Due to magnetic field diffusion and structural dynamics, the relationship between magnetic field and strain in
Ni-Mn-Ga changes significantly as the frequency of applied field is increased. In order to describe this behavior,
which is critical for actuator applications, we present a strain model for Ni-Mn-Ga driven with dynamic magnetic
fields. The magnitude and phase of the magnetic field inside the sample are modeled as a 1-D magnetic diffusion
problem, from where an averaged or effective field is calculated. A continuum thermodynamics constitutive
model is used to quantify the hysteretic response of the martensite volume fraction due to this effective magnetic
field. The evolution of volume fractions with effective field is proposed to behave as a zero order system. To
quantify the dynamic strain output, the actuator is represented as a lumped-parameter 1-DOF resonator with
force input dictated by the twin-variant volume fraction. This results in a second order, linear ODE whose
periodic force input is expressed as a summation of Fourier series terms. The total dynamic strain output is
obtained by superposition of strain solutions due to each harmonic force input. The model accurately describes
experimental measurements at frequencies of up to 250 Hz.
A unified thermodynamic model is presented which describes the bulk magnetomechanical behavior of singlecrystal
ferromagnetic shape memory Ni-Mn-Ga. The model is based on the continuum thermodynamics approach,
where the constitutive equations are obtained by restricting the thermodynamic process through the
Clausius-Duhem inequality. The total thermodynamic potential consists of magnetic and mechanical energy
contributions. The magnetic energy consists of Zeeman, magnetostatic, and anisotropy energy contributions.
The microstructure of Ni-Mn-Ga is included in the continuum thermodynamic framework through the internal
state variables domain fraction, magnetization rotation angle, and variant volume fraction. The model quantifies
the following behaviors: (i) stress and magnetization dependence on strain (sensing effect), and (ii) strain and
magnetization dependence on field (actuation effect).
This paper is focused on the dynamic characterization of field-induced mechanical stiffness changes under varied
bias magnetic fields in commercial-quality, single-crystal ferromagnetic shape memory Ni-Mn-Ga. Prior to the
dynamic measurements, a specified variant configuration is created in a prismatic Ni-Mn-Ga sample through
the application and subsequent removal of collinear or transverse bias magnetic fields. Base excitation is used
to measure the acceleration transmissibility across the sample, from where the resonance frequency is directly
identified. These measurements are repeated for various collinear and transverse bias magnetic fields ranging
from 0 to 575 kA/m, which are applied by a solenoid and an electromagnet, respectively. A 1-DOF model for
the Ni-Mn-Ga sample is used to calculate the mechanical stiffness from resonance frequency measurements. A
resonance frequency increase of 21% and a stiffness increase of 52% are observed in the collinear field tests. In
the transverse field tests, a resonance frequency decrease of -36% is observed along with a stiffness decrease of
-61%. The damping exhibited by this material is low in all cases (≈ 0.03). The measured dynamic behaviors
make Ni-Mn-Ga well suited for vibration absorbers with electrically-tunable stiffness.
Due to their large magnetic field induced strains and fast response
potential, ferromagnetic shape memory alloys have mainly been
studied from the perspective of actuator applications. This paper
presents characterization measurements on a commercial Ni-Mn-Ga
alloy with a goal to investigate its feasibility as a deformation sensor. Experimental determination of flux density as a function of
quasistatic strain loading and unloading at various fixed magnetic
fields gives the bias field needed for maximum recoverable flux
density change. This bias field is shown to mark the transition from
irreversible (quasiplastic) to reversible (pseudoelastic)
stress-strain behavior. A reversible flux density change of 145 mT
is observed over a range of 5.8 % strain and 4.4 MPa stress at a
bias field of 368 kA/m. The alloy investigated therefore shows
potential as a high-compliance, high-displacement deformation
sensor.
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