Analysis of axisymmetric indentation of functionally graded piezoelectric coating or substrate systems under an insulator indenter

Axisymmetric indentation problem of a rigid perfect electrical insulator indenter on a functionally graded piezoelectric coating bonded to a piezoelectric substrate is investigated. The electromechanical properties of the functionally graded piezoelectric coating are assumed to vary as an exponential function along the thickness direction. The technique of the Hankel integral transform is applied to reduce the indentation problem to a singular integral equation. The numerical methods are developed and applied to compute the contact pressure for a cylindrical indenter and a spherical indenter. The effects of the material property gradient on the contact pressure, contact region, indentation depth, and electrical potential are analyzed. The numerical results are also obtained for the indentation responses of three different piezoelectric substrates.