Influence of inclined electric fields on the effective fracture toughness of piezoelectric ceramics

Abstract

Electric fields effectuate the fracture behavior of ferroelectrics on different scales. On the atomic scale, forces in covalent bonds are influenced. On the mesoscopic scale, the ferroelectric domain wall motion shields the crack tip or leads to an additional loading. Based on classical approaches, on the macroscopic scale, the electric field has a major impact on the energy release rate and the electric displacement intensity factor; however, it scarcely influences the mechanical stress intensity factors. The situation is different if Maxwell stresses at crack faces, as a consequence of the jump of dielectric properties, are incorporated in the crack tip loading analysis. First, general considerations deal with the question how a fracture criterion has to be formulated, incorporating all three scales. On the macroscopic scale, the influence of an arbitrarily inclined electric field on the critical mechanical crack loading is investigated. The extended model, in particular, reveals the significance of electric fields parallel to the crack faces. A combined analytical–numerical approach is applied to solve the coupled two-domains problem of solid and crack dielectric, supporting the well-established capacitor approach even for inclined electric fields.