Buckle Formation Research Articles

THE INFLUENCE OF EXTERNAL DISTURBANCE ON BUCKLING PATTERNS IN WEDGE-SHAPED Fe FILMS

A wedge-shaped iron (Fe) film system, quenched by silicone oil during deposition, has been prepared on glass substrates by direct current magnetron sputtering, and the influence of external disturbance on buckling patterns is investigated. The experiment shows that the wedge-shaped Fe film possesses a high compressive stress, which is relieved by spontaneous formation of telephone cord buckles in the atmosphere condition. The growth process can last several days to more than a month. When the film is disturbed by an external force, the stored stress energy will release drastically to form straight-sided buckles within several seconds. The morphological characteristics, edge effect and formation mechanism of the straight-sided buckles are discussed in detail.

Controlled formation of straight-sided buckles in patterned Ta films on glass substrates

We report on the controlled formation of buckle driven delaminations in patterned Ta films composed of parallel strips with different widths. It is found that the strip width can precisely control the morphologies of the buckling patterns due to the edge effect. For narrower strips, complete straight-sided buckles perpendicular to the strip edges are always observed. For wider strips, straight-sided buckles form at the edges while irregular buckle networks form in the central regions. For the strips with a critical width, various buckling phenomena, including complete and half straight buckles, wavy buckles, bifurcation and coalescence behaviors, can coexist in the same strip. The structures and morphologies of the straight-sided buckles appeared in the strips with different widths have been characterized and analyzed in detail.

Mechanical behavior of representative volume elements of lithium-ion battery cells under compressive loading conditions

The mechanical behaviors of lithium iron phosphate battery cells are investigated by conducting in-plane and out-of-plane compression tests of representative volume element (RVE) specimens of dry cells. The test results of cell RVE specimens under in-plane constrained compression indicate that the load carrying behavior of the cell RVE specimens is characterized by the buckling, the kink and shear band formation, and the final densification of the cell components. The SEM images of the active materials on electrodes and the test results of the cell RVE specimens under out-of-plane compression suggest that the porosity in the components and the macroscopic gaps between the components is up to 40%. The test results suggest that the lithium-ion battery cells can be modeled as anisotropic foams or cellular materials. The elastic buckling analyses for a beam with lateral constraints indicate that the higher order buckling modes and the critical buckling stresses in general agree with those observed in experiments. The elastic buckling analyses also justify the length selection of the cell RVE specimens. Finally, an idealized kinematic model is presented to explain the physical mechanisms of the kink and shear band formation in the cell RVE specimens under in-plane constrained compression.

Hydrogen-induced microstructural changes of Pd films

The development of the microstructure in nanocrystalline, polycrystalline and epitaxial Pd films loaded with hydrogen is investigated. Structural changes in Pd films loaded with hydrogen were characterized by positron annihilation spectroscopy combined with electron microscopy and X-ray diffraction. It was found that hydrogen charging causes plastic deformation which leads to an increase of the defect density in all Pd films studied. Moreover, the formation of buckles was observed in nanocrystalline and polycrystalline Pd films loaded above a certain critical hydrogen concentration. Buckling leads to detachment of the film from the substrate and this is accompanied with in-plane stress relaxation and plastic deformation of the film.

Local stress determination in chromia-former thanks to micro-Raman spectroscopy: A way to investigate spontaneous delamination processes

Spontaneous delamination process for α-Cr2O3 thermal oxide films growing on NiCr-30 alloys is studied thanks to micro Raman spectroscopy. In particular, stress maps are performed through and around buckles developed on chromia films. Depending on the cooling rate at the end of the oxidation process, different buckle types appear which are investigated. Associated residual stress distribution clearly evidences the stress release field. In addition, geometrical features are determined for the different buckle types, and from comparison with modelling describing buckle formation and propagation, it is possible to get the interface toughness distribution.

Detailed modelling of delamination buckling of thin films under global tension

Tensile specimens of metal films on compliant substrates are widely used for determining interfacial properties. These properties are identified by the comparison of experimentally observed delamination buckling and a mathematical model which contains the interface properties as parameters. The current two-dimensional models for delamination buckling are not able to capture the complex stress and deformation states arising in the considered uniaxial tension test in a satisfying way. Therefore, three-dimensional models are developed in a multi-scale approach. It is shown that, for the considered uniaxial tension test, the buckling and associated delamination process are initiated and driven by interfacial shear in addition to compressive stresses in the film. The proposed model is able to reproduce all important experimentally observed phenomena, like cracking stress of the film, film strip curvature and formation of triangular buckles. Combined with experimental data, the developed computational model is found to be effective in determining interface strength properties.

