Numerical Simulations of Wrinkling and Wrinkling-induced Delaminations

Wrinkling is a structural instability phenomena occurring in material systems comprising a stiff layer deposited on a compliant foundation. The present study is concerned with wrinkling instabilities in multi-layered systems, with a special focus on thin film systems. Thin films play an important role in many technological applications including microelectronic devices, magnetic storage media and surface coatings. Films are typically deposited on substrates at high temperatures and upon cooling to room temperature the mismatch in the thermo-mechanical properties of the film and the substrate can result in significant residual compressive stresses in the thin film system, often resulting in wrinkling instabilities. In the present work, a novel numerical solution procedure is developed for full-field simulations of wrinkling. The system is modeled as a von Karman plate on a foundation. A Spectral Method is employed to solve the governing differential equations. Two new formulations are developed: (a) a total strain formulation for wrinkling on a spatially heterogeneous foundation, (b) an incremental strain formulation for consideration of irreversible constitutive relations for the foundation. The numerical solution procedure is first applied to study the wrinkling of a bi-layer thin film system on a patterned substrate. Films are assumed to be perfectly bonded with no damage occurring at the interface. Wrinkling amplitudes of films above patterned regions on the substrate are shown to be strongly coupled to wrinkling amplitudes in surrounding non-patterned regions. It is shown that depending on the size of the patterns and their relative spacing, wrinkling of films above patterned regions can be suppressed. The solution procedure is then applied, in an incremental form, to study cases of wrinkling-induced irreversible deformation of the foundation, and the initiation and propagation of wrinkling-induced delaminations. It is shown that the initiation of delaminations at the interface leads to a transition from uniform wrinkles to localized regions with high out-of-plane deflection. The critical temperature for the transition from wrinkles to delaminations is shown to relate to the cohesive strength of the interface. Also, it is shown that in the presence of an initial crack, the system buckles without wrinkling, and that the post-buckling out-of-plane displacement is a function of the cohesive energy of the foundation