Indentation of a transversely loaded functionally graded rectangular plate by a rigid spherical indentor

Abstract

Functionally graded materials are multiphase composites mainly composed of a ceramic and a metal; thus, they merge the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. Many of the present and possible applications of functionally graded materials involve contact loading. Here, the contact problem of a functionally graded simply supported plate with finite dimensions by a rigid spherical punch is studied by an analytical–numerical method. The contact rule will be derived by solving the equations of equilibrium analytically in terms of the displacement field components and by taking advantage of a numerical method in finding the contact parameters. The stress–strain relation is assumed to be linear and is represented by a refined volume fraction based model originally proposed by Tamura–Tomota–Ozawa model. The results of the analytical–numerical approach are validated by using ABAQUS finite element package. The analytical–numerical results are used to investigate the effect of parameters such as material distribution, punch radius, plate span and thickness on the contact rule and stress distribution in the plate. The obtained results show that the influence of the material non-homogeneity on the contact rule and stress distribution is quite significant. In addition, the acquired results illustrate that increasing the indentor diameter and the thickness of the plate increase the contact force for equal amount of indentation.