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

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.