Mechanical testing of two-dimensional materials: a brief review

ABSTRACT Two-dimensional (2D) materials have dominated nanoscience for the last two decades. Among all 2D materials, graphene, MoS2, and h-BN are extremely popular and have been tentatively scaled up to fabricate nanocomposites, energy storage devices, flexible electronics, etc., ex situ and in situ mechanical characterization of 2D crystals can help us understand their mechanical behavior and measure their mechanical properties, which are of great significance in both fundamental science and practical engineering. To date, a great effort has been devoted to both theoretical and experimental mechanics with a focus on unveiling mechanical behaviors and quantifying mechanical properties. Beyond original research, several insightful review works have been published with a specific focus on the mechanics of 2D materials. To have a complementary contribution to the overview of the mechanics of 2D materials, we would like to review the developed experimental techniques being used to mechanically characterize 2D materials. The working mechanism and associated advantages and disadvantages of the techniques will be briefly discussed. Based on the existence of arguments in mechanical properties and behaviors of 2D crystals, and immature mechanical characterization of 2D materials, more intensive and comprehensive studies are expected toward a full understanding of these novel and promising materials.

One of the most representative 2D materials is graphene, in which all carbon atoms are densely packed in a regular sp 2 -bonded atomic-scale hexagonal pattern. Graphene can be described as an one-atom-thick layer of graphite [37] which is also the basic structural element of other allotropes including graphite, charcoal, carbon nanotubes, and fullerenes. For example, graphene can be wrapped up into zero-dimensional (0D) fullerenes, rolled into 1D nanotubes, or stacked into three-dimensional (3D) graphite. Graphene, as one of the strongest materials ever measured, is reported to have Young's modulus of 1 TPa and intrinsic strength of 130 GPa [38]. Such values are, respectively, five and twenty times greater than those of steels, at just one-third the weight [39,40]. Thus, graphene sheets are expected to serve as mechanical reinforcement for lightweight composites [41][42][43][44][45][46].
As a member of layered van der Waals solids, graphene has many analogues including the family of TMDs which have been conceived and investigated [47][48][49][50][51][52]. Such 2D crystals are formed in an MX 2 type stoichiometry, where M is a transition element from group IV, V, or VI, and X is part of the chalcogen species S, Se, or Te [53]. Layered TMDs consist of tiers of hexagonal lattices that are governed by the transition metal-chalcogen interaction. Molybdenum disulfide (MoS 2 ) is one of the most intensively studied TMDs [54][55][56][57][58][59][60][61] in which a layer of hexagonal Mo atoms is sandwiched by two layers of hexagonal S atoms. The driving force to integrate MoS 2 into MEMS/NEMS is that, unlike graphene, monolayer MoS 2 has a direct bandgap of 1.9 eV, which is important for semiconductor applications [62]. MoS 2 could be a promising material for the fabrication of flexible electronics because of its low cost and high performance [63][64][65].
Hexagonal boron nitride (h-BN) has previously been used as a lubricant and has recently accrued interest because of its chemical stability, intrinsic insulation, dielectric property, and anticorrosion capability [66][67][68][69]. The alternating boron and nitrogen atoms in the h-BN sheet are held together by covalent bonds, while the layers are attached by weak van der Waals interaction. Such weak interlayer bonding facilitates exfoliation and fabrication of single and few-layer h-BN crystals. h-BN has a wide bandgap of 5.56 eV and is highly transparent over a broad UV-visible range [70]. A large-area film would allow for fabrication of 2D graphene-based electronics [71][72][73][74][75].
The mechanical stability of each 2D component is critical to the reliability of the fabricated devices such as flexible electronics and energy storage systems. If one suffers damage during mechanical deformation, the entire device may malfunction. The mechanical study on 2D materials can not only predict their service life in different applications but also reveal their unique mechanical behaviors. To date, great effort has been devoted to both theoretical and experimental mechanics with a focus on unveiling mechanical behaviors and quantifying mechanical properties including, elastic modulus, fracture strength, and fracture toughness [25,[76][77][78][79][80][81][82][83][84][85][86][87][88]. In addition, work of fracture, sliding friction, and interface adhesion have been determined with different strategies as well [86,[89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106]. Beyond original research, several insightful review works have been published with a specific focus on the mechanics of 2D materials. For example, Gao et al. [85] reviewed the progress of experimental and theoretical studies on the fracture behavior of graphene, specifically focusing on theoretical strength, mode I fracture toughness, mixed mode fracture, impact fracture, and sonication fracture; Suk et al. [107] reviewed the adhesion properties of 2D materials, mainly focusing on measurement methods and characteristics of adhesion behaviors with target materials of graphene and MoS 2 ; Wei et al. [108] reviewed the in situ techniques based on scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM) in the characterization of mechanical properties of 2D materials; Akinwande et al. [86] comprehensively reviewed the theoretical and experimental studies related to mechanics and mechanical properties of 2D materials as well as addressed the coupling between the mechanical and other physical properties.
Here, we would like to review the developed experimental techniques including atomic force microscopy (AFM)-enabled nanoindentation, micro-/nano-mechanical devices, pressurized bulge testing, etc., to visualize mechanical behaviors and quantify mechanical properties of 2D materials, such as monolayer and multilayer graphene, MoS 2 , h-BN, and other emerging 2D structures. The working mechanism and associated advantages and disadvantages of the techniques will be discussed. The mechanical properties including elastic modulus, fracture strength, and fracture toughness will be generally summarized.

Setup of AFM-enabled nanoindentation
AFM belongs to the family of scanning probe microscopy (SPM), having the resolution on the order of a fraction of a nanometer. The surface information of a sample is collected by a mechanical probe through 'feeling' or 'touching.' Tiny but accurate and precise movement of the probe is controlled by the piezoelectric elements installed in the AFM. The AFM is also capable of positioning single atoms at ambient conditions, giving the potential to build future nanoscale devices. Figure 2 demonstrates a sketch of laser alignment from the laser diode to probe cantilever and then to the split photodiode detector.
AFM has usually been used for imaging, force measurement, and manipulation [109][110][111][112]. The image is obtained by recording the height of the probe with respect to a constant probesample interaction through raster scanning of the sample surface. High-resolution 2D and 3D images can be exported with a pseudo-color. Figure 3 shows an AFM image of a Faraday plate. The image was scanned by a Veeco Dimension 3100 AFM. The major advantages of using AFM to take images include: (i) the ability to export both 2D and 3D images with illumination and precisely placed observation angles; (ii) the electrical conductivity of the imaged sample is not required. Both conducting and insulating materials can be scanned with true atomic resolution.
In force measurement, AFM can be used to measure the force between AFM probe and sample as a function of their mutual separation. Assume the applied load on the AFM probe is P and the resulted deflection is δ if the deflection is small compared to the suspended length of the AFM probe cantilever, e.g. 1/6, the relationship between the force and the deflection can be simplified as follows: where k is the spring constant of the AFM probe. The spring constant of commercial AFM probes ranges from 0.01 N/m to 450 N/m. AFM-enabled nanoindentation has been proven to be an effective tool in characterizing mechanical properties of 1D nanostructures [112][113][114][115][116].

