Frictionless elastic contact analysis of a functionally graded vitreous enameled low carbon steel plate and a rigid spherical indenter

Frictionless elastic contact of a functionally graded vitreous enameled low carbon steel plate and a rigid spherical punch is studied in this paper. The graded modulus of elasticity of the plate is assumed to vary through the thickness and is found experimentally by means of nano-indentation technique and also estimated mathematically by a mathematical model originally proposed by Tamura, Tomota and Ozawa (TTO model). The contact problem of the plate and the rigid sphere is studied both analytically and numerically by means of ABAQUS finite element package. In the analytical approach, a higher order displacement field plate theory along with an exact Green’s function is used to find the contact parameters. The acquired results are then used to investigate the effect of material distribution, punch radius and plate span on the contact parameters. The results show that increasing the metal phase volume fraction of graded medium increases both the contact force and stress in the graded plate. In addition, in the vitreous enameled graded plates, if a polynomial function is fitted to the contact force–indentation relation, the power is equal to 2.0 regardless of the material distribution and plate geometry.