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

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Open access
Authors
Huang, Y.
Liu, X.
Zhou, Y.
Ma, Z.
Lu, Chungsheng
Date
2011
Type
Journal Article

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Huang, Yongli and Liu, Xiaofang and Zhou, YiChun and Ma, Zengsheng and Lu, Chungsheng. 2011. Mathematical Analysis on the Uniqueness of Reverse Algorithm for Measuring Elastic-plastic Properties by Sharp Indentation. Journal of Materials Science and Technology. 27 (7): pp. 577-584.
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Journal of Materials Science and Technology
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Department of Mechanical Engineering
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NOTICE: This is the author’s version of a work that was accepted for publication in Journal of Materials Science and Technology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Materials Science and Technology, 27, 7, 2011

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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.