Microcrack initiation at the tip of a finite rigid conducting line in piezoelectric media

Abstract

In this paper is proposed a dislocation emission mechanism for microcrack initiation at the tip of a finite rigid conducting line in a piezoelectric solid. When a finite rigid conducting line is embedded in a piezoelectric matrix, because of the highly concentrated stress and electric displacement fields at its tips, dislocations of one sign are driven away from the tip, while the stationary dislocations of the opposite sign are left behind. As a result, a micro Zener-Stroh crack is initiated at each tip for the in-plane case, and two microcracks at each tip for the antiplane case. We obtain analytical solutions of both in-plane and anti-plane extension forces for microcracks initiated at the tip of a finite rigid conducting line. By obtaining the stress and electric displacement fields at the tip under nonzero net Burgers vectors, we observe two critical crack lengths. We find that the inplane and anti-plane critical extension forces for a finite rigid conducting line are related to those for a conventional crack in the same piezoelectric materials.