ANALYSIS OF ELASTO-PLASTIC POSTBUCKLING AND ENERGY RELEASE RATE FOR DELAMINATED FIBER METAL LAMINATED BEAMS IN THERMAL ENVIRONMENT

The elasto-plastic postbuckling of fiber metal laminated beams with delamination and the energy release rate along the delamination front are discussed in this paper. Considering geometrical nonlinearity, thermal environment and geometrical initial imperfection, the incremental nonlinear equilibrium equations of delaminated fiber metal laminated beams are established,which are solved using the differential quadrature method and iterative method. Based on these,according to the J-integral theory, the elasto-plastic energy release rate is studied. The effects of some important parameters on the elasto-plastic postbuckling behavior and energy release rate of the aramid reinforced aluminum laminated beams are discussed in details.     

含分层损伤复合材料层合板分层扩展研究

采用基于Ｍｉｎｄｌｉｎ－阶剪切理论的四节点板单元,分析了含椭圆分层合板分层扩展行为。利用虚裂纹闭合技术计算分层前缘处的总能量释放率,并采用总能量释放率准则作为扩展准则,结合自适应网格移动技术,并考虑了分层前缘闭合接角效应,对 合材料层合板的分层扩展行为进行了模拟分析。结果表明,初始分层形状对其扩展有方式有限大影响。     

Delamination growth of laminated composite cylindrical shells

The local buckling may occur in delaminated cylindrical shells under axial compression. This often causes delamination growth and structure failure. Based on the variational principle of moving boundary, in this paper, the postbuckling governing equations for the laminated cylindrical shells are derived, and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells is analyzed, and the effects of delamination sizes and depths, the boundary conditions, the material properties and the laminate stacking sequences on delamination growth are discussed.     

The LS1 model for delamination propagation in multilayered materials at 0°/θ° interfaces: A comparison between experimental and finite elements strain energy release rates

The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only depends on the stacking sequence and the position of delamination is presented.     

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.     

Postbuckling deformation and vibration of a delaminated beam-plate with arbitrary delamination location

In this paper, we consider a homogeneous isotropic beam-plate subjected to axial compressive load along two clamped edges. It is assumed that, an arbitrary distance from the top surface of the beam-plate, an across-the-width delamination is located arbitrary. Based on the continuity conditions of both delaminated tips, the explicit formula of the postbuckling deformation was obtained. Furthermore, the small amplitude vibration of the delaminated beam-plate with respect of a postbuckled state was studied. The numerical results show that the delaminated length and thickness affect the postbuckling deformation and vibration frequencies significantly.     

具脱层的正交铺设圆柱壳的初始后屈曲分析

基于非线性弹性理论,建立了含脱层正交铺设圆柱壳的后屈曲控制方程,应用Koiter初始后屈曲理论和小参数摄动法,导出了系统的一阶和二阶摄动控制方程,以及相应的边界条件、位移连续条件和力平衡条件,然后逐阶求解．算例中,讨论了不同脱层深度和长度对脱层复合材料圆柱壳屈曲和初始后屈曲特性的影响,并与已有文献进行了比较．     

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     

Study on failure process of delaminated stiffened composite plates under compression

Failure behavior of the delaminated stiffened composite plates under compression is studied by the finite element method, based on a Global-Local variational model. A virtual crack closure technique and a self-adaptive grid moving scheme are proposed to predict the delamination growth process. The contact effect along the delamination front is considered. The numerical results show that the influences of the distribution and location of the stiffeners, the configuration and size of the delamination, the boundary condition and the contact upon the failure behavior of the plates are significant. The project supported by the National Natural Science Foundation of China (59975014)     

Analysis of energy release rate for composite delaminated cylindrical shells subjected to axial compression

In this paper, the postbuckling governing equations and the analytical expression of the energy release rates associated with delamination growth in a compression-loaded cylindrical shell are derived by using the variational principle of moving boundary and the Griffith fracture criterion. The finite difference method is used to generate the postbuckling solutions of the delaminated cylindrical shells, and with these solutions, the values of the energy release rates are determined. In simulational examples, the effects of a wide range of parameters, such as delamination sizes and depths, boundary conditions, geometrical parameters, material properties and laminate stacking sequences on the energy release rates of axisymmetrical laminated cylindrical shells are intensively discussed.The English text was polished by Yunming Chen.     