Mechanical testing of 2D materials
The mechanical behavior of 2D materials can be described macroscopically by continuum elasticity theory. Starting from this point, AFM-enabled nanoindentation technique is well suited to measure macroscopic mechanical properties of 2D materials [38,[117][118][119][120]. This technique is the easiest way to mechanically characterize 2D materials and has been popularly adopted to investigate graphene, MoS 2 , h-BN, etc. Elastic modulus can be calculated from the load-displacement data. The thickness of a sheet of 2D materials can be accurately identified from AFM imaging. The challenges in characterizing 2D monolayer materials using AFM include: (i) well-defined sample geometries; (ii) stress concentration at clamping points; (iii) loading force resolution; (iv) defect; and (v) developing mechanical models to determine stress.

Mechanical testing of graphene
Lee et al. [38] pioneered the AFM-enabled indentation on mechanically exfoliated monolayer graphene suspended on a Si wafer with circular holes (diameter: 1 μm and 1.5 μm) as shown in Figure 4. The configuration has precise boundary conditions and is independent of the substrate, which makes indentation to be one of the ideal ways to measure elastic modulus and strength of graphene. Moreover, no observable slippage occurs during indentation or scanning, presumably due to van der Waals interactions between the graphene and the substrate. Monolayer graphene is a 2D material, so the strain energy density can be normalized by the area of graphene sheet. The mechanical behavior under tensile loading can be described by 2D stress and elastic constant. A nonlinear elastic response is governed by the third-order stress-strain relationship: where σ is the symmetric second Piola-Kirchhoff stress, ε is the uniaxial Lagrangian strain, E is the Young's modulus, and D is the third-order elastic modulus. Based on statistical analysis, the Young's modulus of exfoliated graphene is calculated to be 1.0 ± 0.1 TPa (2D elastic constant E 2D = 342 N/m) assuming an effective graphene thickness of 0.335 nm. For the first time, Lee et al. [38] presented the comprehensive measurement of elastic properties of monolayer graphene, which is a milestone for the mechanical characterization of 2D crystals. In addition to the mechanical characterization of monolayer graphene, Lee et al. [121] applied AFM-enabled nanoindentation to quantify mechanical properties of the bilayer and trilayer graphene sheets. During the test, all load-displacement behaviors are identical upon loading and unloading, which sheds light on the fact that no slippage or plastic deformation occurs. The calculated Young's moduli of the bilayer and trilayer graphene sheets are 1.04 TPa and 0.98 TPa, respectively, which are equal to that of monolayer graphene. Annamalai et al. [122] also adopted the same technique and presented the Young's moduli of graphene sheets. The Young's modulus of monolayer graphene is ~1.12 TPa, which is similar to the findings from Lee et al. [121]. Surprisingly, the Young's moduli of graphene sheets with two, three, and five layers jump to 3.2 TPa. Such phenomenon was speculated from the increased pre-tension due to the different adhesion forces of graphene to substrate and the stacking faults in multilayer graphene [123]. Moreover, the adhesion force in multilayer graphene sheets is also different from that of monolayer graphene and substrate [124,125]. Graphene produced by mechanical exfoliation is proven to be single crystalline with a low defect density. The measured strength can be viewed as the intrinsic strength of graphene. Using AFM-enabled indentation, the maximum stress as a function of applied load for a clamped, linear elastic, circular membrane under a spherical indenter can be derived. Assuming the indenter has a spherical shape and ignoring the nonlinear elasticity, the maximum stress under this configuration can be modeled as: where σ 2D m is the maximum stress at the center of the film, F is the maximum load, and R is the radius of the indenter. The average breaking strength is 55 N/m, though this value might be overestimated due to the ambiguity of nonlinear elasticity. Lee et al. [38] also carried out numerical simulations to investigate the theoretical intrinsic strength. Combining nonlinear elasticity principles, the converted intrinsic strength is 130 ± 10 GPa at the strain of 25%, which is very close to the value obtained by Griffith theory.
Gómez-Navarro et al. [126] developed a similar method to measure elastic properties of monolayer and bilayer graphene sheets. Instead of preparing suspended graphene over a circular hole, the sample was fabricated into a rectangle shape shown in Figure 5. The mechanically exfoliated monolayer and bilayer graphene sheets were first sandwiched by polymethyl-methacrylate (PMMA). The rectangular area was machined by e-beam exposure, which can provide full control over the size and position of the suspended area. Regarding that there is no critical-point drying being used, surface tension leading to the collapse of the suspended sheet would not occur. The nanoindentation combined with an AFM was employed to perform mechanical characterization of the suspended graphene sheets. The elastic constant (k) of the suspended graphene sheet in the linear regime can be used to calculate the elastic modulus of graphene. The valid calculation for a doubleclamped beam under point load can be expressed as follows: where t, w, and l are the thickness, width, and the suspended length of the graphene sheet, respectively. The thickness of monolayer graphene was assumed to be 0.34 nm. T is the built-in tension of the sheet. The calculated elastic modulus is only 0.43 TPa, which is less than half of the elastic modulus obtained by Lee et al. The tested graphene was found to have much lower built-in tension than the exfoliated graphene on a SiO 2 substrate, which allows access to the intrinsic properties of suspended graphene and provides predictable and reproducible resonant frequencies. The variation in elastic modulus might be due to the following reasons: (i) the crystallographic orientation of graphene with respect to the PMMA windows [15]; (ii) clamping condition and point load configuration [127]; (iii) the graphene thickness selection; (iv) substrate effect due to the soft PMMA; and (v) PMMA residue on the sheets inducing local thickness change.
Single-atom-thick graphene sheets with sizes ranging up to square meters can be grown by chemical vapor deposition (CVD) which makes polycrystalline structures almost unavoidable in the graphene [128]. Hashimoto et al. [129] observed individual dislocations in graphene using TEM. Theoretically, graphene grain boundaries are predicted to have distinct electronic, magnetic, chemical, and mechanical properties that strongly depend on their atomic arrangement. Due to the five orders of magnitude size difference between grains and grain boundaries, the mechanical behavior of polycrystalline graphene compared to that of single graphene would be interesting. Huang et al. [130] examined the failure strength of CVD-grown polycrystalline graphene membranes using AFM-enabled indentation ( Figure 6(a)). With the AFM tip pushing down, the membrane broke and the crack propagated along graphene grain boundaries ( Figure 6(b)), indicating that the strength of polycrystalline graphene is dominated by grain boundaries. The failure occurs at loads of ~100 nN, which is an order of magnitude lower than typical fracture loads of 1.7 µN reported for single-crystal-exfoliated graphene. Therefore, grain boundary can severely weaken the mechanical strength of graphene membranes. Park et al. [131] also used AFM to perform indentation tests on graphene membranes obtained by the CVD method and got the same conclusion that grain boundaries significantly decrease the breaking strength of graphene. The upper bound for the in-plane breaking stress is about 35 GPa, which is only one-fourth of that of single-crystal graphene. In addition, out-of-plane ripples can effectively soften graphene's in-plane stiffness.
Generally, ripples found in free-standing [132,133] and supported [134] graphene provide an inhomogeneous strain distribution, which would degrade elastic stiffness of graphene. Recently, Lee et al. [135] proposed a mechanism to the creation of ripples and an improved technique to keep graphene intact during fabrication. It is known that CVDgrown graphene is typically synthesized on metals (e.g., copper). During the transfer process, PMMA is coated on top of graphene as a support layer and then the copper substrate is etched away by ferric chloride (FeCl 3 ) solution. After stamping graphene onto the target substrate, the PMMA layer will be removed. The etching solvents and the removing step might generate ripples. However, if the copper etchant is replaced by ammonium persulfate (NH 4 ) 2 S 2 O 8 , the air-baking step will be eliminated during PMMA removal. As a result, ripples can be greatly reduced [136]. The breaking strength of graphene with large and small grains and mechanically exfoliated graphene was measured by Lee et al. [135]. The results demonstrated that graphene with large grains and exfoliated graphene have an equivalent strength of 118 GPa, and graphene with small grains has a slightly lower strength of 98.5 GPa. The difference can be attributed to defects and grain boundaries. Figure 6(c-e) show that the crack went through the grain instead of propagating along grain boundaries. Using atomistic calculations, Ruoff et al. [137] found that graphene sheets with large-angle tilt boundaries that have a high density of defects are as strong as the exfoliated ones and, unexpectedly, are much stronger than those with low-angle boundaries having few defects. These results are completely contrary to the natural intuition that as the number of defects increases, the strength of a material decreases. Therefore, the argument of the effect of grain boundary on the strength of graphene is continuing [78,138].
Generally, the presence of lattice defects in sheets synthesized by scalable routes might degrade mechanical properties. López-polín et al. [118] reported that the inplane Young's modulus increases with increasing defect density up to almost twice as much as the initial value for a vacancy content of ~0.2%. Once missing atoms are over ~0.4%, the elastic modulus will significantly decrease with defect inclusions. Figure 7 demonstrates the schematic indentation and measured the mechanical performance of defected graphene. The change of Young's modulus indicates that the softening effect of vacancies would be suppressed as the vacancy concentration approaches the percolation threshold, where the elastic coefficients are expected to decrease linearly with the number of vacancies. The direct relationship between Young's modulus and density of defects can be expressed: where k and c are constants, b is a geometrical factor of the order of the inverse of the area of the drumhead that accounts for boundary conditions, l 0 is the localization length for flexural phonons in pristine graphene and n i is the density of defects induced by irradiation [118]. In contrast to the increase and decrease of Young's modulus, the fracture strength continues decreasing with defect density, which follows the standard fracture continuum models. As the defect density increases, the fracture strength first drops to 30% of original strength, and then reach a saturation tendency.