The influence of surface ply fibre angle on the compressive strength of composite laminates containing delamination

AbstractA combination of uniaxial compression tests and Strip Model and Finite Element analyses of laminates artificially delaminated to create circular (±θ) sublaminates is used to assess the influence of fibre angle on the compressive strength of composite laminates.Sublaminates with 0° < θ < 40° are found to fail by sublaminate-buckling-driven delamination propagation and provide poor tolerance of delamination. This is a consequence of their relatively high axial stiffnesses, low sublaminate buckling strains, Poisson’s ratio induced compressive transverse strains and extension-twist coupling which produces unexpected sublaminate buckling mode shapes. Sublaminates with 40° < θ < 60° are most tolerant to delamination; axial and transverse stiffnesses are minimal, formation of sublaminate buckles is resisted, high laminate buckling strains reduce interaction between laminate and sublaminate buckling mode shapes and extension-twist coupling is minimal. Sublaminates with 60° < θ < 90° are shown to produce varied tolerance of delamination. Sublaminate buckling is generally prevented owing to transverse tensile strains induced by mismatches between laminate and sublaminate Poisson’s ratios but may occur in laminates with low Poisson’s ratios.

Crash performance of notch triggers and variable frequency progressive-triggers on patterned box beams during axial impacts

Embedding complex sinusoidal patterns on the wall surfaces of box beam impact absorbers has been recently proposed in literature and demonstrated to significantly improve energy absorption capability of box beams during axial impacts. However, no suitable trigger has yet been devised for these absorbers. This paper evaluates the viability of using conventional notch triggers on patterned beams. A progressive triggering mechanism on box beams with embedded patterns is also proposed by a novel idea of using a variable pattern throughout the length of the beam. In the proposed progressively triggered beams, the reaction force slightly increases with each progressive collapse buckle formation throughout the collapse. An extensive FEM study is performed using the commercial pre-processor HyperCrash™ and the commercial explicit FEM solver RADIOSS™. It is found that, as opposed to point triggers, progressive triggering through variable pattern formulation effectively triggers and initiates a more stable collapse. More importantly, progressive triggers cause less stray deformations elsewhere along the beam and are consequently much more robust against global bending.

Adaptive anisotropic remeshing for cloth simulation

We present a technique for cloth simulation that dynamically refines and coarsens triangle meshes so that they automatically conform to the geometric and dynamic detail of the simulated cloth. Our technique produces anisotropic meshes that adapt to surface curvature and velocity gradients, allowing efficient modeling of wrinkles and waves. By anticipating buckling and wrinkle formation, our technique preserves fine-scale dynamic behavior. Our algorithm for adaptive anisotropic remeshing is simple to implement, takes up only a small fraction of the total simulation time, and provides substantial computational speedup without compromising the fidelity of the simulation. We also introduce a novel technique for strain limiting by posing it as a nonlinear optimization problem. This formulation works for arbitrary non-uniform and anisotropic meshes, and converges more rapidly than existing solvers based on Jacobi or Gauss-Seidel iterations.

Carbon Nanotube Fiber Based Stretchable Conductor

AbstractCarbon nanotube (CNT) based continuous fiber, a CNT assembly that could potentially retain the superb properties of individual CNTs on a macroscopic scale, belongs to a fascinating new class of electronic materials with potential applications in electronics, sensing, and conducting wires. Here, the fabrication of CNT fiber based stretchable conductors by a simple prestraining‐then‐buckling approach is reported. To enhance the interfacial bonding between the fibers and the poly(dimethylsiloxane) (PDMS) substrate and thus facilitate the buckling formation, CNT fibers are first coated with a thin layer of liquid PDMS before being transferred to the prestrained substrate. The CNT fibers are deformed into massive buckles, resulting from the compressive force generated upon releasing the fiber/substrate assembly from prestrain. This buckling shape is quite different from the sinusoidal shape observed previously in otherwise analogous systems. Similar experiments performed on carbon fiber/PDMS composite film, on the other hand, result in extensive fiber fracture due to the higher fiber flexural modulus. Furthermore, the CNT fiber/PDMS composite film shows very little variation in resistance (≈1%) under multiple stretching‐and‐releasing cycles up to a prestrain level of 40%, indicating the outstanding stability and repeatability in performance as stretchable conductors.

