圆形脱层的轴对称屈曲及扩展分析

利用高阶摄动结合打靶法，分析了固支圆板在均匀径向力作用下的轴对称屈曲和过屈曲，所得结果与文（６）的ＦＥＭ结构吻合得很好，应用于薄膜－基底结构，研究了受压薄膜脱层的屈曲、扩展问题，得到了在一定的残余压应力作用下，脱层屈曲的临界尺寸Ｒｃ和扩展尺寸Ｒｇ。     

The growth simulation of circular buckling-driven delamination

Some closed-form equations for the coupling problem of buckling and growth of circular delamination are derived by recourse to the moving boundary variational principle. The axisymmetric buckling of a circular delamination subjected to an equal bi-axial compression is analysed by using high-order perturbation expansion. The axisymmetric buckled delamination has the following properties : under a certain residual pressure, there exist two characteristic radii, namely the critical radius R_c and growing radius R_g; for a certain interface toughness, the blister has three configuration of stationary, stable growth and unstable growth with increasing the loads. Under a higher edge thrust, the nonaxisymmetric secondary buckling will occur on the base of axisymmetric buckling and then the toughness and the driving force of the interface crack will be different along the delamination front. So the growth of circular delamination will not be self-similar. Without any assumption regarding the delamination front, the configurations of the blister with several nonaxisymmetric buckling modes n = 2, 3, 6, 8 are simulated. The nonaxisymmetric growth process for the nonaxisymmetric buckling mode n = 2 is simulated also under a sequence of loads.     

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.     

The effects of bridging in a 3D composite on buckling, postbuckling and growth of delamination

Summary Buckling and postbuckling solutions to circular delamination constrained by transversal restoring forces, which occur extensively in stitched or woven composites with three-dimensional (3D) reinforcement, are obtained by using von Karman's geometrically nonlinear thin plate theory by means of Taylor's series expansion. The through-thickness tows are assumed to provide continuous and linear restoring tractions, opposing the deflection of the annular delaminated region adjacent to a penny-shaped crack. When the end of the delaminated layer is clamped, and the deflection is permitted in the positive direction of the z-axis only, there exists a characteristic delamination radius a _* for initial buckling. In the case that the initial delamination radius a ₀ exceeds a _*, it will consist of waves whose sizes decrease gradually, as they are apart from the delamination center with larger distances, and will usually not span the whole crack region. Therefore, buckling profiles can be divided into two types: (1) lacking contact phenomena between the delaminated layer and the base plate; (2) having contact surfaces inside the delamination region. In this paper, growth laws of buckling, postbuckling and growth of delamination at lacking contact surface are discussed. The corresponding stability of the delamination growth under fixed boundary load is studied, and the dependence of stable scope upon the fracture toughness of the composite and the elastic constant of bridging fiber is summarized. It follows from the analysis that bridging can increase the load-bearing capacity of composite structure, improve its mechanical performances and restrain the growth of delamination. Received 23 November 1998; accepted for publication on 13 January 1999     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis

The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.     

Buckling of delaminated bi-layer beam-columns

An improved analytical model is presented to analyze the delamination buckling of a bi-layer beam-column with a through-the-width delamination. Both the transverse shear deformation and local delamination tip deformations are taken into consideration, and two delaminated sub-layers as well as two substrates in the intact (un-delaminated) regions are modeled as individual Timoshenko beams. A deformable interface is introduced to establish the continuity condition between the two substrates in the intact regions. Consequently, a flexible joint is formed at the delamination tip, and it is different from the conventional rigid joint given in most of studies in the literature, in which the local delamination tip deformations are completely ignored. In contrast to the local delamination buckling in our previous study (Qiao et al., 2010), the present model accounts for the global deformations of the intact region in the delaminated composite beam-column, thus capable of capturing the buckling mode shape transitions from the global, to global–local coexistent, and to local buckling for asymmetric delamination as the interface delamination increases. Good agreement of the present analytical solutions with the full 2-D elastic finite element analysis demonstrates the local deformation effects around the delamination tip and verifies the accuracy of the present model. Parametric studies are conducted to investigate the effects of loading eccentricity, delaminated sub-layer thickness ratio, and interface compliance on the critical buckling load for the delaminated composite beam-column. Transitions of buckling modes from the global to local delamination buckling are also disclosed as the thickness of one sub-layer reduces from the thick sub-layer to a thin film. The developed delamination buckling solution facilitates the design analysis and optimization of laminated composite structures, and it can be used with confidence in buckling analysis of delaminated composite structures.     

