引入界面耦合系数的长片型磁电层状复合材料的等效电路模型

摘要

针对长片型磁电层状复合材料,提出了一种适用于准静态和动态磁场激励的引入界面耦合系数的等效电路模型,旨在为基于长片型磁电层状复合材料的传感器、换能器等器件的设计、制作和应用提供理论指导.考虑到磁电层状复合材料实际工作过程中磁致伸缩层和压电层的应变并不相同,首先利用运动方程分别对磁致伸缩层和压电层进行建模,提出了一个从物理上反映相间应变传递的界面耦合系数表达式,然后利用一个变比恰为界面耦合系数的理想变压器将两层材料的等效电路耦合,构成改进的磁电层状复合材料的等效电路模型,得到包含界面耦合系数的磁电电压系数和最佳层合比的表达式.对12个具有不同尺寸和负载条件的样品进行实验,制作过程中承受500 g砝码负载的样品的界面耦合系数为0.15,最佳层合比为0.57;承受100 g砝码负载的样品的界面耦合系数为0.10,最佳层合比为0.50.磁电电压系数和最佳层合比的实验值与各自包含界面耦合系数的理论值基本符合,证明了改进的等效电路模型的合理性和正确性.%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 piezo-electric 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 magne-tostrictive 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 αv 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 αv 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 αv 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.