Modelling of the poling process in functionally graded materials

Materials, containing an one- or multidimensional gradient of structural or chemical properties, connected with a changing of the material properties, are called functionally graded materials (FGM). They have a high potential in a wide range of applications, for instance to improve the interface between two different materials. Moreover, new functions of materials can be created by them. Piezoelectric FGM can be used in actuator or ultrasonic applications. It is known that FGM ultrasonic transducers show a broader frequency bandwidth. There are different ways and technologies to prepare ceramics with a functional gradient. One possibility is the preparation of ceramics with a gradient of the chemical composition along the thickness direction. The chemical gradient will be transformed into a gradient of the electromechanical properties by a poling process. Usually, there is a very inhomogeneous distribution of the poling field inside the graded material due to a corresponding gradient of the dielectric coefficient. Or et al. have shown that the electric field distribution is not constant in time and depends on the electric conductivity of the used materials. Their model describes the poling process of two layer system using a modified tanh function for the ferroelectric hysteresis loop. We enhanced this model by implementation of the Preisach model, an established approach of hysteresis effects in ferromagnetics and ferroelectrics. This allows the modelling of the electric field distribution and the polarization of each layer at arbitrary applied voltages for different poling regimes as well as the time-dependent modelling of switching processes. The numerical model can be used for multilayer structures of two or more materials and is therefore a good approximation of functionally graded materials. We compare the modelling with experimental results of the measurement of the electric field distribution in multilayers based on BaTi_1-xO₃-BaSn_xO₃ ceramics, where the Sn content changes from 7.5 to 15 mol%. Additionally, the electromechanical properties were characterized by bending measurements. The results were compared with FGM ceramics with the same chemical composition.