Concomitant wrinkling and buckle-delamination of elastic thin films on compliant substrates

Abstract

Compressing a thin elastic film attached to a thick compliant substrate can lead to buckling instability. Two commonly observed buckling modes, buckle-delamination and wrinkling, have each been analyzed separately in previous studies. Recent experiments have observed that the two modes can co-exist and co-evolve. In this paper, by analytical and finite element methods, we present a study on concomitant wrinkling and buckle-delamination for an elastic film on a highly compliant substrate. First, without delamination, we present an analytical solution for wrinkling that takes into account the effect of Poisson’s ratio of the substrate. In comparison with a nonlinear finite element analysis, an approximate formula is derived to estimate the normal traction at the interface and to predict initiation of wrinkle-induced delamination. Next, with a pre-existing delamination crack, the critical strain for the onset of buckling instability is predicted by finite element eigenvalue analysis. For an intermediate delamination size, a mixed buckling mode is predicted with the critical compressive strain lower than previous solutions for both wrinkling and buckle-delamination. Post-buckling analyses show a significant shear-lag effect with an effective load transfer length three orders of magnitude greater than the film thickness. Finally, concomitant wrinkling and buckle-delamination is simulated to illustrate the interaction between the two buckling modes, and the results are discussed in view of failure mechanisms and applications in thin film metrology.