Enhancement of fracture toughness of graphene via

Diamond & Related Materials 74 (2017) 90–99

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Enhancement of fracture toughness of graphene via crack bridging with stone-thrower-wales defects G. Rajasekaran ⁎, Avinash Parashar Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee 247667, India

a r t i c l e

i n f o

Article history: Received 27 January 2017 Received in revised form 14 February 2017 Accepted 17 February 2017 Available online 20 February 2017 Keywords: Graphene Defect engineering Stone-Thrower-Wales defect Crack bridging Stress intensity factor Fracture toughness

a b s t r a c t Ever increasing applications of graphene motivates researchers to synthesize large scale graphene sheets. In general, large scale graphene sheets are synthesized with some inherent topological defects such as vacancies, Stone Thrower Wales (STW) and grain boundaries. In this article, effect of STW defects on the fracture toughness of graphene was studied with the help of molecular dynamics based simulations. In this numerical study, different atomistic configurations of graphene containing a centrally embedded crack with or without STW defects were modelled. It can be predicted from the simulations that STW defects could be used for tailoring the fracture toughness as well as fracture behaviour of graphene. Significant improvement in the fracture toughness of graphene has been observed while applying load in zig-zag direction with STW defects were positioned next to the crack faces. Interaction of stress fields generated from crack tip as well as from STW defects helps in tailoring the fracture behaviour of graphene. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Graphene is a two-dimensional (2D) monolayer of honeycomb lattice packed carbon structure that was discovered and successfully isolated from bulk graphite [1]. Owing to its outstanding physical properties [2], graphene is a promising candidate in a number of mechanical, thermal and electrical applications [2–6]. In addition to various nano-technological applications, graphene also attracts prodigious attention as reinforcing element in nanocomposites [7–10]. Characterization of graphene in terms of mechanical strength or fracture toughness is essential for its reliable applications as well as to understand its failure morphology under different boundary conditions [11–13]. Defect engineering has been widely employed by researchers to alter properties of several materials such as metals [14–15], ceramics [16] and diamonds [17]. Similarly, defects have also opened up possibilities to tailor properties of graphene for applications in diversified field such as molecule capacitors [18], ion separation and water desalination [19–20]. Due to application of graphene in diversified fields, researchers are focusing more on synthesizing large scale graphene sheets. Synthesizing of large scale graphene sheets by methods such as chemical vapour deposition usually results in a defective graphene, and these topological defects includes vacancies [2], 5-7 defects [21–24], pentagon-octagonpentagon (5-8-5) defects [25], Stone-Thrower-Wales (STW) defects [2], adatoms, substitution atoms, impurities [26] and crack-like flaws such as slits, holes [27–28]. ⁎ Corresponding author. E-mail address: [email protected] (G. Rajasekaran).

http://dx.doi.org/10.1016/j.diamond.2017.02.015 0925-9635/© 2017 Elsevier B.V. All rights reserved.

So far, several investigations have been carried out to investigate the effect of topological defects on the intrinsic properties of graphene. A recetly published work on 5-7 defects [29] has predicted that higher percentage of grain boundary (GB) defects could intuitively give rise to higher strength in tilt GBs. Wei et al. [30] predicted with the help of their atomsitic models that strength of GB in graphene can either increase or decrease with tilt angle. Rajasekaran and Parashar [31] has predicted a shift in the mechanical behaviour of graphene with the help of STW defects. In addition to numerical simulations, the fundamental importance of the effect of defects on the mechanical properties of graphene has also been studied by means of experimental methods [32–33]. Eventough many research have been carried out to understand the physics of defects on intrinsic properties of graphene, very limited research have been carried out to investigate the effect of topological defects on the fracture behaviour of graphene with existing cracks. Recently in 2015, Meng et al. [34] studied dislocation shielding of a nanocrack in graphene using atomistic as well as continuum scale models. It can be inferred from their work that dislocation shielding mechanism can help in enhancing the fracture toughness of graphene. Jung et al. [35] also employed classical mechanics based approach to predict 50% improvement in the fracture toughness of polycrystalline graphene with randomly distributed GB as compared to its pristine form. Zhang et al. [36–37] also studied fracture behaviour of a sinusoidal graphene ruga [38] containing periodically distributed disclination quadrupoles. In their atomistic smulations mode-I fracture toughness of sinusoidal graphene was predicted as 25.0 J/m2, which is twice that of pristine graphene [36]. Recently in 2016, Wang et al. [39] investigated

