In this work, the magnetoelectric cantilever composed of a layer of Galfenol and a layer of PZT-5H is studied for
novel applications such as surgical ablation tools and cutting tools for machining applications. For developing a
suitable model for the magnetoelectric cantilever, an energy based approach for the non-linear constitutive behavior of
the magnetostrictive material and linear piezoelectric constitutive equations will be coupled with Euler Bernoulli
model for composite beams. The cantilever is held in a uniform magnetic field and the magnetic field is measured by a
Gaussmeter. The tip-deflection of the cantilever is detected by a laser triangulation sensor. The piezoelectric response
can be studied with low noise preamplifier. Four PZT-5H layers with different thickness are separately bonded on the
top of the same Galfenol layer and characterized to study the thickness ratio effects on the quasistatic actuation and
sensing behavior of the composite cantilever.
This work investigates the equivalence of thermodynamic potentials utilizing stress-induced anisotropy energy
and potentials using elastic, magnetoelastic, and mechanical work energies. The former is often used to model
changes in magnetization and strain due to magnetic field and stress in magnetostrictive materials. The enthalpy
of a ferromagnetic body with cubic symmetry is written with magnetization and strain as the internal
states and the equilibrium strains are calculated by minimizing the enthalpy. Evaluating the enthalpy using
the equilibrium strains, functions of the magnetization orientation, results in an enthalpy expression devoid
of strain. By inspecting this expression, the magnetoelastic, elastic, and mechanical work energies are identified to be equivalent to the stress-induced anisotropy plus magnetostriction-induced fourth order anisotropy.
It is shown that as long as the value of fourth order crystalline anisotropy constant <i>K</i><sub>1</sub> includes the value of
magnetostriction-induced fourth order anisotropy constant Δ<i>K</i><sub>1</sub>, energy formulations involving magnetoelastic,
elastic, and mechanical work energies are equivalent to those involving stress-induced anisotropy energy. Further,
since the stress-induced anisotropy is only given for a uniaxial applied stress, an expression is developed for a
general 3D stress.
This paper explores a unified energy-based approach to model the non-linear behavior of both
magnetostrictive and piezoelectric materials. While the energy-approach developed by Armstrong has been
shown to capture the magnetostrictive behavior of materials such as Terfenol-D<sup>1</sup> and Iron-Gallium<sup>2</sup> along
different crystallographic directions, extending this approach to piezoelectric materials presents a
considerable challenge. Some piezo-electric materials such as PMN-PT and BaTiO<sub>3</sub> may undergo phase
changes under applied electric fields and stress in addition to polarization switching. A modeling approach
is developed in this paper to capture these effects. Finally, it is shown that the constitutive behavior for the
piezo-electric/magnetostrictive layers, coupled by a simple blocked-force approach, is likely to model the
behavior of magneto-electric composites.
This paper attempts to model the actuation and sensing behavior of polycrystalline magnetostrictive samples by
treating them as composed of multiple grains of single-crystals, each with a different orientation to the loading axis.
The texture analysis of a typical cross-section of the sample will be used to estimate the fraction of grains that are
close to <100>, <110> and <111> orientation. A simple model based on the law of mixtures will be proposed to
represent the behavior of the polycrystal in terms of the behavior of <100>, <110> and <111> oriented single
crystals. However, the magnetomechanical behavior along each of the crystallographic directions will be simulated
using an energy based model as discussed in Ref. 5 and Ref. 9
Iron-Gallium alloys demonstrate moderate magnetostriction (~350 ppm) and saturation material induction (~1 T) under low magnetic fields (~400 Oe) as well as high tensile strength (~500 MPa) and limited dependence of magnetomechanical properties on temperatures between -20°C and 80°C, making them promising materials for sensing and actuation applications. However, the mechanical and magnetic properties of these materials vary significantly with the percentage of gallium, which motivates this study on the effect of stoichiometry on the behavior of Fe-Ga alloys. Major loop compressive tests (loading to 110 MPa and unloading, at magnetic fields ranging from 0 to 891 Oe) were performed on single crystal 19% Ga and 24% Ga samples with longitudinal axis in the  direction. The effect of % Ga on Young's modulus, saturation magnetization (M<sub>sat</sub>), ΔE-effect and d*<sub>33</sub> are discussed and explained. Furthermore, it was found that the magnetic field (H) through the sample changed with applied stress. A simple magnetic circuit analysis is developed in the latter part of the paper to model this effect. The ramification of both stoichiometry effects and variation in field on the design of Fe-Ga sensors is discussed.