Acta Mechanica Solida Sinica

, Volume 32, Issue 3, pp 339–355 | Cite as

Fracture Toughnesses and Crack Growth Angles of Single-Layer Graphyne Sheets

  • Zonghuiyi Jiang
  • Rong Lin
  • Junhua ZhaoEmail author


Recently, Shang et al. (Angew Chem Int Ed 57(3):774–778, 2018) have developed a method to synthesize ultrathin (around 1.9 nm) graphyne nanosheets. We reported here the mixed-mode I–II fracture toughnesses and crack growth angles of single-layer graphyne sheets using molecular dynamics (MD) simulations and the finite element (FE) method based on the boundary layer model, respectively. The various carbon–carbon bonds of graphyne sheets in the FE method are equated with the nonlinear Timoshenko beams based on the Tersoff–Brenner potential, where all the parameters of the nonlinear beams are completely determined based on the continuum modeling. All the results from the present FE method are reasonable in comparison with those from our MD simulations using the REBO potential. The present results show that both the critical stress intensity factors (SIFs) and the crack growth angle strongly depend on the chirality and loading angle \(\varphi \) (\(\varphi =90^{\circ }\) and \(\varphi =0^{\circ }\) representing pure mode I and pure mode II, respectively). Meanwhile, the fracture properties of single-layer cyclicgraphene and supergraphene sheets are also studied in order to compare with those of the graphyne sheets. The critical equivalent SIFs are derived as \(1.55<K_{{\text {eq-cy}}}\) (cyclic) \(<1.95\) nN Å\(^{-3/2}\), \(1.64<K_{{\text {eq-gy}}}\) (graphyne) \(<2.64\) nN Å\(^{-3/2}\) and \(0.61<K_{{\text {eq-su}}}\) (super)\(<2.04\) nN Å\(^{-3/2}\) in the corresponding zigzag and armchair sheets using the MD simulations, while the SIFs are \(0.32<K_{{\text {eq-cy}}}\) (cyclic) \(<0.48\) nN Å\(^{-3/2}\), \(1.96<K_{{\text {eq-gy}}}\) (graphyne) \(<2.49\) nN Å\(^{-3/2}\) and \(1.42<K_{{\text {eq-su}}}\) (super) \(<2.95\) nN Å\(^{-3/2}\) using the FE method. These findings should be of great help for understanding the fracture properties of carbon allotropes and designing the carbon-based nanodevices.


Fracture toughness Graphyne Molecular dynamics Finite element 



We gratefully acknowledge supports from the National Natural Science Foundation of China (Grant Nos. 11572140 and 11602096), the Natural Science Foundation of Jiangsu Province (Grant No. BK20180031, BK20160158), the National First-Class Discipline Program of Food Science and Technology (Grant No. JUFSTR20180205), the 111 Project (Grant No. B18027), the Programs of Innovation and Entrepreneurship of Jiangsu Province, Primary Research and Development Plan of Jiangsu Province (Grant No. BE2017069), Science and Technology Plan Project of Wuxi, the Fundamental Research Funds for the Central Universities (Grant Nos. JUSRP11529 and JG2015059), Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant No. KYCX17_1473), Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201909), the Project of Jiangsu Provincial Six Talent Peaks in Jiangsu Province and the Thousand Youth Talents Plan.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and TechnologyJiangnan UniversityWuxiChina
  2. 2.Institute of Mechanics and Advanced Materials, School of Mechanical EngineeringJiangnan UniversityWuxiChina

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