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. 2017 Nov 22;7:16053. doi: 10.1038/s41598-017-14734-w

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Comparison of numerical and experimental results of hardness in single crystal Cu, based on available literature and the results with tip radius of 100 nm obtained in this paper. The hardness trends are opposite in nano-scale (black) and micro-scale (blue). The simulation result (black) is two orders higher than the experiment one (blue). There is a gap in simulation and experiment between 1 nm to 100 nm from literature. The simulation (green) and experiment (red) results in this paper are in the same order and the trends are similar to each other, the hardness curves all go up then go down as the indentation depth deceases.