Buckling modes of elastic thin films on elastic substrates

Abstract

Two buckling modes have been observed in thin films: buckle-delamination and wrinkling. This Letter identifies the conditions for selecting the favored buckling modes for elastic films on elastic substrates. Transition from one buckling mode to another is predicted as the stiffness ratio between the substrate and the film or the interfacial defect size varies. The theoretical results are demonstrated experimentally by observing the coexistence of both buckling modes and mode transition in one film-substrate system.

The Mexican hat effect on the delamination buckling of a compressed thin film

“…2. As the constraints at the delamination edges relax from the clamped ones (zero displacement and rotation) to the hinged ones (zero displacement and bending moment), the buckling load reaches the lower limit of ∆ 2 c−c /4 [8]. In Fig.…”

“…(13) implicitly assumes that only delamination buckling occurs and there is no wrinkling. However, Mei et al [8] showed that when E * s /E * f is very small (less than 10 −3 ) with relatively small b/t ratio (b/t = 5, 10, and 20, respectively), which corresponds to the B < 2 scenario, the wrinkling load/stress is smaller than that of delamination buckling. Therefore, wrinkling occurs before the delamination buckling, and the Yu-Hutchinson model becomes inapplicable [8], which implies that the lower limit is unphysical.…”

“…(18) is in fact a combined parameter of the geometry parameter of b/t and the elastic mismatch property of the first Dundurs' parameter. Mei et al [8] used b/t and E * s /E * f as two independent parameters to study the buckling stress of a delaminated thin film, which shows the same asymptotic trend of the buckling stress approaching σ c−c . Here the amplitude ratio of δ 2 /δ 1 is used to characterize the Mexican hat effect.…”

“…The spring stiffnesses are dependent on b/t and two Dundurs' parameters [3]. Because the second Dundurs' parameter plays a less important role than the first one [8,21] …”

Nano-wrinkling of diamond-like carbon thin films on amorphous polycarbonate and semicrystalline polyethylene terephthalate

“…Especially wrinkling mechanisms can be used to create tunable patterns [1], to fabricate functional surfaces [2], to design flexible electronics [3] and/or to measure the mechanical properties of materials [4]. It refers to periodic or chaotic surface undulations appearing on an originally flat surface.…”