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 s hapes and to fold into complex patterns. In this paper, such shapes an d 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 funct ional has the following key properties: it contains two terms, namely, the membrane and bending energies, the latter being a singular pertur bation of the former; and the membrane energy functional is nonconvex and, consequently, its infimum is generally not attained. In keeping w ith the conventional mathematical treatment of these problems, we cons truct solutions by a matched asymptotic expansion. The outer solution follows by membrane energy minimization and determines the essential f olding pattern of the film. The inner solution is obtained by fitting boundary layers at sharp edges in the membrane solution. The film defl ections thus constructed are found to match, in surprising detail, the observed complex folding patterns adopted by delaminated films. In ad dition, the boundary layer analysis permits one to accord a well-defin ed line tension to sharp edges in the membrane solution, and, in parti cular, to the boundary of the blister. This provides a simple device f or assessing the configurational stability of some blister morphologie s. In particular, the analysis predicts the transition from straight-s ided to telephone-cord morphologies at a critical mismatch strain.