Shear lag analysis by a cohesive bilinear model for the interface stress transfer in a graphene monolayer nanocomposite

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The research objectives can be summarized as follows:1. Study of a configuration model of a graphene monolayer attached to a PMMA substrate and covered by an additional thin PMMA top layer. For this configuration a simple system of governing ordinary differential equations will be derived from the originally two-dimensional system of partial differential equations. The possible interface cohesive delamination will be studied under the assumption of pure mode II behaviour along the interface. 2. Using a trapezoidal (or bilinear) law describing the interface behaviour, the shear lag model will be applied together with a simple criterion serving for finding the cohesive debond length. After determining the elastic bond length the slipping interface length has to be determined and finally the cohesive one. The three respective solutions of the system of ordinary differential equations (for elastic, slipping and cohesive zones) will be matched to each other with appropriate continuity conditions. The effect of the length of the graphene on the cohesive interface debonding will be also studied.Computational methodology The proposed research will be done in the frame of a one-dimensional linear model for the graphene/polymer structure with a zero/finite thickness of the interface. The structure is loaded by a tensile strain. The choice of the modified shear lag method as an analytical tool is based on its well-known advantages for different problems in lightweight structures and composite materials. Although the method is already approved in this field, its further development and extension will go along with a constitutive trapezoidal (or bilinear) law for the interface, describing its cohesive behaviour. Thus, the analytical modelling is performed first by the derivation of the modified shear lag system of ordinary differential equations and second by the formulation of suitable boundary and continuity conditions matching the solutions for elastic, slipping and cohesive zones for the overlap between the graphene monolayer and hosting polymer substrate under tensile strain. The hitherto accumulated experience by the applicants for these kinds of problems is a guarantee for overcoming the computational problems discussed above.