Understanding delamination behaviour in a circular laminate

Composite materials are prone to a wide range of defects and damage which may significantly reduce their residual strength. Of the various types of defects possible, interply delaminations arising from in-service damage are probably the most insiduous because of their effects on residual compressive strength and difficulties associated with their detection. In this study, a finite element analysis of the self similar growth of a circular delamination in a compressed laminate is undertaken, and the results are compared with an analytical solution.     

A multi-scale simulation of tungsten film delamination from silicon substrate

To bridge the different spatial scales involved in the process of tungsten (W) film delaminating from silicon (Si) substrate, a multi-scale simulation procedure is proposed via a sequential approach. In the proposed procedure, a bifurcation-based decohesion model, which represents the link between molecular and continuum scales, is first formulated within the framework of continuum mechanics. Molecular dynamics (MD) simulation of a single crystal W block under tension is conducted to investigate the effect of specimen size and loading rate on the material properties. The proposed decohesion model is then calibrated by using MD simulation of a single crystal W block under tension and using available experimental data, with a power scaling law to account for the size effect. A multi-scale model-based simulation of W film delamination from Si substrate is performed by using the proposed procedure within the framework of the material point method. The simulated results provide new insights into the mechanisms of the film delamination process.     

An analysis of axisymmetric buckling and growth of circular-shaped delamination

The buckling and post-buckling of clamped circular plate subjected to distributed radial compressed load is presented by using the high-order perturbation analysis and shooting method. The sixth-order solution shows good agreement with the FEM results in [11]. The results in this paper are applied to investigate the buckling and growth of pressed thin film delamination in the film/substrate system. Under a certain residual pressure in the thin film, two characteristic blister radiiR _c andR _g, the critical radius and growing radius respectively, are obtained. The numerical result shows that the growth criterion of delamination in [9,10] is not perfect. In variant residual stress or interface toughness, the conditions of no growth, stable growth and unstable growth of the delamination are obtained by comparing the driving force at the interface crack tip with the interface toughness.This project is supported by National Natural Science Foundation of China.     

On delamination growth from channel cracks in thin-film coatings

Interfacial fracture (delamination) originating from channel or tunnel cracks is a common failure mode in layered structures. While this subject has been addressed extensively, little is known on the actual process of fracture. It is this aspect which is of concern here. The evolution of delamination damage is followed in situ using an all-transparent system designed to reduce material variability and thermal stresses. The specimen is composed of two glass plates glued onto a polycarbonate slab by a RT epoxy resin. With a proper control of the glass surface, stable delamination growth from a single channel crack occurs. This growth evolves smoothly from the tip of the channel crack, although the delamination area is generally irregular and non-symmetric. The fracture resistance varies greatly between nominally identical samples, attesting to a great sensitivity to such irregularity as well as to bonding surface conditions. The effect of system variables on delamination growth is evaluated using a 2D FEA. The analysis predicts general trends observed in the tests, and it indicates means for an optimal design against premature failure. Finally, the merit of evaluating fracture toughness of ultra-thin films using the channel cracking approach is discussed.     

Numerical analysis of delamination growth for stiffened composite laminated plates

A study of postbuckling and delamination propagation behavior in delaminated stiffened composite plates was presented. A methodology was proposed for simulating the multi-failure responses, such as initial and postbuckling, delamination onset and propagation, etc. A finite element analysis was conducted on the basis of the Mindlin first order shear effect theory and the von-K6rm~n nonlinear deformation assumption. The total energy release rate used as the criteria of delamination growth was estimated with virtual crack closure technique (VCCT). A self-adaptive grid moving technology was adopted to model the delamination growth process. Moreover, the contact effect along delamination front was also considered during the numerical simulation process. By some numerical examples, the influence of distribution and location of stiffener, configuration and size of the delamination, boundary condition and contact effect upon the delamination growth behavior of the stiffened composite plates were investigated. The method and numerical conclusion provided should be of great value to engineers dealing with composite structures.     

