The characterization of telephone cord buckling of compressed thin films on substrates

The topology of the telephone cord buckling of compressed diamond-like carbon films (DLC) on glass substrates has been characterized with atomic force microscopy (AFM) and with the focused ion beam (FIB) imaging system. The profiles of the several buckles have been measured by AFM to establish the symmetry of each repeat unit, revealing similarity with a circular buckle pinned at its center. By making parallel cuts through the buckle in small, defined locations, straight-sided buckles have been created on the identical films, enabling the residual stress in the film to be determined from the profile.It has been shown that the telephone cord topology can be effectively modeled as a series of pinned circular buckles along its length, with an unpinned circular buckle at its front. The unit segment comprises a section of a full circular buckle, pinned to the substrate at its center. The model is validated by comparing radial profiles measured for the telephone cord with those calculated for the pinned buckle, upon using the residual stress in the film, determined as above. Once validated, the model has been used to determine the energy release rate and mode mixity, G(ψ).The results for G(ψ) indicate that the telephone cord configuration is preferred when the residual stress in the DLC is large, consistent with observations that straight-sided buckles are rarely observed, and, when they occur, are generally narrower than telephone cords. Telephone cords are observed in many systems, and can be regarded as the generic morphology. Nevertheless, they exist subject to a limited set of conditions, residing within the margin between complete adherence and complete delamination, provided that the interface has a mode II toughness low enough to ensure that the buckle crack does not kink into the substrate.     

Telephone cord buckles—A relation between wavelength and adhesion

Thin films with low adhesion and large residual stresses may buckle. The resulting morphologies are varied, but one of the most commonly observed is an intriguing oscillating pattern – the so-called “telephone cord” – which has been extensively investigated in the recent years. We have studied the kinematics of formation of telephone cords using a geometrically non-linear plate model and mode dependent interfacial toughness, captured via a cohesive zone. Through extensive Finite Element Simulations, we have demonstrated a simple, non-trivial relation between telephone cord wavelength and interfacial toughness. To validate this prediction, highly stressed Mo thin films were deposited on Si wafers, with a well defined interface and very reproducible adhesion. Studying the morphology of the resulting buckles for different film thicknesses and stresses, we observed a trend which was fully consistent with our simulation results. From the data fit, an adhesion energy of 0.58±0.04 J m⁻² for the SiO₂/Ag interface was inferred, which compares well with literature estimates.     

<Emphasis Type="BoldItalic">In situ</Emphasis> Study of Cracking and Buckling of Chromium Films on PET Substrates

Chromium (Cr) films are widely used as interlayers to promote the adhesion of copper or gold to substrates. However, the Cr interlayer usually fractures at lower strains than the ductile metal films. In this paper, the cracking and buckling behavior of Cr films on polyethylene terephthalate (PET) substrates were studied in situ under tensile loading with the Atomic Force Microscope (AFM) and optical microscope imaging. Cr films with three nominal thicknesses of 15, 70 and 140 nm were studied. The depth and width of the cracks, as well as the height and width of the buckles, were measured from AFM images acquired at incremental loading steps. The buckle shapes at different strain levels were carefully examined using AFM line profile. It was found that at large strain levels the measured buckle shapes usually deviated from the elastic buckling mode shapes. Further in situ AFM imaging of the buckles at a smaller scan area revealed that in some cases the buckles were cracked at the apex. These in situ nanoscale measurements provided experimental observations and data for further model development and more accurate measurement of the interfacial fracture energy at the Cr-PET interface.     

Critical cooling rates to avoid transient-driven cracking in thermal barrier coating (TBC) systems

This paper presents critical cooling rates to avoid cracking in thermal barrier coatings (TBCs) driven by thermal transients. A complete thermomechanical model is presented for multilayers; it determines the history of temperature, deformation and stress distributions in the layers, as well as the steady-state energy release rate (ERR) for delamination for all possible crack locations. The model is used to analyze bilayers over a broad range of properties and cooling rates; critical cooling rates are identified that distinguish scenarios in which the transient delamination driving force is higher than that associated with the fully cooled state. Implications for coating the durability are discussed.     

