Elastic straining of free-standing monolayer graphene

Graphene, a two-dimensional (2D) material with a near-perfect crystal structure, has garnered significant attention for its potential in various applications due to its exceptional properties including high strength, transmittance, thermal conductivity, and electron mobility. While theoretical studies predict extraordinary mechanical properties for graphene, including a Young's modulus of around 1 TPa and tensile strength exceeding 100 GPa, experimental verification has been challenging due to difficulties in sample preparation and testing. Previous experimental approaches, such as nanoindentation and burst tests, have yielded results that either probe only local regions or are influenced by factors like wrinkles and defects, hindering a comprehensive understanding of graphene's mechanical performance at larger scales. This study addresses these challenges by developing a novel protocol for sample transfer, shaping, and straining, enabling in situ tensile tests of large-area, free-standing single-crystalline monolayer graphene to directly measure its mechanical properties under well-controlled conditions. The ultimate goal is to determine if large-area graphene can exhibit near-ideal mechanical properties that are critical for numerous technological applications, particularly in the realm of flexible electronics and mechatronics where substantial elastic deformation is desirable. This would provide direct experimental validation of theoretical predictions and move beyond previous limitations of local measurements which often do not represent the whole-sample mechanical behavior.

The literature extensively discusses the theoretical mechanical properties of graphene. Theoretical investigations predict a Young's modulus around 1 TPa and an ideal tensile strength of 100–130 GPa, with strain to failure ranging from 13–19% along the armchair and 20–26% along the zigzag directions. However, the presence of defects, such as point defects, grain boundaries, and edge defects, in large-area CVD-grown graphene significantly impacts the measured tensile strength, often reducing it considerably from the theoretical ideal. Previous attempts at experimentally determining the mechanical properties of graphene have relied on indirect methods like nanoindentation, which provides localized measurements and is sensitive to geometrical effects. Burst tests, while direct, have shown large variations in burst pressure due to wrinkles and defects. The limitations of these methods emphasize the need for direct tensile tests on crack-free, large-area graphene samples to obtain reliable and representative mechanical properties, thus facilitating the realization of strain-engineering applications.

The researchers developed a novel methodology for preparing and testing free-standing monolayer graphene samples. CVD-grown monolayer graphene samples on copper foil were transferred to a push-to-pull (PTP) micromechanical device using a PMMA-assisted wet transfer method. The graphene was then carefully shaped into ribbon-like structures using focused ion beam (FIB) milling, with the suspended portion being precisely controlled in terms of size and area. The suspended graphene was characterized by Raman spectroscopy and high-resolution transmission electron microscopy (TEM) to confirm its monolayer nature and crystalline structure. In situ tensile tests were performed inside a scanning electron microscope (SEM) using the Hysitron pico-indenter to apply controlled strain to the suspended graphene ribbons while simultaneously capturing images and force-displacement data. The tensile strain was measured directly from SEM image sequences. The tensile stiffness of the sample was obtained by subtracting the inherent stiffness of the PTP device from the measured force-displacement curves. Both two-dimensional (2D) and three-dimensional (3D) Young's moduli were calculated using established formulas and validated by finite element method simulations accounting for the stress/strain state of the sample and experimental configuration. In parallel, molecular dynamics (MD) simulations were performed using the AIREBO potential to model the fracture behavior of graphene ribbons with different edge defects and configurations, enabling a direct comparison between experimental results and simulations. This combined experimental and computational approach allowed for a comprehensive evaluation of the mechanical properties of the free-standing monolayer graphene and interpretation of the observed fracture behavior.

The in situ tensile tests revealed that the monolayer graphene exhibited excellent elastic behavior, with up to ~6% fully recoverable elastic strain. The measured Young's modulus was close to 1 TPa, consistent with theoretical predictions for pristine graphene. The engineering tensile strength reached approximately 50-60 GPa, significantly higher than values reported in previous studies that used pre-cracked samples. The fracture behavior was typically brittle, initiating at edge defects introduced during FIB milling. Molecular dynamics simulations were consistent with experimental findings, showing that the presence of edge defects reduces the graphene's tensile strength, and that the fracture initiates at locations of high stress concentration near clamping ends, and those of pre-existing edge defects. The simulations also indicated that the maximum principal stress was not a reliable indicator of fracture initiation in this material due to significant anisotropy in the hexagonal lattice, which determines crack propagation directions. The crack propagation path was characterized by post-mortem TEM analysis, which revealed a combination of armchair and zigzag cleavage directions, explained by recent theoretical works on graphene fracture behavior under anisotropic stress states.

The findings significantly advance our understanding of graphene's mechanical properties. The demonstration of substantial sample-wide elastic strain (up to ~6%) validates the potential of graphene for strain engineering applications, enabling controlled modulation of its electronic and optoelectronic properties. The high tensile strength and stiffness, even with the presence of edge defects, highlight the resilience and robustness of this material. The discrepancy between the measured tensile strength and theoretical predictions is well-explained by the presence of FIB-induced edge defects, and can be minimized by optimizing the sample preparation process. The consistency between the experimental data and MD simulations supports the validity of the adopted methods and the inferences made about the fracture mechanisms. These results demonstrate the potential of using large-area CVD graphene in real-world applications, paving the way for novel flexible electronics and ultra-high strength composites.

This study successfully demonstrated the near-ideal mechanical performance of large-area, free-standing single-crystalline monolayer graphene under in situ tensile testing, revealing remarkable elastic stretchability and strength. The methodology developed for sample preparation and testing offers a significant advance in characterizing 2D materials and can be extended to other materials. The findings underscore the potential of graphene for applications requiring significant elasticity and high strength. Future work could focus on minimizing edge defects during sample preparation to further enhance the tensile strength and explore the potential of graphene in a broader range of flexible electronics and other applications that benefit from elastic strain engineering.

The study's main limitation is the introduction of edge defects during the FIB milling process, which inevitably affects the measured tensile strength. While the study utilized MD simulations to quantify this effect, further optimization of the sample preparation method is needed to reduce the density of edge defects and achieve even higher tensile strengths. Additionally, the assumption of a uniaxial stress state in the calculations of the Young’s modulus simplifies the complex stress field within the sample; however, the authors validated this approximation with FEM simulations and provided a sensitivity analysis. Future research may benefit from more sophisticated methods to resolve and account for the stress distribution of the sample during testing.