G. Rajasekaran, A. Parashar Diamond & Related Materials 74 (2017) 90–99

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the effect of GB and its different misorientation angles on fracture toughness of bi-crystal graphene and also they studied the interactions between cracks and GB's using molecular dynamics. Similar to the the above studies recently Li et al. [40] studied the role of functional groups on graphene oxide in epoxy nanocomposites and Bortz et al. [41] improved the fracture toughness of epoxy composites by considering graphene oxide as a reinforcement candidate. Despite the fact that several efforts has been directed towards developing an understanding for the fracture and failure in graphene sheet, the effect of STW defects on the fracture behaviour of graphene with excisting cracks remains largely elusive. STW defects are particularly important because it has been estabilished that interfacial bonding in graphene based nanocomposites preferebly takes place at STW defected regions [42]. It has also been predicted by Dumitrica and Yakobson [43–44] that while, subjecting carbon based nanofillers such as carbon nanotubes (CNT's) to an increasing logitudinal strain, STW formation energy decreases rapidly and causes massive generation of STW defects. This further motivates the authors to study the interaction of STW defects with the pre-existing embedded crack in a graphene sheet. In the literature, it has been reported that there exists at least three mechanisms contributing towards the toughness enhancement in graphene such as dislocation shielding, stress reduction by out-ofplane deformation and atomic-scale crack bridging [27]. Thus, concise knowledge of crack-STW defect interactions is key in understanding the structural evoluation and ripping of graphene. In this article, molecular dynamics based atomistic modelling was performed to study the effect of STW defects on threshold stress intensity factor and fracture morphology of graphene.

time step of 0.5 fs. In order to eliminate the effect of free edges, periodic boundary conditions (PBCs) were imposed along in-plane directions. After finishing relaxation of atoms for a sufficiently long period of time (30 ps), tensile strain was applied by pulling the sheet along x-direction (zig-zag) or along y-direction (armchair) at a strain rate of 0.001/ps. In order to maintain the desired boundary conditions, isothermal-isobaric (NPT) ensemble was enforced in all the simulations. Stress in the graphene sheet was computed by averaging over 100 time-steps of all the carbon atoms in the model. Atomic stress of individual carbon atoms in the graphene sheet was calculated using virial stress [2,52–55], which is defined as

2. Modelling details and methodology

pffiffiffiffiffiffiffiffi K I ¼ Yσ n πa0

In this article, large-scale atomistic models of graphene were developed in the environment of molecular dynamics. All the simulations were performed in open source code LAMMPS (Large-scale Atomic/ Molecular Massively Parallel Simulator) package [45]. In the proposed atomistic models, interatomic interactions between carbon atoms were simulated with the help of adaptive intermolecular reactive empirical bond order (AIREBO) potential [46]. AIREBO potential consists of three sub components, which are the reactive empirical bond order (REBO) potential [47], the Lennard-Jones (LJ) potential and the torsional component. REBO potential evaluates energy stored in atomic bonds, LJ potential accounts for the non-bonded interactions and the torsional component includes the energy due to torsional interactions between atoms. In order to avoid spurious behaviour of interatomic potential in predicting the failure properties, a single cut-off value of 1.95 Å was used in the simulations [31–32,48–49]. In order to avoid finite size effect [50–51], all the simulations performed either with pristine or with defective graphene, dimensions of the graphene were kept fixed at 27 nm, for length as well as for width, which constitutes 27,468 carbon atoms. All the simulations were performed at 300 K with an integration

