Characterization and modeling of the magnetic field-induced strain and work output in ${\mathrm{Ni}}_2\mathrm{MnGa}$ magnetic shape memory alloys

Abstract

This paper is concerned with the experimental characterization and the constitutive modeling of magnetic shape memory alloys (MSMA), in terms of their applicability as actuator materials. The key properties that determine the actuation characteristics are the magnetic field-induced strain (MFIS) and the blocking stress. With the goal of increasing the corresponding actuation output, a material selection strategy was followed which was aimed at obtaining a higher magnetocrystalline anisotropy energy, while keeping the detwinning stress low. This was achieved by choosing a composition in which the separation of the Curie temperature and the martensitic transformation temperatures was large, and then selecting an operating temperature just below the phase transformation temperature. In the selected ${\mathrm{Ni}}_{51.1}{\mathrm{Mn}}_{24.0}{\mathrm{Ga}}_{24.9}$ composition a more than 50% increase of the actuation work output was observed, compared to corresponding data reported in the literature for other off-stoichiometric compositions of the ${\mathrm{Ni}}_2\mathrm{MnGa}$ intermetallic compound. The second part of the paper describes a phenomenological constitutive model that predicts the MFIS hysteresis curves observed in the first part. The model is concerned with the field-induced reorientation of martensitic variants and changes in the magnetic microstructure. Dissipative effects are captured by introducing internal state variables into the free energy function. In its most general form the contributing energy terms are the elastic strain energy, the Zeeman energy, the magnetocrystalline anisotropy energy and appropriate mixing terms. Typical loading cases are considered and the accuracy of the model predictions is evaluated by comparison with the experimental data presented in the first part of this work.

Introduction

As a new class of active materials, magnetic shape memory alloys (MSMA) have recently drawn considerable research interest due to their ability to produce magnetic field-induced strains (MFIS) at least one order of magnitude higher than those of ordinary magnetostrictive or piezomagnetic materials [1], [2], [3]. MSMA have exhibited a greater actuation bandwidth than conventional shape memory alloys (SMA), since their actuation frequency is not limited by heat transfer [3], [4]. The MFIS response is nonlinear, stress-dependent and hysteretic in nature and it is coupled to a nonlinear change in the magnetization of the material. Therefore MSMA are not only interesting materials for actuator and sensor design [4], [5], [6], but also candidates for advanced magnetic material applications, for example, in solenoid transducers [7], or as voltage generators [8].

Although magnetic field-induced phase transformations are possible under certain conditions [9], [10], the MFIS in MSMA are most often a result of the reorientation of martensite variants under the influence of the magnetic field, and this is how it will be treated in this work. The volume fraction of those variants whose magnetic easy axes are favorably oriented with respect to the external magnetic field grows at the expense of less favorable ones. Additionally the magnetic field-driven alignment of the magnetization with the applied field is accommodated by the mechanisms of magnetic domain wall motion and rotation of the magnetization away from preferred directions.

The key properties of MSMA, when considered as actuator materials, are the actuation stress and the actuation strain, in this case the MFIS and the resulting actuation work output. The maximum actuation stress is denoted the blocking stress, the stress level above which the variant reorientation is completely suppressed. Among the known MSMA, NiMnGa alloys are the most widely explored due to their low detwinning stress, and sufficiently high magnetocrystalline anisotropy energy [11], [12], [13], [14], [15], [16], [17]. Maximum MFIS of 6% for five-layered tetragonal martensite and 10% for the seven-layered orthorhombic martensite have been reported [11], [14], [15], [18]. However, the maximum MFIS usually is observed at compressive stress levels below 2 MPa. One of the main research goals therefore is to produce MSMA in which large MFIS can be induced at high stress levels, for the purpose of maximizing the work output.

The main experiment in the characterization of the MSMA actuation properties in this work, is the measurement of MFIS as a function of the applied magnetic field under different stress levels. The composition of the material under study was selected to maximize the work output. This material selection strategy has led to the choice of a $\mathrm{NiMnGa}$ alloy with a composition of ${\mathrm{Ni}}_{51}{\mathrm{Mn}}_{24}{\mathrm{Ga}}_{25}$, in which a MFIS of 5.9%, with a blocking stress of 6 MPa, were obtained near $M_{\mathrm{s}}$, corresponding to an increase of the work output of more than 50%. The selection criteria are described in detail below. Analysis of the obtained MFIS data is used to explain the reason for an increase in the work output observed in the selected composition. The material response is also investigated with respect to the nature of the MFIS behavior beyond the first magnetic cycle. This aspect is motivated by the fact that most studies in the literature have focused only on the first cycle response of $\mathrm{NiMnGa}$ MSMA. Multiple cycle behavior, however, is important in the context of actuation. The mechanisms leading to the observed difference of the material response in the first and subsequent cycles are described.

In addition to the experimental work concerned with improving the actuation performance of MSMA, the other essential factor in the successful development of MSMA actuators is the constitutive modeling of the observed material response. It is demonstrated in the second part of this paper how the constitutive model, whose governing equations are presented in Section 3.1, is directly applied to predict the material response observed in the MFIS experiments conducted in this work.