Two interfacial failure modes, shear sliding and buckling, of graphene on a flexible substrate subjected to uniaxial compression are investigated. The shear sliding starts at the edge region, and buckling starts at the middle region of graphene. Using shear-lag cohesive zone models and finite element (FE) simulations, the critical strain and maximum strain of graphene are predicted for the interfacial sliding failure. Then, the critical strain for the onset of buckling is derived via the theory of continuum mechanics with the van der Waals (vdW) interaction between graphene and the substrate surface taken into consideration. By comparison of the two critical failure strains and maximum strain of graphene, it is found that there exists a critical length of graphene. As the graphene length is larger than it, interfacial failure goes through four stages of development with increasing loading, including sliding and buckling. Conversely, the buckling of graphene will not occur. Finally, the influence of the interfacial adhesion energy and geometric size of graphene on the critical strains for interfacial sliding and buckling are discussed.
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