Fracture analysis of a functionally graded piezoelectric strip

In the present paper, the electroelastic behavior of a Griffith crack in a functionally graded piezoelectric strip is investigated. It is assumed that the elastic stiffness, piezoelectric constant and dielectric permittivity of the functionally graded piezoelectric strip vary continuously as an exponential function, and that the strip is under out of plane mechanical loading and in plane electrical loading. By using the Fourier transform and defining the jumps of displacement and electric potential components across the crack surface as unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties on the stress and electric displacement intensity factors.