Effects of electrical breakdown on a conducting crack or electrode in electrostrictive solids

Based on the strip dielectric breakdown (DB) model, the two-dimensional problem for a conductive crack in an infinite electrostrictive material is studied by means of the complex variable method. Explicit solutions are obtained for the electric fields and electroelastic fields, respectively. Then, the intensity factors of total stresses are presented in closed-form. Finally, all the solutions are extended to the case of a soft electrode in an infinite electrostrictive material. It is found that for a conducting crack, the applied electric field parallel to the crack retards its growth before DB, but it may enhance its growth once DB takes place ahead of the conductive crack. For the soft electrode, it can be seen that DB can produce the singularity of electric fields ahead the tip of electrode and induce the cracking of the electrostrictive material since the tensile stress has a traditional singularity of r−1/2 at the tip of the electrode.