In their correspondence, Taheri Mousavi et al. presented molecular dynamics (MD) calculation results of nano-twined Cu (nt-Cu) with twinning spacing below 3 nm under Vickers indentation shear deformation in the (001)[110] direction of the nt-Cu supercell, which showed the same strain-stiffening effect similar to what was reported for nano-twined BN (nt-cBN) and nano-twined diamond (nt-Dia) in our previous papers1, 2. They argued that as the early experiments3 reported nt-Cu softening under tensile deformation below a critical twinning spacing (λ < 15 nm), their finding places significant doubt on the validity of our model in explaining the observed Vickers hardness enhancement of nt-cBN and nt-Dia4, 5, where the twinning spacing is about 4– 5 nm. First of all, the strain-stiffening effect found by first principles and MD calculations for nt-cBN, nt-Dia in our work1, 2 and nt-Cu in the correspondence comes from the transformation of atomic bonding on twin boundaries from easy sliding configurations to hard sliding configurations under indentation shear deformation, and such strain-stiffening mechanism does not exist in tensile deformation, as we showed in our works1, 2. The comparison of the calculated strain-stiffening effect of nt-Cu under indentation shear deformation with its experimental tensile strength made in the correspondence is not meaningful. Second, the authors of the correspondence seem to be not aware of the recent experimental report, where unprecedented strengthening of the tensile strength up to 3 GPa was observed experimentally for nano-twined metal Ni83.6Mo14W2.4 with twinning spacing at λ = 1.8 nm6, which has a nano-twinning enhanced tensile strength more than two times of those of nano-crystalline Ni and nano-twined Cu. These recent findings6 suggest that even the effects of nano-twinning on the tensile strengths of nano-twining metals depend critically on the sample qualities, structures, material compositions, and experimental processes. Third, the strain-stiffening effect we found in nt-cBN (or nt-Dia)1, 2 is different from the Hall-Petch effect, with the former describing the intrinsic indentation shear strength of ideal nt-cBN (or nt-Dia) without defects and dislocations, while the later describing the blocking of dislocation motions by nano-twin or other grain boundaries. In addition to the Hall-Petch effect, our results show that nano-twining in nt-cBN (or nt-Dia) can flip the easy atomic bonding to hard atomic bonding across the twining interfaces under indentation, which suppresses the original easy shear mode in single-crystal cBN (or diamond) and enhances the ideal indentation strength of nt-cBN (or nt-Dia) to twice that of single-crystal cBN (or diamond)1, 2, consistent with the experimental results4, 5. It should be noted, however, the measured hardness of real nano-twining materials, including nt-cBN, nt-Dia or nt-Cu, also depends on other qualities, such as defects, dislocations, other grain boundaries, different mechanisms of dislocation motions, etc. of the samples.
References
Li, B., Sun, H. & Chen, C. F. Large indentation strain-stiffening in nanotwinned cubic boron nitride. Nat. Commun. 5, 4965 (2014).
Li, B., Sun, H. & Chen, C. F. Extreme mechanics of probing the ultimate strength of nanotwinned diamond. Phys. Rev. Lett. 117, 116103 (2016).
Lu, L., Chen, X., Huang, X. & Lu, K. Revealing the maximum strength in nanotwinned copper. Science 323, 607 (2009).
Tian, Y. et al. Ultrahard nanotwinned cubic boron nitride. Nature 493, 385 (2013).
Huang, Q. et al. Nanotwinned diamond with unprecedented hardness and stability. Nature 510, 250 (2014).
Sim, G. et al. Nanotwinned metal MEMS films with unprecedented strength and stability. Sci. Adv. 3, e1700685 (2017).
Author information
Authors and Affiliations
Contributions
B.L., H.S. and C.C. discussed the correspondence and H.S. wrote the reply.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
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/.
About this article
Cite this article
Li, B., Sun, H. & Chen, C. Reply to ‘Anisotropy governs strain stiffening in nanotwinned-materials’. Nat Commun 9, 1585 (2018). https://doi.org/10.1038/s41467-018-03967-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-018-03967-6
This article is cited by
-
Continuous strengthening in nanotwinned diamond
npj Computational Materials (2019)