Indentation responses of piezoelectric films ideally bonded to an elastic substrate

The influences of elastic substrate on the indentation force, contact radius, electric potential and electric charge responses of piezoelectric film/substrate systems are investigated by the integral transform method. The film is assumed to be ideally bonded to the substrate and the contact interaction between the indenter and the film is assumed to be frictionless, with three kinds of axisymmetric insulating and conducting indenters (i.e., punch, cone and sphere) considered. Obtained results show that when the ratio of the contact radius to the film thickness is close to zero, the influences of the elastic substrate disappear and the indentation behaviors converge to the piezoelectric half space solutions while the indentation responses approach the corresponding ones of elastic half space as the ratio gets to infinity. The transition between the piezoelectric and the elastic half space indentation solutions for the film/substrate system is quantified in terms of the film thickness and the elasticity of the substrate. Finite element analysis on an insulating sphere indentation is conducted to verify the numerical calculations and good agreement is observed. The obtained results are believed to be useful for developing experimental techniques to extract the material properties of piezoelectric film/substrate systems.