Journal of Materials Research


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

Jack C. Haya1, A. Bolshakova2 and G. M. Pharra3 c1

a1 IBM Research, T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598

a2 Baker Hughes Inteq, P.O. Box 670968, Houston, Texas 77267-0968

a3 Department of Materials Science and Engineering, The University of Tennessee, 434 Dougherty Engineering Building, Knoxville, Tennessee 37996-2200 and Oak Ridge National Laboratory, Metals and Ceramics Division, P.O. Box 2008, Oak Ridge, Tennessee 37831-6116


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.

(Received September 14 1998)

(Accepted March 08 1999)


c1 Address all correspondence to this author at the university of Tennessee.