Research Papers

Molecular Dynamics Simulations and Continuum Modeling of Temperature and Strain Rate Dependent Fracture Strength of Graphene With Vacancy Defects

[+] Author and Article Information
M. A. N. Dewapriya

School of Engineering Science,
Simon Fraser University,
Burnaby, BC V5A 1S6, Canada
e-mail: mandewapriya@sfu.ca

R. K. N. D. Rajapakse

Faculty of Applied Sciences,
Simon Fraser University,
Burnaby, BC V5A 1S6, Canada
e-mail: rajapakse@sfu.ca

1Corresponding author

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 6, 2014; final manuscript received May 11, 2014; accepted manuscript posted May 15, 2014; published online June 2, 2014. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(8), 081010 (Jun 02, 2014) (9 pages) Paper No: JAM-14-1159; doi: 10.1115/1.4027681 History: Received April 06, 2014; Revised May 11, 2014; Accepted May 15, 2014

We investigated the temperature and strain rate dependent fracture strength of defective graphene using molecular dynamics and an atomistic model. This atomistic model was developed by introducing the influence of strain rate and vacancy defects into the kinetics of graphene. We also proposed a novel continuum based fracture mechanics framework to characterize the temperature and strain rate dependent strength of defective sheets. The strength of graphene highly depends on vacancy concentration, temperature, and strain rate. Molecular dynamics simulations, which are generally performed under high strain rates, exceedingly overpredict the strength of graphene at elevated temperatures. Graphene sheets with random vacancies demonstrate a singular stress field as in continuum fracture mechanics. Molecular dynamics simulations on the crack propagation reveal that the energy dissipation rate indicates proportionality with the strength. These findings provide a remarkable insight into the fracture strength of defective graphene, which is critical in designing experimental and instrumental applications.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Lee, C., Wei, X., Kysar, J. W., and Hone, J., 2008, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science, 321(5887), pp. 385–388. [CrossRef] [PubMed]
Singh, V., Irfan, B., Subramanian, G., Solanki, H. S., Sengupta, S., Dubey, S., Kumar, A., Ramakrishnan, S., and Deshmukh, M. M., 2012, “Coupling Between Quantum Hall State and Electromechanics in Suspended Graphene Resonator,” Appl. Phys. Lett., 100(23), p. 233103. [CrossRef]
Klimov, N. N., Jung, S., Zhu, S. Z., Li, T., Wright, C. A., Solares, S. D., Newell, D. B., Zhitenev, N. B., and Stroscio, J. A., 2012, “Electromechanical Properties of Graphene Drumheads,” Science, 336(6088), pp. 1557–1561. [CrossRef] [PubMed]
Espinosa-Ortega, T., Luk'yanchuk, I. A., and Rubo, Y. G., 2013, “Magnetic Properties of Graphene Quantum Dots,” Phys. Rev. B, 87(20), p. 205434. [CrossRef]
Chen, C., Rosenblatt, S., Bolotin, K. I., Kalb, W., Kim, P., Kymissis, I., Stormer, H. L., Heinz, T. F., and Hone, J., 2009, “Performance of Monolayer Graphene Nanomechanical Resonators With Electrical Readout,” Nat. Nanotechnol., 4(12), pp. 861–867. [CrossRef] [PubMed]
Chen, C. Y., Lee, S., Deshpande, V. V., Lee, G. H., Lekas, M., Shepard, K., and Hone, J., 2013, “Graphene Mechanical Oscillators With Tunable Frequency,” Nat. Nanotechnol., 8(12), pp. 923–927. [CrossRef] [PubMed]
Novoselov, K. S., Fal'ko, V. I., Colombo, L., Gellert, P. R., Schwab, M. G., and Kim, K., 2012, “A Roadmap for Graphene,” Nature, 490(7419), pp. 192–200. [CrossRef] [PubMed]
Banhart, F., Kotakoski, J., and Krasheninnikov, A. V., 2011, “Structural Defects in Graphene,” ACS Nano, 5(1), pp. 26–41. [CrossRef] [PubMed]
Gao, L. B., Ni, G. X., Liu, Y. P., Liu, B., Neto, A. H. C., and Loh, K. P., 2014, “Face-To-Face Transfer of Wafer-Scale Graphene Films,” Nature, 505(7482), pp. 190–194. [CrossRef] [PubMed]
Zandiatashbar, A., Lee, G. H., An, S. J., Lee, S., Mathew, N., Terrones, M., Hayashi, T., Picu, C. R., Hone, J., and Koratkar, N., 2014, “Effect of Defects on the Intrinsic Strength and Stiffness of Graphene,” Nat. Commun., 5, p. 3186. [CrossRef] [PubMed]
Kotakoski, J., Krasheninnikov, A. V., Kaiser, U., and Meyer, J. C., 2011, “From Point Defects in Graphene to Two-Dimensional Amorphous Carbon,” Phys. Rev. Lett., 106(10), p. 105055. [CrossRef]
Datta, D., Li, J. W., and Shenoy, V. B., 2014, “Defective Graphene as a High-Capacity Anode Material for Na- and Ca-Ion Batteries,” ACS Appl. Mater. Interfaces, 6(3), pp. 1788–1795. [CrossRef] [PubMed]
