Micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in piezoelectric solids

A dislocation emission mechanism for micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in a piezoelectric solid is proposed in the present paper. For a rigid line inhomogeneity embedded in a piezoelectric matrix, dislocations of one sign are driven away from the tip due to high stress level, while the stationary dislocations of the opposite sign are left behind near the tip of the inhomogeneity. As a result, a micro-Zener-Stroh crack is initiated ahead of the line inhomogeneity. In the current study, a dislocation pileup mechanism for micro-crack initiation at the inhomogeneity tip is proposed. An interesting result is that the critical stress intensity factors for a line inhomogeneity perpendicular to the poling direction can be related to the fracture toughness of a conventional crack in the same material. Analytical solutions show that the critical plane shear stress intensity factor depends on the plane shear mechanical and displacement loadings, and the critical opening stress and electric displacement intensity factors depend on not only the mechanical and displacement loadings, but the electric field and displacement loadings as well.