Analysis on small scale bridging in fibrous monolithic ceramics

Based on shear lag model of interface between fiber and matrix, a new formula that relates the crack opening displacement and bridging force in fibrous monolithic ceramics was constructed under the framework of small scale bridging. This formula was applied to predict the fracture resistance orR-curve response of a three-point bending specimen made of fibrous monolithic ceramics. A parametric investigation on the influences of fiber volume fraction, fiber radius, characteristics of constituents, BN's fracture toughness and specimen's geometry on the bridging forces and fracture resistance in Si₃N₄/BN composite was carried out. The upper and lower limits of theR-curve of Si₃N₄/BN in small scale bridging were derived. This research revealed the role played by the above parameters in the fracture toughness of fibrous monolithic ceramics. Supported by National Natural Science Foundation of China (59632090).     

Numerical and Experimental Investigation of Liquid Residue in 90° Bend Microchannel Based on Gas–Liquid Two-Phase Flow

The microfluidic chip for nucleic acid detection in vitro is an essential application of microfluidic technology to the process of in vitro diagnosis. The 90° bend microchannels in chip designed for facilitating assay reagent delivery may cause reagent residues and cast mutual contamination between detection reagents, which significantly affects the detection accuracy. In this paper, a two-dimensional gas–liquid two-phase flow model is constructed to simulate the liquid residue phenomenon. Using the results of simulation, the residual liquid generation can be observed and the area of residual liquid can be obtained. The accuracy of the numerical simulation is verified by comparison with the experimental results. The effects of the fillet radius R, the diameter ratio d₁/d₂ of the vertical to horizontal sections, the flow velocity v, and the surface roughness R_a on the residual amount are studied. We find that the fillet radius is inversely proportional to the residual amount within the range v = 20–100 mm/s and there is almost no liquid residue in the channel when the radius increases to R = 1 mm. When the channel diameter ratio d₁/d₂ increases, the liquid residual amount also increases by approximately 98%. The increased surface roughness R_a significantly increases the residual amount. The results of this study provide a reference for the optimal design of microchannels on chips.

     

Effects of near-tip rotation on pre-buckle crack growth of compressed beams bonded to a rigid substrate

The macroscopic pre-cracked line scratch test (MPLST), in which a debonded edge of a film is loaded in in-plane compression, has been modeled as a generic, coupled fracture–buckle problem using simple beam theory. Near crack-tip beam rotation (also called root rotation in literature), which always exists due to the eccentric loading in this type of test, has been incorporated into the governing equations. An analytical solution to the augmented problem has been derived. It is found that the near-tip rotation can introduce pre-buckle bending in the film. One important consequence of this pre-buckle bending is that it leads to the reduction of the critical buckling condition. This agrees well with the results of [Int. J. Fract. 113 (2002) 39] obtained by solving the full elastic field near the crack-tip. Furthermore, the pre-buckle bending moment at crack-tip remains negative (leading to crack closure) as long as the pre-buckle crack length is small, but it becomes positive (leading to crack opening) at larger pre-buckle crack length. The negative bending moment causes the crack-tip energy release rate to decrease as the crack propagates, which results in a stable pre-buckle crack growth. Once it becomes positive, however, the bending moment causes crack-tip energy release rate to increase rapidly as crack length increases and hence leads to an unstable (pre-buckle) crack growth. Further, the nominal phase angle is initially larger than the classic prediction of 52.1° owing to the existence of the negative crack-tip bending moment, but it drops quickly upon approaching the buckle point. All these results are confirmed by a rigorous 2D FEM calculation using cohesive zone modeling (CZM) approach. Finally the derived analytical solution has been used to analyze a set of PLST data reported in the literature. It has been demonstrated that plasticity in the adhesive layer and in the bonded film is responsible for the strong R-curve toughening characteristics in the deduced interface toughness data. It has also been shown that, once the deduced interface toughness is incorporated into a CZM simulation, both the axial loading and buckling point can be accurately predicted.     

