Abstract
This paper describes the modeling of magnetoelectric (ME) effects for disk-type Terfenol-D (Tb0.3Dy0.7Fe1.92)/PZT (Pb(Zr,Ti)O3) laminate composite at low frequency by combining the advantages of the static elastic model and the equivalent circuit model, aiming at providing a guidance for the design and fabrication of the sensors based on magnetoelectric laminate composite. Considering that the strains of the magnetostrictive and piezoelectric layers are not equal in actual operating due to the epoxy resin adhesive bonding condition, the magnetostrictive and piezoelectric layers were first modeled through the equation of motion separately, and then coupled together with a new interface coupling factor kc, which physically reflects the strain transfer between the phases. Furthermore, a theoretical expression containing kc for the transverse ME voltage coefficient αv and the optimum thickness ratio noptim to which the maximum ME voltage coefficient corresponds were derived from the modified equivalent circuit of ME laminate, where the interface coupling factor acted as an ideal transformer. To explore the influence of mechanical load on the interface coupling factor kc, two sets of weights, i.e., 100 g and 500 g, were placed on the top of the ME laminates with the same thickness ratio n in the sample fabrication. A total of 22 T-T mode disk-type ME laminate samples with different configurations were fabricated. The interface coupling factors determined from the measured αv and the DC bias magnetic field Hbias were 0.11 for 500 g pre-mechanical load and 0.08 for 100 g pre-mechanical load. Furthermore, the measured optimum thickness ratios were 0.61 for kc = 0.11 and 0.56 for kc = 0.08. Both the theoretical ME voltage coefficient αv and optimum thickness ratio noptim containing kc agreed well with the measured data, verifying the reasonability and correctness for the introduction of kc in the modified equivalent circuit model.
Highlights
The magnetoelectric (ME) effect is defined as a dielectric polarization of a material when a magnetic field is applied, or, a magnetization of a material when an electric field is applied [1,2,3]
31,m, which is a function of the DC bias for T-T mode is proportional to the piezomagnetic coefficient d31,m, which is a function of the DC bias magnetic field
The respective respective equivalent equivalent circuit circuit models models of of magnetostrictive and piezoelectric piezoelectric layers layers can can be be combined with an ideal transformer whose turn-ratio is just the interface coupling factor
Summary
The magnetoelectric (ME) effect is defined as a dielectric polarization of a material when a magnetic field is applied, or, a magnetization of a material when an electric field is applied [1,2,3]. They proposed a simple static elastic model, in which the magnetic and piezoelectric layers were assumed to be perfectly bonded and the strains in the both layers along the transverse directions were equal Compared to this simple model, Nan developed a rigorous Green’s function technique to solve the constitutive equations [14,15], which is universal to the ME composites with various connectivity, 2-2 type laminate composite. Bichurin et al proposed another generalized static elastic model [16,17] to calculate the effective ME coefficient at low frequency by introducing an interface coupling k, which represents the actual bonding condition between the magnetic and piezoelectric layers In their modeling, the laminate composite was considered as a homogeneous bilayer whose effective material parameters in the constitutive equations were estimated by an averaging method, which is similar to the Green’s function. This paper focuses on the modeling of disk-type ME laminate composite and aims to provide guidance for the design, fabrication and application of the ME laminate based devices, such as current sensor, magnetic sensor, energy harvester and wireless energy transfer system
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