Limiting speed of false-twist texturing: a possible explanation of the post-surging mode

The1 speed of false-twist texturing is limited by tension surging, which has been explained as flipping between a good pre-surging mode and an unsatisfactory post-surging mode. Fundamental research on the mechanics of rotating rods has shown that buckling occurs above a critical speed for a rod under a given torque and tension. In false-twist texturing, it is postulated that this leads to formation of buckles in the feed→spindle zone, which pass through the system giving rise to the irregular behaviour of the post-surging mode.

How Does Adhesion Induce the Formation of Telephone Cord Buckles?

Compressively stressed thin films with low adhesion frequently buckle and delaminate simultaneously into telephone cords. Although these buckles have been studied for decades, no complete understanding of their propagation has so far been presented. In this study, we have coupled a nonlinear plate deformation with a cohesive zone model to simulate the kinematics of a propagating telephone cord buckle in very close agreement with experimental observations. Proper inclusion of the dependence of an adhesion upon the mode mixity proved to be central to the success of the approach. The clarification of the mechanism promises better understanding of buckle morphologies.

Higher Recovery and Better Energy Dissipation at Faster Strain Rates in Carbon Nanotube Bundles: An in-Situ Study

We report mechanical behavior and strain rate dependence of recoverability and energy dissipation in vertically aligned carbon nanotube (VACNT) bundles subjected to quasi-static uniaxial compression. We observe three distinct regimes in their stress-strain curves for all explored strain rates from 4 × 10(-2) down to 4 × 10(-4)/sec: (1) a short initial elastic section followed by (2) a sloped plateau with characteristic wavy features corresponding to buckle formation and (3) densification characterized by rapid stress increase. Load-unload cycles reveal a stiffer response and virtually 100% recoverability at faster strain rates of 0.04/sec, while the response is more compliant at slower rates, characterized by permanent localized buckling and significantly reduced recoverability. We propose that it is the kinetics of attractive adhesive interactions between the individual carbon nanotubes within the VACNT matrix that governs morphology evolution and ensuing recoverability. In addition, we report a 6-fold increase in elastic modulus and gradual decrease in recoverability (down to 50%) when VACNT bundles are unloaded from postdensification stage as compared with predensification. Finally, we demonstrate energy dissipation capability, as revealed by hysteresis in load-unload cycles. These findings, together with high thermal and electrical conductivities, position VACNTs in the "unattained-as-of-to-date-space" in the material property landscape.

Load-induced subsidence of the Ancestral Rocky Mountains recorded by preservation of Permian landscapes

The Ancestral Rocky Mountains (ARM) formed a system of highlands and adjacent basins that developed during Pennsylvanian–earliest Permian deformation of interior western North America. The cause of this intracratonic deformation remains debated, although many have linked it to far-field compression associated with the Carboniferous–Permian Ouachita-Marathon orogeny of southern North America. The ultimate disappearance of the ARM uplifts has long been attributed to erosional beveling presumed to have prevailed into the Triassic–Jurassic. New observations, however, indicate an abrupt and unusual termination for the largest of the ARM uplifts. Field evidence from paleohighlands in the central ARM of Oklahoma and Colorado indicates that Lower Permian strata onlap Pennsylvanian-aged faults and bury as much as 1000 m of relief atop the paleohighlands. In parts of Oklahoma and Colorado, late Cenozoic partial exhumation of these paleohighlands has revealed landscapes dating from Permian time. These relationships suggest cessation of uplift followed by active subsidence of a broad region that encompassed both basins and uplifted crustal blocks and that commenced in Early Permian time, directly following the Pennsylvanian tectonic apogee of the ARM. Independent from these geological observations, geophysical data reveal a regional-scale mafic load underpinning these paleohighlands, emplaced during Cambrian rifting associated with the southern Oklahoma aulacogen. Geophysical modeling of the effects of such a load in the presence of a horizontal stress field, such as that implied by ARM orogenesis, indicates that the amplitude of flexurally supported features is modulated nonlinearly. This leads to buckling and thrust formation with the application of sufficient compressive stress, and subsidence of topography formed by buckling upon relaxation of the high compressional stresses. We therefore infer that the core ARM highlands subsided owing to the presence of a high-density upper crustal root, and that this subsidence began in the Early Permian owing to relaxation of the in-plane compressional stresses that had accompanied the last phase of the Ouachita-Marathon orogeny of southern and southwestern Laurentia. Our results highlight the importance of tectonic inheritance in intraplate orogenesis and epeirogenesis, including its potential role in hastening the reduction of regional elevation, and enabling the ultimate preservation of paleolandscapes.