Parametric studies of failure mechanisms in elastic EB-PVD thermal barrier coatings using FEM

Catastrophic failure of thermal barrier coatings (TBCs), usually occurs due to large scale buckling and spallation, primarily originating at the bond coat and TGO interface. Spallation in TBCs is preceded by a competition between buckling and interface delamination that is stimulated by the waviness of the interface. In the presence of thermal loading, the waviness is responsible for growth of interfacial delamination. In this paper, a finite element model of the two and three layer TBC’s is developed in the commercial code ANSYS to investigate the buckle and interface delamination mechanisms and develop a simplified parametric understanding of these mechanisms. The models for simulation are validated with analytical and experimental results. Parametric relations, in terms of geometric and material parameters representing constituents of the TBC, are developed in this paper for critical stresses and energies causing buckling and debonding initiated instabilities. Through these relations, critical parameters that control failure mechanics are identified for a fail-safe design space.     

Quantitative characterization of the interfacial adhesion of Ni thin film on steel substrate: A compression-induced buckling delamination test

A compression-induced buckling delamination test is employed to quantitatively characterize the interfacial adhesion of Ni thin film on steel substrate. It is shown that buckles initiate from edge flaws and surface morphologies exhibit symmetric, half-penny shapes. Taking the elastoplasticity of film and substrate into account, a three-dimensional finite element model for an edge flaw with the finite size is established to simulate the evolution of energy release rates and phase angles in the process of interfacial buckling-driven delamination. The results show that delamination propagates along both the straight side and curved front. The mode II delamination plays a dominant role in the process with a straight side whilst the curved front experiences almost the pure mode I. Based on the results of finite element analysis, a numerical model is developed to evaluate the interfacial energy release rate, which is in the range of 250–315 J/m² with the corresponding phase angle from −41° to −66°. These results are in agreement with the available values determined by other testing methods, which confirms the effectiveness of the numerical model.     

Adhesion-governed buckling of thin-film electronics on soft tissues

Stretchable/flexible electronics has attracted great interest and attention due to its potentially broad applications in bio-compatible systems. One class of these ultra-thin electronic systems has found promising and important utilities in bio-integrated monitoring and therapeutic devices. These devices can conform to the surfaces of soft bio-tissues such as the epidermis, the epicardium, and the brain to provide portable healthcare functionalities. Upon contractions of the soft tissues, the electronics undergoes compression and buckles into various modes, depending on the stiffness of the tissue and the strength of the interfacial adhesion. These buckling modes result in different kinds of interfacial delamination and shapes of the deformed electronics, which are very important to the proper functioning of the bioelectronic devices. In this paper, detailed buckling mechanics of these thin-film electronics on elastomeric substrates is studied. The analytical results, validated by experiments, provide a very convenient tool for predicting peak strain in the electronics and the intactness of the interface under various conditions.     

基底上薄膜结构的非线性屈曲力学进展

基底上薄膜结构中的过大残余压应力常常通过屈曲不稳定性诱发薄膜结构和功能的失效。屈曲不稳定性、演化与斑图形成是近年来非线性力学研究的热点。此类屈曲不稳定性受薄膜-基底的力学性质以及界面相互作用影响,进而呈现出复杂的屈曲模式如褶皱、翘曲和折痕等。论文简要综述褶皱、翘曲和折痕等屈曲模式的形成机制、影响因素和后屈曲形貌相关方面的进展。褶皱部分,重点介绍了褶皱的形成、多级褶皱结构、局域化的褶皱、各向异性褶皱和曲面上的褶皱。翘曲部分,介绍了翘曲结构包括一维翘曲结构、“电话线”屈曲泡,网络状屈曲泡等的形成与生长过程,并讨论了曲面几何、界面滑移、开裂等因素的影响。折痕及其它复杂屈曲模式部分,介绍了折痕、叠痕及隆起失稳的形成机制与临界条件.     

Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending

The interaction of multiple delaminations in a laminated composite plate loaded dynamically under plane strain conditions (cylindrical bending) is studied by a simple but accurate model that represents the delaminated plate as a set of Timoshenko beams joined by cohesive interfaces. Behavioral maps are derived, which distinguish conditions under which multiple delaminations tend to propagate with equal lengths from those under which one of them tends to grow as a dominant crack with relatively high velocity. In homogeneous systems, equal length growth is favored when the delaminations are equally spaced through the thickness. While the behavioral maps are similar to those for static loading conditions, significant dynamic effects arise in the details of propagation: the maximum energy release rate depends strongly on the loading rate, duration and profile; dynamic effects and crack-interaction effects are generally coupled; and strong hammering effects (chaotic collisions of sub-laminates) can occur during the free wave motions that arise after the load is removed. The hammering effect can be suppressed by imposing a large-scale bridging mechanism (bridging extending far in the crack wake, as from pins or stitches), whereupon energy release rates tend to show smooth oscillations associated with waves propagating on the scale of the whole specimen. The energy absorbed during failure will depend significantly on whether conditions favor multiple delaminations propagating with equal lengths or a single delamination growing dominantly.     

Stress and Moisture Effects on Thin Film Buckling Delamination

Deposition processes control the properties of thin films; they can also introduce high residual stresses, which can be relieved by delamination and fracture. Tungsten films with high 1–2 GPa compressive residual stresses were sputter deposited on top of thin (below 100 nm) copper and diamond-like carbon (DLC) films. Highly stressed films store large amounts of strain energy. When the strain energy release rate exceeds the films' interfacial toughness, delamination occurs. Compressive residual stresses cause film buckling and debonding, forming open channels. Profiles of the buckling delaminations were used to calculate the films' interfacial toughness and then were compared to the adhesion results obtained from the superlayer indentation test. Tests were conducted in both dry and wet environments and a significant drop in film adhesion, up to 100 times was noticed due to the presence of moisture at the film/substrate interface.     

纳米薄膜屈曲模式的实验研究

薄膜/基底系统在信息科学以及微电子机械系统中有着十分重要的地位.薄膜中常会有压或拉的残余应力,因此薄膜/基底结构通常是工作在残余应力以及外加应力的联合作用下.根据结构的功用不同,其载荷方式也有不同,从而也导致了不同的破坏模式.压缩载荷下的脱粘屈曲是薄膜基底结构主要的破坏形式之一.本文使用磁控溅射镀膜技术,制作了压缩薄膜...     

The use of stereo X-ray and deply techniques for evaluating instability of composite cylindrical panels with delaminations

The buckling loads of eight-ply AS4/3501-6 graphite/epoxy cylindrical panels with delaminations were determined experimentally. The delaminations fabricated into the laminate with Mylar and Teflon inserts, represent the effect of low-velocity projectile impact damage. The Mylar was found to cause partial delamination while the Teflon inserts caused total delamination. Two types of insert positions were considered; eccentric or off-midsurface, and midsurface. The eccentric delaminations were placed progressively through the thickness of the laminate. STAGSC-1 finite-element computer code results for undelaminated composite panels were compared to the experimental results to obtain a percent strength degradation. The experimental testing was accomplished by the Air Force Flight Dynamics Laboratory. The test device provided boundary conditions of clamped top and bottom edges and simply supported vertical sides. Two destructive techniques, stereo X-ray and deply, were used to determine the total delaminated areas and locations. Based in part on these results, one equivalent delamination was obtained corresponding to the total area of the multiple partial delaminations. The panels with multiple delaminations were found to be approximately five-percent weaker than a single delaminated area of the same total size. Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.     

Buckling analysis of laminated composite plates containing delaminations using the enhanced assumed strain solid element

This study investigates buckling behaviors of laminated composite structures with a delamination using the enhanced assumed strain (EAS) solid element. The EAS three-dimensional finite element (FE) formulation described in this paper, in comparison with the conventional approaches, is more attractive not only because it shows better accuracy but also it converges faster, especially for distorted element shapes. The developed FE model is used for studying cross-ply or angle-ply laminates containing an embedded delamination as well as through-the-width delamination. The numerical results obtained are in good agreement with those reported by other investigators. In particular, new results reported in this paper are focused on the significant effects of the local buckling for various parameters, such as size of delamination, aspect ratio, width-to-thickness ratio, stacking sequences, and location of delamination and multiple delaminations.     

