Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters

The elastic problem of the contact between an axisymmetric indenter and a general anisotropic (21 independent elastic constants) half space has not been solved explicitly in closed form. Implicit methods to determine the indentation modulus originate from the work of Willis [J. Mech. Phys. Solids 14 (1966) 163]; and are now available for conical, parabolic and spherical indenters [Philos. Mag. A 81 (2001) 447; J. Mech. Phys. Solids 51 (2003) 1701]. The particular case of orthotropy has also been investigated [ASME J. Tribol. 115 (1193) 650, 125 (2003) 223]. This paper proposes an explicit solution for the indentation moduli of a transversely isotropic medium and a general orthotropic medium under rigid conical indentation in the three principal material symmetry directions. The half-space Green's functions are interpolated from their exact extreme values, then integrated and finally simplified. The proposed closed form expressions are in very good agreement with the implicit solution schemes of [Philos. Mag. A 81 (2001) 447; J. Mech. Phys. Solids 51 (2003) 1701]. (C) 2004 Elsevier Ltd. All rights reserved.