Buckling Of Film Research Articles

Spontaneous Buckling of Multiaxially Flexible and Stretchable Interconnects Using PDMS/Fibrous Composite Substrates

An original strategy is described to address a critical issue for flexible and stretchable electronics. For the first time, buckling of prestrain‐free stiff film (spontaneous buckling) is achieved on composite substrate benefiting from fibrous nature of daily life substrates such as paper, textiles or bandage. This new strategy allows the processing of microstructures which are directly embedded in a fibrous substrate during fabrication process. Multiaxially compressive strain due to fibrous material shrinkage is strong enough to induce multiaxially stiff film buckling. Moreover, additional fibrous material prestretching leads to enhance the buckling effect allowing buckled ribbons use as interconnections. As a result, 80% maximum elongation is obtained before interconnections mechanical and electrical failure.

Mechanics of Graded Wrinkling

The properties and behavior of a surface as well as its interaction with surrounding media depend on the inherent material constituency and the surface topography. Structured surface topography can be achieved via surface wrinkling. Through the buckling of a thin film of stiff material bonded to a substrate of a softer material, wrinkled patterns can be created by inducing compressive stress states in the thin film. Using this same principle, we show the ability to create wrinkled topologies consisting of a highly structured gradient in amplitude and wavelength, and one which can be actively tuned. The mechanics of graded wrinkling are revealed through analytical modeling and finite element analysis, and further demonstrated with experiments.

Large-Area Buckled MoS2 Films on the Graphene Substrate.

In this study, a novel buckled structure of edge-oriented MoS2 films is fabricated for the first time by employing monolayer graphene as the substrate for MoS2 film growth. Compared to typical buckling methods, our technique has several advantages: (1) external forces such as heat and mechanical strain are not applied; (2) uniform and controllable buckling over a large area is possible; and (3) films are able to be transferred to a desired substrate. Dual MoS2 orientation was observed in the buckled film where horizontally aligned MoS2 layers of 7 nm thickness were present near the bottom graphene surface and vertically aligned layers dominated the film toward the outer surface, in which the alignment structure was uniform across the entire film. The catalytic ability of the buckled MoS2 films, measured by performing water-splitting tests in acidic environments, shows a reduced onset potential of -0.2 V versus reversible hydrogen electrode (RHE) compared to -0.32 V versus RHE for pristine MoS2, indicating that the rough surface provided a higher catalytic activity. Our work presents a new method to generate a buckled MoS2 structure, which may be extended to the formation of buckled structures in various 2D materials for future applications.

Voltage-induced buckling of dielectric films using fluid electrodes

Accurate and integrable control of different flows within microfluidic channels is crucial for further development of lab-on-a-chip and fully integrated adaptable structures. Here, we introduce a flexible microactuator that buckles at a high deformation rate and alters the downstream fluid flow. The microactuator consists of a confined, thin, dielectric film that buckles into the microfluidic channel when exposed to voltage supplied through conductive fluid electrodes. We estimate the critical buckling voltage and characterize the buckled shape of the actuator. Finally, we investigate the effects of frequency, flow rate, and pressure differences on the behavior of the buckling structure and the resulting fluid flow. These results demonstrate that the voltage-induced buckling of embedded microstructures using fluid electrodes provides a means for high speed, repeatable attenuation of microfluidic flow.

Dynamic stability of flexible electronic structures under step loads

Abstract The flexible electronic structure is based on the buckling of a thin film on a compliant substrate. This paper studies the dynamic stability of this structure under a uniaxial step load. Dynamic equilibrium equation is deduced according to the Euler–Lagrange equation. The dynamic response of the film is solved analytically by using Jacobi elliptic functions. It is a periodic vibration influenced by the step load. The critical load in dynamic buckling is determined by the characteristics of phase graphs and Budiansky–Roth criterion. It is the same as that in static buckling. In dynamic buckling, the amplitude of vibration is larger than that in static buckling. With the increment of the load and initial amplitude, the period of vibration decreases.

Buckling of a stiff thin film on a compliant substrate under anisotropic biaxial prestrain

The structure of stretchable electronics is based on the buckling of a thin film on a compliant substrate. Under anisotropic biaxial prestrains, this structure may buckle into several patterns, including cylindrical, checkerboard, and undulating patterns. The displacement and energy of each pattern are deduced analytically. By comparing their minimum potential energies, the critical buckling condition of each pattern is determined. After secondary bifurcation, the checkerboard pattern occurs just above the critical prestrains, but the undulating pattern dominates other regions. The buckling amplitude and wavenumber of the undulating pattern are shown under biaxial prestrains. Even if the structure is under equi-biaxial prestrains, it may buckle into an asymmetric undulating pattern.

