Constrained piezoelectric thin film for sensing of subsurface cracks

Abstract

A semi-analytical model for analysis of a constrained piezoelectric thin film as a subsurfacecrack sensor is developed. The model and the analytical study reported in thispaper are applicable to linear elastic fracture involving a finite mode-I or mode-IIcrack within a structure having specified traction conditions at the surfaces. Theapproach is based on the concept of embedding the crack tip field in a finiteelastic continuum by introducing additional perturbation functions. This takes intoaccount the interaction between the crack tips and the surfaces. A piezoelectricthin film on the surface of the substrate or host structure is considered as thecrack sensor. The voltage distribution over the span of the film is obtained byusing an analytical model of a plane strain piezoelectric continuum across the filmthickness. This model requires the interfacial displacement and traction conditions,which are calculated for various locations and sizes of mode-I and mode-II cracksin the host structure. The numerical simulations show that for a mode-I crackthe film response can be used as a direct indicator of the span-wise location ofthe crack. The growth of a mode-II crack can be correlated to the arrival of thekinks in the voltage distribution, which is introduced by the oscillatory strainingof the surfaces near the crack tips. The spatial gradient of the voltage is notinfluenced by the depth-wise location of the mode-II crack, although the magnitude ofthe voltage can be used as an indicator of the depth-wise location of the crack.