Constitutive and failure models for relaxor ferroelectric ceramics

A non-linear constitutive model for relaxor ferroelectrics developed by Hom and Shankar is examined and verified with electromechanical experiments. This model links polarization and strain to the electric field and stress in an electrostrictive material. A set of tests were performed to study the quasi-static electrical behavior of PMN-PT-BT materials under prestress. Another set of tests investigate the effect of DC electric field on the elastic modulus of the material. The results show excellent correlation between the predicted behavior of the model and the experiments. Failure models for electrostrictive ceramic materials are presented which address the issues of actuator reliability. The constitutive model of Hom and Shankar is incorporated into a nonlinear finite element code. A new finite element technique for computing the J-Integral for cracks in electromechanical materials is developed. This technique is based on the domain integral method and computes both the mechanical and electrical contributions to the energy release rate. The finite element code and the J-Integral computation are used to study crack growth in multilayered electrostrictive ceramic actuators.