Theoretical Investigations On Bidirectional Interfacial Shear Stress Transfer Of Graphene/Substrate Structure

Interfacial mechanical behaviors have great influences on the overall mechanical properties of graphene/substrate structure.Therefore,it is necessary to study interfacial shear stress transfer between graphene and substrate.In this dissertation,a twodimensional nonlinear shear-lag model(2-D model)which can be used to study the bidirectional shear stress transfer at the interface is developed based on the onedimensional nonlinear shear-lag model(1-D model)describing unidirectional shear stress transfer between a graphene and a substrate.And the bidirectional interfacial shear stress transfer of graphene/substrate structure subjected to uniaxial and biaxial tension is investigated by the 2-D model,respectively.Taking the effects of Poisson's ratio of the graphene and substrate into consideration,the bidirectional interfacial shear stress transfer of graphene/substrate structure subjected to uniaxial tension is studied by the 2-D model.In the elastic bonding stage,the semi-analytical solutions of the bidirectional normal strains of the graphene and interfacial shear stresses and the analytical solution of the critical strain for interfacial sliding are derived.In the interfacial sliding stage,the finite element simulations are made to calculate the distributions of graphene's normal strains and interfacial shear stresses.For the two cases that the Poisson's ratio of substrate is larger and smaller than that of graphene,the distributions of graphene's normal strains and interfacial shear stresses at different positions are specifically illustrated both in the elastic bonding and interfacial sliding stage.And the influences of graphene's width and Poisson's ratio of substrate on the critical strain for interfacial sliding are discussed.Furthermore,by comparing the results obtained via 1-D and 2-D models,it can be found that the graphene's normal strains,interfacial shear stresses and critical strain for interfacial sliding show great difference for two kinds of models when the width of graphene is large,and the difference can be neglected when the width is small enough.Finally,by fitting the Raman experimental results,the reliability of the 2-D model is verified,and the interfacial stiffness(100 TPa/m)and shear strength(0.295 MPa)between graphene and Polyethylene terephthalate(PET)substrate are calculated.The bidirectional interfacial shear stress transfer of graphene/substrate structure under biaxial tension is studied by 2-D model.The bidirectional normal strains of the graphene and interfacial shear stresses are calculated,and their distributions at different positions are illustrated both in the elastic bonding and interfacial sliding stage for the case that the substrate is subjected to equal biaxial tension.Finally,the critical strain for interfacial sliding is derived by the 2-D model,and the influence of the width of graphene on the critical strain is discussed under different loading conditions.