Applicability of Sneddon relationships to the real case of a rigid cone penetrating an infinite half space

The analytical solution for a "rigid" axisymmetric indenter penetrating an elastic half-space has been investigated as it pertains to the techniques used in the analysis of experimental nanoindentation data. It is observed that the analytical Sneddon solution and finite element simulations, with the same boundary conditions, deviate significantly from the physical interpretation of a rigid conical indenter. The severity of the deviations depends on both the half-included angle of the indenter and the Poisson ratio of the material being indented. The solution is found to underestimate the actual contact radii by up to 9% and 27% for rigid conical indenters with half-included angles of 70.32 degrees and 42.28 degrees, respectively. Approximate analytical corrections to the Sneddon relationships are presented for the case of a right circular cone of arbitrary included angle. Finite element simulations of a rigid indenter corroborate the deviations of the Sneddon solution, and provide support for the modified solutions.