A critical examination of the fundamental relations used in the analysis of nanoindentation data

Methods for analyzing nanoindentation load-displacement data to determine h ardness and elastic modulus are based on analytical solutions for the inden tation of an elastic half-space by rigid axisymmetric indenters. Careful ex amination of Sneddon's solution for indentation by a rigid cone reveals sev eral largely ignored features that have important implications for nanoinde ntation property measurement. Finite element and analytical results are pre sented that show corrections to Sneddon's equations are needed if accurate results are to be obtained. Without the corrections, the equations underest imate the load and contact stiffness in a manner that leads to errors in th e measured hardness and modulus, with the magnitudes of the errors dependin g on the angle of the indenter and Poisson's ratio of the half-space. First order corrections are derived, and general implications for the interpreta tion of nanoindentation data are discussed.