On thin film delamination growth in a contracting cylinder (Q580023)

The problem corresponding to growth of a pre-existing delamination at the interface of a thin layer and a contracting cylindrical substrate is considered. The problem is approached as a moving boundary problem in the calculus of variations by employing the principle of stationary potential energy in conjunction with a Griffith type energy balance. A shallow arch theory is used as the mathematical model for the layer while the behavior of the substrate is assumed to be effectively unaltered by the presence of the layer and hence is modeled as a ``rigid'' but contracting ``foundation''. An analytical solution along with an associated growth criterion is found. Specific numerical results are obtained for both the case of a layer delaminating from the exterior surface of the substrate as well as for that of a layer debonding from the corresponding interior surface. These results reveal several characteristic features associated with the phenomena of interest and are seen in some cases to differ qualitatively from, and in others to be qualitatively similar to corresponding results obtained for flat layers.