An Electrically Charged Crack in a Piezoelectric Material Under Remote Electromechanical Loading

The problem of electrically charged crack in a piezoelectric material under the action of remote electromechanical load is considered. The material is polarized in the direction orthogonal to the crack faces. Assuming that all fields are independent of the coordinate co-directed with the crack front and using the special presentations of electromechanical quantities via sectionally-analytic function, the problem is reduced to the vector Hilbert problem and solved exactly. All required electromechanical quantities are presented by means of simple formulas. The behavior of stresses, electric field and electric displacement jump are analyzed. It is shown that the electric charge can eliminate the field singularities at one of the two crack tips. The proposed solution, together with the presented table of parameters for some widely used piezoceramics materials, like PZT-4 and many others, can be easily used by the reader for an engineering calculation of the near-crack-tip electromechanical fields in these materials.