153
Views
24
CrossRef citations to date
0
Altmetric
Original Articles

Theoretical strength of 2D hexagonal crystals: application to bubble raft indentation

, , &
Pages 2177-2195 | Received 02 Apr 2004, Accepted 27 Oct 2004, Published online: 21 Feb 2007
 

Abstract

By means of lattice and molecular dynamics we study the theoretical strength of homogeneously strained, defect-free 2D crystals whose atoms interact via pair potentials with short- and longer-ranged interactions, respectively. We calculate the instability surface, i.e. the boundary in the 3D homogeneous strain space (ε xx , ε yy , ε xy ), at which the first vanishing of the frequency of a vibrational mode occurs, taking into account all 2(N − 1) + 3 modes of a 2D periodic system of N atoms. We also compute the strain energies of the crystal on the instability surface, thus defining the most dangerous direction(s) of strain where the critical energy density is small. A theory is developed to incorporate the effect of loading device–sample interactions in the lattice instability criterion. The results are applied to the model problem of bubble raft indentation. We analyse the distribution of the unstable phonon modes in the first Brillouin zone as a function of the loading parameter, and discuss the post-critical behaviour of the lattice in the presence of strain gradients as in nano-indentation experiments.

Acknowledgements

We thank Krystyn J. Van Vliet and Sidney Yip for the inspiring discussions during the IUTAM Meeting in Osaka, July 2003. We also thank Takayuki Kitamura, Yoshitaka Umeno and Kisaragi Yashiro for very helpful discussions. J.L. acknowledges support from Honda R&D Co., Ltd. and the Ohio State University Transportation Research Endowment Program.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 786.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.