The electric breakdown problem in piezoelectric material containing a semi-permeable crack

This paper studies the electric breakdown problem of a semi-permeable crack in piezoelectric material under combined mechanical and electric loads. According to Stroh formalism, the differences of the electric potential and the displacement of the crack are first derived and the quadratic equation containing the electric displacement inside the crack is obtained. Meanwhile, the electric field is also acquired based on the electric displacement and field relation. Then, the critical electric breakdown condition inside the crack is discussed as the breakdown criterion. Finally, the electric field distribution and the criterion curves for electric breakdown are numerically shown in the condition of different dielectric constants under remote mechanical and electric loadings. It is found that the applied mechanical stress, electric field and dielectric ratio have influence on the occurrence of electric breakdown inside the crack.