Mathematical Analysis on the Uniqueness of Reverse Algorithm for Measuring Elastic-plastic Properties by Sharp Indentation

Abstract

The reverse analysis provides a convenient method to determine four elastic-plastic parameters through an indentation curve such as Young's modulus E, hardness H, yield strength σy and strain hardening exponent n. In this paper, mathematical analysis on a reverse algorithm from Dao model (Dao et al., Acta Mater., 2001, 49, 3899) was carried out, which thought that only when 20≤E*/σ0:033≤26and 0.3<n≤0.5, the reverse algorithm would yield two solutions of n by dimensionless function Π2. It is shown that, however, there are also two solutions of n when 20≤E*/σ0:033≤26 and 0≤n<0.1. A unique n can be obtained by dimensionless function Π3 instead of Π2 in these two ranges. E and H can be uniquely determined by a full indentation curve, and σy can be determined if n is unique. Furthermore, sensitivity analysis on obtaining n from dimensionless function Π3 or Π22 has been made.