Secondary instability and evolution of straight-sided blisters in cylindrical film-substrate systems

Abstract

The regulation of buckle delamination morphologies in compressed thin films is crucial for ensuring material stability, particularly in systems with curved substrates. While substrate curvature is known to influence surface instabilities, its specific role in governing buckle delamination remains insufficiently understood. This paper investigates the secondary instability and evolution of straight-sided blisters in cylindrical film-substrate systems with both positive and negative curvature through theoretical analysis and finite element simulations. Linear stability analysis elucidates the dependence of critical buckling stress and wavelength on the amplitude and sign of curvature and Poisson’s ratio, revealing distinct instability regimes. The calculated phase diagrams for secondary instability mode selection indicate that symmetric modes dominate at small curvature and low Poisson’s ratios, while antisymmetric modes prevail at larger values. Finite element simulations not only validate the linear stability predictions, but also capture nonlinear evolution of straight-sided blisters into dendritically branched morphologies with dimple-like structures beyond secondary instability. These findings provide new insights into the interplay between curvature, material properties, and instability modes in compressed film-substrate systems.