Asynchronous cracking with dissimilar paths in multilayer graphene

Flaw-size-dependent mechanical interlayer coupling and edge-reconstruction embrittlement in van der Waals materials

Van der Waals (vdW) materials consisting of two-dimensional (2D) building blocks have strong in-plane covalent bonding and weak interlayer interactions. While monolayer 2D materials exhibit impressive fracture resistance, as demonstrated in hexagonal boron nitride (h-BN), preserving these remarkable properties in vdW materials remains a challenge. Here we reveal an anomalous mechanical interlayer coupling that involves interlayer-friction toughening and edge-reconstruction embrittlement during the fracture of multilayer h-BN. Both asynchronous and synchronous fracture modes and their flaw-size dependence are identified. Edge reconstruction in the synchronous fracture mode can eliminate a toughening mechanism induced by lattice asymmetry in monolayer h-BN, leading to embrittlement of the multilayer h-BN, while the asynchronous fracture mode results in greater fracture resistance. Such findings will provide fundamental guidelines for engineering interlayer interactions in vdW materials including heterostructures and layered architectures for better mechanical and functional performances.

Fracture Behavior of a 2D Imine-Based Polymer

2D polymers have emerged as a highly promising category of nanomaterials, owing to their exceptional properties. However, the understanding of their fracture behavior and failure mechanisms remains still limited, posing challenges to their durability in practical applications. This work presents an in-depth study of the fracture kinetics of a 2D polyimine film, utilizing in situ tensile testing within a transmission electron microscope (TEM). Employing meticulously optimized transferring and patterning techniques, an elastic strain of ≈6.5% is achieved, corresponding to an elastic modulus of (8.6 ± 2.5) GPa of polycrystalline 2D polyimine thin films. In step-by-step fractures, multiple cracking events uncover the initiation and development of side crack near the main crack tip which toughens the 2D film. Simultaneously captured strain evolution through digital image correlation (DIC) analysis and observation on the crack edge confirm the occurrence of transgranular fracture patterns apart from intergranular fracture. A preferred cleavage orientation in transgranular fracture is attributed to the difference in directional flexibility along distinct orientations, which is substantiated by density functional-based tight binding (DFTB) calculations. These findings construct a comprehensive understanding of intrinsic mechanical properties and fracture behavior of an imine-linked polymer and provide insights and implications for the rational design of 2D polymers.

Exploring fracture of H-BN and graphene by neural network force fields

Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture often lead to catastrophic failure of materials and structures. Understanding the nucleation and growth of cracks is challenged by their multiscale characteristics spanning from atomic-level structures at the crack tip to the structural features where the load is applied. Atomistic simulations offer 'first-principles' tools to resolve the progressive microstructural changes at crack fronts and are widely used to explore the underlying processes of mechanical energy dissipation, crack path selection, and dynamic instabilities (e.g. kinking, branching). Empirical force fields developed based on atomic-level structural descriptors based on atomic positions and the bond orders do not yield satisfying predictions of fracture, especially for the nonlinear, anisotropic stress-strain relations and the energy densities of edges. High-fidelity force fields thus should include the tensorial nature of strain and the energetics of bond-breaking and (re)formation events during fracture, which, unfortunately, have not been taken into account in either the state-of-the-art empirical or machine-learning force fields. Based on data generated by density functional theory calculations, we report a neural network-based force field for fracture (NN-F3) constructed by using the end-to-end symmetry preserving framework of deep potential-smooth edition (DeepPot-SE). The workflow combines pre-sampling of the space of strain states and active-learning techniques to explore the transition states at critical bonding distances. The capability of NN-F3is demonstrated by studying the rupture of hexagonal boron nitride (h-BN) and twisted bilayer graphene as model problems. The simulation results elucidate the roughening physics of fracture defined by the lattice asymmetry in h-BN, explaining recent experimental findings, and predict the interaction between cross-layer cracks in twisted graphene bilayers, which leads to a toughening effect.