High-finesse cavities fabricated by buckling self-assembly of a-Si/SiO_2 multilayers

Arrays of half-symmetric Fabry-Perot micro-cavities were fabricated by controlled formation of circular delamination buckles within a-Si/SiO(2) multilayers. Cavity height scales approximately linearly with diameter, in reasonable agreement with predictions based on elastic buckling theory. The measured finesse (F > 10(3)) and quality factors (Q > 10(4) in the 1550 nm range) are close to reflectance limited predictions, indicating that the cavities have low roughness and few defects. Degenerate Hermite-Gaussian and Laguerre-Gaussian modes were observed, suggesting a high degree of cylindrical symmetry. Given their silicon-based fabrication, these cavities hold promise as building blocks for integrated optical sensing systems.

Interface failure and adhesion measured by focused ion beam cutting of metal–polymer interfaces

New developments in flexible electronics require metal films to adhere to polymer substrates. Measuring the interfacial adhesion of these systems is challenging, requiring the formulation of new techniques and models. A strategy to measure the adhesion of Cr–polyethylene terephthalate (PET) interfaces using tensile straining and buckle formation is presented in this article. Focused ion beam cross-sectioning of the buckles reveals that the polymer substrate can locally fail, which may lead to an overestimate of adhesion. Cr–PET adhesion energy of 9.4 ± 1.6 J/m2 is determined with the present approach.

In situ SEM Observation of Column-like and Foam-like CNT Array Nanoindentation

Quantitative nanoindentation of nominally 7.5 and 600 μm tall vertically aligned carbon nanotube (VACNT) arrays is observed in situ within an SEM chamber. The 7.5 μm array consists of highly aligned and weakly interacting CNTs and deflects similarly to classically defined cylindrical columns, with deformation geometry and critical buckling force well estimated using the Euler-Bernoulli theory. The 600 μm array has a highly entangled foam-like morphology and exhibits sequential buckle formation upon loading, with a buckle first forming near the array bottom at approximately 2% strain, followed by accumulating coordinated buckling at the top surface at strains exceeding 5%.

Length dependent foam-like mechanical response of axially indented vertically oriented carbon nanotube arrays

The axial compressive mechanical response of substrate-supported carbon nanotube (CNT) arrays with heights from 35 to 1200 μm is evaluated using flat punch nanoindentation with indentation depths to 200 μm. The compressive behavior is consistent with that of an open-cell foam material with array height playing a role similar to that of occupation density for traditional foam. Mechanical yielding of all arrays is initiated between 0.03 and 0.12 strain and arises from localized coordinated plastic buckling. For intermediate CNT array heights between 190 and 650 μm, buckle formation is highly periodic, with characteristic wavelengths between 3 and 6 μm. Buckle formation produced substantial force oscillations in both the compressive and lateral directions. The compressive elastic modulus of the arrays is obtained as a continuous function of penetration depth and attains a value between 10 and 20 MPa for all arrays during mechanical yield. A qualitative model based upon concepts of cellular foam geometry is advanced to explain the observed CNT buckling behavior.

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

Abstract 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.

Thermal tuning of hollow waveguides fabricated by controlled thin-film buckling

We describe the thermal tuning of air-core Bragg waveguides, fabricated by controlled formation of delamination buckles within a multilayer stack of chalcogenide glass and polymer. The upper cladding mirror is a flexible membrane comprising high thermal expansion materials, enabling large tuning of the air-core dimensions for small changes in temperature. Measurements on the temperature dependence of feature heights showed good agreement with theoretical predictions. We applied this mechanism to the thermal tuning of modal cutoff conditions in waveguides with a tapered core profile. Due to the omnidirectional nature of the cladding mirrors, these tapers can be viewed as waveguide-coupled, tunable Fabry-Perot filters.