Secondary buckling patterns of a thin plate under in-plane compression

We study the nonlinear deformations of a long rectangular elastic plate clamped along its edges and submitted to in-plane biaxial compression. Using the F?ppl-von Kármán equations, we predict various secondary buckling modes according to the applied longitudinal and transverse compressions. A model experiment is carried out in a thin polycarbonate film, and the observed buckling patterns are found in good agreement with theory. Pattern selection in the delamination of compressed thin films is discussed in the light of these results. Received 22 January 2002     

How does crystalline substrate plasticity modify thin film buckling?

We report experimental atomic force microscopy observations and analytical modeling of buckling structures of thin films deposited on single crystal substrates. The formation of straight-sided blisters just above the step structures resulting from the dislocations emergence has been observed and explained in the framework of the F?ppl-von Karman theory of thin plates. A critical step height above which the buckling may occur has been determined and the asymmetry of the resulting blisters has been explained. Finally, the new buckling criterion has been compared with the classical one in the plane case and allows us to explain the blisters localization on step structures.     

Self-similar structures near boundaries in strained systems

We study the buckling of thin elastic plates caused by residual strains concentrated near a free edge. This is a model for plant leaves and torn plastic sheet morphologies. We derive new governing equations explaining self-similar patterns reported earlier in experiments. We reveal the cascade mechanism, determine the bounds for its wavelengths, and predict a similarity factor of 3 in agreement with experiments. This is confirmed by numerical solutions with up to five generations of wrinkles.     

Topological crossovers in the forced folding of self-avoiding matter

We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of three-dimensional plates to the folding of two-dimensional sheets, and further to the packing of one-dimensional strings, are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry, we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.     

Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson's ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.     

CLUSTER NUCLEATION LIMITED BY GROWTH PATTERN COVERAGE IN THIN FILM PREPARATION FROM VAPOR

In the early stage of thin film preparation from vapor, growth patterns consisting of stable clusters will gradually cover almost the entire substrate surface. During this process, the density of single atoms is zero on growth patterns and the nucleation of clusters will proceed in the substrate parts uncovered by these patterns. The influence of growth pattern coverage on the nucleation of thin films has not been considered wholly in the classical theory of thin films. We will systematically study the influence of growth pattern coverage and give some correction formulas for the widely used classical theory of thin films. It was found that the classical nucleation rate is proportional to the square of the uncovered area. The corrected formulas are of particular importance in the dominant coverage case.     

Lyotropic mixture made of potassium laurate/1-undecanol/K2SO4/water presenting high birefringences and large biaxial nematic phase domain: a laser conoscopy study

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson??s ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.     

Dynamical pattern formation for diblock copolymer films under stretch by moving walls

We propose a computational method that takes into account the dynamical influence of moving rigid walls over the pattern formation for thin films of diblock copolymers. The competition between the surface field energy and elastic stretching energy, and the effects of the molecular relaxation on pattern formation are studied. Finally, it is also observed that stretching the film enhances the ordering of patterns in it.     

Effect of deformation on the metal-semiconductor phase transition in vanadium dioxide thin films

It has been demonstrated that a small plastic deformation of aluminum substrates with vanadium dioxide thin films deposited on the substrate surfaces is accompanied by the appearance of elastic stresses in the films. Depending on the deformation technique, the elastic stresses can have different signs and the range of the metal-semiconductor phase transition in VO₂ shifts toward higher or lower temperatures as compared to the equilibrium phase temperature.     

Mechanical properties of Al/a-C nanocomposite thin films synthesized using a plasma focus device

The Al/a-C nanocomposite thin films are synthesized on Si substrates using a dense plasma focus device with alu- minum fitted anode and operating with CH4/Ar admixture. X-ray diffractometer results confirm the formation of metallic crystalline Al phases using different numbers of focus shots. Raman analyses show the formation of D and G peaks for all thin film samples, confirming the presence of a-C in the nanocomposite thin films. The formation of Al/a-C nanocomposite thin films is further confirmed using X-ray photoelectron spectroscopy analysis. The scanning electron microscope results show that the deposited thin films consist of nanoparticles and their agglomerates. The sizes of th agglomerates increase with increasing numbers of focus deposition shots. The nanoindentation results show the variations in hardness and elastic modulus values of nanocomposite thin film with increasing the number of focus shots. Maximum values of hardness and elastic modulus of the composite thin film prepared using 20 focus shots are found to be about 10.7 GPa and 189.2 GPa, respectively.     

