Indentation of a piezoelectric FGM-coated half-space by a conical conductive punch: Approximated analytical solution

Abstract

Indentation of the coated piezoelectric transversely isotropic half-space by a conical conductive punch is modeled. The coating is assumed to be functionally-graded (continuously inhomogeneous in depth) with all group of electromechanical properties varying independently in depth according to arbitrary continuous functions or piecewise homogeneous. The problem is described mathematically in terms of linear electroelasticity and reduced to solution of a system of dual integral equations using the Hankel’s integral transformations. Closed-form approximated analytical solution of this system is obtained using the bilateral asymptotic method taking into account asymptotic properties of the kernel transforms. Expressions for the contact pressure, electric induction are obtained in an analytical form suitable for engineering analysis as well as the relations for the indentation force, total electric charge, indentation depth, contact radius and electric potential. Analytical form of results clearly demonstrates the contribution of mechanical and electric loading to the total solution and influence of the coating’s thickness and its properties on contact characteristics. Numerical results for homogeneous and two types of functionally-graded coatings illustrate features of the theoretical results in a wide range of values of relative coatings thickness.