  Periodic wrinkling of a rigid capping layer on a deformable substrate
provides a useful method for templating surface topography for a variety of
novel applications. Many experiments have studied wrinkle formation during the
compression of a rigid film on a relatively soft pre-strained elastic
substrate, and most have focused on the regime where the substrate thickness
can be considered semi-infinite relative to that of the film. As the relative
thickness of the substrate is decreased, the bending stiffness of the film
dominates, causing the bilayer to transition to either local wrinkling or a
global buckling instability. In this work optical microscopy was used to study
the critical parameters that determine the emergence of local wrinkling or
global buckling of freestanding bilayer films consisting of a thin rigid
polymer capping layer on a pre-strained elastomeric substrate. The thickness
ratio of the film and substrate as well as the pre-strain were controlled and
used to create a buckling phase diagram which describes the behaviour of the
system as the ratio of the thickness of the substrate is decreased. A simple
force balance model was developed to understand the thickness and strain
dependences of the wrinkling and buckling modes, with excellent quantitative
agreement being obtained with experiments using only independently measured
material parameters.
