A parametric cohesive zone beam theory analysis of mixed-mode graphene transfer

Competing interface fracture paths in the transfer of 2D materials from their growth substrate to a flexible polymer substrate are examined by developing finite element and semi-analytical beam theory models. With limited data on interface characterization for 2D materials, a parameter space is chosen based on the polyimide-graphene-copper foil system. Cohesive zone models with two different damage initiation criteria are explored. Algebraic equations to predict load, crack length, damage zone length, rotation and mode-mix are extracted through scaling analysis and correlation of the numerical data. Successful transfer of graphene to a polymer substrate is observed to be dependent on relative interface strengths rather than fracture energies.