Nonlinear Simulation of Piezoceramic Materials Using Micromechanical Approach

Abstract

Nowadays piezoelectric and ferroelectric materials are becoming very important materials in scientific and engineering applications. Precision machining in manufacturing area, micropositioning in metrology, common rail systems with piezo fuel injection control in automobile industry, and ferroelectric random access memories (FRAM) in microelectromechanical systems (MEMS) besides commercial piezo actuators and sensors can be very good examples for the application of piezoceramic and ferroelectric materials. According to their substitutional elements, piezoceramic materials can be divided into two categories which are called soft and hard piezoceramics. The material constants to describe the behavior are the basic differences between hard and soft piezoceramics. The substitutional elements of piezoceramic materials also affect the phase types of the material. Piezoceramic material generally exists as tetragonal or rhombohedral phase in nature. BaTiO3, PZT and PLZT are very well known piezoelectric materials which have a perovskite type tetragonal microstructure. In spite of having good characteristics, piezoelectric and ferroelectric materials have significant nonlinearities which make them limiting in high performance usage. Domain switching (ferroelastic or ferroelectric) is the main reason for the nonlinearity of ferroelectric materials. External excessive electromechanical loads (mechanical stress and electric field) are driving forces for domain switching. In this study the nonlinear behavior of tetragonal perovskite type piezoceramic materials is simulated theoretically using a micromechanical model. In our simulations we consider a bulk piezoceramic material that has 1000 grains. Each grain has random orientation in properties of polarization and strain. Randomness is given by Euler angles equally distributed between 0 and 360°. External cyclic electrical loading is applied uniaxially and gradually starting from zero. The calculations are performed at each grain based on linear constitutive equations, nonlinear domain switching and a probability for domain switching. In order to fit the simulations to the experimental data, some parameters such as spontaneous polarization, spontaneous strain, piezoelectric and dielectric constants are chosen from literature. The domain switching of each grain is determined by an electromechanical energy criteria. Depending on the actual energy related to a critical energy a certain probability is introduced for switching the polarization direction. It is assumed that intergranular effects between grains can be modeled by such probability functions. Regarding the microstructure of a perovskite type tetragonal element, there are two possible types (90° and 180° domain switching) and six possible orientations for the polarization direction. Various energy levels are applied for 90° and 180° domain switching during the simulations. The response of the material to the applied loading is calculated by using transformations and averaging the individual grains. Properties of piezoelectric materials under fixed mechanical stresses are also investigated by applying constant compressive stress in addition to cyclic electrical loading in the simulations. In computer simulations, the effect of different domain switchings (90° or 180° domain switching for