Equivalent circuit model for plate-type magnetoelectric laminate composite considering an interface coupling factor

Abstract

We describe the modeling of magnetoelectric (ME) effect in the plate-type Terfenol-D/PZT laminate composite by introducing a newly proposed interface coupling factor into the equivalent circuit model, aiming at providing a guidance for designing, fabricating and using the ME laminate composite based devices, such as current sensor, magnetic sensor, energy harvester, and wireless energy transfer system. Considering that the strains of the magnetostrictive and piezoelectric layers are not equal in actual operation due to the epoxy resin adhesive bonding condition, the equivalent circuit models of magnetostrictive and piezoelectric layers are created based on the constitutive equation and the equation of motion, respectively. An interface coupling factor kc is introduced which physically reflects the strain transfer condition between the magnetostrictive and piezoelectric phases. Specifically, the respective equivalent circuit models of magnetostrictive and piezoelectric layers are combined with an ideal transformer whose turn-ratio is just the interface coupling factor. Furthermore, the theoretical expressions containing kc for the longitudinal ME voltage coefficient v and the optimum thickness ratio noptim to which the maximum ME voltage coefficient corresponds are derived from the modified equivalent circuit model of ME laminate, where the interface coupling factor acts 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, are placed on the top of the ME laminates, each with the same thickness ratio n in the sample fabrication for comparison. A total of 12 L-T mode plate-type ME laminate samples with different-thickness configurations are fabricated. The interface coupling factors determined from the measured v and the DC bias magnetic field Hbias are 0.15 for 500 g pre-mechanical load and 0.10 for 100 g pre-mechanical load, respectively. Furthermore, the measured optimum thickness ratios are 0.57 for kc=0.15 and 0.50 for kc=0.10, respectively. Both the measured ME voltage coefficient v and optimum thickness ratio containing kc agree well with the corresponding theoretical predictions. The relationship between the optimum thickness ratios under two different mechanical loads remains unchanged, i.e., the measured optimum thickness ratio for kc=0.15 is larger than for kc=0.10. The experimental results verify the reasonability and correctness of the introduction of kc in the modified equivalent circuit model. The possible reasons for different interface coupling factors under different loads are also qualitatively discussed in this paper.