Experimental study on buckle evolution of thin inorganic layers on a polymer substrate

In this paper the behavior of a 250 nm and a 350 nm thick Indium tin oxide (ITO) layers deposited on a 200 μm thick high temperature aromatic polyester substrate (Arylite™) and spin coated with a 3 μm silica-acrylate hybrid coating (Hard Coat) is discussed. In-situ optical microscopy of the layered structures under uniaxial compressive strain was used to determine the buckle delamination rate at different applied strains. The effect of applied uniaxial compressive strain and layer thickness on the evolution of buckle width and height was investigated. The biaxial-residual stress, uniaxial compressive stress, poor adhesion at the interface and Poisson’s ratio are believed to be responsible for the formation of telephone-cord buckling.     

Influence of substrate compliance on buckling delamination of thin films

A thin film subject to in-plane compressive stress is susceptible to buckling-driven delamination. This paper analyzes a straight-sided delamination buckle with a focus on the effects of substrate compliance, following earlier work by B. Cotterell and Z. Chen. The critical buckling condition, the energy release rate and the mode mix of the interface delamination crack are calculated as a function of the elastic mismatch between the film and substrate. The average energy release rate at the curved end of a tunneling straight-sided blister is also determined. The more compliant the substrate, the easier for the film to buckle and the higher the energy release rates. The effect becomes significant when the modulus of the substrate is appreciably less than that of the film. When the substrate modulus is comparable to that of the film, or higher, the usual assumption is justified to the effect that the film is clamped along its edges. When the substrate is very compliant the energy release rate at the curved front exceeds that along the straight sides.     

Evaluation of thin film adhesion to a compliant substrate by the analysis of progressive buckling in the fragmentation test

The interface toughness of a thin coating/compliant substrate system is estimated based on the evolution of coating buckle patterns in the fragmentation test. The linear density of coating buckles as a function of applied strain is determined experimentally for a SiO_x coating deposited on a polyethylene terephthalate film. A three-dimensional non-linear finite element model is developed to simulate the process of buckle formation in a single narrow coating strip. The elastic energy released during buckling-driven delamination is obtained from the energy balance in the system before and after the buckling event. Both the interface adhesion and the total energy release rate, which includes the plastic dissipation in the substrate during debonding, are evaluated. The apparent interfacial toughness, equal to 15 J/m² at the onset of buckling, is found to increase with strain. This is tentatively explained by the probabilistic features of the buckle accumulation process, reflected also in the random locations of buckles evolving towards a log-normal distribution of buckle spacings at high strains.     

Effect of a hard coat layer on buckle delamination of thin ITO layers on a compliant elasto-plastic substrate: An experimental–numerical approach

Layer buckling and delamination is a common interfacial failure phenomenon in thin film multi-layer structures that are used in flexible display applications. Typically, the substrate is coated on both sides with a hybrid coating, called a hard coat (HC), which acts as a gas barrier and also increases the scratch resistance. In this paper 250 nm thick indium tin oxide (ITO) layers have been deposited on a 200 μm thick high temperature aromatic polyester substrate (Arylite^TM), with and without a 3 μm HC. In order to study the influence of this HC layer on delamination phenomena, two-point bending experiments are performed from which buckle width and height values are measured after straightening of the sample. An analytical model and a finite element (FE) model are developed to estimate the adhesion properties from the measured buckle geometries. In the numerical model, the initiation and propagation of the delamination process is described by cohesive zone elements, of which the parameters are extracted from response surface model (RSM) results. Furthermore, the numerical model is used to illustrate the significant change in buckle geometry upon load reversal, i.e. from loaded to straightened state, which is governed by the elasto-plastic behavior of the substrate material. It is concluded that the addition of a HC layer significantly decreases the adhesion of the ITO layer. The latter is determined as function of the actual mode angle.     

A non-contact, thermally-driven buckling delamination test to measure interfacial fracture toughness of thin film systems

Interfacial fracture toughness measurements of thin film-substrate systems are of importance in many applications. In the microelectronics industry, the interfacial adhesion between the dielectric-barrier-metal layers on a semiconductor chip is critical for chip reliability. In this paper, we propose a thermally-driven patterned buckling delamination test that does not use a pre-existing weak interface. The test relies on causing a patterned film to debond from its substrate by inducing a compressive stress due to heating of the film on a thick silicon substrate. The compressive stress causes the film to buckle and debond from the substrate. A model for the propagation of the buckling-induced debond is then developed to estimate interfacial fracture toughness. The efficacy of the thermally-driven buckling test is demonstrated on a model Al/SU8/Si film-substrate system wherein the Al film debonds along its interface to SU8. The interfacial toughness of the Al/SU8 interface is estimated using the proposed test and is compared to the toughness for the same system obtained using an alternative test with a weakened interface to validate the developed elastic-plastic model for buckling-induced debond propagation.     

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

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.     

