The electro-mechanics of a coating/substrate system under charged spherical contact

A general theory of the piezo-electric contact mechanics for a transversely isotropic piezo-electric elasticity coated system (TIPECS) under charged spherical contact is presented. Three-dimensional exact solutions for the stresses, displacements, electric displacements and electric potential are derived. The contact radius versus the total load relation is obtained to guide the indentation experiments. The relations of coating thickness versus voltage and coating thickness versus voltage are studied. The optimal thickness can be determined with an optimization procedure. The interfacial delamination area of the TIPECS can be predicted with the interfacial failure criterion. The theoretical results are helpful for the prediction of some transient electrical effects, which can be combined with experiments to estimate some elastic constants, dielectric constants and piezo-electric constants in the indentation process.