Research On The Magneto-mechanical-thermo-electric Coupling For The Tri-layer Symmetrical Magnetoelectric Laminates

The tri-layer symmetric magnetoelectric(ME) laminates made of giant magnetostrictive materials Terfenol-D and piezoelectric materials have become a hot topic in recent years for their strong direct magnetoelectric(DME) coupling effect in ME sensors, energy harvesters, and their strong converse magnetoelectric(CME) in electric write-magnetic read memory devices and other multi-functional devices. The DME would exhibit different nonlinear characteristics under different temperature and stress levels, but yet no comprehensive theoretical model can explain the phenomenon. The CME would also show different nonlinear characteristics under the action of bias magnetic fields. And the ratio of piezoelectric layers in laminates also could affect the nonlinear characteristics. However,no theoretical model can describe this nonlinearity at present.In response to these problems, we carried out the following tasks:Firstly, the equivalent circuit method was adopted to analyze the L-T mode Terfenol-D/PZT/Terfenol-D laminate. We chose the nonlinear magnetostrictive constitutive with variable coefficients and the linear piezoelectric constitutive to obtain the vibration equation for the laminates. The surface force and displacement speed were equivalent to the circuit voltage and current in the equivalent circuit for the laminated composites. According to the equivalent circuit, a model of the static DME field coefficient for the strong nonlinear thermo-magneto-mechanical coupling was obtained. Without considering the pre-stress, the comparisons of the static ME coefficient versus temperature curves for the experimental and theoretical results were in good agreement both qualitatively and quantitatively for low and moderate magnetic fields. The theoretical results were smaller than the experimental results under high magnetic fields. The comparisons proved the validity of the model presented in this chapter. On this basis, this model was adopted to predict variations in the ME coefficients in the laminates under different bias magnetic fields, temperatures,and stresses. This showed that: the laminated composites had the strongest DME effect at 0°C; a large compressive stress effectively suppressed the DME effectattenuation caused by high temperatures; an appropriate tensile stress improved the maximum DME coefficient and lowered its bias magnetic field near room temperature. These results provide a theoretical basis for the design and application of high-performance and miniaturized ME devices, operating under extreme temperature conditions.Secondly, an equivalent circuit was proposed for the converse magnetoelectric coupling in PMN-PT/Terfenol-D/PMN-PT which was wrapped by the ideal coil. This equivalent circuit model adopted the nonlinear magneto-thermo-mechanical magnetostrictive constitutive and the linear mechanical-thermo-electric piezoelectric constitutive, and was made in accordance with Newton’s second law and the current loop theorem. Then we based on this equivalent circuit and built a theoretical model of the CME coefficient. Without considering the pre-stress and temperature, the predicted CME coefficient versus temperature curves coincided well with the experimental results qualitatively and quantitatively, which verified the validity of the model. On this basis, this model was adopted to predict the influences of the volumes occupied by the piezoelectric layers, temperatures, pre-stress and bias magnetic fields on the CME coefficients. This found that: the existence of an optimal volume ratio made the CME coefficient achieve the maximum; the laminated composites had the strongest CME effect at 0°C; an appropriate tensile stress further improved the maximum CME coefficient and lowered its bias magnetic field corresponding to the maximum CME coefficient; in the high-temperature or variable temperature environment, applying a compressive stress would contribute to lower the CME effect attenuation caused by variable temperatures. The study in this chapter could provide a theoretical basis for the design and application of high-performance and miniaturized ME devices and for the further study of the CME in laminates.Finally, a theoretical model for the nonlinear thermo-magneto-electric coupling effect in Terfenol-D/PZT/Terfenol-D laminates was established from the perspective of continuum mechanics. This theoretical model adopted the nonlinear magneto-thermo-mechanical magnetostrictive constitutive and the linear mechanical-thermo-electric piezoelectric constitutive and introduced the interface coupling factor to describe the strain transfer efficiency between layers. Then the theoretical model which was nonlinear and calculated in an iterative approach was built. The predictions of ME coefficient versus temperature curves coincide well with experiments qualitatively and quantitatively, which verified the validity of the model.On this basis, this model then was adopted to predict the influences of the temperature,interface coupling factor and thermal expansion coefficient of the giant magnetostrictive materials on ME coupling. It showed that: the laminates had the strongest ME effect at 0 °C; increasing the coupling factor would contribute to obtaining a larger ME coupling in a smaller bias magnetic field and lowering the ME effect attenuation caused by temperature variations; a smaller thermal expansion coefficient was also conducive to obtaining a larger ME coupling in a smaller bias magnetic field and decreasing the ME effect attenuation caused by temperature variations. This model can provide a theoretical basis for the preparation and application of ME devices under different temperature conditions.