σ aij ¼

1 Ωa

1 a a a i j f aβ m vi v j þ ∑ raβ 2 β¼1;n

! ð1Þ

where i and j denote indices in Cartesian coordinate system; α and β are the atomic indices; mα and vα are mass and velocity of atom α; rαβ is the distance between atoms α and β; fiαβ is the force along direction i on atom α due to atom β; Ωα is the atomic volume of atom α. The atomic volume can be taken from the relaxed graphene sheet with a thickness of 0.34 nm [2]. In the current study, authors have followed the approach taken by Pei et al. [56] and Grantab et al. [29], i.e. the strength of the graphene sheet is computed by averaging the stress over all the carbon atoms in the sheet at failure. Authors have further verified that stress computed with this approach is in good agreement with the experimental data [57]. Because of the brittle nature of graphene, its useful strength with engineering relevance should be dictated by fracture toughness, which is conventionally characterized by the critical stress intensity factor (SIF), which was evaluated as, ð2Þ

where, Y is the dimensionless parameter [34] (Y ≈ 1 in our model systems) and σn is the far field (or near the boundary) normal stress values at the instant of first bond rupture and a0 is half of the central crack length. They have been calculated by averaging the normal stress over all the carbon atoms in the graphene sheet at failure. The fracture toughness is also often given by the critical strain energy (Γc) release rate of fracture, which was evaluated as, Γc ¼ σ 2n πa0 =E

ð3Þ

where, E is the Young's modulus of graphene. 3. Results and discussion Stone-Thrower-Wales (STW) defect also referred as pentagon-heptagon-heptagon-pentagon (5-7-7-5) defect is formed by rotating a C\\C bond by 90°, which transforms 4 hexagons into 2 pentagons and 2 heptagons, as illustrated in Fig. 1. Due to hexagonal and symmetric atomic

Fig. 1. Structure of STW defects. (a) Encircled vertical C\ \C bond b11 rotates by 90° to form STW1 defect. (b) Encircled inclined C\ \C bond b22 rotates by 90° to form STW2 defect.

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configuration of graphene, only two types of STW defects are possible, STW1 and STW2 that are well explained with the help of Fig. 1. One of the main feature of graphene with STW defects is that it retains the same number of atoms as in the pristine graphene, and do not create any dangling bonds. Initially, simulations were performed with pristine graphene as well as graphene containing single STW (STW1 or STW2) defect subjected to uniaxial tensile load. Stress-strain response of graphene containing STW1 and STW2 defects along zig-zag as well as armchair directions are plotted in Fig. 2. It can be inferred from Fig. 2a and Fig. 2b that STW1 and STW2 are highly detrimental for the graphene strength along the armchair and zig-zag directions, respectively. Explanation for this selective behaviour of graphene containing STW1 or STW2 defects is provided in earlier work by the authors in research article [31]. Stress-strain response of pristine as well as defected graphene plotted in Fig. 2 are in good agreement with the experimental [57] values and other simulations results [31,48]. After examining the stress-strain response of pristine as well as defective graphene, molecular dynamics based simulations were performed with an embedded crack of length 1.5 nm (=2a). Separate simulations were performed for crack aligned with armchair and zig-zag directions of graphene. After relaxing graphene with an embedded crack for a time period of 30 ps, crack tips and crack surfaces displays out of the plane displacement. The crack tips and crack surfaces are free edges, deformation of free edges of graphene sheet arises due to difference in the energy stored in edge atoms and interior atoms [58]. It

