### Wednesday, May 14

9:15 AM-10:00 AM

*Chair: Graeme W. Milton, University of Utah*

*Peale C Room*

## IP8

Delamination of Thin Films

Portions of a thin film may buckle away from the substrate, thereby forming a blister. Blisters may grow by interfacial fracture, a process, which under the appropriate conditions, may result in the catastrophic failure of the component. Blisters are often observed to adopt convoluted---even bizarre---shapes and to fold into intricate patterns.

The speaker will address the problem of determining the possible shapes of thin-film blisters. The requisite driving force for delamination at the boundary is furnished by Eshelby's energy-momentum tensor. Therefore, the speaker will begin by discussing the energetics of blister growth and deriving the expression of the energy-momentum tensor for a thin film. This requires consideration of energy densities which depend on displacement gradients of up to second order. A far-reaching outcome of the analysis is that the driving force for delamination is completely determined by the normal bending strain at the boundary. Using singular perturbation theory and a simple `sand-heap' construction to approximate the membrane solution, the requisite bending strain follows conveniently from a boundary layer analysis. The normal bending strain is found to depend on the local curvature of the boundary and its derivatives with respect to the arc-length. By setting the driving force for delamination equal to the static or kinetic fracture energy resistance, the ordinary differential equations which govern the shape of stationary and growing blisters, respectively, are discussed. The solutions of these equations compare well with the experimentally observed telephone-cord geometries.

**Michael Ortiz**

*Graduate Aeronautical Laboratories, California Institute of Technology*

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*MMD, 1/14/97*