An experimental study on the static and impact torsional buckling of cylindrical shells

In this paper, experimental studies are carried out on the buckling of circular cylindrical thin shells under impact torque. Experiments of impact buckling are made on a Hopkinson torsional bar. The torsional bar gives a step torque on the shells. Through an analysis of the strain-time curve obtained in experiment, the dynamic buckling critical torqueM _er and buckling waves numbern of the shell with different geometric data and some qualitative results are obtained. The buckling behavior of circular cylindrical thin shells under static and impact torque is compared.     

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...     

Elastic waves guided by a material interface

The propagation of interfacial small-amplitude waves along a rectilinear thin film separating two pre-stressed, incompressible, elastic media is addressed. The film is modelled as a material surface possessing its own mass density and normal and flexural stiffnesses. It is shown that these features induce dispersion as the obtained secular equations are polynomials of the second degree in the wavenumber when bending stiffness is absent (membrane-like interface), and of the fourth degree otherwise (plate-like interface). In both case, beyond the modified Stoneley mode, a bending mode for the interface, an additional propagating wave can exist, with amplitude polarized along the interface (extensional mode). The associated bifurcation problem is analyzed with focus on the effects of compressive residual forces at the interface. The buckling strain of a compressed metal layer embedded in an elastomeric medium is computed also with an exact approach, to provide the range of validity of the proposed simplified model of material interface.     

Nonlinear analysis of compressed elastic thin films on elastic substrates: From wrinkling to buckle-delamination

Nonlinear buckling of elastic thin films on compliant substrates is studied by modeling and simulations to reveal the roles of pre-strain, elastic modulus ratio, and interfacial properties in morphological transition from wrinkles to buckle-delamination blisters. The model integrates an interfacial cohesive zone model with the Föppl–von Kármán plate theory and Green function method within the general framework of energy minimization. A kinetics approach is developed for numerical simulations. Subject to a uniaxial pre-strain, the numerical simulations confirm the analytically predicted critical conditions for onset of wrinkling and wrinkle-induced delamination, with which a phase diagram is constructed. It is found that, with increasing pre-strain, the equilibrium configuration evolves from flat to wrinkles, to concomitant wrinkles and buckle-delamination, and to an array of parallel straight blisters. The height and width of the buckle-delamination blisters can be approximately described by a set of scaling laws with respect to the pre-strain and interfacial toughness. Subject to an equi-biaxial pre-strain, the critical conditions are determined numerically to construct a similar phase diagram for the buckling modes. Moreover, by varying the pre-strain, modulus ratio, and interfacial toughness, a rich variety of equilibrium configurations are simulated, including straight blisters, and network blisters with or without wrinkles. These results provide considerable insight into diverse surface patterns in layered material systems as a result of the mechanical interactions between the film and the substrate through their interface, which suggests potential control parameters for designing specific surface patterns.     

Experimental and theoretical study of the buckling of narrow thin plates on an elastic foundation under compression

The paper describes the processes of elastic deformation of thin films under mechanical loading. The film is modeled longitudinally by a compressed plate arranged on an elastic foundation. A computer model of the buckling of the narrow thin plate with a delamination portion located on an elastic foundation is constructed. This paper also touches upon the supercritical behavior of the plate–substrate system. The experiments on the axial compression of a metal strip adhered to a rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. It is shown that there is the possibility of progressive delamination of the metal plate from the foundation if the critical load is exceeded. It is found that the use of the proposed approach, which, in contrast to other approaches, accounts for the elastic deformation of the substrate, causes the dependence between the critical bending stress and the stiffness of the foundation.     