can be seen in Fig. 3 that out-of-plane deformation in a relaxed atomistic configuration of graphene is localized around the crack tip and crack surface. However, when the strain was gradually raised to 0.01, the deformed shape of the crack tip changes to a localized ripple that further propagates in the graphene sheet and encompasses the whole sheet with any further increase in strain. In order to examine the effects of STW defects on the fracture toughness of graphene, authors modelled several crack-STW configurations, which are illustrated with the help of schematic in Fig. 4. Separate models were developed to simulate crack propagation under mode-I loading in armchair as well as zig-zag directions of graphene. In all the simulations, STW defects were introduced in pairs to maintain the symmetry of atomistic configuration, which can also be observed in Fig. 4. Position of STW defects with respect to centrally embedded crack in graphene is illustrated in Fig. 4, where rx and ry corresponds to the distance of STW defect from crack tip and crack surface, respectively. In order to validate the accuracy of AIREBO potential to simulate the fracture toughness of graphene, simulations were performed with pristine form of graphene containing a centrally embedded crack of length 1.5 nm. In both the atomic configurations with crack aligned either with armchair or zig-zag directions, uniaxial load was applied perpendicular to crack surfaces to simulate crack propagation under mode-I loading. Stress-strain response obtained from the uni-axial loading of graphene containing crack is plotted in Fig. 5. It can be observed in Fig. 5a that the stress increases monotonically until the onset of crack propagation that is indicated by sudden drop in stress. Stress intensify factor

Fig. 2. Stress-strain response of graphene containing STW defects along (a) zig-zag direction (b) armchair direction (c) arm chair and zig-zag configuration of graphene indicated with the help of red arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


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Fig. 3. Ripples in a graphene sheet at various strain level. Direction of applied strain is aligned with y-axis. Colours of the atoms indicate the out of plane (z) coordinate with red and blue corresponds to maximum positive and negative out of plane displacement respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(SIF) for graphene sheet was estimated with the help of Eq. 2 as KIZZ = 3.20 MPa m1/2 and KIAC = 2.60 MPa m1/2 under mode-I loading aligned with zig-zag and armchair directions, respectively. These estimated values for stress intensity factor are in good agreement with the values estimated by Zhang et al. [59] using MD simulation and by Zhang et al. [12] using experimental means. A clean brittle cleavage fracture can be observed in Fig. 5b, which corresponds to crack aligned with zig-zag direction and loading along armchair direction. On the other hand, crack deflection and the serrated crack path were observed for crack aligned with armchair direction and loading in zig-zag direction as shown in Fig. 5c. Also, it can be observed in Fig. 5b and 5c that for both type of crack configurations aligned either with armchair or zig-zag directions, the crack propagation is preferably along the armchair edge. The preference of crack propagation along armchair edge can be attributed to the fact that the fracture energy of the armchair edge is lower than that of the zig-zag edge due to the orientation of C\\C bond with respect to the loading directions (refer Table 1). Table 1. provides the calculated Young's modulus (E) and

fracture energy (Γ) from the current work, where fracture energy of graphene sheet was calculated using Eq. 3. Next set of simulations were performed with STW defects positioned in front of crack tip for both armchair and zig-zag configuration of graphene as demonstrated in Fig4a and Fig. 4c, respectively. Simulations were performed for three different set of positions for STW defects, which are referred by distance rx in Fig. 4. Stress-strain response obtained for armchair and zig-zag configuration of graphene with an embedded crack in conjunction with STW defects are plotted in Fig. 6. It can be inferred from Fig. 6a that the fracture stress of graphene sheet along armchair direction in conjunction with STW2 defects placed at a distance of 0.5 nm from the crack tip are almost same as that of graphene without STW defects. On the other hand, an increase in the fracture stress in armchair direction of graphene was noticed when STW2 defects were placed at a distance of 1.0 nm and 1.5 nm from the crack tip. This improvement in fracture toughness of graphene in armchair direction with STW2 defects placed at 1.0 nm and 1.5 nm can be well explained with the help of atomic stress distribution shown in

Fig. 4. Schematic of graphene containing an embedded crack with symmetrically aligned STW defects (a–b) Crack-STW2 defect configuration aligned with zig-zag direction and loaded in armchair direction. (c–d) Crack-STW1 defect configuration aligned with armchair direction and loaded in zig-zag direction.

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Fig. 5. (a) Stress-strain response of cracked graphene sheet along armchair and zig-zag direction (b) Atomic stress configurations at the crack tip and crack surface in armchair direction (c) Atomic stress configurations at the crack tip and crack surface in zig-zag direction.