Adhesion measurements using telephone cord buckles

Thin film adhesion energies can be calculated using buckles with the telephone cord geometry. The buckles can be measured through the point of inflection of the buckle or through the center of the buckle and modeled as a straight buckle of uniform width and height. In the tungsten-silica system, a unique delamination morphology involved a transition from the straight to telephone cord buckle. This structure was used to compare various measurement techniques. The stability range between the straight and telephone cord morphology has been shown to be broader than previously described and exhibits a smooth transition from the straight to telephone cord structure. Measurements of the straight-sided buckles produce adhesion energies which are within 15% of the values calculated when approximating the telephone cord as a straight-sided structure at the inflection point of the buckle.     

Calculations of Buckle-Driven Delamination Using Cohesive Elements

Plane strain, elastic calculations of buckle-driven thin film delamination from compliant substrates using finite element models are considered. The interfacial properties between the film and the substrate are modeled using cohesive elements with a tractionseparation law formulated in terms of a potential. The model yielded the geometry of the buckles given the properties of the film and the substrate, the interfacial toughness and the value of the compressive equi-biaxial stress. Results for the relation between the buckle width and the interfacial toughness were very close to similar results by Yu and Hutchinson (2002), thus giving confidence that the cohesive element approach presented can be used in applications where buckle-driven delamination of thin films is an issue.     

基于弯曲刚度最大分层临界载荷的层压板局部屈曲预测

提出了一种预测含特定分层损伤层压板发生局部屈曲时整体应变的方法。认为含分层子板的局部屈曲载荷由其弯曲刚度最大的分层决定, 因而含有相同最大弯曲刚度分层的不同子板具有相同的屈曲载荷。在已知弯曲刚度最大分层的屈曲载荷的情况下, 根据层压板的轴向刚度公式, 计算出发生局部屈曲时弯曲刚度最大的分层与完好的基板分别承受的载荷, 即得到总载荷, 进而得到层压板的整体应变。用ABAQUS有限元分析软件建立含分层损伤的层压板模型, 使用准静态加载进行了多种分层深度和分层位置下的局部屈曲仿真, 所得局部屈曲载荷符合上述推论。用所提方法预测发生局部屈曲时的整体应变, 结果与有限元结果吻合较好, 此方法可用于建立分层参数识别的参照样本库。     

Performance of a fiber reinforced polymer web core skew bridge superstructure. Part I: field testing and finite element simulations

An analytical method is presented to investigate hydrothermal effects on locally buckling for an elliptical delamination near the surface of cylindrical laminated shells. The critical strain of non-linear buckling for a locally elliptic delamination of cylindrical laminated shells is obtained by considering transverse displacements of the elliptically sub-laminated shells. The stacking sequence of sub-laminated shells may be multilayer and asymmetric. The geometrical axis of sub-laminated shells may be arbitrary. The Young's modulus and the thermal and humidity expansion coefficients of the material are considered as functions of temperature change in base-laminated shells. The critical strains of locally buckling for cylindrical laminated shells subjected to hydrothermal effects are extracted for different stacking sequences, and different radii of base-laminated shells, by applying Rayleigh–Ritz method based on second variation of potential energy. From results carried out, it is found that the critical strain from the non-linear buckling for a locally elliptic delamination near the surface of a cylindrical laminated shell presents a lower value than that from linear considerations.     

Determining buckling strain energy release rate through indentation-induced delamination

An oscillating indentation load was applied to delaminate a diamond-like-carbon film from a silicon substrate. After delamination occurred, a two-stage behavior was exhibited in the load-depth results; then, a three-stage behavior was exhibited after buckling occurred due to a long enough delamination length. After removing the indentation load, the debonding film was single-buckled and suspended over the substrate; thus, the delamination length was obtained via the residual profile. Through analysis of the deflection of the buckled film, the buckling strain energy release rate was evaluated.     

Buckling and Delamination Growth Analysis of Composite Laminates Containing Embedded Delaminations

The objective of this work is to study the post buckling behavior of composite laminates, containing embedded delamination, under uniaxial compression loading. For this purpose, delamination initiation and propagation is modeled using the softening behavior of interface elements. The full layer-wise plate theory is also employed for approximating the displacement field of laminates and the interface elements are considered as a numerical layer between any two adjacent layers which delamination is expected to propagate. A finite element program was developed and the geometric non-linearity in the von karman sense is incorporated to the strain/displacement relations, to obtain the buckling behavior. It will be shown that, the buckling load, delamination growth process and buckling mode of the composite plates depends on the size of delamination and stacking sequence of the laminates.     

Finite element analysis of interface delamination and buckling in thin film systems by wedge indentation

A finite element method is used to study the interface delamination and buckling of thin film systems subject to microwedge indentation. In the formulation, the interface adjoining the thin film and substrate is assumed to be the only site where cracking may occur. Both the thin film and the substrate are taken to be ductile materials with finite deformation. A traction-separation law, with two major parameters: interface strength and interface energy, is introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. The effects of the interface adhesive properties and the thickness of the thin film on the onset and growth of interface delamination and the film buckling are investigated.     