微尺度金属薄膜屈曲稳定性的实验研究

微尺度金属薄膜的脱粘和屈曲严重影响着膜基结构的性能和使用寿命。本文对微尺度的金属铜薄膜在残余应力和外部压力共同作用下的脱粘屈曲和后屈曲模式进行了研究,用自行设计的单轴对称加载装置进行压力加载,用一台光学显微镜观察薄膜表面的屈曲形貌。在外力作用下薄膜会出现垂直于加载方向的直线型屈曲,但在外力卸载过程中该屈曲并不稳定,会演化成电话线型屈曲,完全卸载后形成泡状屈曲。再次加载后,恢复到直线型屈曲。研究表明:直线型屈曲的不稳定现象主要与薄膜的残余应力、基底的泊松比以及薄膜沿纵向与横向的应力比有关。     

Optimizing strength and toughness of nanofiber-reinforced CMCs

Nanofibers used in current ceramic matrix composites (CMCs) are usually wavy and of finite length. Here, a shear-lag model for predicting the tensile strength and work of fracture of a composite containing a “single matrix crack”, as a function of all the material parameters including constant plus Coulomb interfacial friction, is presented for a CMC containing wavy, finite-length nanofibers having a statistical distribution of strengths. Literature results are recovered for straight infinite fibers, with strength and toughness depending on a characteristic strength σ_c and a characteristic length δ_c. For nanofibers of finite length L, radius of curvature R, and with Coulomb friction coefficient μ, the strength and toughness are found to depend only on σ_c, δ_c, and two new dimensionless parameters μδ_c/R and L/δ_c. Parametric results for a typical carbon nanotube CMC show an optimal region of morphology (L and R) that maximizes composite strength and toughness, exceeding the properties of composites with straight (R=∞) and/or long (L=∞) reinforcements. Therefore, while factors such as the nanofiber strength distribution and the nanofiber–matrix interface sliding resistance may not be easily controlled, the tuning, via processing, of purely geometrical properties of the nanofibers (L and R) alone can aid in maximizing composite properties. These results have important application in hybrid CMCs such as “fuzzy fiber” CMCs, where micron-scale fibers are covered with a forest of nanofibers such that the nanofiber array can bridge longitudinal cracks and thus improve delamination resistance.     

Some asymptotic results concerning the buckling of a spherical shell of arbitrary thickness

For a spherical shell of arbitrary thickness which is subjected to an external hydrostatic pressure, symmetrical buckling takes place at a value of μ₁ which depends on and the mode number, where A₁ and A₂ are the undeformed inner and outer radii, and μ₁ is the ratio of the deformed inner radius to the undeformed inner radius. In the large mode number limit, we find that the dependence of μ₁ on has a boundary layer structure: it is a constant over almost the entire region of and decreases sharply from this constant value to unity as tends to unity (the thin-shell limit). Simple asymptotic expressions for the bifurcation condition are obtained. The classical result for thin shells is recovered directly from the equations of finite elasticity, and an asymptotic critical neutral curve (which envelops the neutral curves corresponding to different mode numbers) is obtained.     

Measurement of liquid film thickness in micro square channel

In micro channels, slug flow becomes one of the main flow regimes due to strong surface tension. In micro channel slug flow, elongated bubble flows with the thin liquid film confined between the bubble and the channel wall. Liquid film thickness is an important parameter in many applications, e.g., micro heat exchanger, micro reactor, coating process etc. In the present study, liquid film thickness in micro square channels is measured locally and instantaneously with the confocal method. Square channels with hydraulic diameter of D_h = 0.3, 0.5 and 1.0 mm are used. In order to investigate the effect of inertial force on the liquid film thickness, three working fluids, ethanol, water and FC-40 are used. At small capillary numbers, liquid film at the channel center becomes very thin and the bubble interface is not axisymmetric. However, as capillary number increases, bubble interface becomes axisymmetric. Transition from non-axisymmetric to axisymmetric flow pattern starts from lower capillary number as Reynolds number increases. An empirical correlation for predicting axisymmetric bubble radius based on capillary number and Weber number is proposed from the present experimental data.     

Delamination of compressed thin layers at corners

An analysis of delamination for a thin elastic layer under compression, attached to a substrate at a corner is carried out. The analysis is performed by combining results from interface fracture mechanics and the theory of thin shells. In contrast with earlier results for delamination on a flat substrate, the present problem is not a bifurcation problem. Crack closure at sufficiently high stress levels are shown to occur. Results show a very strong dependency on fracture mechanical parameters of the angle of the corner including the range of parameters where crack closure occurs. Analytical results for the fracture mechanical properties have been obtained, and these are applied in a study of the effect of contacting crack faces. Special attention has been given to analyse conditions under which steady state propagation of buckling driven delamination takes place.