Fig. 7. It can be inferred from Fig. 7b and Fig. 7c (corresponds to STW2 defect positioned at 1.0 nm and 1.5 nm, respectively) that the stress field developed by crack tip and STW2 defects are tensile in nature. These tensile stress field interactions at a distance of 1.0 nm and 1.5 nm helps in re-distributing the stress between crack tip and STW2 defects and ultimately it helps in improving the failure strength of graphene. When STW2 defects were placed at 1.0 nm and 1.5 nm from the crack tip, the overall reduction in the atomic stress at crack tip was observed in Fig. 7b and Fig. 7c, whereas with 0.5 nm distance from the crack tip, STW2 stress field interact with the crack tip stresses and compensates the overall improvement in the fracture strength of graphene. The position and alignment of rotated bond in STW2 defects helps in reducing crack tip stresses for STW2 defects placed at 1.0 nm and 1.5 nm. In Fig. 6b, stress-strain responses for graphene sheet with STW1 defects placed in front of crack tip is plotted for mode-I tensile load aligned with zig-zag direction. It can be observed from Fig. 6b that the fracture stress of graphene sheet with STW1 defects placed at a distance of 0.5 nm and 1.0 nm from the crack tip are almost same as that of graphene sheet without STW1 defects. On the other hand, the fracture stress of graphene sheet with STW1 defects placed at a distance of 1.5 nm from the crack tip is much lower than that of the graphene Table 1 Calculated Young's modulus and fracture energy. Parameters

Calculated

Reference [34]

Young's modulus, E (TPa) ΓZZ (J/m2) ΓAC (J/m2)

0.875 11.03 8.54

0.955 10.04 10.04

sheet without STW1 defects. It can be inferred from Fig. 7f that the atomic stress distribution developed by crack tip is tensile in nature but the stress field developed by STW1 defects is compressive in nature. Hence, the interaction between tensile and compressive stress fields at a distance of 1.5 nm will creates a huge energy difference that ultimately leads to reduce the failure strength of graphene. On the other hand, in the case of STW1 defects at 0.5 nm and 1.0 nm, the stress field developed by crack tip is tensile and STW defects are also tensile in nature but they are very close to each other, hence it provides same failure strength as that of graphene sheet without STW defects. The position and distance of rotated bond in STW1 defect with respect to crack tip plays the important role in re-distributing the stresses around the crack tip. In the last phase of simulations, STW defects were placed symmetrically above and below the crack surfaces as shown in Fig. 4b and Fig. 4d. Stress-strain response of graphene sheet containing STW defects in the lateral direction of the crack surfaces are plotted in Fig. 8. It can be inferred from Fig. 8a that the fracture stress in armchair direction of graphene with STW2 defects placed at a distance of 1.0 nm and 1.5 nm from the crack surface are almost same as that of graphene sheet without STW2 defects, whereas in the case of 0.5 nm, fracture stress is reduced than that of graphene sheet without STW2 defects. In simulations performed with STW2 defects placed at 1.0 nm and 1.5 nm from crack surfaces, the stress field developed by crack-tip and crack surfaces (refer atomic stress distribution in Fig. 9b and Fig. 9c) are tensile and compressive in nature, respectively. In simulations with STW2 defects placed at 1.0 nm and 1.5 nm from the crack surfaces and mode-I loading aligned with armchair direction of graphene, the atomic stress field from crack-tip and STW2 defects behaves independently and do not interact, as shown in Fig. 9b and Fig. 9c, respectively.


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Fig. 6. Stress-strain response of graphene sheet with an embedded crack and STW defects positioned in front of crack tip at three different set of values of rx. (a) crack aligned with zig-zag, whereas loading in arm chair direction (b) crack aligned with armchair, whereas loading in zig-zag direction.

