Magnetostrictive materials belong to a class of smart materials that have been proposed for magneto-responsive materials. Terfenol-D (Te0.3Dy0.7Fe2) is a giant magnetostrictive material consisting of rare earth elements terbium, dysprosium and iron. The positive magnetostrictive response refers to the increase of the mechanical strain in the material as the magnitude of an external magnetic field is raised. A ‘giant’ magnetostrictive material, as opposed to just a magnetostrictive material, has a maximum strain usually in the hundreds part per million when saturated with a magnetic field. Terfenol-D was developed in the 1970s at the Naval Ordnance Laboratory which was used as a component in sonar transducers (Olabi and Grunwald 2008). This material is unique for its huge magnetostriction compared to other materials, such as Galfenol or nickel. This unique property has also led many proposals for its applications in actuation and energy harvesting (Ashley 1998; Goodfriend and Shoop 1992; Fenn et al. 1996). Magnetostriction can be attributed to the rotation of the magnetic moments for the alignment with the external magnetic field direction (Engdahl 2000). In Terfenol-D specifically, the large deformation results from the complementary magnetic anisotropies of terbium and dysprosium (Clark et al. 1984). The energy involved with magnetostriction is related to both the energy to deform the material and the magnetic field energy (Xe and Zheng 2005). A common issue in experiments with magnetostrictive material is the observation of large amount of scatterers. These can be attributed to the material quality, such as the number of defects. These alloys are capable of a large response in a wide range of operating temperatures (Clark 1992). Statistical analysis of the material properties can be accomplished with a coefficient of variation (CV) of approximately 5% (Dapino et al. 2006). Higher temperatures can affect the saturation strain or the maximum strain under magnetic field stimulation (Clark and Crowder 1985). These materials also display anisotropic magnetostriction properties depending on the direction of the load and prestress application. The origins and the stress dependence of the magnetostrictive effect have been discussed by Bulte and Langman (Bulte and Langman 2002). The presented hypothesis is based on an atomic level theory of the origins of the magnetomechanical behaviour whereby spin-spin and spin-orbit coupling interact with magnetic moments to alter the magnetocrystalline anisotropy and exchange energies. Terfenol-D particles have a C15 cubic Laves crystal structure (contributing to high brittleness and hardness). This intermetallic phase has a polymorphic structure, meaning that it can change into different crystalline structures maintaining the same chemical composition (Alexander and Myers 2014). An enhanced magnetostriction is observed with Terfenol-D with higher ratios of the rare earth element Tb/Dy ratio at the same volume fraction of RFe2 due to the increase of magnetocrystalline anisotropy, which is controlled by the Tb/Dy ratio within a crystal (Kwon et al. 2005). To quantify the quality of the magnetostrictive material, a technique is needed for the estimation of the spatial variability in responses. Such a technique can potentially help identifying the origin for variations and most importantly enable radical changes in manufacturing procedures, resulting in enhanced responses and the ability in engineering magnetostrictive properties.
Here, we report the study of the magnetostriction in Terfenol-D under periodic variations of the magnetic field with phase sensitive thermography (PST) (Breitenstein et al. 2010). In this method, a lock-in amplifier infers the magnetic state with the thermal images with a reference signal. This technique is particularly useful for isolating small temperature variations from the intense background noise. A load (or magnetic field) is applied at a preset frequency enough to induce adiabatic conditions. As the specimen is loaded, an infrared camera captures these load related thermal changes and correlates them with a reference signal provided by the load machine (Greene et al. 2008). The advantage of this technique is in filtering camera noises and ambient temperature fluctuations. As a result, the detection of small temperature in the mK range becomes feasible. This thermography technique has been previously used in various engineering mechanics measurements (e.g., stress gradients) or defect evaluations when the thermoelastic effect is present (i.e., infrared signals related to sum of principal stresses) (Wu et al. 1994; Meola et al. 2006; Elhajjar et al. 2014; Haj-Ali et al. 2008). Here, PST is investigated for evaluating the fabrication quality of magnetostrictive materials.
During the alignment of the magnetic moments, thermal energy is released in the form of heat. This release of heat is also known as the magnetocaloric effect (MCE). The internal energy of the material system is at a high energy state which is the result of the energy input into the material system during its formation (Gomez et al. 2013). The applied magnetic field direction is a low energy state. When the magnetic moments align towards the magnetic field, the moments go from a high energy state to a lower energy state. Under adiabatic conditions, this change in energy is compensated through the release of heat in the material (Tishin and Spichkin 2003). In adiabatic conditions, the change of temperature due to the change of the magnetic field (or magnetocaloric effect), ΔT can be defined as (Tishin and Spichkin 2014):
$$ \varDelta T={\displaystyle \underset{H_1}{\overset{H_2}{\int }}\frac{T}{C_H}{\left(\frac{\partial M}{\partial T}\right)}_H dH} $$
(1)
Where C
H
is the heat capacity under constant magnetic field, H is the magnetic field strength, and M is the magnetization. In the case of thermoelastic effect, under adiabatic conditions and applying Lamé elastic parameters which are assumed to be independent of temperature, we arrive at the classical theory of thermoelastic stress (Pitarresi and Patterson 2003), the change in temperature ΔT becomes:
$$ \varDelta T=-\frac{\alpha}{\rho {c}_p}{T}_o\varDelta \left({\sigma}_1+{\sigma}_2\right) $$
(2)
Where α is the coefficient of thermal expansion, ρ is the density, c
p
is the specific heat capacity at constant pressure, T
o
is the initial temperature, and σ
1 and σ
2 are the first and second principal stresses, respectively.