On the effect of remanent polarization on electro-mechanical fields near an elliptic cavity in poled or depolarized piezoelectric ceramics

In this paper the effect of remanent polarization on electric-mechanical fields near an elliptic cavity in piezoelectric ceramics is studied. The analysis is based on the application of exact electric boundary conditions at the rim of the elliptic cavity, thus avoiding the common assumption of electric impermeability. Expressions for electromechanical fields near the elliptic cavity are derived in a closed form in terms of complex potentials. The result shows that the problem of remanent polarization is similar to the problem of general strain mismatch and the effect of remanent polarization on fracture in poled or depolarized piezoelectric ceramics can not be omitted. When the permitivity of the medium in a cavity is small, the effect of remanent polarization is identical to the effect of a considerable strong positive electric field and the tangent stress at the major axial apex of the elliptical cavity is tensile. Such behavior explains why the positive electric field promotes the crack growth while the negative electric field retards the crack growth and accounts for the anisotropy of fracture toughness under mechanical loads. The results show that the effect of remanent polarization on electromechanical fields near an elliptic cavity depends not only on the geometry of the elliptic cavity, i.e. the ratio of the minor semi-axis to major semi-axis, but also on the ratio of permitivity of the medium in the cavity to permitivity of the piezoelectric ceramic.