Equivalent Circuit Model of Low-Frequency Magnetoelectric Effect in Disk-Type Terfenol-D/PZT Laminate Composites Considering a New Interface Coupling Factor

Abstract

This paper describes the modeling of magnetoelectric (ME) effects for disk-type Terfenol-D (Tb_0.3Dy_0.7Fe_1.92)/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 k_c, which physically reflects the strain transfer between the phases. Furthermore, a theoretical expression containing k_c for the transverse ME voltage coefficient α_v and the optimum thickness ratio n_optim 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 k_c, 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 α_v and the DC bias magnetic field H_bias 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 k_c = 0.11 and 0.56 for k_c = 0.08. Both the theoretical ME voltage coefficient α_v and optimum thickness ratio n_optim containing k_c agreed well with the measured data, verifying the reasonability and correctness for the introduction of k_c in the modified equivalent circuit model.