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Nanoindentation and Indentation Size Effects: Continuum Model and Atomistic Simulation

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Handbook of Mechanics of Materials

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Abstract

Nanoindentation is one of the most widely used methods to measure the mechanical properties of materials at the nanoscale. For spherical indenters, when radius decreases, the hardness increases. The phenomenon is known as the indentation size effect (ISE). Nix and Gao developed a continuum model to explain the ISE in microindentation. However, the model overestimates the hardness at the nanoscale. The objective of this study is to develop proper methods to probe key quantities such as hardness and geometric necessary dislocation (GND) density from the quasi-static version of molecular dynamics (MD) simulations and to develop a mechanism-based model to elucidate the ISE phenomenon at the nanoscale. A reliable method is presented to extract the GND directly from dislocation length and the volume of plastic zone in the MD simulations. We conclude that the hardness determined directly from MD simulations matches well with the hardness determined from the Oliver–Pharr method. The ISE can be observed directly from the MD simulations without any free parameters. The model by Swadener et al. rooted from the Nix and Gao model underestimates the GND density at the nanoscale. However, this model can accurately predict the hardness size effects in nanoindentation if it uses the GND density directly calculated from the MD simulations.

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Acknowledgments

This research was supported by the Ministry of Science and Technology in Taiwan. We are also grateful to the National Center for High-Performance Computing for providing the computational resources required for this study.

Author information

Authors and Affiliations

  1. R&D division, CoreTech. (Moldex3D), Hsinchu, Taiwan

    Chi-Hua Yu

  2. Structural Engineering, Univeristy of Califorinia, San Diego, California, USA

    Kuan-Po Lin

  3. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

    Chuin-Shan Chen

Authors
  1. Chi-Hua Yu
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  2. Kuan-Po Lin
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  3. Chuin-Shan Chen
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Corresponding author

Correspondence to Chuin-Shan Chen .

Editor information

Editors and Affiliations

  1. Materials Science and Strength of Materials, University of Stuttgart Institute for Materials Testing, Stuttgart, Germany

    Siegfried Schmauder

  2. Department of Civil Engineering, National Taiwan University Department of Civil Engineering, Taipei, T´ai-pei, Taiwan

    Chuin-Shan Chen

  3. BEC 254, University of Alabama at Birmingham, Birmingham, Alabama, USA

    Krishan K. Chawla

  4. Fulton School of Engineering, Arizona State University, Tempe, Arizona, USA

    Nikhilesh Chawla

  5. Engineering Mechanics, Zhejiang University Engineering Mechanics, Hangzhou, China

    Weiqiu Chen

  6. Katayanagi Advanced Research Laboratorie, Tokyo University of Technology Katayanagi Advanced Research Laboratorie, Tokyo, Japan

    Yutaka Kagawa

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Yu, CH., Lin, KP., Chen, CS. (2018). Nanoindentation and Indentation Size Effects: Continuum Model and Atomistic Simulation. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6855-3_26-1

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  • DOI: https://doi.org/10.1007/978-981-10-6855-3_26-1

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  • Print ISBN: 978-981-10-6855-3

  • Online ISBN: 978-981-10-6855-3

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