Crack Propagation and Fracture Toughness of Graphene Probed by

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Crack Propagation and Fracture Toughness of Graphene Probed by Raman Spectroscopy Zilong Zhang, Xuewei Zhang, Yunlu Wang, Yang Wang, Yang Zhang, Chen Xu, Zhenxing Zou, Zehao Wu, Yang Xia, Pei Zhao, and Hong Tao Wang ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.9b03999 • Publication Date (Web): 19 Aug 2019 Downloaded from pubs.acs.org on August 19, 2019

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Crack Propagation and Fracture Toughness of Graphene Probed by Raman Spectroscopy

Zilong Zhang,†,‡,§ Xuewei Zhang,†,‡,§ Yunlu Wang,†,‡,§ Yang Wang,†,‡,§ Yang Zhang,†,‡,§ Chen Xu,†,‡,§ Zhenxing Zou,†,‡,§ Zehao Wu,†,‡,§ Yang Xia,|| Pei Zhao,*,†,‡,§ Hong Tao Wang,*,†, ‡,§

†Center

‡Institute

for X-Mechanics, Zhejiang University, Hangzhou 310012, P. R. China

of Applied Mechanics, Zhejiang University, Hangzhou 310012, P. R. China

§Key

Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Hangzhou 310012, P. R. China

||Institute

of Microelectronics, Chinese Academy of Science, Beijing 100029, P. R. China

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KEYWORDS: graphene, fracture toughness, crack propagation, Raman spectroscopy, chemical vapor deposition

ABSTRACT

Fracture behaves as one of the most fundamental issues for solid materials. As a one-atom-thick crystal, many aspects in fracture mechanics of graphene are of high significance, such as the crack propagation and its fracture toughness. Here we present a method to study the fracture characteristics of graphene using Raman spectroscopy and designed chemical-vapor-deposited monolayer graphene with pre-set cracks. The dynamic fracture process of graphene was experimentally observed, and its fracture toughness was obtained using Griffith’s criterion based on the strain distribution derived from the frequency shifts of Raman bands. The fracture toughness of Kc=6.1±0.5 MPa m and Gc=37.4±5.5 J/m2 is comparable with the previously reported theoretical and experimental values, and we believe that this simple and easy-to-operate approach of characterizing the fracture of graphene using Raman spectroscopy can also be extended to other two-dimensional materials.


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Fracture is one of the most fundamental issues for solid materials, and has been focused by mankind as early as there have been artificial structures.1 However, many aspects for the in-depth understanding of fracture remain uncovered. As a one-atom-thick carbon material with honeycomb-like lattices, graphene has the simplest crystalline structure.2 Therefore, graphene can behave as an ideal platform to study fracture with a nanoscale resolution, which is essential for the comprehensive fracture theory of bulk solids. The fracture characteristics of graphene is usually studied by the stresses near the tip of a crack and the associated energy during the crack propagation,3,4 which can be quantitatively expressed by the Griffith’s criterion5,6

c 

2 E  a0

(1)

where  c and E are the failure strength and Young’s modulus of graphene, respectively,  is the edge energy at the crack, and a0 is the crack half length. The fracture toughness of graphene, i.e., the ability of graphene to resist the fracture, is usually characterized by its critical stress intensity factor K c   c  a0 , or the critical strain energy release rate Gc   c2 a0 / E . The crack propagation and fracture toughness are of high significance for the stability of materials, especially for brittle materials such as graphene. Most of the previous studies were conducted by numerical methods such as molecular dynamics (MD) or finite element analysis (FEA).7-19 For instance, from the results of MD simulations, single-crystal graphene exhibits a fracture toughness of K c  4.7MPa m ,7 and this value is higher for polycrystalline graphene due to the existence of domain boundaries.8 The crack propagation in graphene follows the armchair or zigzag orientations, and the zigzag one is more preferable.9 Compared with the theoretical works, by far there have been few experimental studies on the fracture of graphene,6,20-24 due to the difficulties of applying loads to a material with nanoscale dimensions, as well as its fast