Elastic interaction of multiple delaminations in plates subject to cylindrical bending

This paper deals with the elastic interaction of multiple through-width delaminations in laminated plates subject to static out of plane loading and deforming in cylindrical bending. A model has been formulated utilizing the classical theory of the bending of beams and plates and accounting for non-frictional contact along the delamination faces. Strong interaction effects arise between the delaminations including shielding and amplification of the energy release rate and modification of the mode ratio as compared to a structure with only a single delamination. Such behavior has been summarized in maps that completely characterize the response of a system of two delaminations in a cantilever beam. The quasi-static propagation of the system of delaminations is also strongly controlled by the delamination interactions, which lead to local snap-back and snap-through instabilities, crack arrest and crack pull-along. The results show similarity to those for cracked infinite bodies, but the finite-thickness of the plate plays an important role and gives rise to more complex behaviors. The stability of the equality of length of a system of n delaminations is controlled by their spacing. Finite element calculations confirm that the model proposed here is accurate, except when the difference in the length of the interacting delaminations is less than a few times the separation of their planes.     

含内埋圆形或椭圆形脱层复合材料层合板的屈曲分析

用瑞里-李兹方法来建立含内埋圆形或椭圆形脱层板的屈曲分析模型．首先利用Heaviside阶梯函数，假定一种适合于脱层板的位移模式．然后由变分原理并进行线性化得出了含内埋圆形或椭圆形脱层板的屈曲特征方程．最后通过将含表面脱层的各向同性和各向异性板的屈曲载荷与其它文献进行比较，验证了该文分析方法的正确性，并分析了含内埋圆形或椭圆形脱层的各向同性、正交各向异性和角铺层层合板各种参数对屈曲载荷的影响．     

Delamination in patterned films

When the dielectric constant of an insulator in an interconnect is reduced, mechanical properties are often compromised, giving rise to significant challenges in interconnect integration and reliability. Due to low adhesion of the dielectric an interfacial crack may occur during fabrication and testing. To understand the effect of interconnect structure, an interfacial fracture mechanics model has been analyzed for patterned films undergoing a typical thermal excursion during the integration process. It is found that the underlayer pattern generates a driving force for delamination and changes the mode mixity of the delamination. The implications of our findings to interconnect processes and reliability testing have been discussed.     

Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites

An element-failure algorithm is proposed and incorporated into a finite element code for simulating dynamic crack propagation and impact damage in laminated composite materials. In this algorithm, when a crack is propagating within a finite element, the element is deemed to have partially failed, but not removed from the computations. Consequently, only a fraction of the stresses that were computed before the crack tip entered the element contribute to the nodal forces of the element. When the crack has propagated through the element, the element is completely failed and therefore can only resist volumetric compression. This treatment of crack propagation in isotropic solids allows fracture paths within individual elements and is able to accommodate crack growth in any arbitrary direction without the need for remeshing. However, this concept is especially powerful when extended to the modeling of damage and delamination in fibre-reinforced composite laminates. This is because the nature of damage in composite laminates is generally diffused, characterized by multiple matrix cracks, fibre pullout, fibre breakage and delaminations. It is usually not possible to define or identify crack tips in the tradition of fracture mechanics. Since parts of a damaged composite structure are often able to partially transmit load despite the presence of some damage, it is advantageous to model the damaged portions with partially failed elements. The damage may be efficiently modeled and tracked using element-failure concepts, with the application of appropriate failure criteria and damage evolution laws. The idea is to embody the effects of damage into the effective nodal forces of the finite element. In this paper, we report the novel use of element-failure concepts in the analysis of low-velocity impact damage of composite laminates. The initiation and propagation of delaminations arising from the impact are predicted and the results show qualitative agreement with experimental observation of the formation of multiple delaminations in impact-damaged specimens. While such delaminations do not permit transmission of tensile stress waves across the cracked surfaces, transmission of compressive stress waves are allowed in the simulation. It is further shown that, when elements are allowed to fail, the dynamic stress wave distributions are altered significantly. In the element-failure algorithm, the issue of interpenetration of delamination surfaces in the model does not arise. This is a significant advantage over the conventional method of explicitly modeling the delamination surfaces and crack front, where generally, much computational time must be spent in employing contact algorithms to ensure physically admissible solutions. Finally, we also demonstrate the simulation of crack propagation of pre-notched specimens of an isotropic material under initial conditions of mode II loading using the element-failure algorithm. The numerical results showed that the cracks propagated at an angle of about 70° with respect to the notches, in agreement with the experimental results of Kalthoff.     