On the other hand, the orientation of rotated bond in STW2 defect at 0.5 nm from the crack surface increases atomic stresses at the crack tip. Also, the alignment and position of rotated bond in STW2 defect at 0.5 nm distribute the atomic stresses around the crack tip in an asymmetric manner, as shown in Fig. 9a, one crack tip is ensuring higher atomic stresses as well as crack opening, which ultimately leads to earlier crack propagation and reduces the fracture toughness of graphene. In contrast to predictions along armchair direction, increase in fracture stress was observed in zig-zag direction of graphene in conjunction

with STW1 defects placed along the crack surfaces as shown in Fig. 8b. This improvement in the fracture toughness of graphene in zig-zag direction for mode-I loading can be explained with the help of atomic stress distribution around the crack tip in conjunction with the stresses from STW1 defect, as shown in Fig. 9. It can be inferred from Fig. 9d (STW1 defect at 0.5 nm) and Fig. 9e (STW1 defect at 1.0 nm) that orientation of rotated bond in STW1 defect is aligned perpendicular to the crack surface. Compressive atomic stresses from STW1 rotated bond helps in bringing the crack surfaces closer to each other as seen in

Fig. 7. Atomic stress configuration of graphene sheet with an embedded crack and STW defects placed in front of crack tip at different values of rxat 4% strain. (a–c) Atomistic stress distribution around the crack tip and crack surface in conjunction with STW2 defect for mode-I loading in armchair direction at rx = 0.5 nm, rx = 1.0 nm and rx = 1.5 nm respectively. (d–f) Atomistic stress distribution around the crack tip and crack surface in conjunction with STW1 defect for mode-I loading in zig-zag direction at rx = 0.5 nm, rx = 1.0 nm and rx = 1.5 nm respectively.

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Fig. 8. Stress-strain response of graphene sheet containing STW defects in lateral side of crack surface at different values of ry (a) STW2 defect and mode-I loading in armchair direction (b) STW1 defect and mode-I loading in zig-zag direction.

Fig. 9d and Fig. 9e. The closing of crack surfaces helps in developing new bonds or atomic bridges between the crack surfaces as shown in Fig. 9d and Fig. 9e. These new bonds act as self-healing for the cracked graphene surfaces and ultimately improves the fracture toughness of graphene. In another case with STW1 defect placed at 1.5 nm, the atomic stresses at crack surfaces is not sufficient to bring the surfaces close enough to obverse the self-healing phenomenon, but still helps in reducing the crack opening and improving the fracture toughness. In order to quantify the effect of STW defects on the fracture toughness of graphene, mode-I stress intensity factor (SIF) for pristine sheet

of graphene with embedded crack as well as graphene containing STW defects is plotted in Fig. 10, as a function of distance rx and ry. SIF value for graphene sheet containing a centrally embedded crack is estimated as 3.20 MPa m1/2 and 2.60 MPa m1/2 for mode-I loading applied along zig-zag and armchair directions, respectively. The calculated results are in good agreement with the values obtained by Zhang et al. [59]. It can be inferred from Fig. 10a that maximum improvement in the fracture toughness (≈ 16%) was observed in zig-zag direction of graphene when STW1 defect was placed at a distance of 0.5 nm as well as at 1.0 nm from the crack surfaces and also it has been observed

Fig. 9. Atomic stress distribution in graphene with an embedded crack and STW defects placed in lateral direction of crack surface at various distance of ryat 4% strain (a–c) atomistic stress distribution around the crack tip and crack surface in conjunction with STW2 defect for arm chair direction at ry = 0.5 nm, ry = 1.0 nm and ry = 1.5 nm respectively (d–f) atomistic stress distribution around the crack tip and crack surface in conjunction with STW2 defect for zig-zag direction at ry = 0.5 nm, ry = 1.0 nm and ry = 1.5 nm respectively.