Mechanical testing of graphene oxide (GO)
GO is a compound of carbon, oxygen, and hydrogen in variable ratios obtained by treating graphite with strong oxidizers [139][140][141][142][143]. The oxidized bulk product is a yellow solid with a C:O ratio between 2.1 and 2.9 [144]. The thickness of GO layers is 1.1 ± 0.2 nm and oxygen atoms are arranged in a rectangular pattern with a lattice constant of about 0.27 nm × 0.41 nm [145,146]. The edges of each layer are terminated with carboxyl and carbonyl groups, which make GO bulk materials disperse in solution. The mechanical properties of GO and reduced GO (rGO) have been investigated by both experimental and theoretical approaches. Suk et al. [147] employed AFM in contact mode to measure the effective Young's modulus and prestress in monolayer and multilayer GO membranes. Figure 8 shows the transferred membrane and the histogram of the effective Young's modulus and SAED patterns of GO membranes. The prestress in GO membranes is between 39.7 MPa and 76.8 MPa. Monolayer GO has a much lower effective Young's modulus of 207.6 ± 23.4 GPa compared to pristine graphene. Regarding that GO was obtained by oxidation of graphene, 40% original sp 2 bonded carbon atoms of graphene were reconstructed into sp 3 -bonded atoms via bonding with oxygen [146]. Due to the heavily 'defected' structure, the GO membrane does not have attractive mechanical performance. Assume that the membrane is in monolayer form, the effective Young's moduli of bilayer and trilayer GO membranes increase to 444.8 ± 25.3 GPa and 666.5 ± 34.6 GPa, respectively. After using the real thickness, the Young's moduli of bilayer and trilayer membranes can be recalculated to be 223.9 ± 17.7 GPa and 229.5 ± 27.0 GPa, respectively. Such similarity between monolayer, bilayer, and trilayer GO indicates that the bonding between layers in the bilayer and trilayer membranes is strong enough to avoid any interlayer sliding [147].
To restore the integrity of GO, a chemical reduction can be carried out to reduce the number of oxygen-involved functional groups to get a graphene-like sheet of rGO. For example, GO prepared via the Hummers method [144] can be transferred onto a Si/SiO 2 substrate and reduced by hydrogen plasma treatment. The solution-based route is another way to reduce GO with the advantages of being cheap and up-scalable [148,149]. The sheets obtained with this method may have residual oxygenated functional groups due to the limited efficiency of the reduction process. To understand the mechanical performance of rGO, Gómez-Navarro et al. [150] performed indentation testing. Preselected layers were cut by standard e-beam lithography with Ti/Au electrodes. In order to freely suspend rGO, the samples were etched by hydrofluoric acid, followed by critical point drying to prevent adhesion of the sheets to the substrate. Mechanical characterization of the free-standing rGO monolayers was carried out by indenting an AFM tip at the center of the suspended area. The calculated elastic modulus of the rGO monolayers is 0.25 ± 0.15 TPa, which is much lower than that of monolayer graphene, but similar to those of GO membranes.

