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

Yongli Huang1), Xiaofang Liu1), Yichun Zhou1), Zengsheng Ma1) and Chunsheng Lu2) 1) Key Laboratory of Low Dimensional Materials and Application Technology of Ministry of Education, and Faculty of Materials, Optoelectronics and Physics, Xiangtan University, Xiangtan 411105, China 2) Department of Mechanical Engineering, Curtin University, Perth, WA 6845, Australia

摘 要：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≤ 26 and 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 Π2 has been made.

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