Yield Point of Semiconducting Polymer Films on Stretchable Substrates Determined by Onset of Buckling.

Mechanical buckling of thin films on elastomeric substrates is often used to determine the mechanical properties of polymers whose scarcity precludes obtaining a stress-strain curve. Although the modulus and crack-onset strain can readily be obtained by such film-on-elastomer systems, information critical to the development of flexible, stretchable, and mechanically robust electronics (i.e., the range of strains over which the material exhibits elastic behavior) cannot be measured easily. This paper describes a new technique called laser determination of yield point (LADYP), in which a polymer film on an elastic substrate is subjected to cycles of tensile strain that incrementally increase in steps of 1% (i.e., 0% → 1% → 0% → 2% → 0% → 3% → 0%, etc.). The formation of buckles manifests as a diffraction pattern obtained using a laser, and represents the onset of plastic deformation, or the yield point of the polymer. In the series of conjugated polymers poly(3-alkylthiophene), where the alkyl chain is pentyl, hexyl, heptyl, octyl, and dodecyl, the yield point is found to increase with increasing length of the side chain (from approximately 5% to 15% over this range when holding the thickness between ∼200 and 300 nm). A skin-depth effect is observed in which films of <150 nm thickness exhibit substantially greater yield points, up to 40% for poly(3-dodecylthiophene). Along with the tensile modulus obtained by the conventional analysis of the buckling instability, knowledge of the yield point allows one to calculate the modulus of resilience. Combined with knowledge of the crack-onset strain, one can estimate the total energy absorbed by the film (i.e., the modulus of toughness).

Primary and secondary instabilities in soft bilayered systems

AbstractWrinkling phenomena emerging from mechanical instabilities in inhomogeneously compressed soft bilayered systems can evoke a wide variety of surface morphologies. Applications range from undesired instabilities in engineering structures such as sandwich panels, via fabricating surfaces with controlled buckling patterns of unique properties, to wrinkling phenomena in living matter such as lungs, mucosas, and brain convolutions. While moderate compression evokes periodic sinusoidal wrinkles, higher compression induces secondary instabilities ‐ the surface bifurcates into increasingly complex morphologies. Periodic wrinkling has already been extensively studied, but the rich pattern formation in the highly nonlinear post‐buckling regime remains poorly understood. Here, we establish a computational model of differential growth to explore the evolving buckling pattern of a growing layer bonded to a non‐growing substrate. Our model provides a mechanistic understanding of growth‐induced primary and secondary instabilities. We show that amongst all possible secondary bifurcations, the mode of period‐doubling is energetically favorable. We experimentally validate our numerical results by examining buckling of a compressed polymer film on a soft foundation. Our computational studies have broad applications in the microfabrication of distinct surface patterns as well as in the morphogenesis of living systems, where growth is progressive and the formation of structural instabilities is critical to biological function. (© 2015 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Coupling In Situ TEM and Ex Situ Analysis to Understand Heterogeneous Sodiation of Antimony.

We employed an in situ electrochemical cell in the transmission electron microscope (TEM) together with ex situ time-of-flight, secondary-ion mass spectrometry (TOF-SIMS) depth profiling, and FIB-helium ion scanning microscope (HIM) imaging to detail the structural and compositional changes associated with Na/Na(+) charging/discharging of 50 and 100 nm thin films of Sb. TOF-SIMS on a partially sodiated 100 nm Sb film gives a Na signal that progressively decreases toward the current collector, indicating that sodiation does not proceed uniformly. This heterogeneity will lead to local volumetric expansion gradients that would in turn serve as a major source of intrinsic stress in the microstructure. In situ TEM shows time-dependent buckling and localized separation of the sodiated films from their TiN-Ge nanowire support, which is a mechanism of stress-relaxation. Localized horizontal fracture does not occur directly at the interface, but rather at a short distance away within the bulk of the Sb. HIM images of FIB cross sections taken from sodiated half-cells, electrically disconnected, and aged at room temperature, demonstrate nonuniform film swelling and the onset of analogous through-bulk separation. TOF-SIMS highlights time-dependent segregation of Na within the structure, both to the film-current collector interface and to the film surface where a solid electrolyte interphase (SEI) exists, agreeing with the electrochemical impedance results that show time-dependent increase of the films' charge transfer resistance. We propose that Na segregation serves as a secondary source of stress relief, which occurs over somewhat longer time scales.