Mechanical testing of MoS 2
MoS 2 is one of the most extensively studied TMDs [56,60,64,65,[151][152][153][154], which has a hexagonal structure consisted of Mo and S atoms at alternating corners. The driving force to integrate MoS 2 into MEMS/NEMS is that, unlike graphene, it has an indirect bandgap of 1.29 eV [62]. The transition from indirect to direct bandgap occurs only if thickness approaches monolayer [155]. MoS 2 could be a promising candidate for flexible electronics because of its low cost and high performance. To make MoS 2 best serve potential applications with strong stability and reliability, the mechanical characterization of MoS 2 is necessary.
A defect-free material would have fracture strength at an upper theoretical limit of ~10% of its Young's modulus [156]. The in-plane stiffness of a defect-free monolayer MoS 2 is proportional to the effective spring constant of the bond between Mo and S. As AFMenabled indentation has been used to characterize mechanical properties of graphene, GO, and rGO, Bertolazzi et al. [157] adopted the same technique to investigate the mechanical properties of MoS 2 . Figure 9 shows optical and AFM images and associated indentation testing on a monolayer MoS 2 flake transferred onto the prepatterned SiO 2 substrate, which contains an array of circular holes with a diameter of 550 nm. The measured Young's modulus of MoS 2 with a thickness of 0.65 nm is 270 ± 100 GPa; however, such value drops down to 200 ± 60 GPa for bilayer MoS 2 . As a reference, the Young's modulus of steel and bulk MoS 2 is 210 GPa and 238 GPa, respectively. The discrepancy of Young's modulus of MoS 2 with the different number of layers is attributed to the possible effect of interlayer sliding or defects in the MoS 2 [158]. Similar studies have also been done on MoS 2 films ranging from 5 to 25 layers by Castellanos-Gomez et al. [151,159]. The obtained Young's modulus is 330 ± 70 GPa which is close to that of bulk MoS 2 , suggesting that there is no size dependence for the Young's modulus of MoS 2 .

Mechanical testing of WSe 2
Zhang et al. [160] reported the elastic properties of suspended multilayer WSe 2 . The suspended WSe 2 membranes were fabricated by mechanical exfoliation of bulk WSe 2 . The exfoliated multilayer WSe 2 flakes were transferred onto SiO 2 /Si substrates pre-patterned with hole arrays. Figure 10 shows the transferred WSe 2 and AFM-enabled indentation test. The mechanical tests were performed on membranes with various layers to obtain their elastic constants. The elastic moduli are 170.3 ± 6.7 GPa, 166.3 ± 6.1 GPa, 167.9 ± 7.2, and 164.8 ± 5.7 GPa for samples with 5, 6, 12, and 14 layers, respectively. Such results indicate that the Young's modulus of WSe 2 is independent of its thickness. The interlayer interaction in WSe 2 was observed to be strong enough to prevent the interlayer sliding during the indentation experiments. The Young's modulus of multilayer WSe 2 is about two-thirds of that of other 2D semiconducting TMDs, including MoS 2 and WS 2 , and one-sixth of graphene [157,161].

Mechanical testing of h-BN
Similar to MoS 2 , the boron and nitrogen atoms in h-BN are held together by covalent bonds, while the layers are attached by weak van der Waals interactions. This weak interlayer bonding facilitates exfoliation and fabrication of monolayer and few-layer crystals. Mechanical properties of h-BN have been theoretically predicted to be extremely strong, much like graphene [162,163]. For example, the density functional theory (DFT) simulation results show that the E 2D can reach 275.9 N/m and the Poisson's ratio is around 0.22 [164,165]. Song et al. [70] performed AFM-enabled nanoindentation to measure the elastic constant of multi-layer h-BN. Figure 11(a-c) shows the experimental setup and measured force-displacement curves. The obtained E 2D and σ 2D of the tested bilayer h-BN are 223 ± 16 N/m and 8.8 ± 1.2 N/m, respectively [70]. The maximum stress held by the h-BN film is far below 55 N/m found in monolayer graphene. Regarding that the maximum stress of graphene, 55 N/m was obtained from mechanically exfoliated graphene, the lower maximum stress could result from a large number of vacancy defects in h-BN grown by the CVD method. Interestingly, both E 2D and σ 2D significantly increase as the thickness of h-BN increases. For example, once the film contains five layers, the E 2D and σ 2D surprisingly reach 505 ± 30 N/m and 15.7 ± 1.5 N/ m. Such result E 2D is even close to two times higher than the theoretical prediction of 292.1 N/ s and is much higher than 342 N/m, the elastic constant of graphene. The associated results, probably, cannot be fully explained by the dependence of the in-plane stiffness on intrinsic defects present in the film. Generally, the materials may contain more defects as the size increases, which suggests that the trend of maximum stress in the study might be different. The layer distribution of stacking faults in the CVD-grown films, the error in estimating the exact diameter of the holes, and the position of membrane contact with the substrate would be the reasons for the discrepancy of the measured elastic constants and maximum stress but are not enough. Li et al. [166] tested boron nitride nanosheets with thicknesses of 25-300 nm using AFM enabled three-point bending tests. Figure 11(d-f) demonstrate the schematic diagram illustrating a clamped h-BN nanosheet for an AFM bending test, comparative experimental approaching and detaching load-displacement curves obtained in the center of a nanosheet and on the Au substrate, respectively, and bending modulus versus nanosheet thickness. The bending moduli were found to increase with a decrease in sheet thickness and approach to 31.2 GPa, the theoretical value of a bulk h-BN for sheet thicknesses below 50 nm [167]. The highly thickness-dependent bending modulus is attributed to the layer distribution of stacking faults.

Mechanical testing of black phosphor (BP)
Wang et al. [168] transferred BP nanosheets and performed nanoindentation to get their mechanical properties. Figure 12(a-c) shows the AFM image of BP nanosheet before and after the indentation test. The BP nanosheets were suspended over circular holes and scanned by an AFM. The continuum mechanic model was introduced to calculate the elastic modulus and pretension of BP nanosheets with thicknesses ranging from 14.3 to 34 nm. The elastic modulus of BP nanosheets was found to decrease as the thickness decreases. The maximum elastic modulus is 276.6 ± 32.4 GPa. When the thickness is larger than 30 nm, the modulus remains at 89.7 ± 26.4 GPa which is equal to that of bulk BP [169]. Besides, the effective strain of BP ranges from 8% to 17% with a breaking strength of 25 GPa. Regarding that BP is not stable in ambient condition, Moreno-Moreno et al. [79] investigated mechanical properties of BP nanosheets with a few layers in both high-vacuum condition and as  Figure 12(d-f) show the evolution of the mechanical properties and topography of the BP drumheads under ambient conditions. The tested BP flakes were with thicknesses ranging from 4 to 30 nm. AFM-enabled nanoindentation was performed on the samples suspended over circular holes. For the samples tested in high-vacuum condition, an elastic modulus of 46 ± 10 GPa and breaking strength of 2.4 ± 1 GPa were obtained, which are significantly lower than the values measured by Wang et al. [168]. In addition, both magnitudes are independent of the thickness of the flakes, which are contrary to the finding from Wang et al. [168]. The elastic modulus barely decreases in atmospheric condition for thick flakes, while the exposure to air has substantial influence in the mechanical response of flakes thinner than 6 nm.