Effects of voids on postbuckling delamination growth in unidirectional composites

This work examines the effects of manufacturing induced voids on the postbuckling behavior of delaminated unidirectional composites. In the finite element model developed, a through-width delamination is introduced close to one surface of a flat panel, and a void is placed in the delamination plane ahead of each delamination front. The panel is subjected to compression in the fiber direction. The postbuckling delamination growth is studied by calculating the strain energy release rate (SERR) using the virtual crack closure technique. Local stress analyses of the region near the delamination front are also performed to further investigate the void effects. It is found that although the presence of void does not significantly alter the postbuckling transverse displacement of the delaminated panel, the induced stress perturbation by the void affects the SERR. The Mode II SERR as well as the total SERR increase depending on the size of the void and its distance from the delamination front. Since the Mode I SERR shows non-monotonic behavior with the applied load, the effects of voids are studied on its maximum value.     

含圆孔拉伸板的近场动力学数值模拟

首先推导了非普通状态为基础的近场动力学基本方程,引入损伤理论.在对非普通状态为基础的近场动力学基本方程进行离散化后,编制了非普通状态为基础的近场动力学数值分析程序.利用非普通状态为基础的近场动力学理论对圆孔拉伸板的断裂和非断裂问题进行了数值模拟.数值结果表明近场动力学理论不仅能模拟非断裂问题,也能模拟断裂问题,而且该方法不需要借助任何外部断裂准则就能很好地模拟裂纹的扩展和连接过程,相对于其它的数值模拟方法具有很大的优势,同时它也为材料断裂问题提供了一种新方法和新思路.     

Analytical model for delamination growth during small mass impact on plates

An analytical model is presented for delamination initiation and growth and the resulting response during small mass impact on orthotropic laminated composite plates, which typically is caused by runway debris and other small objects. The solution is obtained by a fast stepwise numerical solution of a single integral equation. Delamination size, load and deflection history are predicted by extension of an earlier elastic impact model by the author. Good agreement is demonstrated in comparisons with finite element simulations and experiments.     

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     

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.     

Homogenization of delamination growth in an ACA flip-chip joint based on micropolar theory

In the present paper the delamination mechanism of a typical internal structure of the anisotropic conductive adhesive (ACA) interconnect for electronic packaging is modeled on the basis of micropolar theory and computational homogenization. The interface is treated as a finite Representative Volume Element (RVE), across which the macroscopic deformation is expressed in terms of regularized strong displacement and rotational discontinuities. For the microstructure of the RVE, the micro-macro kinematical coupling is considered as a Taylor series expansion in the regularized macroscopic discontinuities, and, connected to that, a discontinuous fluctuation field representing the microstructural variation is included to describe delamination on the microlevel. As to the microlevel delamination modeling, on the basis of the discontinuous fluctuation field, a damage coupled to slip and dilation formulation is used to model the interface degradation. The constitutive relations are established in a thermodynamic setting, where the interfacial free energy involves internal variables of damage and plastic deformation. The parameters of the interface are calibrated so that a predefined amount of fracture energy is dissipated in mode I. In the numerical example, the response of a planar interface is considered when it is subjected to the basic modes I-II and also the non-conventional rotational discontinuity mode. Case studies on fracture and geometry parameters have also been carried out. Finally, an uncoupled thermomechanical analysis of a microsystem involving a representative ACA microstructure has been made for the understanding of the microscopic delamination during a thermal cycling procedure.     

Axisymmetric large eddy simulation of a circular source of buoyancy

Axisymmetric large-eddy simulations (LES) of published experiments on vertical mixing above a circular source of buoyancy are performed. Numerical results confirm the existence of a mixing boundary layer just above the buoyancy source (freshwater injected into saline water). As experiments suggested, the calculated normalized shape of the boundary layer seems independent of source size, freshwater injection rate and background solute concentration. This validates a restrictive but numerically efficient assumption of axisymmetric turbulence for the LES calculations. It also lends additional credibility to the theoretical boundary-layer analysis of Epstein and Burelbach [Epstein, M., Burelbach, J.P., 2001. Vertical mixing above a steady circular source of buoyancy. Int. J. Heat Mass Trans. 44, 525–536], even at marginally high Froude numbers.     

