An analytical model for a bridged crack in piezoelectric ceramics

Abstract

A Griffith crack centrally bridged by a single grain in piezoelectric ceramics is modeled and investigated theoretically. Applying the Fourier transform method and the semi-permeable crack-face boundary conditions, various fracture parameters involving the stress intensity factors, the jumps of electrical potential and elastic displacement across the crack, and the energy release rate are given in closed forms. The total force and the electric potential acting on the bridging grain are obtained explicitly. Numerical results are calculated to show the effects of applied electrical fields and the permittivity of crack interior on the fracture parameters of concern. Under the assumption that the crack growth depends on the pull-out of the bridging grain, the obtained results reveal that applied positive electrical loadings enhance the crack growth and applied negative ones retard the crack growth. When one measures the crack length, applied positive electrical loadings will decrease the crack length and applied negative ones may increase the crack length. The above phenomena show that the crack-face bridging grains have contributions to various effects of applied electrical fields on the crack growth of piezoelectric solids.