Hydrogen-Induced Buckling of Pd Films Deposited on Various Substrates

A Pd-H system is a model system suitable for studying interactions of hydrogen with metals. In the present work, we studied hydrogen-induced buckling of thin Pd films deposited on various substrates with different bonding strengths (sapphire, glimmer) and also the effect of deposition temperature. Lattice expansion and phase transitions were investigated by X-ray diffraction of synchrotron radiation. The influence of the substrate and microstructure of the film on the buckling process and phase transformation to palladium hydride are discussed.

Micro-wrinkling and delamination-induced buckling of stretchable electronic structures

This paper presents the results of experimental and theoretical/computational micro-wrinkles and buckling on the surfaces of stretchable poly-dimethylsiloxane (PDMS) coated with nano-scale Gold (Au) layers. The wrinkles and buckles are formed by the unloading of pre-stretched PDMS/Au structure after the evaporation of nano-scale Au layers. They are then characterized using atomic force microscopy and scanning electron microscopy. The critical stresses required for wrinkling and buckling are analyzed using analytical models. The possible interfacial cracking that can occur along with film buckling is also studied using finite element simulations of the interfacial crack growth. The implications of the results are discussed for potential applications of micro-wrinkles and micro-buckles in stretchable electronic structures and biomedical devices.

Phase-field model coupling cracks and dislocations at finite strain

A new 3D continuum model is developed to simultaneously describe cracks and dislocations in materials undergoing finite strain deformations. Significant advances are made to account for fracturing in a cubic symmetrical system and to correctly model the microscopic dislocation properties into a Time-Dependent Ginzburg–Landau formalism. In addition, the interaction between dislocations and free borders (crack lips, surfaces…) is naturally described. As an example, the model is used to investigate the effects of plasticity on the delamination and buckling of thin films deposited on substrates. It may also be helpful in any other situation where cracks and dislocations take place and in which finite strain effects must be considered.

Nodal properties of eigenfunctions of a generalized buckling problem on balls

In this paper we are interested in the following fourth order eigenvalue problem coming from the buckling of thin films on liquid substrates: $$\begin{aligned} {\left\{ \begin{array}{ll} \Delta ^2 u+ \kappa ^2 u=-\lambda \Delta u &{}\text {in } u=\partial _r u= 0 &{}\text {on } \partial B_1, \end{array}\right. } \end{aligned}$$ where $$B_1$$ is the unit ball in $${\mathbb R}^N$$ . When $$\kappa > 0$$ is small, we show that the first eigenvalue is simple and the first eigenfunction, which gives the shape of the film for small displacements, is positive. However, when $$\kappa $$ increases, we establish that the first eigenvalue is not always simple and the first eigenfunction may change sign. More precisely, for any $$\kappa \in \mathopen ]0,+\infty \mathclose [$$ , we give the exact multiplicity of the first eigenvalue and the number of nodal regions of the first eigenfunction.

Delamination buckling of a thin film bonded to an orthotropic substrate

This paper investigates the delamination buckling of an orthotropic film with compressive prestress bonded to an orthotropic substrate. The buckled film detached from the film/substrate structure is solved in the closed form except for the resultant force and bending moment at the ends of the buckled film, which are obtained by matching the solutions for the buckled film and the film/substrate structure in which the buckled part of the film is removed. Special attention is paid to the effects of parameters of orthotropic materials on delamination buckling based on a numerical analysis. The energy release rate and mode mixity induced by buckling are evaluated, and the growth and arrest of the interface crack under mixed loading induced by buckling are discussed based on the energy criterion.

Wrinkling and folding of thin films by viscous stress.

We examine the buckling of a thin elastic film floating on a viscous liquid layer which is itself supported on a prestretched rubber sheet. Releasing the prestretch in the rubber induces a viscous stress in the liquid, which in turn induces a compressive stress in the elastic film, leading to buckling. Unlike many previous studies on wrinkling of floating films, the buckling process in the present study is dominated by viscous effects whereas gravitational effects are negligible. An approximate shear lag model predicts the evolution of the stress profile in the unbuckled film that depends on three parameters: the rate at which the prestretch is released, the thickness of the liquid layer, and the length of the elastic film. A linear perturbation analysis is developed to predict the wavelength of wrinkles. Numerical simulations are conducted to predict nonlinear evolution of the wrinkle wavelength and amplitude. Experiments using elastic polymer films and viscous polymer liquids show trends that are qualitatively consistent with the predictions although quantitatively, the experimentally-observed wrinkle wavelengths are longer than predicted. Although this article is focused only on small-strain wrinkling behavior, we show that application of large nominal strains (on the order of 100%) leads to sharply localized folds. Thus this approach may be useful for developing buckled features with high aspect ratio on surfaces.

