Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material

Analytical solutions for an elliptical cylinder cavity or a crack inside an infinite piezoelectric medium under combined mechanical-electrical loadings are formulated via the Stroh formalism and well confirmed by finite element analysis. The results show that the stress and electric fields in the vicinity of the crack tip are, in general, determined by a complex vector of intensity factors. The complex vector of intensity factors may reduce to be real under certain circumstances. For a vacuum crack, the electric field inside the crack in the direction perpendicular to the crack magnifies the corresponding applied electric field by more than 1000 times. In this case, the electric field strength in the material has a finite value at the crack tip, but the electric displacement approaches infinity at the crack tip due to the piezoelectricity. The self-consistent analysis is developed to determine the deformed crack profile. The energy release rate for the cavity propagation is formulated under the condition that the ratio of the minor semi-axis to the major semi-axis of the ellipse remains unchanged. For an insulating crack, the applied electric field contributes nothing to the energy release rate when the undeformed crack profile is used, while the electric field resists crack propagation when the deformed crack profile is used. For a conducting slit crack, the energy release rate is independent of the applied electric field perpendicular to the crack, and is enhanced by the applied electric field parallel to the crack.