magnetic Shape Memory Alloys ◽  
Twin Boundaries ◽  
Starting Point ◽  
Effectiveness Of Training

Magnetic shape-memory alloys owe their exceptional properties primarily to the accompanying effects of a martensitic phase transformation. The twinning disconnection as elementary carrier of magnetic-field-induced deformation is the starting point of the present study. A disconnection is a line defect similar to a dislocation but located at an interface and exhibiting a step character besides a dislocation character. The mutual interaction of disconnections is fully tractable by the theory of dislocations. Due to the martensitic transformation, a hierarchical twin microstructure evolves, details of which are controlled through disconnection-disconnection interaction. Depending on the mutual orientation of twin boundaries on different hierarchical levels, twinning disconnections are incorporated in higher hierarchical twin boundaries forming disclination walls, or they stand off individually from those interfaces. Disconnections which stand off from interfaces contribute to magnetoelasticity, i.e. recoverable magnetic-field-induced deformation. Disconnections in disclination walls contribute to magnetoplasticity, i.e. permanent magnetic-field-induced deformation, if the twin thickness is large. In self-accommodated martensite with very thin twins, resulting from a martensitic transformation without training, the deformation is fully magnetoelastic and small. In single-domain crystals, resulting from effective thermo-magnetomechanical training, the deformation is fully magnetoplastic and large. Between these limiting cases, there is a continuous spectrum where, as a rule, the fraction of magnetoplastic strain and the total strain increase with increasing effectiveness of training.

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

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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