In situ indentation in SEM
Without AFM laser and photodiode system, AFM cantilever driven by a manipulator in SEM can be independently used to detect force once the deflection is visualized [170]. For example, a mechanical testing system consisting of three independent linear stages, three picomotors, and an AFM probe has been used to investigate the interface strength between CNTs and graphene [170]. The tester can drive and align the AFM probe with three degrees of freedom (x, y, z). The force resolution depends on the spring constant of the installed AFM probe which may range between 0.01 N/m and 450 N/m. The maximum force resulting in mechanical failure can be calculated based on the product of spring constant and the resulted deflection. Therefore, such technique can be used to investigate the mechanical performance of 2D materials. The advantage of in situ indentation in SEM enables a precise control of the tip position over the membranes and observation of fracture during indentation.
Suk et al. [171] performed an indentation test demonstrated in Figure 13 to investigate fracture of polycrystalline graphene membrane in SEM. The polycrystalline graphene was synthesized by the CVD method and then transferred onto 9 μm diameter holes fabricated on the silicon substrate. Circular graphene membranes were subjected to central point loads using a nanomanipulator combined with an AFM cantilever as a force sensor. The grain boundaries of the polycrystalline graphene were visualized by Raman spectroscopy. The suspended graphene membrane consisting only one grain had an average failure strength of 45.4 ± 10.4 GPa, while the suspended graphene composed of multiple grains exhibited much lower average failure strength of 16.4 ± 5.1 GPa. The highest fracture strength of the polycrystalline graphene membranes did not exceed the lowest failure strength of the single-crystal membranes. As the density of grain boundaries increases, the failure strength decreases, suggesting that the grain boundary can significantly weaken the fracture strength of graphene. Such result agrees with the previous finding from AFM-enabled nanoindentation testing that grain boundaries significantly decrease the breaking strength of graphene [131]. Moreover, the obtained failure strength does not exceed the upper bound in-plane breaking stress of graphene, 35 GPa [131].

Micro-/nano-mechanical devices
The local indentation by an AFM tip may result in highly non-uniform stress and strain fields in tested 2D crystals, which makes it difficult to extract the intrinsic mechanical properties from experimental measurements. Moreover, it is impossible to visualize the dynamic fracture processes by performing nanoindentation tests. Recently, several types of micro-/nano-mechanical testing devices have been successfully designed and developed, enabling the uniform in-plane loading on a freestanding membrane of 2D crystals [76,108,[172][173][174][175][176]. As long as selected crystals are transferred onto the testing area, their mechanical properties can be well quantified. The in situ tensile tests can be performed in both SEM and TEM, which allows the fracture process to be easily visualized and further helps with the analysis of fracture behavior of 2D crystals.

Thermal-actuated micromechanical devices
One of the most common micromechanical devices has been developed by Espinosa et al. [177]. There are two types of actuators: one is a thermal actuator and the other is an electrostatic (comb drive) actuator. The thermally driven microelectromechanical systems (MEMS) platform shown in Figure 14(a) includes an on-chip actuator, an electronic load sensor, and a gap for placement of nanostructures [172,177]. A major advance in this design is the introduction of a capacitance load sensor that measures displacement electronically, based on differential capacitive sensing rather than microscope imaging. The MEMS platforms are good for the in situ SEM and TEM tensile tests. The thermally actuated micromechanical device has the capability of testing stiffer structures, such as films and nanowires with larger diameters. In addition, the comb-driven micromechanical device is suitable for compliant structures, such as CNTs and nanowires with smaller diameters. In fact, many MEMS platforms based on this configuration have been designed and developed, including the one demonstrated in Figure 14(b) [173,[178][179][180][181].

Micromechanical Devices with Push-Pull Mechanism
Most recently, Lou et al. [182,183] have designed and developed a micro-fabricated device shown in Figure 15(a), which can perform the tensile testing and pullout experiment [184][185][186][187][188][189]. The microdevice uses a spring-like 'push-pull' mechanism, consisting of three moveable shuttles attached to each other via inclined freestanding beams. A quantitative Agilent InSEM nanoindenter was used to measure the load and  displacement independently. The design can significantly minimize the source of errors and reduce the cost of device fabrication. The actuation is enabled by the nanoindenter that applies a load on the top shuttle in the vertical direction (along the y-axis). Four sets of inclined symmetrical beams transform the motion of the top shuttle into a 2D translation of the sample stage shuttles, resulting in uniaxial tension on the clamped sample. In the micro-mechanical device, both the load applied on the sample and the sample elongation can be derived from the nanoindenter load and displacement data using conversion factors obtained from finite element simulations or by a force reduction method. The resolution of load and displacement of the device is on the order of a few tens of nano-newtons and a few nanometers, respectively. The corresponding stressstrain curve can be used for further fracture analysis. The elastic modulus and fracture strength can be precisely measured. All kinds of 1D nanostructures loaded onto the device can be tested. Such a development in microdevices makes it possible to carry out mechanical tests on graphene and other 2D crystals. Figure 15(c) shows the micromechanical device adopted by Liao et al. [174]. The transferred graphene on the micromechanical device is included in Figure 15(d).

Development of 'Dry-Transfer' technique
A critical step in the mechanical testing of 2D materials is to transfer the atomically thin film onto a sample stage. To address the fact that liquid is unfavorable for the suspended Si working layer of the stage, Zhang et al. [80] developed a unique approach for graphene transfer. Figure 16(a-f) demonstrate the dry transfer of graphene. The as-grown graphene was first coated by PMMA and then attached to a polydimethylsiloxane (PDMS) block. The PDMS block had an open window which is slightly larger than the sample stage in the center, allowing the micromechanical device to go through and capture the suspended graphene/PMMA. Heat treatment enabled the PMMA/graphene film to adhere to the suspended Si layer of the device smoothly and tightly, which was important to prevent wrinkle formation and release pre-strain in the graphene film. Afterward, the graphene/ PMMA film was carefully cut with the tip of a sharp pair of tweezers along the open window contour of the PDMS block, and the sample stage together with the transparent graphene/PMMA film was subsequently picked up with tweezers. After calcining in the air to decompose PMMA, a suspended film of graphene was obtained across the whole device.
The dry transfer technique developed by Zhang et al. [80] was good for film samples, but not for discontinuous crystals. Yang et al. [76] developed another effective 'drytransfer' method. Figure 16(g-j) schematically show the transfer of individual MoSe 2 crystals [76]. The 2D crystals together with the substrate were spin-coated with PMMA with a layer thickness of about 200-300 nm and heated on a hot plate at 180°C for 1 min to ensure adhesion between the 2D crystals and PMMA. The copper was etched away using FeCl 3 and Si/SiO 2 substrate was etched off by NaOH solutions. The floating film was fished out of the etchant using a copper TEM grid. A fine tungsten micromanipulator probe was used to cut the desired area of PMMA coated 2D crystals and to carefully load the 2D material over the test section of the micromechanical device under an optical microscope. The PMMA can then be annealed in a 90% nitrogen and 10% hydrogenmixed CVD tube furnace. Generally, the temperature is raised to 400°C over the course of 40 min and held at 400°C for 2 h with a continuous flow of the gas mixture under atmospheric pressure. The monolayer and bilayer 2D crystals in Figures 16(h,i) are distinguishable, which enables the comparison of the mechanical behaviors of 2D crystals with different numbers of layers. With the effective 'dry-transfer' technique, the suspended monolayer 2D crystals can be easily obtained as demonstrated in Figure 16(j). Moreover, various crystals can be stacked together with a controlled orientation, e.g. a P-N junction is fabricated on a piece of h-BN by vertically stacking a WSe 2 and an MoS 2 together [190].  [191], with permission of Springer Nature.