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Fig. 10. Stress Intensity Factor (SIF) as a function of distance (rx & ry), while mode-I loading was aligned with (a) zig-zag direction. (b) armchair direction.

that fracture toughness of graphene with STW1 defects placed in lateral side of crack is approaching to fracture toughness of graphene without STW defect when STW1 defects where placed 1.5 nm from the crack surface. In addition, it has been observed that fracture toughness of graphene with STW1 defects placed along the crack is decreasing significantly when STW1 defects were placed more than 1.0 nm from the crack-tip. From Fig. 10b, the maximum improvement in fracture toughness (≈ 8%) was observed in armchair direction when STW2 defects was placed at a distance of 1.5 nm from the crack-tip and also it has been observed that fracture toughness of graphene with STW2 defects is increasing when STW2 defects were placed more than 1 nm from the crack-tip and surfaces in along the crack and lateral side of the crack cases respectively.

This increase in mode-I SIF value can be further attributed to distribution of stresses around crack tip and the crack surface by means of stress field interaction between STW defects and the crack surface. As maximum improvement in the fracture toughness is estimated along the zig-zag direction with STW1 defects placed along crack surfaces, hence, author has only considered this case for further calculations. It can be inferred from Fig. 11 that the stress/atom at crack tip in zigzag configuration of graphene with STW1 defects on lateral side of crack surfaces are lower than that of the other two cases (i.e. graphene sheet without STW defects and graphene sheet with STW defects placed in front of the crack-tip). It can also be observed from Fig. 11 that the crack-tip stress at the time of failure is almost consistent in all three cases. From this section one can conclude that STW defects placed in

Fig. 11. Stress/atom for crack-tip with uniaxial load aligned with the zig-zag direction and STW1 defects at various distance of ry. (a) ry = 0.5 nm. (b) ry = 1.0 nm. (c) ry = 1.5 nm.

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lateral side of the crack will help in reducing crack-tip stresses that will ultimately help graphene in bearing higher load and increased fracture toughness. Fig. 12 depicts failure morphology of graphene sheet with STW defects placed in lateral side of crack surface, while mode-I loading was aligned with zig-zag direction. In Fig. 12, each row corresponds to distance ry (first row ry = 0.5 nm, second ry = 1.0 nm and third for ry = 1.5 nm) for STW1 defect from the crack surface for a crack and loading aligned with armchair and zig-zag directions, respectively. In each row, first, second and third snapshots of simulation box corresponds to crack profile before, at and after initiation of crack propagation, respectively. It can be inferred from Fig. 12 that fracture behaviour of graphene with crack aligned in armchair edges and loading in zig-zag direction shifts from perfectly brittle failure (Fig. 5b) to mild ductile with chain formation in conjunction with crack propagation as evident from Fig. 12c, Fig. 12f and Fig. 12i.

electronic and mechanical properties of graphene for achieving new functionalities not found in the pristine graphene. In this research work, systematic molecular dynamics simulation has been carried out to study the effect of STW defects on fracture toughness of graphene sheet. It has been found that designed distribution of STW defects can improve the fracture toughness by ≈ 16% in zig-zag direction when STW1 defects were placed at a distance of 0.5 nm as well as at 1.0 nm from the crack surfaces. Also, it has been observed that the improvement in fracture toughness (≈8%) was observed in armchair direction when STW2 defects was placed at a distance of 1.5 nm from the crack-tip. These significant improvements in the fracture toughness of graphene in zig-zag direction and also in armchair direction are owing to the interaction of stress fields generated from crack tip as well as from STW defects. These stress fields interactions were helps in tailoring the fracture toughness of graphene. Also, it has been observed that interaction of STW defects and crack can change the failure morphology of graphene from perfect brittle to mild ductile.

4. Conclusions Acknowledgements Topological defects in graphene can be intentionally introduced to tailor its local properties. This is very auspicious in the material-bydesign perspective, where defects are engineered in order to tailor the

This work is supported by Nanomission, Department of Science and Technology, India (Grant No. DST-952-MID) and Indian Institute of

Fig. 12. Failure morphology of graphene containing STW1 defect in zig-zag direction. (a-c) STW defects are placed at 0.5 nm. (d–f) STW defects are placed at 1.0 nm. (g–i) STW defects are placed at 1.5 nm.


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