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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.

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Figures

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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.

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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.

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Fig. 3

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

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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.

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Fig. 5

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

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Fig. 6

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

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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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.

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