Constrained piezoelectric thin film for sensing of subsurface cracks

Abstract

A semi-analytical model for analysis of a constrained piezoelectric thin film as a subsurface crack sensor is developed. The model and the analytical study reported in this paper are applicable to linear elastic fracture involving a finite mode-I or mode-II crack within a structure having specified traction conditions at the surfaces. The approach is based on the concept of embedding the crack tip field in a finite elastic continuum by introducing additional perturbation functions. This takes into account the interaction between the crack tips and the surfaces. A piezoelectric thin film on the surface of the substrate or host structure is considered as the crack sensor. The voltage distribution over the span of the film is obtained by using an analytical model of a plane strain piezoelectric continuum across the film thickness. This model requires the interfacial displacement and traction conditions, which are calculated for various locations and sizes of mode-I and mode-II cracks in the host structure. The numerical simulations show that for a mode-I crack the film response can be used as a direct indicator of the span-wise location of the crack. The growth of a mode-II crack can be correlated to the arrival of the kinks in the voltage distribution, which is introduced by the oscillatory straining of the surfaces near the crack tips. The spatial gradient of the voltage is not influenced by the depth-wise location of the mode-II crack, although the magnitude of the voltage can be used as an indicator of the depth-wise location of the crack.