Growth from buckling to buckling-driven delamination in a film/substrate system

Compressing a stiff film bonded to a compliant substrate with finite thickness can lead to various instabilities, including global buckling, local wrinkling, delamination or their concomitant buckling. This paper proposed an analytical model, which integrates global and local interactive effects due to the finite thickness, to reveal the growth from buckling to buckling-driven delamination. The resulting governing non-linear equations (non-autonomous fourth-order ordinary differential nonlinear equations with integral conditions) are then solved by introducing a continuation algorithm, which offers considerable advantages to detect multiple bifurcations and trace a complex post-buckling path. The critical conditions for global buckling, local wrinkling and buckling-driven delamination are carefully studied. Two different growth processes from destabilization to restabilization (snap-back) are captured in the post-buckling range. Moreover, it is found that the interface toughness and the pre-existing delamination crack length dominates the critical strain for the onset of buckling-driven delamination, and further decide the initial instability mode. Finally, two phase diagrams are plotted to predict both initial and advanced instability modes in such a bilayer system. The phase diagrams can be used to guide the design of film/substrate systems to achieve desired modes of instabilities.