Input error sensitivity of hardness and elastic modulus evaluated from indentation load-displacement records by Oliver and Pharr method

Abstract

Due to its straightforwardness and the ease of implementation the Oliver-Pharr method [1] has been used in the analysis of load-displacement records for more than a decade now. This paper provides analytical expressions relating the errors in the hardness and elastic modulus obtained by this method to systematic calibration errors of measured depth, force and frame compliance for spherical and sharp indentation. While in systems with zero frame compliance the sensitivity ratios for depth and force measurement were found to be constant, in systems with a finite frame compliance the error sensitivity changes with the absolute values of applied force and measured depth. The analytical predictions are compared with the true variation in derived materials parameters and the ranges of validity of the expressions are established. The error sensitivity with respect to different input variables and its implications for the actual measurement are discussed.