THE MORPHOLOGY AND FOLDING PATTERNS OF BUCKLING-DRIVEN THIN-FILM BLISTERS

THIN FILMS AND COATINGS in a state of residual compression can, under appropriate conditions, decohere and buckle away from the substrate to form blisters. These blisters are often observed to adopt intricate shapes and to fold into complex patterns. In this paper, such shapes and patterns are given an energetic interpretation, i.e. they follow as energy minimizers. We formulate the energy of the film by recourse to von Karman theory of moderate deflections of a plate. The energy functional has the following key properties: it contains two terms, namely, the membrane and bending energies, the latter being a singular perturbation of the former; and the membrane energy functional is nonconvex and, consequently, its infimum is generally not attained. In keeping with the conventional mathematical treatment of these problems, we construct solutions by a matched asymptotic expansion. The outer solution follows by membrane energy minimization and determines the essential folding pattern of the film. The inner solution is obtained by fitting boundary layers at sharp edges in the membrane solution. The film deflections thus constructed are found to match, in surprising detail, the observed complex folding patterns adopted by delaminated films. In addition, the boundary layer analysis permits one to accord a well-defined line tension to sharp edges in the membrane solution, and, in particular, to the boundary of the blister. This provides a simple device for assessing the configurational stability of some blister morphologies. In particular, the analysis predicts the transition from straight-sided to telephone-cord morphologies at a critical mismatch strain.