The effect of mechanical-driven volumetric change on instability patterns of bilayered soft solids.

If a soft solid is compressible, its volume changes with imposed loading. The extent of the volume change depends on its Poisson's ratio. Here, we study the effect of the mechanical-driven volumetric change on buckling and post-buckling behaviors of a hard thin film perfectly bound on a compliant substrate through the theoretical analysis and finite element method. Poisson's ratio of the substrate has been chosen to be in the range of -1 to 0.5, allowing its volume change during deformation. We find that Poisson's ratio cannot only shift the critical strain for the onset of buckling, but also affect the buckling modes. When Poisson's ratio of the substrate is close to -1, the surface instabilities of the thin film can be suppressed and delayed to large deformation. The present study demonstrates a new way to control surface instabilities of a bilayered system by changing Poisson's ratio of the material.

Buckling of a soap film spanning a flexible loop resistant to bending and twisting

A generalization of the Euler–Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler–Lagrange equations are derived in a parametrized setting and a buckling analysis is performed. A pair of dimensionless parameters govern buckling from a flat, circular ground state. While one of these is familiar from the Euler–Plateau problem, the other encompasses information about the ratio of the torsional rigidity to the bending rigidity, the twist density and the size of the loop. For sufficiently small values of the latter parameter, two separate groups of buckling modes are identified. However, for values of that parameter exceeding the critical twist density arising in Michell's study of the stability of a twisted elastic ring, only one group of buckling modes exists. Buckling diagrams indicate that a loop with greater torsional rigidity shows more resistance to transverse buckling. Additionally, a twisted flexible loop spanned by a soap film buckles at a value of the twist density less that the value at which buckling would occur if the soap film were absent.

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

Because of the interaction between film and substrate, the film buckling stress can vary significantly, depending on the delamination geometry, the film and substrate mechanical properties. The Mexican hat effect indicates such interaction. An analytical method is presented, and related dimensional analysis shows that a single dimensionless parameter can effectively evaluate the effect.

Films in narrow tubes

AbstractWe consider the axisymmetric arrangement of an annular liquid film, coating the inner surface of a narrow cylindrical tube, in interaction with an active core fluid. We introduce a low-dimensional model based on the two-phase weighted residual integral boundary layer (WRIBL) formalism (Dietze &amp; Ruyer-Quil, J. Fluid Mech., vol. 722, 2013, pp. 348–393) which is able to capture the long-wave instabilities characterizing such flows. Our model improves upon existing works by fully representing interfacial coupling and accounting for inertia as well as streamwise viscous diffusion in both phases. We apply this model to gravity-free liquid-film/core-fluid arrangements in narrow capillaries with specific attention to the dynamics leading to flooding, i.e. when the liquid film drains into large-amplitude collars that occlude the tube cross-section. We do this against the background of linear stability calculations and nonlinear two-phase direct numerical simulations (DNS). Due to the improvements of our model, we have found a number of novel/salient physical features of these flows. First, we show that it is essential to account for inertia and full interphase coupling to capture the temporal evolution of flooding for fluid combinations that are not dominated by viscosity, e.g. water/air and water/silicone oil. Second, we elucidate a viscous-blocking mechanism which drastically delays flooding in thin films that are too thick to form unduloids. This mechanism involves buckling of the residual film between two liquid collars, generating two very pronounced film troughs where viscous dissipation is drastically increased and growth effectively arrested. Only at very long times does breaking of symmetry in this region (due to small perturbations) initiate a sliding motion of the liquid film similar to observations by Lister et al. (J. Fluid Mech., vol. 552, 2006, pp. 311–343) in thin non-flooding films. This kickstarts the growth of liquid collars anew and ultimately leads to flooding. We show that streamwise viscous diffusion is essential to this mechanism. Low-frequency core-flow oscillations, such as occur in human pulmonary capillaries, are found to set off this sliding-induced flooding mechanism much earlier.

Combined effect of pressure and geometric imperfection on buckling of stressed thin films on substrates

This paper deals with the combined effect of pressure and geometric imperfection on buckling of stressed thin films on a semi-infinite rigid substrate. Analytical approximate solutions are proposed by using the total potential energy of the system and the Rayleigh–Ritz’s method, and their stabilities are also determined. The present analytical approximate solutions agree very well with the numerical solutions obtained via the improved shooting method. The effect of pressure mismatch together with imperfection on the critical stress (above which the film buckles) and on the film-center deflection is characterized. It is found that, compared with the classical case of the Euler column buckling, the equilibrium solutions and critical stress of the film are strongly dependent on the linear combination of the pressure mismatch and imperfection amplitude.