Electrostatic measures for a piezoelectric thin film with an embedded crack in the substrate: I. Mode I

A quasi-three-dimensional model of a piezoelectric thin film is employed to detect a subsurface mode-I crack in a finite-sized substrate. The emphasis of this paper is on demonstration of the efficacy of the thin film model for sensing an embedded subsurface mode-I crack in the substrate uniquely. Numerical results reported here show the nature of the voltage distribution—peculiar to a mode-I crack—over the piezoelectric film. We have introduced a set of electrostatic measures to capture the influence of the strain concentration gradient due to a mode-I crack. Our analysis shows that the proposed electrostatic measures of the voltage and its gradients are useful in identifying the crack size and the crack location through correlating the relative coordinate of the subsurface cracks with respect to the center coordinate of the film. However, realistic crack identification analysis based on the present type of numerical results would require one to ensure that the background electrostatic field in the film, which is due to the global boundary constraints alone (except the film–substrate interface), is suitably decoupled from the crack front induced deformation of the substrate.