Definitive engineering strength and fracture toughness of graphene through on-chip nanomechanics

Fail-safe design of devices requires robust integrity assessment procedures which are still absent for 2D materials, hence affecting transfer to applications. Here, a combined on-chip tension and cracking method, and associated data reduction scheme have been developed to determine the fracture toughness and strength of monolayer-monodomain-freestanding graphene. Myriads of specimens are generated providing statistical data. The crack arrest tests provide a definitive fracture toughness of 4.4 MPam . Tension on-chip provides Young's modulus of 950 GPa, fracture strain of 11%, and tensile strength up to 110 GPa, reaching a record of stored elastic energy ~6 GJ m-3 as confirmed by thermodynamics and quantized fracture mechanics. A ~ 1.4 nm crack size is often found responsible for graphene failure, connected to 5-7 pair defects. Micron-sized graphene membranes and smaller can be produced defect-free, and design rules can be based on 110 GPa strength. For larger areas, a fail-safe design should be based on a maximum 57 GPa strength.

Metal-Semiconductor Behavior along the Line of Stacking Order Change in Gated Multilayer Graphene

We investigated gated multilayer graphene with stacking order changes along the armchair direction. We consider that some layers cracked to release shear strain at the stacking domain wall. The energy cones of graphene overlap along the corresponding direction in the k-space, so the topological gapless states from different valleys also overlap. However, these states strongly interact and split due to atomic-scale defects caused by the broken layers, yielding an effective energy gap. We find that for some gate voltages, the gap states cross and the metallic behavior along the stacking domain wall can be restored. In particular cases, a flat band appears at the Fermi energy. We show that for small variations in the gate voltage, the charge occupying this band oscillates between the outer layers.

Anisotropic mechanical properties of α-MoO3 nanosheets

The mechanical behaviors of 2D materials are fundamentally important for their potential applications in various fields. α-Molybdenum trioxide (α-MoO3) crystals with unique electronic, optical, and electrochemical properties, have attracted extensive attention for their use in optoelectronic and energy conversion devices. From a mechanical viewpoint, however, there is limited information available on the mechanical properties of α-MoO3. Here, we developed a capillary force-assisted peeling method to directly transfer α-MoO3 nanosheets onto arbitrary substrates. Comparatively, we could effectively avoid surface contamination arising from the polymer-assisted transfer method. Furthermore, with the help of an in situ push-to-pull (PTP) device during SEM, we systematically investigated the tensile properties of α-MoO3. The measured Young's modulus and fracture strengths along the c-axis (91.7 ± 13.7 GPa and 2.1 ± 0.9 GPa, respectively) are much higher than those along the a-axis (55.9 ± 8.6 GPa and 0.8 ± 0.3 GPa, respectively). The in-plane mechanical anisotropy ratio can reach ∼1.64. Both Young's modulus and the fracture strength of MoO3 show apparent size dependence. Additionally, the multilayer α-MoO3 nanosheets exhibited brittle fracture with interplanar sliding due to poor van der Waals interaction. Our study provides some key points regarding the mechanical properties and fracture behavior of layered α-MoO3 nanosheets.

Bioinspired Toughening Mechanisms in a Multilayer Transparent Conductor Structure

With increasing demands and interest in flexible and foldable devices, much effort has been devoted to the development of flexible transparent electrodes. An in-depth understanding of failure mechanisms in nanoscale structure is crucial in developing stable, flexible electronics with long-term durability. The present work investigated the mechanoelectric characteristics of transparent conductive electrodes in the form of dielectric/metal/dielectric (DMD) sandwich structures under bending, including one time and repeated cyclic bending test, and provides an explanation of their failure mechanism. We demonstrate how a thin metallic layer helps to enhance the mechanical robustness of the DMD as compared with that without, tune the mechanical properties of the cohesive layer, and improve the electrode fracture resistance. Abnormal crack propagation and toughening of multilayer DMD structures are analyzed, and its underlying mechanisms are explained. We consider the knowledge of the failure mechanisms of transparent conductive electrodes gained from the present study as a foundation for future design improvements.