含内埋矩形脱层复合材料圆柱壳屈曲分析的混合变量条形传递函数方法

提出了一种分析含内埋矩形脱层正交各向异性圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Mindlin一阶剪切壳理论,通过定义圆柱壳的广义力变量和混合变量,建立了壳的改进混合变量能量泛函;然后,为了便于脱层壳的分区求解,通过引入条形单元,创建了基于混合变量条形传递函数解的含脱层和不合脱层两种超级壳单元;在此基础上,将含内埋矩形脱层的复合材料层合壳划分成两种超级壳单元的组合体,通过各超级壳单元相互之间连接结点处的位移连续和力平衡条件得到脱层壳的屈曲方程;最后由屈曲方程计算含内埋矩形脱层壳的屈曲载荷和屈曲模态。算例分析的结果验证了本方法的正确性,并给出了几种因素对屈曲载荷和屈曲模态的影响。     

Thickness effect on microstructural and mechanical properties of pulse-laser treated Ti/Ni multilayer thin films

Previous work showed that pulse-laser irradiation can strengthen metal multilayer thin films through intermetallic formation and the degree of strengthening is a function of laser pulse energy.In this work,the effect of individual layer thickness(λ)and total multilayer thickness(h)on the resulting microstructure and mechanical strength of laser-treated Ti/Ni multilayers was further investigated.Experiments were carried out on fourλ/hcombinations using individual layer thickness of 20 nm and 50 nm,and total multilayer thickness of 500 nm and1μm,respectively.Obvious intermetallic strengthening was observed in the 500 nm thick multilayers,especially with the 20 nm layer thickness,but not in the 1μm thick multilayers.Further,the multilayer surface morphology after laser treatment was observed to be dominated by competition between laser-induced optical interference and thermal melting,with the former leading to ripple or cross-hatched patterns and the latter leading to melted surfaces with pores and cracks.     

Buckling analysis of two layer delaminated beams with bridging

Stitching has been used as through-thickness reinforcement to reduce the effects of delamination. In stitching, the delamination will be held by stitches in the form of crack/interface bridging. In the present work, the reinforcement of stitching threads is assumed to provide continuous linear restoring tractions opposing the delamination opening. A generalized mathematical model is developed to study the buckling analysis of two layer delaminated beams with bridging by using Rayleigh–Ritz energy method. The delaminated beam is analyzed as four interconnected beams using the delamination as their boundary. Lagrange multipliers are used to enforce the boundary and continuity conditions between the junctions of the interconnected beams. The developed mathematical model is solved as an eigenvalue problem in which the lowest eigenvalue gives the buckling load. Effective-bridging modulus, a new nondimensionalized parameter, is introduced to study the influence of bridging on the delamination buckling. It is shown that bridging strongly influences the buckling load of the delaminated beams and a monotonic relation is observed between the buckling load and the effective-bridging modulus. Parametric studies in terms of delamination sizes and locations along spanwise and thicknesswise positions on the buckling load have been carried out. The bridging is found to be effective for shallow delaminations of moderate length, and for deep and long delaminations. Spanwise positions of delamination strongly influence the buckling loads. In addition, an analytical model for obtaining upper bounds of the buckling load is developed by using Euler–Bernoulli beam theory. Effective-slenderness ratio, a new nondimensionalized parameter is defined and it is found to be controlling the buckling mode configurations, i.e., local, global and mixed modes.