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A coupled quantum/continuum mechanics study of graphene fracture

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Abstract

A new technique is presented to study fracture in nanomaterials by coupling quantum mechanics (QM) and continuum mechanics (CM). A key new feature of this method is that broken bonds are identified by a sharp decrease in electron density at the bond midpoint in the QM model. As fracture occurs, the crack tip position and crack path are updated from the broken bonds in the QM model. At each step in the simulation, the QM model is centered on the crack tip to adaptively follow the path. This adaptivity makes it possible to trace paths with complicated geometries. The method is applied to study the propagation of cracks in graphene which are initially perpendicular to zigzag and armchair edges. The simulations demonstrate that the growth of zigzag cracks is self-similar whereas armchair cracks advance in an irregular manner. The critical stress intensity factors for graphene were found to be 4.21 MPa\({\sqrt {\rm m}}\) for zigzag cracks and 3.71 MPa\({\sqrt{\rm m}}\) for armchair cracks, which is about 10% of that for steel.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Northwestern University, 2145 N. Sheridan Road, Evanston, IL, 60208, USA

    Mei Xu & Ted Belytschko

  2. Department of Mechanical Engineering, University of North Carolina at Charlotte, Charlotte, NC, USA

    Alireza Tabarraei

  3. Department of Chemistry, University of Victoria, Victoria, BC, V8W 3V6, Canada

    Jeffrey T. Paci

  4. Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA

    Jeffrey T. Paci

  5. School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA

    Jay Oswald

Authors
  1. Mei Xu
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  2. Alireza Tabarraei
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  3. Jeffrey T. Paci
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  4. Jay Oswald
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  5. Ted Belytschko
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Correspondence to Jeffrey T. Paci.

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Xu, M., Tabarraei, A., Paci, J.T. et al. A coupled quantum/continuum mechanics study of graphene fracture. Int J Fract 173, 163–173 (2012). https://doi.org/10.1007/s10704-011-9675-x

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  • DOI: https://doi.org/10.1007/s10704-011-9675-x

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