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

Methods for analyzing nanoindentation load-displacement data to determine hardness and elastic modulus are based on analytical solutions for the indentation of an elastic half-space by rigid axisymmetric indenters. Careful examination of Sneddon's solution for indentation by a rigid cone reveals several largely ignored features that have important implications for nanoindentation property measurement. Finite element and analytical results are presented that show corrections to Sneddon's equations are needed if accurate results are to be obtained. Without the corrections, the equations underestimate the load and contact stiffness in a manner that leads to errors in the measured hardness and modulus, with the magnitudes of the errors depending on the angle of the indenter and Poisson's ratio of the half-space. First order corrections are derived, and general implications for the interpretation of nanoindentation data are discussed.