Effect of residual stress on the delamination response of film-substrate systems under bending

The effect of residual stress on the delamination behaviour of thin films is examined under four-point bending. Elastic film-substrate systems with and without the addition of a superlayer are analysed by constructing closed-form expressions for the energy release rate at steady-state delamination. The analytical results obtained with these expressions are compared to finite element results based on cohesive zone modelling, showing an excellent agreement. The closed-form expressions correctly reduce to simpler forms for film-substrate systems without residual stresses, and further include the special case of spontaneous delamination under the presence of a critical residual stress only. The closed-form expression for the elastic film-substrate system without a superlayer is used for indicating errors in alternative analytical expressions presented in the literature. Subsequently, the contribution of substrate plasticity to the delamination resistance is studied by means of finite element analyses for a range of (relative) film thicknesses and various values of the (relative) interfacial strength. For a compressive residual stress the delamination response typically is characterised by a transition from large scale yielding to small scale yielding under increasing film thickness, while for a tensile residual stress the limit of small scale yielding may not be reached at large film thickness when the interfacial strength is relatively high. Furthermore, stress relaxation induced by large scale yielding diminishes the influence of the residual stress on the delamination resistance under bending.