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response to the load for fracture. Especially, considering that the popular atomic force microscopy (AFM) nanoindentation method20,21 always produces complex strain fields that are not applicable using Griffith’s criterion, a uniaxial load on graphene becomes the first step of a successful experiment. Zhang et al. studied the fracture of polycrystalline graphene by in-situ nanomechanical uniaxial stretching in scanning electron microscope (SEM), and obtained its fracture toughness as K c  4  0.6 MPa m and Gc  15.9 J/m 2 .6 However, during their experiments a sudden fracture of graphene occurred, so that no information of the entire fracture process were obtained. Using similar method, Jang et al. reported a fracture toughness

K c  21.25 MPa m for single-crystal graphene,24 and this high value may be caused by the nonlinearity during graphene deformation.25 Kim et al. used transmission electron microscopy (TEM) to study the crack propagation in single-crystal graphene, and observed that most of the cracks are along either the zigzag or armchair orientations.22 Fujihara et al. also reported similar results that for chemical vapor deposition (CVD) graphene on Cu,26,27 the propagation of natural cracks is selectively along its zigzag orientation.23 Therefore, a more effective approach of characterizing the fracture of graphene is necessary. In this work, we present a methodology to study the fracture characteristics of graphene using Raman spectroscopy and designed CVD graphene samples with pre-set cracks. With a mild load from the underlying flexible substrate, the dynamic propagation of cracks in graphene was experimentally observed. Based on the high sensitivity of Raman spectroscopy in detecting the crystal lattice modification, we succeeded in obtaining the strain distribution around the crack tip, which leads to a fracture toughness of Kc=6.1±0.6 MPa m and Gc=37.4±6.7 J/m2 for polycrystalline graphene, comparable with previously reported values using other theoretical and experimental methods.


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RESULTS AND DISCUSSION To experimentally investigate the fracture of graphene, a most fundamental step is to test the graphene sample with pre-set cracks using uniaxial load, so that the strain and stress in graphene are analyzable using Griffith’s criterion. By far the most successful experiments for graphene fracture are in-situ nanomechanical testing using SEM, and the cracks are prepared using gallium focused ion beam (FIB). However, problematic issues exist such as the possible interfacial sliding between the loading device and graphene, the damage near the crack induced by ion deposition, and the fast response of graphene into a sudden fracture. Therefore, it will be of high importance to develop other experimental techniques to fabricate suitable graphene samples, and apply mild uniaxial load to study its fracture properties. As we reported previously,28 a thin buffering layer of formvar resin between graphene and polydimethylsiloxane (PDMS) provides an enhanced interface for stress transfer, and up to 2% uniaxial strain can be obtained for single-crystal graphene when PDMS is stretched. Based on this, we designed polycrystalline graphene samples with preset cracks by a controlled CVD process. The experimental procedure is illustrated in Figure 1a, and a series of optical microscopy (OM) images of the CVD graphene with different growth time is shown in Figure 1b. The samples are treated with a mild oxidation in air, so that the graphene islands are visualized from the Cu substrate by a color contrast. With an extended growth time, graphene on Cu gradually evolves from small domains to a coalesced film, but due to the varied growth rates of the domains, if the CVD time is carefully adjusted, the coalescence of these domains can stop right before the complete film is formed, leaving only several narrow gaps (cracks) in the monolayer film. The formed cracks are usually located between neighbor domains, but owing to that most of the domains are aligned with the same lattice direction by our CVD parameter (as indicated by the blue dashed lines in Figure 1b), these cracks are actually inside


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Figure 1. Preparation and characterization of a graphene film with pre-set cracks. (a) Schematic of the experimental procedure using designed CVD graphene samples, flexible substrate stretching and Raman spectroscopy. (b) A series of OM images that demonstrate the formation of a continuous graphene film with pre-set cracks. The color contrast is formed by mildly oxidizing the samples in air. (c) SEM images of graphene films with pre-set cracks on a Si/SiO2 substrate and on a formvar/PDMS substrate. (d) Typical Raman spectra of the graphene samples measured away and near a crack.

single crystal domains of graphene and will lead to intergranular fracture. However, we still treat the coalesced film as polycrystalline graphene considering that not all of the domains are strictly aligned (black dashed lines). The edges of these graphene islands are preferentially along the zigzag orientations,27 and when most of these islands coalesce the cracks left in the film will exhibit