Specific features of the determination of the mechanical characteristics of thin films by the nanoindentation technique

The hardness and the elastic modulus of Cu thin films on Si, Ti, Cu, and Al substrates are investigated. It is demonstrated that the use of the Oliver-Pharr method in combination with the technique for evaluating the true hardness makes it possible to determine uniquely the hardness of Cu thin films at different ratios between the hardnesses of the film and the substrate. The elastic modulus of thin films can be correctly measured by the Oliver-Pharr method only in the case where the film and the substrate exhibit identical elastic properties. In order to determine the elastic moduli of films with the use of the parameter P/S ², the film and the substrate should have close values of both the hardness and the elastic modulus.     

Thermoelastic behavior of a thermoelectric thin-film attached to an infinite elastic substrate

Abstract

This paper examines the thermoelectric behaviour of a thermoelectric thin film bonded to an elastic substrate. A calculation model for thermoelectric thin films is developed based on the singular integral equation method. The interface shear stress is found to exhibit singular behaviour at the ends of the films. Numerical results for the thermal stress distribution in the film and the film/substrate interface are obtained. Effects of film thickness and the substrate to film stiffness ratio on the stress of the film and the stress intensity factor of the interface are identified. The effects of interface electricity conductivity and the elastic–plastic deformation of the film are discussed.     

空间弹性细杆在扭矩作用下的屈曲

用有限元方法研究了三维弹性细杆在扭矩作用下的屈曲.利用自然坐标形式的细长空间曲杆的能量方程和2节点12个自由度的自然坐标形式的三维曲梁单元,采用特征值分析方法,研究分析了同时受有轴力和扭矩作用时的空间弹性细杆的屈曲问题.数值结果与存在的理论解极为吻合.具有一定曲率和挠率的空间细长曲杆,其临界扭矩值与扭矩的指向有着极其明显的关系.     

A measurement of elastic moduli for tungsten films on polymer substrate using wrinkling analysis

The elastic moduli of ultra thin tungsten (W) films on polymers were assessed with wrinkling analysis. Thin W films with a range of thickness between 17 and 100 nm were deposited on compliant polymers and Si strips using DC magnetron sputtering method, causing the tensile stress in a few GPa scale with respect to the thickness of W films. By applying lateral compression on polymer, wrinkle patterns were developed in the W thin film with well-defined amplitude and wavelength. Using a simple equation on wrinkle analysis, the range of elastic moduli was estimated with increasing the thickness. It was found that the elastic modulus and the tensile stress decreased with increasing the film thickness.     

Self-organized structures in soft confined thin films

We present a mini-review of our recent work on spontaneous, self-organized creation of mesostructures in soft materials like thin films of polymeric liquids and elastic solids. These very small scale, highly confined systems are inherently unstable and thus self-organize into ordered structures which can be exploited for MEMS, sensors, opto-electronic devices and a host of other nanotechnology applications. In particular, mesomechanics requires incorporation of intermolecular interactions and surface tension forces, which are usually inconsequential in classical macroscale mechanics. We point to some experiments and quasi-continuum simulations of self-organized structures in thin soft films which are germane not only to nanotechnology, but also to a spectrum of classical issues such as adhesion/debonding, wetting, coatings, tribology and membranes.     