Mechanical testing of graphene
Cao et al. [191] performed in situ quantitative tensile testing of freestanding CVDgrown monolayer graphene in a scanning electron microscope using the micromechanical device in Figure 15(c). Before testing, the preparation of monolayer graphene was facilitated by robust sample transfer, shaping, and clamping techniques. The measured Young's modulus is close to 1 TPa, witch well agrees with the predicted theoretical values and nanoindentation results [38,135,[192][193][194][195][196][197][198]. The fracture strength measured from multiple samples reaches ~60 GPa, which is considerably reduced but in the same order of magnitude as they are compared to the ideal strength of monolayer graphene (~100-130 GPa). The difference between measured fracture strengths could be attributed to the edge defects implanted during the sample cutting process by FIB. However, the obtained maximum strain is only ~6% demonstrated in Figure 17, which is far below ~35%, the maximum strain of graphene from theoretical calculations [192][193][194]199,200]. Compared with the previous study on tensile testing of pre-cracked graphene [80], the result clearly indicates much higher elastic stretchability and tensile strength for free-standing graphene without crack.
Fracture toughness characterization on monolayer or multilayer graphene is challenging due to the requirements of particular design and equipment carrying on the nanoscale tensile test. The intrinsic strength governs a uniform breaking of atomic bonding in perfect graphene. However, the graphene with defects, such as single vacancies (SV), stone-wales (SW), and slit, may have both low elastic performance and fracture strength. The strength of large-area graphene with engineering relevance is usually determined by its fracture toughness. Zhang et al. [80] reported an in situ tensile testing of suspended graphene using a micromechanical device in a scanning electron microscope. Figure 18 shows nanomechanical testing of fracture of graphene with a pre-crack. During tensile loading, the pre-cracked graphene sample fractures in a brittle manner with sharp edges at a breaking stress substantially lower than the intrinsic strength of graphene. Such brittle feature is in agreement with previous studies [201]. Combining experiments and modeling verifies the applicability of the classic Griffith theory of brittle fracture to graphene. The fracture toughness of graphene is measured as the critical stress intensity of 4.0 ± 0.6 MPa·m 1/2 . The result has a significant implication on the strength of large-area graphene that should be determined by its fracture toughness, rather than intrinsic strength. Regarding that nanoindentation is unable to measure fracture toughness of 2D materials, the tensile testing of notched graphene enabled by the micromechanical device advances the understanding of mechanics of 2D materials and triggers the investigation of fracture toughness of other 2D materials.

Mechanical testing of rebar graphene
Perfect graphene is believed to be one of the strongest materials, yet its resistance to fracture is much less impressive [80]. The modest fracture toughness is thought to be related to the generally brittle nature in the fracture process of graphene and its 2D analogous [76]. The brittleness also makes it extremely difficult to assess the mechanical properties of 2D materials. Yan et al. [202] integrated CNTs into graphene to form a unique rebar graphene, which has been expected to be a tougher and stronger 2D material. Hacopian et al. [176] got freely suspended rebar graphene over the micromechanical devices. The tensile testing was performed inside an SEM and demonstrated in Figure 19. A zigzag crack propagation is presented in Figure 19(c). This fracture surface is due to the CNTs redirecting the motion of the crack and guiding the propagation in a zigzag formation. Graphene alone is brittle and exhibits a direct fracture, while rebar graphene shows a longer fracture path, suggesting a higher fracture energy consumption during mechanical failure. The average elastic modulus and fracture strength of the tested unnotched rebar graphene samples are 466.8 ± 29.95 GPa and 6.02 ± 1.53 GPa, respectively. The stress intensity factor of rebar graphene reaches 10.50 ± 5.73 MPa/m 2 , which is much higher than that of graphene [80]. Such results indicate rebar graphene requires a higher amount of stress than pristine graphene to complete fracture. Both experimental observation and theoretical prediction reveal that graphene fractures in a linear, brittle manner, while rebar graphene displays a zigzag fracture surface, guided, and redirected by the embedded CNTs.

Mechanical testing of MoSe 2
Yang et al. [76] transferred monolayer MoSe 2 onto the micromechanical device, quantified its fracture strength and elastic modulus, and investigated the effect of defects on the mechanical properties of MoSe 2 . All the tests were conducted in SEM through realtime observation [76]. Figure 20 shows the SEM snapshots during a typical tensile test until catastrophic failure. The corresponding stress-strain curve is plotted in Figure 20 respectively [76]. The elastic modulus from the above experimental measurement is consistent with the theoretical value of 162.1 GPa from the first-principles density functional theory (DFT) calculations [203]. However, the measured fracture strengths vary from 2.2 GPa to 9.9 GPa, with a considerably large standard deviation of 2.9 GPa. The variation in size of preexisting flaws/cracks is responsible for the large scattering of measured fracture strengths. The Griffith theory of brittle fracture is applicable to a 2D material of graphene by combining in situ fracture testing and atomistic modeling [80]. On this basis, the Griffith theory was applied to estimate the size of a dominant fracture-producing crack/flaw in the 2D MoSe 2 [204]. For a central crack of length 2a 0 , the Griffith theory of brittle fracture can be expressed as where E is the elastic modulus and γ is the surface energy which is defined as the edge energy of a 2D crystal divided by its thickness. Then, the length of the fracture-producing crack for all samples tested was estimated. The crack lengths range from 3.6 nm to 77.5 nm, with an average value of 33.0 ± 30.9 nm [76]. The large number of invisible defects is responsible for the variation in fracture strength.