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zigzag edges as well, which is very important for the fracture process. Figure 1c shows the SEM images of graphene films with several cracks after being transferred onto a Si/SiO2 substrate and onto a formvar/PDMS substrate. The lengths of these cracks are tens of micrometers. It needs to be mentioned that due to the coalescing randomness of CVD graphene domains, the length of formed cracks in the graphene film cannot be precisely designed, but it can be roughly controlled if the graphene domain sizes are adjusted by the CVD parameters (for instance, ~50 μm in our experiments).The parallel alignment of these cracks in the left image of graphene also implies that they are generated inside single crystals by aligned domains. Moreover, after being transferred onto a formvar/PDMS substrate, the cracks in graphene are almost invisible. This is due to the transfer process that the formvar is deposited onto graphene with a liquid state and then cured, so that the graphene deformation near the crack is minimized. Typical Raman spectra of these graphene samples measured away and near a crack are shown in Figure 1d. The high intensity ratio between the 2D and G band confirms its monolayer nature, and the absence of the D band away from the crack demonstrates the high crystallinity of graphene, whereas the apparent D band from the crack is indicative of the defect sites along its edges. Previous experimental results showed that the fracture of graphene follows a brittle manner,6,24 so that only its initial and final states can be observed. On the other hand, probing the entire process of crack propagation is of fundamental importance for the understanding of graphene fracture. With the assistance of mild stress transferred from the flexible substrate, the propagation of cracks in graphene can be successfully captured. Figure 2 shows a series of OM images for the evolution of a crack (initial length of 15 μm) under an increased uniaxial strain. The load is along the horizontal direction in the figure. The strains marked in the figure are the nominal strains of the substrate instead of the intrinsic strains in graphene, and the blue and red arrows indicate the crack


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Figure 2. OM images and the corresponding schematics of the propagation for a pre-set crack in graphene. The strain values are the nominal strains of the substrate. The blue and red arrows indicate the crack tips and the kink sites of crack propagation, respectively. Scale bar in a: 5 μm, and all the scales in other images are the same as in a. The load is along the horizontal direction of the images.

tips and the kink sites of crack propagation, respectively. Initially, only a slight hint of the pre-set crack can be observed in the image (Figure 2a). When the applied strain increases, the crack starts to propagate along a path perpendicular to the load. It is emphasized that the cracks in all of our experiments exhibit zigzag edges, so the propagation path this crack follows is along the zigzag orientation as well, consistent with the results from TEM observations22 and theoretical works3. This is due to the lower formation energy of zigzag edges than the armchair ones.29,30 Moreover, during the fracture process only one of its tips propagates and the other is frozen, probably due to the existence of a defect to pin the tip. As to the moved tip, its path occasionally exhibits kinks


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(Figure 2f and g), as predicted by the fracture mechanics for brittle materials.31 The occurrence of a kink indicates a higher fracture resistance for the crack to propagate along its original direction. The kink angle for the path is ~128°, close to the angle of a hexagonal graphene domain (120°),27 and after the first kink (Figure 2f, nominal strain 3%) the crack turns back to its original direction by generating the second kink (Figure 2g, nominal strain 4.5%), with the same kink angle of ~128°. The average kink angle derived from eight crack propagation experiments is 123.6±6.6°, and we attribute the deviation of it from 120° to the observation error resulted from the Poisson’s effect during the uniaxial stretching and the surface roughness of the samples. Moreover, during the whole propagation process, no branched cracks evolved from this crack were observed. The propagation of another crack(s) is shown in Figure 3. Different from the crack in Figure 2, in total three cracks are observed to induce the fracture. The load is along the horizontal direction as well. Under lower strain, crack i appears first with both its two tips slowly propagate along a direction not straightly perpendicular to load. The angle between the crack path and the load direction is approximately 78°. When strain increases, the propagation of crack i stops, and crack ii appears next to the upper tip of crack i parallelly, and connects to crack i at a nominal strain of 2.625% (Figure 3d) by generating a new crack and the kink angles are ~120°. The merged crack maintains its length (~60 μm) until a nominal strain of 4.125% is applied, but its contrast keeps increasing. This is probably resulted from the pinning of its both tips by defects as well. With increased strain one more crack of iii appears next to the lower tip of crack i, following the same propagation direction as crack i and ii. However, the connection of crack i and iii is caused by the re-started propagation of crack i, not by the propagation of crack iii. The black lines along the load direction that appear under increased strain are the wrinkles from the Poisson’s effect of graphene. However, as can be seen from Figure 3g–i, with the existence of several wrinkles, crack i can still