The delamination of a growing elastic sheet with adhesion

We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate.     

Dynamics of delamination buckling

The dynamics of delamination growth in layered plates as a result of delamination buckling is studied in the context of the model problem of a two layer circular plate with an initial penny-shaped delaminalion subject to a time dependent radial compressive load. The interaction of delamination buckling and normal impact is modeled through the application of a uniform transverse tension pulse, simulating the effect of a wave front passing through the layer interface, in conjunction with the radial loading. In addition three types of radial loading functions are considered independently and characcteristic features of the response are observed. Comparison is made with growth predictions made using a quasi-static analysis.     

The effects of shear on delamination in layered materials

The effect of transverse shear on delamination in layered, isotropic, linear-elastic materials has been determined. In contrast to the effects of an axial load or a bending moment on the energy-release rate for delamination, the effects of shear depend on the details of the deformation in the crack-tip region. It therefore does not appear to be possible to deduce rigorous expressions for the shear component of the energy-release rate based on steady-state energy arguments or on any type of modified beam theory. The expressions for the shear component of the energy-release rate presented in this work have been obtained using finite-element approaches. By combining these results with earlier expressions for the bending-moment and axial-force components of the energy-release rates, the framework for analyzing delamination in this type of geometry has been extended to the completely general case of any arbitrary loading. The relationship between the effects of shear and other fracture phenomena such as crack-tip rotations, elastic foundations and cohesive zones are discussed in the final sections of this paper.     

The growth of the thermal boundary layer at the inlet to a circular tube

Summary The problem considered is that of the heat transfer occurring at the inlet to a circular tube. Using the method of a previous paper we solve the energy equation in the form of a power series, instead of transforming the equation into an eigenvalue problem by separation of variables, as is usual in such cases. We thus obtain information concerning the temperature distribution at the inlet to the tube which is not provided by the latter method. A sufficient number of coefficients of the power series has been computed to allow the present solution to be joined to one of the second type, thus completing the solution of the problem for all values of the longitudinal variable.     

圆柱绕流流场结构的大涡模拟研究

为进一步揭示绕流现象的形成机理,本文分别对处于层流稳态区、尾流过渡区、剪切层转换区Re分别为26、200、1.4×105的三种典型流态下的单圆柱绕流进行了二维数值模拟研究。Re为26时应用层流模型直接求解N-S方程,而Re分别为200、1.4×105时使用大涡模拟的方法进行计算。数值模拟很好地再现了稳定的涡旋结构、周期性交替脱落的卡门涡街结构、不规则的涡旋结构,在此基础上分析了尾流结构的基本特征及其压强分布规律、平均的流场特性、积分参数(如升力系数、阻力系数、斯特劳哈尔等),并与有关研究成果进行了对比。研究发现,采用不同流动介质时流场特性有所差异,空气为介质时的计算结果更符合实验的成果,而水为介质时计算结果偏差较大,这主要是由尾流涡旋产生的不合理负压造成的。     

Postbuckling growth of a concentric delamination in a circulal plate under axisymmetric compression and bending

Postbuckling growth of a thin circular delamination at the center of a circular plate subjected to axisymmetric edge compression and bending is analyzed. A one-parameter family of solutions of the non-dimensionalized Von Karman's nonlinear equations is obtained by using the shooting method based on the fourth-order Runge-Kutta integration formula. The expression of energy release rate is deduced by means of the path-independent M-integral, and corresponding numerical results are given. The present analysis investigates the various possibilities of bifurcation, snap-through and crack growth.