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

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.

 Tong Qing Lu, Wei Xu Zhang, T.J. Wang   The surface effect on the strain energy release rate of buckling delamination in thin film–substrate systems.  International Journal of Engineering Science 49 (2011) 965-975