Study Of The Buckle Delamination Of The Film-substrate System

The film-substrate system are widely used in industrial production and advance scientific and technological study.When the film is under compression,the buckle-delamination is wildly observed in experiments.So the deeply study on the occurrence and evolution of buckle-delamination are very important for industrial manufacture and advance scientific and technological investigation.On the one hand,we need to suppress the occurrence of the buckle-delamination of the functional film materials to maintain its lifetime;on the other hand,the adjustable buckle-delamination morphology of film-substrate system are wildly applied in surface morphology controlling,microfluidic device design,flexible electronic device manufacturing and measuring the mechanical parameters of the film-substrate system.In this paper,the Foppl-von Karman equations are used to theoretically study the post-buckling instability mode and post-buckling morphology of the buckle-delamination and the buckle-delamination structure affected by the film crack,where the nonlinear numerical simulation method is also applied to validate the theoretical study.Firstly,the influence of the ridge crack on the straight-sided blisters and the telephone-cord blisters are studied.We modify the theoretically study of the previous theory and improve the result of the straight-sided blister with the ridge crack through cosidering the mid-plane displacement caused by the ridge crack.We also extend the results of the straight-sided blister with ridge crack to the telephone-cord blister by using the ring-like blister approximation model.So the morphology of telephone-cord blister with complex periodic ridge crack are investigated.Then the effect of the ridge crack and the interface sliding boundary on the stability of the straight-sided blister are studied.We find that the ridge crack and low Poisson's ratio promote symmetric secondary instability mode and favor bubble-like blisters while interface sliding and high Poisson's ratio facilitate anti-symmetric secondary instability mode and result in telephone cord buckles.We also improve the previous nonlinear simulation model by considering the effect of ridge crack,of which the results validate the linear stability analysis.Then an improved analytical model is established to study the post-buckling of straight-sided blister with secondary instability and the buckling of telephon-cord blister.The results show that the buckling of periodic curving boundary is harder to occur.In addition,we use this model to obtain the first order approximate solution of the buckling after the secondary instability of the straight-sided blister and the one of the simple periodic curving boundary case.The influence of stress is taken into account and the total elastic energy of the buckling after the secondary instability of the straight-sided bliser can be given.However,this result cannot describe the variation height along the ridge line,which may be due to the lack of the effect of higher order terms.Finally,the validity of the improved analysis model is confirmed by numerical method.The first order numerical solutions agree well with the first order theoretical approximate solution,but it still cannot describe the variation height along the ridge line.The improved second-order numerical solution accurately describes the variation height along the ridge line and is in good agreement with the finite element simulation results,which fully validate the improved analysis model for the periodic curving boundary.In addition,the elastic energy of the curved blister can be significantly lower than that of the SS blister even when the initial equi-biaxial compression is a little larger than the Euler buckling stress,significantly lower than the critical stress for secondary buckling instability of SS blisters.This results indicate that the telephone-cord blister may not go through the instability of the straight-sided blister but appears directly through the boundary instability.