Piezoelectric tube-driven testing in TEM
For AFM-enabled indentation testing, if the deflection is too large, the linear relationship between the deflection and the load may not follow a linear relationship, bringing error the calculated elastic modulus and fracture strength. By replacing AFM cantilever with a higher spring constant, the deflection can be controlled in a smaller range. An alternative testing method to precisely monitor the load is to adopt a piezoelectric tubedriven manipulator. The piezoelectric crystal will expand or shrink when a voltage is applied. The force can be calculated based on the equation as follows: where k T is the piezo actuator stiffness (N/m) and ΔL 0 is the maximum nominal displacement without external force. Wei et al. carried out in situ tensile testing in HR-TEM equipped with a side-entry AFM-TEM holder, which combines a force-measuring system and a high-precision piezoelectric tube-driven nanomanipulation system. Both graphene and boronitrene nanosheets were tested. Figure 21 shows the setup of the testing system and TEM images of pristine, notched, and fracture of graphene nanosheets. The fracture toughness of multilayer graphene and boronitrenes with blunt notches was determined to be 12.0 ± 3.9 MPa/ m 1/2 and 5.5 ± 0.7 MPa/m 1/2 , respectively. In addition to quantification of fracture toughness of 2D materials, TEM has been widely used to investigate the fracture surface of 2D materials. For example, Wang et al. [56] found that the sparse vacancy defects can cause crack deflections while increasing defect density shifts the fracture mechanism from brittle to ductile by the migration of vacancies. Ly et al. [77] observed high-frequency emission of dislocations in MoS 2 , which is beyond the previous understanding of the fracture of brittle MoS 2 . The strain analysis reveals that dislocation emission is closely associated with the crack propagation path in nanoscale.

Bulge testing
The bulge test was first reported by J.M. Beams in 1959 [206]. The testing method has advantages of elimination of substrate influence compared to nanoindentation techniques and clamping problems required by tensile tests [207]. Bulge testing has been widely used to characterize mechanical properties of freestanding thin films made of various materials including metals, semiconductors, and dielectric materials [208][209][210][211]. In bulge tests, the mechanical properties of the thin film can be obtained from the relationship between the imposed uniform pressure and the corresponding out-of-plane deflection of the bulged film. The out-of-plane deflection can be measured via optical microscopy with a calibrated vertical displacement, laser interferometry, and other techniques [212][213][214]. The measured curvature of the bulged membrane, which is equivalent to the out-of-plane deflection, can be used to analyze the stress. If a circular membrane is pressurized, the relationship between pressure, deflection, Young's modulus, and equibiaxial stress can be expressed as follows [207]: where E and v are Young's modulus and Poisson's ratio of the membrane, respectively. P is the pressure and h is the thickness of the sample. w 0 is the maximum deflection and α is the radius of the sample (w 0 ≪ α). σ and σ 0 are the equi-biaxial stress and residual stress before pressurization, respectively.

Depressurize inside and form a concave deflection in film
Recently, Hwangbo et al. [215] observed and analyzed the fracture characteristics of the monolayer CVD-grown graphene using the pressurized bulge testing setup demonstrated in Figure 22. The monolayer CVD-graphene appeared to undergo environmentally assisted subcritical crack growth in room condition. Figure 22(b) shows that the crack grew in a discontinuous and complicated manner after the appearance of the minimum detectable crack. The catastrophic failure of the CVD-grown graphene occurred within a time of less than 2 ms but was captured by a high-speed camera. Interestingly, the growth proceeded as a succession of crack arrest and re-initiation similar to the behavior frequently observed in 3D bulk materials. The fracture toughness of the CVD-grown graphene has turned out to be exceptionally high, 10.7 ± 3.3 MPa·m 1/2 , as compared to the critical stress intensity of 4.0 ± 0.6 MPa·m 1/2 obtained from the tensile test using a micromechanical device [80]. The difference in fracture toughness might result from the different testing conditions, regarding that the pressurized bulge testing was carried out at ambient conditions and the tensile testing was performed in a high-vacuum condition. The advantages of tensile testing in characterizing fracture toughness of graphene include: (1) the tensile test can superbly reflect the mechanical behavior of tested materials; and (2) the in situ tensile test in SEM can minimize the experimental and calculation errors. Likewise, the advantage of pressurized bulge testing is that it demonstrates the crack propagation scenario through the use of a high-speed camera.

Depressurize outside and form a convex deflection in film
Most recently, mechanical behaviors of 2D crystals have been demonstrated indirectly using Raman spectroscopy. Raman spectroscopy is usually employed to observe vibrational, rotational, and other low-frequency modes in a system, which can be used to investigate the intrinsic properties of graphene. The Raman spectrum of graphene is sensitive to mechanical deformations. Red-shift and splitting of Raman G and 2D bands have been experimentally demonstrated when graphene is under uniaxial strain [216][217][218][219]. The Young's modulus of graphene layers can be deduced by measuring the strain induced on pressurized graphene balloons using Raman spectroscopy and comparing the strain with a numerical calculation based on the finite element method. Figure 24 shows a schematic diagram of the experimental setup for measuring Young's modulus of graphene using Raman spectroscopy. The Young's modulus of single-layer graphene is calculated to be 2.4 ± 0.4 TPa [220] which is much larger than the reported values [121,221,222]. Cheong et al. [220] analyzed that the Young's modulus may not be constant in different strain ranges. If graphene has significant softening at a higher strain range, the estimated Young's modulus would be smaller than the value estimated in the small strain range. Although accurate quantitative analysis is not possible due to the large uncertainty caused by trivial Raman peak shifts, the estimated Young's modulus value is consistently larger than those in the previous reports [38,135].

Electrostatic force triggered drum structure
Palaniapan et al. [221] fabricated a graphene drum which can be electrostatically deflected. To determine the induced static deflection, a scan of the unbiased device was first taken to determine the initial state of the drum and another scan of the same region was taken while a voltage (V s ) was applied to the back gate. By performing the profile subtraction, the deflection resulting from the applied electrostatic force can be derived. The elastic modulus of deflected graphene can be obtained via fitting to the plate theory. The electrostatic force F was calculated using the parallel plate equation and applied as a uniformly distributed load over the circular surface in the model: where ε 0 = 8.854 × 10 −12 F/m is the permittivity of free space, ε r is the effective relative permittivity, A is the area of the graphene drum, V s is the applied voltage, g is the initial gap and d 0 is the peak deflection. With the load calculated, the 2D stress and elastic constant can be derived. Figure 23 shows the optical micrograph of a suspended graphene drum device. The number of graphene layers is up to 40. The calculated Young's modulus is about 1 TPa. The mechanical behavior of the graphene drum structure was also simulated using finite element modeling. The derived mechanical properties match the experimental results very well. Other mechanical parameters of the drums, such as linear and nonlinear spring constant, can also be deduced from the experimental forcedeflection data. The drum was found to have a linear spring constant ranging from 3.24 to 37.4 N/m and could be actuated to about 18-34% of their thickness before exhibiting nonlinear deflection. It is also found that the thicker or stiffer devices may actually be more resilient to nonlinear behavior. The graphene drum holds prospective applications as resonators and mass sensors.

