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

Abstract

A quasi-three-dimensional model of a piezoelectric thin film is employed to detect asubsurface mode-I crack in a finite-sized substrate. The emphasis of this paper is ondemonstration of the efficacy of the thin film model for sensing an embedded subsurfacemode-I crack in the substrate uniquely. Numerical results reported here show the nature ofthe voltage distribution—peculiar to a mode-I crack—over the piezoelectric film. We haveintroduced a set of electrostatic measures to capture the influence of the strainconcentration gradient due to a mode-I crack. Our analysis shows that the proposedelectrostatic measures of the voltage and its gradients are useful in identifying the cracksize and the crack location through correlating the relative coordinate of the subsurfacecracks with respect to the center coordinate of the film. However, realistic crackidentification analysis based on the present type of numerical results would requireone to ensure that the background electrostatic field in the film, which is due tothe global boundary constraints alone (except the film–substrate interface), issuitably decoupled from the crack front induced deformation of the substrate.