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Figure 3. OM images and the corresponding schematics of the propagation for another pre-set crack in graphene. The blue and red arrows indicate the crack tips and the crack connection sites, respectively. Scale bar in a: 5 μm, and all the scales in other images are the same as in a. The load is along the horizontal direction of the images as well.

grow downwards to connect with crack iii, suggesting that these wrinkles actually have no influence on the propagation of cracks. This is due to that a wrinkle is usually at micrometer scale with strain relaxation, but the crack tip is at nanometer scale with considerably large strain concentration. Therefore, the propagation direction of the crack still follows the lattice structure of graphene rather than being hindered by the wrinkles. Besides of crack propagation, the fracture roughness of graphene is a subject of more interests and significance. As reported by Zhang et al.,6 the fracture of graphene follows the manner of a


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brittle material and its Mode I fracture toughness can be evaluated from the Griffith’s criterion, using the failure strength near the crack (σc) and the initial crack half length (a0). In previous studies, the failure strength was usually derived indirectly from simulations such as FEA,6,24 whose set parameters may vary from the real case of tested samples in experiments. Therefore, a more direct approach to detect the stress fields near the crack needs to be explored. As a technique to detect lattice vibrations, Raman spectroscopy is sensitive to strains by shifting its bands to lower (tension) or higher (compression) frequencies.28,32,33 We adopted this technique to probe the stress and strain distributions near a graphene crack by mapping the region for the frequency contour. We chose the Raman 2D band as the strain indicator due to its high sensitivity.28 Figure 4a shows the spectral evolution of the 2D band as a function of the intrinsic strain in graphene. Due to the relatively small strain that is applied on graphene, the 2D band exhibits only a redshift but no splitting. The intrinsic strain that graphene has is obtained by its relation with the Raman frequency shift

1     0 ( ll   tt )   0 ( ll   tt ) 2

(2)

where ω± is the shifts of splitted Raman band, ω0 is the initial frequency of the Raman band, εll and εtt are the strains parallel and perpendicular to the load, respectively, γ is the Grüneisen parameter, and β is the shear deformation potential. Considering that the strain distribution that Raman probes are the region that has a single crystallinity, we chose parameters of single-crystal graphene for the following analysis instead of those of polycrystalline graphene, such as a shifting rate of  /   60 cm–1/% for the 2D band as we derived previously,28 and a Young’s modulus of 1 TPa.20


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Figure 4. Raman spectroscopic analysis of the stress near a crack tip in graphene. (a) Raman 2D band evolution as a function of the graphene intrinsic strain. (b) OM image of a crack tip zone for Raman mapping, boxed by red dash lines. (c,d) The contours of Raman 2D band frequencies and stress distribution for the region boxed in (b), respectively. The crack tip is marked in both maps by dash curves.

Figure 4b shows the OM image of a crack, with its tip zone for the Raman mapping is boxed by red dash lines. The contour of Raman 2D band for this zone is shown in Figure 4c, and the crack tip is denoted by the dashed curve. It needs to be emphasized that the region with lower frequencies is not where the tip locates. Moreover, the 2D bands within the crack are still observable due to the signal average within the Raman laser spot (1.4 μm). The corresponding contour of the stress under the load is shown in Figure 4d, which is gained by multiplying the Young’s modulus of graphene with the strains derived from the frequency shifts. Apparently, the stress is concentrated within a region near the crack tip, and for other regions the stress stays at a lower level, which is considered as the critical stress for the fracture, i.e., the failure strength. However, although the


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Table 1. Experimental data of half initial crack length a0, critical fracture stress σc and calculated fracture toughness of three graphene samples. No.

a0 (μm)

σc (GPa)

 c a0 (MPa m)

Kc ( MPa m )

Gc (J/m2)

