Two-dimensional electromechanical analysis of piezoelectric ceramics

The linear piezoelectric theory is used to study two-dimensional electromechanical interaction in piezoelectric materials with the consideration of the effect of surrounding dielectric medium, such as air. Using integral transforms, general expression of stresses, displacements, electric potential and electric displacements for transversely isotropic piezoelectric materials of the hexagonal crystal class 6mm have been obtained for several specific problems. Two special problems are considered here. The first is the Griffith crack in an infinite piezoelectric material under uniform electric loading. By including electrostatic energy in the calculation of crack driving force, the energy release rate is found to be a third power function of the electric field intensity. The second one is the contact problem between a symmetric rigid electrode and a semi-infinite piezoelectric medium. A square root singularity of normal stress and charge density in the contact zone is found at the edges of the electrode for a plane electrode. Such a stress singularity at the edge of the electrode will eventually induce the initiation of a crack and introduce mechanical and electric instability.