Delaminating buckling model based on nonlocal Timoshenko beam theory for microwedge indentation of a film/substrate system

A novel model built on the basis of nonlocal Timoshenko beam theory is presented for delaminating buckling in the microwedge indentation test of a thin film on an elastic substrate. Two size effects are accounted for in the proposed model. One is the delamination size effect, and the other is the film thickness effect. The influence of the elastic deformation in the substrate and the indentation-induced impression or notch on the buckling behaviors are taken into consideration by employing coupled line springs as the boundary conditions of the buckled film. The critical stress for buckling, the energy release rate and the phase angle of the interface delamination crack are calculated and compared with those by classical beam theories. Sensitivity of the two size effects is observed.     

有横向纤维搭桥的脱层扩展稳定性分析

本文利用von Karman 非线性薄板理论, 求解了复合材料中有横向纤维搭桥作用的圆形薄膜脱层的后屈曲问题, 获得了桥联脱层均匀扩展的能量释放率和断裂韧性。通过大量的计算和分析得到一个重要结论: 搭桥纤维的存在不仅对脱层的初始扩展起到了增韧作用, 而且避免了脱层扩展的灾难性。同时定量地给出了搭桥作用对脱层初始扩展的增韧程度, 并且确定了桥联脱层扩展稳定与不稳定的分区, 对不稳定脱层还给出了失稳扩展的范围及动态效应的估计。      

Mechanical integrity analysis of multilayer insulator coatings on flexible steel substrates

The cohesive and adhesive properties, and related critical radius of curvature of thin multilayer insulator coatings on a 152 μm thick flexible steel substrate were investigated using tensile experiments carried out in-situ in an optical microscope. This method was found to be well adapted for the two types of coatings studied: SiO₂ single layers with different thickness and SiO₂/SiN_x/polyimide stacks. Special attention was paid to the influence of surface roughness and yielding of the steel substrate. Coating delamination and spallation was observed at low strain in case of SiO₂ coatings on unpolished steel, resulting from roughness-induced stress concentrations and slippage of grain boundaries. Polishing the steel substrate, or using a polyimide interlayer, was found to be useful to avoid premature delamination of the layers. In all investigated cases, a critical radius of curvature for layer damage of approximately 5 mm was found.     

Swelling-induced delamination causes folding of surface-tethered polymer gels

When a polymer film that is weakly attached to a rigid substrate is exposed to solvent, swelling-induced compressive stress nucleates buckle delamination of the film from the substrate. Surprisingly, the buckles do not have a sinusoidal profile, instead, the film near the delamination buckles slides toward the buckles causing growth of sharp folds of high aspect ratio. These folds do not result from a wrinkle-to-fold transition; instead, the film goes directly from a flat state to a folded state. The folds persist even after the solvent evaporates. We propose that patterned delamination and folding may be exploited to realize high-aspect ratio topological features on surfaces through control of a set of boundary constraints arising from the interrelation of film-surface adhesion, film thickness and degree of swellabilty.     

Light‐Induced Buckles Localized by Polymeric Inks Printed on Bilayer Films

Buckling instabilities generate microscale features in thin films in a facile manner. Buckles can form, for example, by heating a metal/polymer film stack on a rigid substrate. Thermal expansion differences of the individual layers generate compressive stress that causes the metal to buckle over the entire surface. The ability to dictate and confine the location of buckle formation can enable patterns with more than one length scale, including hierarchical patterns. Here, sacrificial “ink” patterned on top of the film stack localizes the buckles via two mechanisms. First, stiff inks suppress buckles such that only the non‐inked regions buckle in response to infrared light. The metal in the non‐inked regions absorbs the infrared light and thus gets sufficiently hot to induce buckles. Second, soft inks that absorb light get hot faster than the non‐inked regions and promote buckling when exposed to visible light. The exposed metal in the non‐inked regions reflects the light and thus never get sufficiently hot to induce buckles. This second method works on glass substrates, but not silicon substrates, due to the superior thermal insulation of glass. The patterned ink can be removed, leaving behind hierarchical patterns consisting of regions of buckles among non‐buckled regions.     

A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green’s function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness. Also, the transition of buckling from the first to the second mode is captured in the simulation.     

Buckling Of Thin Film Thermoelectrics

This work investigates buckling behavior of thin film thermoelectrics subjected to a temperature gradient. Both a single-layer thermoelectric film and multilayered structures are studied. The multilayered structure consists of a p-type and n-type thermocouple separated by an insulating layer with or without additional supporting membrane layers. The temperatures, and thermoelectrically induced stresses and membrane forces are first presented. The elastic stability theories of homogeneous plates and laminated composites are subsequently used to determine the temperature differential between the hot and cold junctions that causes buckling of the thin film structures. The numerical results show that a single-layer thermoelectric film could buckle at a temperature differential of around 10 K for large length-to-thickness ratios. The multilayered thermoelectric thin film structures exhibit significantly higher buckling temperature differentials due to reduced overall length-to-thickness ratios.