Thermodynamics-based models for the magneto-mechanical response of magnetic shape memory alloys.

摘要

Magnetic shape memory alloys (MSMAs) are a relatively new class of smart material that exhibit large recoverable strain (up to 10%) [1] and fast response time (higher than 1 kilohertz) [2]. MSMAs are comprised of martensitic variants arranged as tetragonal unit cells with one short side, denoted by c, and two longer sides, denoted by a. With single crystal MSMAs, these variants align with one of the three Cartesian directions, and the volume fraction of variants with short side aligned in the i-direction is given by &xgr;i. The boundary between two variants, called the twin boundary, moves as one variant volume fraction grows at the expense of the other. Under an applied compressive stress in the i-direction, variants will reorient into the &xgr;i configuration to align the short side of the unit cell with the compressive stress. Each variant has an internal magnetization vector of length Msat that is approximately [3] aligned with the short length of the unit cell in the absence of an external applied magnetic field. This internal magnetization vector tends to align with an externally applied field to minimize the energy in the MSMA. The magnetization vector may align with the external field by: 1) changing internal magnetic domains, 2) rotating magneti- zation vectors away from the easy axis, or 3) variant reorientation . The fraction of the magnetic domains in the &xgr;i variant with easy-axis in the i-direction is denoted by &agr;i, and the domain fraction of the &xgr;i variants with easy axis in the direction opposite to the i-direction is given by (1 - &agr;i). Under an applied field in the i-direction, the &agr;i domain will grow at the expense of the (1 - &agr;i) domain, and vice versa for an applied field in the -i-direction. When the volume fraction &agr;i reaches either 1 or 0, this domain wall motion ceases and the domains are said to be saturated. After domains in &xgr;i have saturated, increasing the magnetic field further may rotate the magnetization vectors in other variants toward this i-direction. The energy required to rotate these magnetization vectors is called the anisotropy energy. Because MSMAs have unusually high anisotropy energy requirements [4, 5], it can become more energetically favorable to reorient variants into &xgr;i and align the magnetic easy axis with the applied magnetic field, rather than to rotate the magnetization vector in the i-direction, toward the hard axis. In this manner, an MSMA can experience the same response to magnetic field as it does to a compressive stress: variant reorientation. As variants reorient, the MSMA will compress in one direction and elongate in another direction, enabling their use as actuators. Additionally, magnetization vectors change direction as they align with the short length of the reorienting variant. As the internal magnetization changes, the MSMA can produce changes in the external magnetic field, which can induce a current within a surrounding coil. Utilizing this can lead to the design of either power harvesters or sensors. This work builds upon that of others, notably that of Kiefer and Lagoudas [6-9], to present several thermodynamic-based continuum models to predict the response of an MSMA to magneto-mechanical loading. The first model is 2D, and allows for any magneto-mechanical loading in two directions. The 2D model includes evolution rules for domain fractions, magnetization vector rotation, and variant reorientation. The next two models are 3D, and include evolution rules for domain wall motion and variant re- orientation. The first 3D model neglects magnetization vector rotation to present a simpler model that is less computationally intensive, while the second 3D model in- cludes all known mechanisms present in the microstructure to give a more generalized and complete model. These models are all more general than any other continuum, thermodynamics-based model in the literature. No other 2D continuum, thermodynamics-based model allows for general 2D magneto-mechanical loading. Furthermore, this 2D model is substantially less empirical than other, as it only includes three model parameters, where other models have five or more [6-10]. A simple method for calibrating these three parameters to easily-obtained experimental results is also presented. With fewer parameters and a more generalized formulation, this model can make reasonable predictions validated by experimental data. The 3D model is also unique, as no other continuum model exists for 3D loading which includes a third variant and magnetization rotation, and is fully derived from thermodynamics.