13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Molecular Dynamics Simulation of Fracture of Graphene Dewapriya M. A. N.1, Rajapakse R. K. N. D.1,*, Srikantha Phani A.2 1 School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada 2 Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada * Corresponding author: rajapaks@sfu.ca Abstract A molecular dynamics (MD) simulation to assess the effect of crack length on the ultimate tensile strength of infinitely large armchair and zigzag graphene sheets is presented. The strength of graphene is inversely proportional to the square-root of crack length as in continuum fracture theories. Further comparison of the strength given by MD simulations with Griffith’s energy balance criterion demonstrates a reasonable agreement. Armchair and zigzag graphene sheets with 2.5 nm long crack exhibit around 55% of the strength of pristine sheets. Investigation of the influence of temperature on the strength of graphene indicates that sheets at higher temperatures fail at lower strengths, due to high kinetic energy of atoms. We also observe out-of-plane deformations of the crack tip at equilibrium configuration of both types of sheets due to compressive forces acting on the crack surface. This deformation propagates with applied strain in the direction normal to the crack and eventually generates ripples in the entire sheet. Keywords Graphene, Fracture, Molecular Dynamics, Vacancy Defects 1. Introduction Experimental investigations with atomic force microscope (AFM) have revealed that the ultimate tensile strength and Young's modulus of graphene are around 130 GPa and 1 TPa, respectively [1]. Researchers have found experimental evidence for the existence of defects such as the absence of carbon atoms in graphene sheets [2]. The absence of carbon atoms in graphene is known as vacancy defects. The influence of vacancy defects on the strength of graphene has not been studied experimentally. However, a number of theoretical studies have been conducted, and it has been found that vacancy defects could reduce the strength of graphene by around 50% [3-9]. Khare et al. [4] studied the effects of large defects and cracks on the mechanical properties of carbon nanotubes and graphene using a coupled quantum mechanical/molecular mechanical method. They found that the weakening effects of holes, slits, and cracks vary only moderately with the shape of the defect, and instead depend primarily on the cross section of the defect perpendicular to the loading direction. Ansari et al. [5], using MD simulations, showed that the presence of vacancy defects significantly reduces the ultimate strength and strain of graphene, while it has a minor effect on Young's modulus. They also showed that defects have a lower effect in armchair direction compared to zigzag direction. Wang et al. [6] studied the effect of vacancy defects on the fracture strength of graphene sheets using MD. They found that vacancies can cause significant strength loss in graphene and also concluded that temperature and loading directions affect the fracture strength. Omeltchenko et al. [7] estimated the fracture toughness of armchair graphene from Griffith analysis and local-stress distributions, and the toughness values are 4.7 MPa m1/2 and 6 MPa m1/2, respectively. The study was conducted using MD simulations. A recent work from Xu et al. [8] revealed that the critical stress intensity factors of graphene are 4.21 MPa m1/2 and 3.71 MPa m1/2 for armchair and zigzag directions, respectively. They used a coupled quantum/continuum mechanics model for the study. Coupled quantum mechanics models are generally computationally expensive and those models cannot incorporate temperature effects. Therefore, it is useful to have a simple MD model, which can be used to investigate the fracture of nanoscale systems such as graphene. This paper presents a MD simulation of fracture of armchair and zigzag graphene at temperatures of 1 K and 300 K.
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