Morphological evolutions of iron films on PDMS substrates under uniaxial compression/tension

We report on the morphological evolutions of iron films sputtering deposited on elastic polydimethylsiloxane (PDMS) substrates under uniaxial compression/tension. The experiment shows that the as-prepared film (no external strain) spontaneously forms cracks and wrinkles due to the residual thermal stresses stored up during/after the film deposition. The external uniaxial compression can generate delaminated buckles perpendicular to the loading direction (transverse direction) and new cracks in the loading direction (longitudinal direction). Subsequent reloading and further straining result in the formation of transverse cracks and longitudinal buckles. It is found that there exists a significant coupling effect between the cracking and buckling patterns during the compression/tension process. The morphological evolution behaviours and underlying physical mechanisms are discussed and analysed in depth in this paper.     

Low-field vortex dynamics in various high-T c thin films

We present a novel ac susceptibility technique for the study of vortex creep in superconducting thin films. With this technique we study the dynamics of dilute vortices in c-axis oriented Y-123, Hg-1212, and Tl-1212 thin films, as well as a axis oriented Hg-1212 thin films. Results on the Hg-1212 and Tl-1212 thin films indicate that dislocation-mediated plastic flux creep of single vortices dominates at low temperatures and fields. As the temperature (or the field) is increased, the increasing vortex-vortex interactions promote a collective behavior, which can be characterized by elastic creep with a non-zero μ exponent. Also, in some of these samples effects of thermally assisted quantum creep are visible up to 45 K in some of these samples. In Y-123 thin films, creep is found to be collective down to the lowest temperatures and fields investigated, while the quantum creep persists only up to 10–11 K.     

Annealing effect on microstructure and mechanical properties of amorphous Al-C-N films

Al-C-N thin films with different Al contents were deposited on Si (1 0 0) substrates by closed-field unbalanced reactive magnetron sputtering in the mixture of argon and nitrogen gases. These films were subsequently vacuum-annealed at 700 °C and 1000 °C, respectively. The microstructures of as-deposited and annealed films were characterized by X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM); while the hardness and elastic modulus values were measured by nano-indention method. The results indicated that the microstructure of both as-deposited and annealed Al-C-N films strongly depended on Al content. For thin films at low Al content, film delamination rather than crystallization occurred after the sample was annealed at 1000 °C. For thin films at high Al content, annealing led to the formation of AlN nanocrystallites, which produced nanocomposites of AlN embedded into amorphous matrices. Both the density and size of AlN nanocrystallites were found to decrease with increasing depth from the film surface. With increasing of annealing temperature, both hardness and elastic modulus values were decreased; this trend was decreased at high Al content. Annealing did not change elastic recovery property of Al-C-N thin films.     

一种在线测量微机械薄膜残余应力的新结构

提出了一种利用临界屈曲法在线测量微机械薄膜残余应力的新结构，并采用表面微加工技术制作了两种测试样品.搭建了在线观测实验装置来实时监控释放过程中结构出现的临界屈曲变形模态，由此判断出结构内部的应力状态，同时在测得临界刻蚀深度的情况下，采用有限元方法计算出残余应力大小.借助有限元方法，先研究了多个参数对临界屈曲应力的影响，然后利用这种新结构对薄膜残余应力进行了实际测量，所得结果与微旋转结构的应力测量结果基本吻合.分析及实验表明，新结构在测量薄膜残余应力方面有许多优点，具有较高的实用价值，不仅能满足大量程的应力检测要求，而且只用一个结构就可以同时测量压应力和拉应力，从而极大提高了器件版图空间的利用率.     

Origin of the short-range, strong repulsive force between ionic surfactant layers

We study the electrostatic interaction between two ionic surfactant layers by performing molecular dynamic simulations of salt-free thin water films coated by surfactants (Newton black films). We find a strong exponentially decaying short-range repulsion not explained by classical Poisson-Boltzmann theory. This electrostatic force is shown to be mainly due to the anomalous dielectric response of water near charged surfactant layers. This result clarifies the much debated physical mechanism underlying the controversial "hydration forces" observed in experiments. In the case of ionic thin films, the "hydration forces" can be identified with the electrostatic forces induced by the layers of highly polarized water originated at the interfaces.