Rafiee, M. A., Rafiee, J., Srivastava, I., Wang, Z., Song, H. H., Yu, Z. Z., and Koratkar, N., 2010, “Fracture and Fatigue in Graphene Nanocomposites,” Small, 6(2), pp. 179–183. [CrossRef] [PubMed]
Zhu, S., and Li, T., 2014, “Wrinkling Instability of Graphene on Substrate-Supported Nanoparticles,” ASME J. Appl. Mech., 81(6), p. 061008. [CrossRef]
Carpenter, C., Maroudas, D., and Ramasubramaniam, A., 2013, “Mechanical Properties of Irradiated Single-Layer Graphene,” Appl. Phys. Lett., 103(1), p. 013102. [CrossRef]
Xu, L. Q., Wei, N., and Zheng, Y. P., 2013, “Mechanical Properties of Highly Defective Graphene: From Brittle Rupture to Ductile Fracture,” Nanotechnology, 24(50), p. 505703. [CrossRef] [PubMed]
Zhao, H., and Aluru, N. R., 2010, “Temperature and Strain-Rate Dependent Fracture Strength of Graphene,” J. Appl. Phys., 108(6), p. 064321. [CrossRef]
Jhon, Y. I., Jhon, Y. M., Yeom, G. Y., and Jhon, M. S., 2014, “Orientation Dependence of the Fracture Behavior of Graphene,” Carbon, 66, pp. 619–628. [CrossRef]
Cao, A. J., and Qu, J. M., 2013, “Atomistic Simulation Study of Brittle Failure in Nanocrystalline Graphene Under Uniaxial Tension,” Appl. Phys. Lett., 102(7), p. 071902. [CrossRef]
Kim, K., Artyukhov, V. I., Regan, W., Liu, Y. Y., Crommie, M. F., Yakobson, B. I., and Zettl, A., 2012, “Ripping Graphene: Preferred Directions,” Nano Lett., 12(1), pp. 293–297. [CrossRef] [PubMed]
Zhang, B., Mei, L., and Xiao, H. F., 2012, “Nanofracture in Graphene Under Complex Mechanical Stresses,” Appl. Phys. Lett., 101(12), p. 121915. [CrossRef]
Yi, L. J., Yin, Z. N., Zhang, Y. Y., and Chang, T. C., 2013, “A Theoretical Evaluation of the Temperature and Strain-Rate Dependent Fracture Strength of Tilt Grain Boundaries in Graphene,” Carbon, 51, pp. 373–380. [CrossRef]
Dewapriya, M. A. N., Rajapakse, R. K. N. D., and Phani, A. S., 2014, “Atomistic and Continuum Modelling of Temperature-Dependent Fracture of Graphene,” Int. J. Fract., 187(2), pp. 199–212. [CrossRef]
Dewapriya, M. A. N., Phani, A. S., and Rajapakse, R. K. N. D., 2013, “Influence of Temperature and Free Edges on the Mechanical Properties of Graphene,” Modell. Simul. Mater. Sci. Eng., 21(6), p. 065017. [CrossRef]
Rokni, H., and Lu, W., 2013, “Surface and Thermal Effects on the Pull-In Behavior of Doubly-Clamped Graphene Nanoribbons Under Electrostatic and Casimir Loads,” ASME J. Appl. Mech., 80(6), p. 061014. [CrossRef]
Plimpton, S., 1995, “Fast Parallel Algorithms for Short-Range Molecular-Dynamics,” J. Comp. Phys., 117(1), pp. 1–19. [CrossRef]
Stuart, S. J., Tutein, A. B., and Harrison, J. A., 2000, “A Reactive Potential for Hydrocarbons With Intermolecular Interactions,” J. Chem. Phys., 112(14), pp. 6472–6486. [CrossRef]
Brenner, D. W., 1990, “Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor-Deposition of Diamond Films,” Phys. Rev. B, 42(15), pp. 9458–9471. [CrossRef]
Shenderova, O. A., Brenner, D. W., Omeltchenko, A., Su, X., and Yang, L. H., 2000, “Atomistic Modeling of the Fracture of Polycrystalline Diamond,” Phys. Rev. B, 61(6), pp. 3877–3888. [CrossRef]
Dewapriya, M. A. N., 2012, “Molecular Dynamics Study of Effects of Geometric Defects on the Mechanical Properties of Graphene,” M.A.Sc. thesis, The University of British Columbia, Vancouver, Canada.
Nose, S., 1984, “A Molecular-Dynamics Method for Simulations in the Canonical Ensemble,” Mol. Phys., 52(2), pp. 255–268. [CrossRef]
Hoover, W. G., 1985, “Canonical Dynamics–Equilibrium Phase-Space Distributions,” Phys. Rev. A, 31(3), pp. 1695–1697. [CrossRef] [PubMed]
Humphrey, W., Dalke, A., and Schulten, K., 1996, “VMD: Visual Molecular Dynamics,” J. Mol. Graphics Modell., 14(1), pp. 33–38. [CrossRef]
Tsai, D. H., 1979, “The Virial Theorem and Stress Calculation in Molecular Dynamics,” J. Chem. Phys., 70(3), pp. 1375–1382. [CrossRef]
Bailey, J., 1939, “An Attempt to Correlate Some Tensile Strength Measurements on Glass: III,” Glass Ind., 20, pp. 95–99.
Freed, A. D., and Leonov, A. I., 2002, “The Bailey Criterion: Statistical Derivation and Applications to Interpretations of Durability Tests and Chemical Kinetics,” Z. Angew. Math. Phys., 53(1), pp.160–166. [CrossRef]
Arrhenius, S., 1889, “On the Reaction Rate of the Inversion of the Non-Refined Sugar Upon Souring,” Z. Phys. Chem., 4, pp. 226–248.
Kuo, T. L., Garcia-Manyes, S., Li, J. Y., Barel, I., Lu, H., Berne, B. J., Urbakh, M., Klafter, J., and Fernandez, J. M., 2010, “Probing Static Disorder in Arrhenius Kinetics by Single-Molecule Force Spectroscopy,” PNAS, 107(25), pp. 11336–11340. [CrossRef] [PubMed]
Anderson, T. L., 1991, Fracture Mechanics: Fundamentals and Applications, CRC Press, Boca Raton, FL, Chap. II.