1

8.5

1.29

3.76

6.6

43.56

2

9

1.17

3.51

6.2

38.44

3

11

0.93

3.08

5.5

30.25

stress distribution exhibits a hint of singular behavior, it does not show the typical pattern around the crack tip as predicted by the Griffith’s criterion. A possible reason is that the scale that Raman spectroscopy probes is significantly larger (at least 103) than the theory. The failure strength of graphene in Figure 4d is obtained as 1.17 GPa from the dark blue region, and the half initial length of the crack is approximately 9 μm. They yield a Mode I critical stress intensity factor of K c   c  a0 as 6.2 MPa m and a critical strain energy release rate of Gc   c2 a0 / E as 38.44 J/m2. Table 1 lists the fracture toughness results measured from Raman

scanning on three crack tips, which give an average value of Kc=6.1±0.6 MPa m and Gc=37.4±6.7 J/m2. It is noted that although equation (1) for fracture toughness is accurate only for one center crack in an infinite plate, considering the cracks we chose to conduct the Raman mapping are relatively isolated in the scanning fields, these equations are still applicable, as also can be seen from the close  c a0 values in Table 1. The fracture toughness we derive is compared with other theoretical and experimental methods in Figure 5. Another two reports of fracture toughness by experiments are not shown due to their exceptional high values (Kc as 10.7±3.3 MPa m in Ref. 34 and 21.25 MPa m in Ref. 24). Our larger fracture toughness for graphene may be caused by


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Figure 5. Theoretical and experimental values of fracture toughness for graphene.

several factors as follows. Compared with a sharp crack tip propagating in a single crystal graphene, the blunt crack tip and polycrystalline nature of our samples can significantly enhance the measured fracture toughness,6,8,35,36 Moreover, other factors will also contribute to the increased fracture toughness of graphene, such as the defects induced by the synthesis, the crack branching and bridging,22 etc. For a point defect at the crack tip such as a vacancy, it enables an extra opening at the tip to facilitate stress relaxation and energy release, so that the fracture toughness is enhanced as well.37 It is worth mentioning that when the crack speed reaches the critical crack-tip speed (50–60% of the Rayleigh wave speed depending on the applied strain), branches are generated at the crack tip to increase the fracture toughness.7 In our experiments, such branched cracks were not observed during the propagation of all cracks, suggesting that the fracture toughness is the statics/quasi-statics fracture toughness rather than the dynamic one.

CONCLUSIONS


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In conclusion, we present a method to study the fracture toughness of graphene using Raman spectroscopy and designed CVD graphene samples with pre-set cracks. The dynamic fracture process of graphene was experimentally observed, and its fracture toughness was obtained using Griffith’s criterion based on the strain distribution measured by Raman frequency shifts. The fracture toughness of Kc=6.1±0.6 MPa m and Gc=37.4±6.7 J/m2 is comparable with previously reported theoretical and experimental values, and we believe that this simple and easy-to-operate approach of characterizing the fracture of graphene can also be extended to other two-dimensional materials.

EXPERIMENTAL Graphene synthesis Commercially available Cu foils (25-µm-thick, #46365, Alfa Aesar China Chemical Co., Ltd.) were used for the CVD growth of graphene, as we reported previously.27 In details, a piece of Cu foil was heated at 150 ºC in air by a hot plate for 8 min to create a layer of metal oxide. It was then loaded into a quartz chamber and the temperature was increased to and maintained at 1060 ºC. To grow graphene, 27 sccm diluted CH4 (0.05% in Ar by volume), 12 sccm H2 and 300 sccm Ar was employed with a total pressure of 1 atm. The typical growth time of a graphene film with pre-set cracks is approximately 30 min. Graphene transfer The transfer of graphene onto a flexible substrate was conducted by formvar-assisted method.28 A thin layer of formvar resin (1 wt.% in chloroform) was first dip-coated and cured onto the surface of graphene, followed by brought into close contact with the polydimethylsiloxane (PDMS, 0.7 mm thick, Sylgard 184 elastomer Kit, Dow Corning, USA) substrate. Finally, a


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graphene/formvar/PDMS sample was obtained after the Cu foil was etched by FeCl3 aqueous solution. Fracture toughness measurement A home-made tensile testing machine with displacement-controller was used to apply uniaxial load to the samples, and the resolution of the testing machine is 0.01 mm. The morphological evolution of pre-set cracks in graphene was monitored by in-situ micro-Raman spectroscopy (LabRAM HR Evolution, Horiba Co., Ltd) equipped with an optical microscope (Olympus BXFM-ILHS, Olympus Co., Ltd). A long-focal-depth 50× objective lens with NA=0.95 and a grating of 1800 g/mm were used in the experiments. The laser spot size was estimated to be 1.4 µm and the obtained Raman spectra had a resolution of

Crack Propagation and Fracture Toughness of Graphene Probed by

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