The surface effect on the strain energy release rate of buckling delamination in thin film–substrate systems

Abstract

Gurtin–Murdoch continuum surface elasticity model is employed to study the buckling delamination of ultra thin film–substrate system. The effects of surface deformation and residual stress on the large deflection of ultra thin film are considered in analysis. A concept of effective bending rigidity (EBR) for ultra thin plate is proposed on the basis of Gurtin–Murdoch continuum theory and the principle of minimum potential energy. The governing equations with EBR are formally consistent with the classical plate theory, including both small deflection and large deflection. A surface effect factor is introduced to decide whether there is need to consider the surface effect or not. Combining the buckling theory and interface fracture mechanics, we obtain analytical solutions of the critical buckling load and the energy release rate of the interface crack in the film–substrate system. It is seen that the surface deformation and residual stress have significant effects on the buckling delamination of ultra thin film–substrate system.