The stress transfer mechanism from a polymer substrate to a nanoinclusion, such as a graphene flake, is of extreme interest for the production of effective nanocomposites. Previous work conducted mainly at the micron scale has shown that the intrinsic mechanism of stress transfer is shear at the interface. However, since the interfacial shear takes its maximum value at the very edge of the nanoinclusion it is of extreme interest to assess the effect of edge integrity upon axial stress transfer at the submicron scale. Here, we conduct a detailed Raman line mapping near the edges of a monolayer graphene flake that is simply supported onto an epoxy-based photoresist (SU8)/poly(methyl methacrylate) matrix at steps as small as 100 nm. We show for the first time that the distribution of axial strain (stress) along the flake deviates somewhat from the classical shear-lag prediction for a region of ∼2 μm from the edge. This behavior is mainly attributed to the presence of residual stresses, unintentional doping, and/or edge effects (deviation from the equilibrium values of bond lengths and angles, as well as different edge chiralities). By considering a simple balance of shear-to-normal stresses at the interface we are able to directly convert the strain (stress) gradient to values of interfacial shear stress for all the applied tensile levels without assuming classical shear-lag behavior. For large flakes a maximum value of interfacial shear stress of 0.4 MPa is obtained prior to flake slipping.

The mechanical behavior of high quality two-dimensional (2D) crystals offers exciting opportunities for new material design, such as the combination of extremely high in-plane stiffness and bending flexibility, compared to existing three-dimensional (3D) material forms. By combining different 2D crystals vertically or by in-plane stitching, unusual properties can arise due to nonlinear mechanical interactions between them. Van der Waals forces between vertically stacked crystals give rise to a wide range of useful phenomena such as layer-number dependent friction, superlubricity, creasing, and spatial modulation of elastic properties through Moiré structures. In the present article, we review and explain the mechanical behavior of 2D materials and heterostructures (graphene, hexagonal boron nitride, transition metal dichalcogenides). Linear elastic properties of these 2D crystalline monolayers are well-studied using membrane nanoindentation towards their application in nano-electro-mechanical systems (NEMS) devices. On the other hand, a more thorough understanding of friction, fracture and stress transfer mechanisms between 2D layers and with the substrate or matrix is still lacking. More in-depth understanding of geometry-dependent behavior could enable the application of these materials in multi-functional composites. We discuss emerging opportunities achievable by assembling 2D heterostructures to tailor their mechanical behavior, and perhaps even break the traditional bounds limiting the properties of the bulk homostructures. Furthermore, to accelerate the design and discovery of the infinite combinations of new 2D heterostructures, we construct a crowd-sourced searchable online database to record and exploit the studies reporting on the complex arrangements of these crystals.

Exfoliated monolayer graphene flakes were embedded in a polymer matrix and loaded under axial compression. By monitoring the shifts of the 2D Raman phonons of rectangular flakes of various sizes under load, the critical strain to failure was determined. Prior to loading care was taken for the examined area of the flake to be free of residual stresses. The critical strain values for first failure were found to be independent of flake size at a mean value of –0.60% corresponding to a yield stress up to -6 GPa. By combining Euler mechanics with a Winkler approach, we show that unlike buckling in air, the presence of the polymer constraint results in graphene buckling at a fixed value of strain with an estimated wrinkle wavelength of the order of 1–2 nm. These results were compared with DFT computations performed on analogue coronene/PMMA oligomers and a reasonable agreement was obtained.

Thin membranes, such as monolayer graphene of monoatomic thickness, are bound to exhibit lateral buckling under uniaxial tensile loading that impairs its mechanical behaviour. In this work, we have developed an experimental device to subject 2D materials to controlled equibiaxial strain on supported beams that can be flexed up or down to subject the material to either compression or tension, respectively. Using strain gauges in tandem with Raman spectroscopy measurements, we monitor the G and 2D phonon properties of graphene under biaxial strain and thus extract important information about the uptake of stress under these conditions. The experimental shift over strain for the G and 2D Raman peaks were found to be in the range of 62.3 ± 5 cm–1/%, and 148.2 ± 6 cm–1/%, respectively, for monolayer but also bilayer graphenes. The corresponding Grüneisen parameters for the G and 2D peaks were found to be between 1.97 ± 0.15 and 2.86 ± 0.12, respectively. These values agree reasonably well with those obtained from small-strain bubble-type experiments. The results presented are also backed up by classical and ab initio molecular dynamics simulations and excellent agreement of Γ-E2g shifts with strains and the Grüneisen parameter was observed.