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

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 sigma(y) 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*/sigma(0.033)<= 26 and 0.3 < n <= 0.5, the reverse algorithm would yield two solutions of V, by dimensionless function Pi(2). It is shown that, however, there are also two solutions of n when 20 <= E*/sigma(0.033)<= 26 and 0 <= n < 0.1. A unique n can be obtained by dimensionless function Pi(3) instead of Pi(2) in these two ranges. E and H can be uniquely determined by a full indentation curve, and sigma(y) can be determined if n is unique. Furthermore, sensitivity analysis on obtaining n from dimensionless function Pi(3) or Pi(2) has been made.