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

Abstract

This paper is a successor to the previous paper by Ali et al (2008 Smart Mater. Struct. 17 025037); it presents the analysis for sensing an embedded mode-II crack in a substrate. The displacement field kinematics for the film–substrate system is extended to the problem of applied surface shear stress. This extension requires modifying the model presented in the previous paper to include the differences due to changes in boundary and excitation conditions. The film response in terms of voltage pattern over the film area—peculiar to the presence of a mode-II crack in the substrate—is illustrated here through the results of numerical simulations. Our analysis shows that the proposed electrostatic measures of the voltage and its gradients are useful in identifying the axial and depth-wise location, as well as the crack-face area of a planar mode-II crack. There is a marked difference in the pattern of results presented in this paper with the results in part I of this work for a mode-I crack. This distinction is of utmost importance, for it singularly suffices to identify the mode of crack in a substrate for a given set of boundary conditions.