The fracture behavior of functionally graded piezoelectric materials with dielectric cracks

This article provides a comprehensive investigation on the fracture behavior of cracked functionally graded piezoelectric materials (FGPMs). To account for the effect of dielectric medium inside the crack upon the fracture behavior of FGPMs, a dielectric crack model is used in this work, in which the electric boundary condition along crack surfaces is deformation-dependent and is nonlinear. The analytical formulations are developed using Fourier transform technique and solving the nonlinear singular equations using Chebyshev polynomials. A solution technique is developed to determine the desired deformation mode of the crack. Numerical simulations are given to show the effects of material gradient and the dielectric medium filling the crack upon the fracture behavior of FGPMs. The results obtained from this dielectric crack model clearly demonstrate how the transition between electrically impermeable and permeable crack models occurs with the change of crack opening displacement in response to the applied electromechanical loads. It is also observed that a critical state for the applied electromechanical loading exists for FGPMs that determines whether the impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric crack model considering the effect of dielectric medium filling the crack