Surface Instability of Composite Thin Films on Compliant Substrates: Direct Simulation Approach

Abstract

Surface instability via wrinkle formation is a common feature in thin films attached to a compliant substrate. Wrinkled thin-film structures have been increasingly exploited to enhance device performance. In this study, a numerical technique utilizing embedded imperfections is employed for direct simulations of wrinkle formation, extending from a single-film structure to composite films involving two or more layers. The incorporation of material elements, bearing different elastic properties at the film-substrate interface, assists in triggering buckling instability when the compressive strain reaches a critical value. The wrinkle wavelength and amplitude obtained from the numerical modeling show excellent agreements with available theoretical solutions involving bi-layer composite films, over the entire span of volume ratios of the constituent layers. A valid range of imperfection distribution, resulting in uniform wrinkle formation, is identified. The current numerical approach is robust and easy to implement and yields great promises in generating reliable wrinkling patterns. It can be readily applied to cases where realistic features cannot be captured by theories, such as the generalized plane strain deformation, indirect compression, and multilayer composite films.

Instabilities of Thin Films on a Compliant Substrate: Direct Numerical Simulations from Surface Wrinkling to Global Buckling

“…As a consequence the critical strain for instability becomes higher. Note that if PE is used in the numerical modeling, the predicted critical strain also agrees with the analytical solutions 37 . Figure 3c presents the surface wrinkling amplitude as a function of the applied strain, for the two film materials with various domain widths.…”

“…These elements carry material properties the same as the film material. The applicability of this approach in generating wrinkling instability was demonstrated in our previous studies, first for single-layer thin film/thick substrate systems discretized by four-noded linear elements 36 and then extended to composite-film/thick substrate systems with higher order eight-noded elements 37 . In the present work, a thorough investigation of model geometry from thick to thin substrates and from large to small widths, are undertaken, to demonstrate the full capability of the numerical approach.…”

“…The embedded imperfection approach 36,37 is used for triggering instabilities. The embedded imperfections are selected regular finite elements immediately below the perfectly bonded film/substrate interface (in the substrate layer).…”

“…The choice of the greatest width in this study, 110λ, is worthy of elaboration. It is based on our prior finding 36,37 that, if more than one imperfections are to be included in the model, their maximum spacing, when normalized by the wavelength, should not be greater than 55 in order to generate uniform sinusoidal wrinkles conforming to the theoretical solution. As a consequence, to include only one central imperfection in the present study for making the model a "representative volume element, " a total width of 110λ (55λ on each side of the imperfection) is the maximum allowed.…”

“…In this approach, termed "embedded imperfections," perturbed elastic properties are assigned to one or more regular elements at the interface of the film-substrate structure, for the purpose of triggering the formation of wrinkles without the need of any multi-step process. This work is originated from our recent development 36,37 , but is now expanded into a comprehensive study of the effects of model dimensions and boundary condition, using only one embedded imperfection, to fully assess the modeling capability. Most importantly, we illustrate that the formation of surface wrinkles and overall structural buckles can both be predicted from a single numerical implementation, and that concurrent wrinkling and buckling can actually occur and be directly simulated.…”