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A critical examination of the relationship between plastic deformation zone size and Young's modulus to hardness ratio in indentation testing

Published online by Cambridge University Press:  03 March 2011

J. Chen  and
S.J. Bull
J. Chen
Affiliation:
Department of Chemical Engineering and Advanced Materials, University of Newcastle, Newcastle Upon Tyne NE1 7RU, United Kingdom
S.J. Bull*
Affiliation:
Department of Chemical Engineering and Advanced Materials, University of Newcastle, Newcastle Upon Tyne NE1 7RU, United Kingdom
*
a) Address all correspondence to this author. e-mail: s.j.bull@ncl.ac.uk
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Abstract

Existing indentation models (both analytical models and numerical analysis) show a linear relationship between δr/δm and H/Er, where δr and δm are the residual and maximum indentation depth, and Er and H are the reduced Young's modulus and hardness of the test material. Based on the analysis of Oliver and Pharr, a new relationship between δr/δm and H/Er has been derived in a different way without any additional assumptions, which is nonlinear, and this has been verified by finite element analysis for a range of bulk materials. Furthermore, this new relationship for residual depth is used to derive an analytical relationship for the radius of the plastic deformation zone Rp in terms of the residual depth, Young’s modulus, and hardness, which has also been verified by finite element simulations for elastic perfectly plastic materials with different work hardening behavior. The analytical model and finite element simulation confirms that the conventional relationship used to determine Rp developed by Lawn et al. overestimates the plastic deformation, especially for those materials with high E/H ratio. The model and finite element analysis demonstrate that Rp scales with δr, which is sensible given the self-similarity of the indentations at different scales, and that the ratio of Rp/δr is nearly constant for materials with different E/H, which contradicts the conventional view.

Keywords

Hardness

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Type
Articles
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Journal of Materials Research , Volume 21 , Issue 10 , October 2006 , pp. 2617 - 2627
Copyright
Copyright © Materials Research Society 2006

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