On the Stress Transfer and Mode Mixity for a Film of Finite Length Bonded to an Elastic Substrate

The configuration of film-substrate structure is widely involved in many aspects of technologies. To ensure high reliability and sound performance, it is of importance to understand the stress distribution and the adhesion at the interface. In the present work, within mind the film of finite width, a mechanical model has been proposed to analyze the traction at the interface between the film and an elastic substrate that may be subjected to either uniaxial stretching or bending. For incompressible substrates, the problem may be reduced to the solution of singular integral equations of Cauchy type and the tractions at the film’s edges have been revealed to exhibit the square-root singularity. Mode mixity has been calculated. By comparing the strain in the film when the system is subjected to uniaxial stretching with that from experiments on the adhesion between graphene and substrates, an agreement has been found and the implications of the present model in the measurement of adhesion energy have been discussed.