Grahic Jump Location
Fig. 1

A graphene sheet, with a single vacancy, is subjected to a strain ε0 along the armchair direction. The zigzag direction is perpendicular to the armchair direction. The applied strain, ε0, induces stress concentrations at the carbon–carbon bonds circled in red.

Grahic Jump Location
Fig. 2

Stress–strain curves of pristine and defective (a) armchair and (b) zigzag sheets at various temperatures. Defective sheets have 2% of randomly distributed vacancies.

Grahic Jump Location
Fig. 3

The fracture of (a) pristine and (b) defective armchair sheets with 2% vacancy concentration. The simulations were done at 300 K.

Grahic Jump Location
Fig. 4

(a) Change in the potential energy (ΔPE) during fracture of armchair graphene with various vacancy concentrations from 0.1% to 4%. Down and up arrows indicate the fracture initiation and completion points, respectively. (b) Correlation between the energy dissipation rate and the strength of defective armchair (ac) and zigzag (zz) sheets with various vacancy concentrations used in Fig. 4(a). The linear regression lines are also shown.

Grahic Jump Location
Fig. 5

Graphical representation of the solutions of Eq. (9) for armchair graphene at various temperatures

Grahic Jump Location
Fig. 6

Comparison of the strength of (a) armchair and (b) zigzag sheets given by the proposed model and the MD simulations

Grahic Jump Location
Fig. 7

Strain rate dependent fracture strength of graphene. MD simulations ware performed at 300 K.

Grahic Jump Location
Fig. 8

Strain rate and temperature dependent strength of (a) pristine armchair and (b) pristine zigzag sheets

Grahic Jump Location
Fig. 9

The strain rate dependent strength of armchair and zigzag sheets with higher vacancy percentages at 300 K

Grahic Jump Location
Fig. 10

Variation of the strength of graphene with the square root of vacancy percentage

Grahic Jump Location
Fig. 11

Stress concentration of armchair graphene (a)–(c) with a single crack of length 2a and (d)–(e) with various vacancy concentrations (α). The simulation temperature is 300 K.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In