Effect of point defects and nanopores on the fracture behaviors in single-layer MoS2 nanosheets

Point defects and nanopores are inevitable and particularly noticeable in single-layer (SL) MoS2. Molecular dynamics (MD) simulations have been done to comprehensively study the influences of point defects and nanopores on tensile deformation behaviors of SLMoS2 nanosheets, and the dependences of fracture properties on defect type and concentration, pore size, temperature and strain rate are discussed. The formation energy of S vacancy (VS) is the lowest one, but that of VMoS6 is the highest one, corresponding to the highest and lowest fracture stress, respectively. The local stress concentration around point defects and nanopores might lead to the early bond breaking and subsequent nucleation of cracks and brittle fracture upon tensile loading. A modified Griffith criterion is proposed to describe the defect concentration and pore size dependent fracture stress and strain. These findings provide us an important guideline for the structural design of 2D materials in future applications.

Mechanics of free-standing inorganic and molecular 2D materials

The discovery of graphene has triggered a great interest in inorganic as well as molecular two-dimensional (2D) materials. In this review, we summarize recent progress in the mechanical characterization of free-standing 2D materials, such as graphene, hexagonal boron nitride (hBN), transition metal-dichalcogenides, MXenes, black phosphor, carbon nanomembranes (CNMs), 2D polymers, 2D metal organic frameworks (MOFs) and covalent organic frameworks (COFs). Elastic, fracture, bending and interfacial properties of these materials have been determined using a variety of experimental techniques including atomic force microscopy based nanoindentation, in situ tensile/fracture testing, bulge testing, Raman spectroscopy, Brillouin light scattering and buckling-based metrology. Additionally, we address recent advances of 2D materials in a variety of mechanical applications, including resonators, microphones and nanoelectromechanical sensors. With the emphasis on progress and challenges in the mechanical characterization of inorganic and molecular 2D materials, we expect a continuous growth of interest and more systematic experimental work on the mechanics of such ultrathin nanomaterials.

In situ tensile fracturing of multilayer graphene nanosheets for their in-plane mechanical properties

The excellent mechanical properties of single- and few-layer graphene have been well-quantified and evidenced by computational methods and local indentation measurements. However, there are less experimental reports on the in-plane mechanical properties of multilayer graphene sheets, despite many practical applications in flexible electronic and energy devices (e.g. graphene flexible electronic display, battery, and storage devices) are actually based on these thicker nanosheets. Here, in-plane fracture behaviors of multilayer graphene nanosheets with thicknesses between ∼10 and 300 nm (∼10-1000 layers) are characterized and quantified by in situ scanning electron microscopy and transmission electron microscopy under tensile loading. We found that, generally, the fracture strengths of graphene nanosheets decrease as the thickness (or layers) increases; however, the fracture strain of thinner graphene sheets is less than that of thicker sheets. The fracture process of the thicker nanosheets includes the initial flattened stage, the stable elastic stage, and the rapid fracture with brittle characteristics, while the thinner nanosheets show obvious delamination between the atomic layers at fracture. This work provides critical experimental insights into the tensile fracture behavior of multilayer two-dimensional materials and a better understanding on their realistic mechanical performance for potential flexible device and composite applications.

Nonlinear fracture toughness measurement and crack propagation resistance of functionalized graphene multilayers

Despite promising applications of two-dimensional (2D) materials, one major concern is their propensity to fail in a brittle manner, which results in a low fracture toughness causing reliability issues in practical applications. We show that this limitation can be overcome by using functionalized graphene multilayers with fracture toughness (J integral) as high as ~39 J/m², measured via a microelectromechanical systems-based in situ transmission electron microscopy technique coupled with nonlinear finite element fracture analysis. The measured fracture toughness of functionalized graphene multilayers is more than two times higher than graphene (~16 J/m²). A linear fracture analysis, similar to that previously applied to other 2D materials, was also conducted and found to be inaccurate due to the nonlinear nature of the stress-strain response of functionalized graphene multilayers. A crack arresting mechanism of functionalized graphene multilayers was experimentally observed and identified as the main contributing factor for the higher fracture toughness as compared to graphene. Molecular dynamics simulations revealed that the interactions among functionalized atoms in constituent layers and distinct fracture pathways in individual layers, due to a random distribution of functionalized carbon atoms in multilayers, restrict the growth of a preexisting crack. The results inspire potential strategies for overcoming the relatively low fracture toughness of 2D materials through chemical functionalization.