The macroscopic delamination of thin films from elastic substrates
- aPhysique et Mécanique des Milieux Hétérogènes, École Supérieure de Physique et de Chimie Industrielles, Universités Paris 6 and 7, Centre National de la Recherche Scientifique Unité Mixte de Recherche 7636, ParisTech, 10 Rue Vauquelin, 75231 Paris Cedex 05, France;
- bLaboratoire de Physique Statistique, École Normale Superieure, Université Pierre et Marie Curie, Paris 06, Université Paris Diderot, Centre National de la Recherche Scientifique, 24 Rue Lhomond, 75005 Paris, France; and
- cDepartment of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
-
Edited by Harry L. Swinney, University of Texas, Austin, TX, and approved May 6, 2009 (received for review February 26, 2009)
Abstract
The wrinkling and delamination of stiff thin films adhered to a polymer substrate have important applications in “flexible electronics.” The resulting periodic structures, when used for circuitry, have remarkable mechanical properties because stretching or twisting of the substrate is mostly accommodated through bending of the film, which minimizes fatigue or fracture. To date, applications in this context have used substrate patterning to create an anisotropic substrate-film adhesion energy, thereby producing a controlled array of delamination “blisters.” However, even in the absence of such patterning, blisters appear spontaneously, with a characteristic size. Here, we perform well-controlled experiments at macroscopic scales to study what sets the dimensions of these blisters in terms of the material properties and explain our results by using a combination of scaling and analytical methods. Besides pointing to a method for determining the interfacial toughness, our analysis suggests a number of design guidelines for the thin films used in flexible electronic applications. Crucially, we show that, to avoid the possibility that delamination may cause fatigue damage, the thin film thickness must be greater than a critical value, which we determine.
Footnotes
- 1To whom correspondence should be addressed. E-mail: preis{at}mit.edu
-
Author contributions: B.R. and P.M.R. designed research; D.V., J.B., A.B., and P.M.R. performed research; D.V. and P.M.R. analyzed data; and D.V. and P.M.R. wrote the paper.
-
The authors declare no conflict of interest.
-
This article is a PNAS Direct Submission.
-
See Commentary on page 10875.
-
↵* A balance-of-forces argument applied at the edge of the sheet perpendicular to the compression direction shows that ΔL is directly related to the globally imposed end-to-end displacement.
-
↵† We assume here that n is chosen to minimize the elastic energy, although the final result may also be obtained by assuming that it is the strain accommodated by each blister, ɛ, that is chosen to minimize the elastic energy.
