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Relationships in instrumented indentation by Berkovich indenter

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Abstract

The relationships among the ratio of indentation hardness HIT over reduced elastic modulus Er, the ratio of elastic work We over total work Wt, and the ratio of permanent depth hp over the maximum indentation displacement hmax were investigated by instrumented indentation of 25 different materials under Berkovich indenter and various maximum indentation loads. Proportional relationships are found among various indentation variables (e.g. We vs. Wt, HIT vs. Er, and hp vs. hmax). Quadratic polynomial can be used to express the dependence of HIT/Er on We/Wt (or hp/hmax), based on which indentation hardness and reduced elastic modulus can be determined by work-based (or displacement-based) approach without requiring area function of the indenter. HIT and Er obtained by work-based and displacement-based approaches are consistent with those obtained by Oliver and Pharr’s method and those reported in literature.

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Data availability

The raw/processed data required to reproduce these findings are available from the corresponding author M.L. on request (mingliu@fzu.edu.cn or mingliuUK@gmail.com).

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Acknowledgments

This project is supported by National Key Research and Development Program of China on the International Scientific Innovation Cooperation among Governments (Grant No. 2019YFE0191800), National Natural Science Foundation of China (Grant No. 51705082), and Innovation Programs from Southwest Institute of Physics (Grant Nos. 202101XWCXRZ001 and 202102XWCXYD001).

Funding

Funding was provided by National Key Research and Development Program of China on the International Scientific Innovation Cooperation among Governments (Grant No. 2019YFE0191800), National Natural Science Foundation of China (Grant No. 51705082), and Innovation Programs from Southwest Institute of Physics (Grant Nos. 202101XWCXRZ001 and 202102XWCXYD001).

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Authors and Affiliations

  1. Fujian Provincial Key Laboratory of Terahertz Functional Devices and Intelligent Sensing, School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108, People’s Republic of China

    Ming Liu & Zhibo Cong

  2. Center for Fusion Science, Southwestern Institute of Physics, No. 5, Huangjing Road, Shuangliu County, Chengdu, 610225, People’s Republic of China

    Haiying Fu & Pengyuan Li

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  1. Ming Liu
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Correspondence to Ming Liu or Haiying Fu.

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Liu, M., Cong, Z., Fu, H. et al. Relationships in instrumented indentation by Berkovich indenter. Journal of Materials Research 37, 4084–4102 (2022). https://doi.org/10.1557/s43578-022-00769-x

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