Phonon dispersion measurement
Phonon dispersion measurement can be used to characterize the mechanical properties of graphene through high-resolution electron energy loss spectroscopy (HREELS), which is a powerful tool to investigate surface phonon dispersion, surface structure, and monitor epitaxial growth. HREELS deals with small energy losses in the range of 10 −3 eV to 1 eV. The main advantages of HREELS include high surface sensitivity, excellent resolution in both energy and momentum domains, and wide energy and momentum windows. In graphene, there are two types of phonons: lattice vibrations in the plane of the sheet giving rise to transverse and longitudinal acoustic and optical branches, and lattice vibrations out of the plane of the layer which give rise to the so-called flexural phonons [223]. The acoustic phonons of graphene can provide information on its elastic properties. The sound velocities of the transverse acoustic and longitudinal acoustic branches could be used to calculate the in-plane stiffness and the shear modulus of 2D materials. Chiarello et al. [223] adopted phonon dispersion measurement to evaluate Young's modulus and the Poisson's ratio of quasi-freestanding graphene samples grown on metal substrates. Figure 25 shows HREEL spectra of monolayer graphene/Pt(111) as a function of the scattering angle. The relationship between the speed of transverse acoustic (ν T ) and longitudinal acoustic (ν L ) branches and in-plane stiffness (κ) and shear modulus (μ) of the graphene can be expressed as: where ρ 2D is the 2D mass density. The Poisson's ratio and in-plane stiffness of graphene are 0.19 and 342 N/m, respectively. Such values are the same as those obtained by Lee et al. through AFM-enabled indentation [135,224]. Hence, phonon dispersion measurement offers the unique opportunity to perform measurements for ripple-free and quasifreestanding graphene sheets.

Mechanical testing techniques
The mechanical characterization techniques, including AFM-enabled nanoindentation, micro-/nano-mechanical devices, bulge testing together with Raman spectroscopy, etc., have been briefly reviewed. AFM-enabled nanoindentation is a facile and user-friendly technique which has been popularly employed to investigate 2D materials. A commonly used wet transfer can facilitate to load mechanically exfoliated and CVD-grown samples over holes with diameter up to 9 μm. The configuration has precise boundary conditions and does not need any special requirement for the substrate. All of these make indentation be one of the ideal ways to quantify the mechanical properties of 2D materials. On the other hand, the local indentation by an AFM tip may result in non-uniform stress and strain fields in the tested 2D materials, which makes it difficult to extract intrinsic mechanical properties. Moreover, it is impossible to visualize the dynamic fracture processes. While in situ indentation in SEM would complement the AFM-enabled nanoindentation tests by bringing precise control of tip position over the tested membrane and observation of fracture scenarios during indentation. Compared to nanoindentation, in situ tensile tests facilitated by the micromechanical devices can enable uniform in-plane loading on a freestanding membrane, which would help obtain intrinsic mechanical properties of 2D materials. If the defect category, distribution, and density can be characterized, the effect of defects on mechanical properties would be easily unveiled. The tensile tests performed in both SEM and TEM would allow to videotape crack propagation and further help with analysis of fracture behavior of 2D materials. If a notch is prepared in the suspended 2D membrane, the fracture toughness can also be measured. Therefore, the tensile testing of pristine and notched 2D materials would advance the understanding of mechanics of 2D materials. Unlike the wet transfer that can be used to prepare samples for nanoindentation tests, dry transfer techniques have to be applied to load 2D materials over the testing area of micromechanical devices, regarding that liquid is unfavorable for the suspended Si working layer. A major concern from the mechanics society is whether the coated PMMA can be fully removed. A small residual of PMMA would give a significant error to the measured mechanical properties due to the tested membrane is in monolayer or a few layers.
Compared to nanoindentation and in situ tensile tests, bulge testing, electrostatic force triggered drum structure, and phonon dispersion measurement cannot collect the load and displacement directly, but monitor pressure, voltage, and lattice vibration. These parameters will be used to derive the mechanical properties of the tested 2D materials. Visualization of crack propagation can be achieved by a high-speed camera. Generally, quantitative analysis is with large uncertainty, resulting in the overestimated Young's modulus.

Mechanical properties of 2D materials
Graphene as one of the strongest materials has drawn significant attention from the mechanics community. In addition, the mechanical properties of the derivatives of graphene, e.g. GO and rGO, emerging TMDs, e.g. MoS 2 and WSe 2 , h-BN, and black phosphor have been investigated. Most 2D materials can be obtained through mechanical exfoliation and CVD growth, which offers the opportunity to get samples with low and high defect densities. Therefore, the effect of defects including SV, SW, slit, and grain boundaries on mechanical properties of 2D materials has been studied. Currently, 2D crystals with monolayer, bilayer, trilayer, and a few nanometers in thickness can be easily obtained through mechanical exfoliation and liquid dispersion, which enables the investigation of the dependence of mechanical performance on thickness, interfacial sliding, etc. In terms of mechanical properties, elastic modulus, fracture strength, fracture toughness, effect of the defect on fracture strength and elasticity have been intensively discussed.
Though mechanical properties and mechanical behaviors of graphene and other 2D crystals have been extensively investigated, the mechanics of 2D materials is still in its infant stage. More effort is required to help clearly understand the mechanical behaviors of 2D materials and accurately quantify their mechanical properties. The debates on mechanical behaviors and mechanical properties continue in the mechanics community. For example, the reported experimental and theoretical elastic modulus of graphene ranges from 0.25 TPa to 5.5 TPa. The measured and calculated fracture strength of graphene is between 55 GPa and 210 GPa. The significant variation in mechanical properties is mainly due to the different experimental techniques and theoretical approaches, sample preparation and transfer, testing environment, etc. In addition to the mechanical measurement, the observed mechanical behaviors may be contrary. For example, it is usually accepted that the grain boundary and initial cracks will greatly weaken the strength of nanocrystalline graphene. It is found that the initial crack and grain boundary may be independent of fracture strength regardless of grain size. Fracture following grain boundaries and passing through grains have been observed. Another major challenge is to correlate the experimental measurements to the theoretical prediction due to the lack of suitable experimental devices and sample manipulation possibilities. Finally, compared to graphene, the mechanical properties of MoS 2 , h-BN, and other 2D crystals have not been fully studied. More robust micro-/nano-devices are in need to facilitate mechanical characterization. Addressing these issues is very challenging but offers an opportunity to advance the understanding of 2D materials.