Calculation of energy release rate in composite delaminated cylindrical shells under circumferential concentrated dynamic load

The delamination growth may occur in delaminated cylindrical shells subjected to external dynamic load and it will further cause structural failure. Based on the variational principle of moving boundary and considering the contact effect between delamination regions, in this paper, the nonlinear governing equations for the delaminated cylindrical shells under the action of circumferential concentrated dynamic load are derived, and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells is analyzed, and the effects of the delamination sizes and depths, the geometrical parameters, the material properties and the laminate stacking sequences on delamination growth are discussed.     

General analytical solution to bending of composite laminated beams with delaminations

Based on the first-order shear deformable beam theory, a refined model for composite beams containing a through-the-width delamination is presented, and the deformation at the delamination front is considered. Different from the ordinary delami- nated beam theory, each of the perfectly bonded portions of the new model is constructed as two separated beams along the interface without assuming a plane section at the de- lamination front. The governing equations of the delaminated portions and bonded ones are established, combined with continuity conditions of displacements and internal forces. Solutions of delaminated composite beams with different boundary conditions, delamina- tion locations and sizes axe shown in excellent agreement with the finite element results, showing efficiency and applicability of the present model.     

Energy release rate analysis of delamination in laminates

Delamination growth caused by local buckling of delaminated laminate under compression may lead the structure to failure. In this paper, a two-dimensional model of delaminated laminates was studied using a combination of post-buckling theory and fracture mechanics. The delaminated laminate under compression is first analysed by the first-order deformable plate thoery. Then, the energy release rateG at every point along the delamination front is derived by means of a variation problem with a moving boundary. Finally, the near-surface elliptical delamination is also discussed. There is a large variation of energy release rateG along the delamination front, the direction in which delamination growth may occur depends upon the delamination aspect ratio, the state of applied load and the orientation of plies.Supported by the Chinese Science Foundation of Aeronautics     

ANALYSIS ON BUCKLING AND POSTBUCKLING OF DELAMINATION IN 3D COMPOSITES

In this paper, the problem of axisymmetric buckling and postbuckling of a circular thin-film delamination bridged by through-thickness fiber tows in 3D composites is presented. An iterativeprocedure based on Taylor's series expansion is used to generate a family of nondimensionalized post-buckling solutions of the above problem by yon Karman's nonlinear plate theory. Attention is fo-cused, herein, on the effects of the bridge force of through-thickness fibers on the buckling and post-buckling behavior of the delamination. It is found that fiber bridge not only increases the ability of re-sisting delamination buckling and postbuckling, but also brings on the jump of the delamination deflec-tion mode during the postbuckling phase. Consequently the behavior of the composite structure with de-lamination is greatly improved, such as increasing the residual strength and prolonging the service life.     

层板脱层的能量释放率分析

含脱层的层板在承受压缩载荷作用时,很容易发生局部屈曲,导致脱层扩展和结构失效.本文利用可动边界变分问题对脱层扩展进行了分析,导出了脱层前缘各点处的能量释放率表达式.本文还对浅部椭圆脱层进行计算分析,指出:其能量释放率沿脱层边界有很大变化,脱层的扩展方向取决于脱层的形状、受载方式及铺层方向.     

Vapor pressure and void size effects on failure of a constrained ductile film

To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth.A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.     

Size effects on void growth in single crystals with distributed voids

The effect of void size on void growth in single crystals with uniformly distributed cylindrical voids is studied numerically using a finite deformation strain gradient crystal plasticity theory with an intrinsic length parameter. A plane strain cell model is analyzed for a single crystal with three in-plane slip systems. It is observed that small voids allow much larger overall stress levels than larger voids for all the stress triaxialities considered. The amount of void growth is found to be suppressed for smaller voids at low stress triaxialities. Significant differences are observed in the distribution of slips and on the shape of the deformed voids for different void sizes. Furthermore, the orientation of the crystalline lattice is found to have a pronounced effect on the results, especially for the smaller void sizes.     

The effects of void cluster size on ductile fracture

The effects of void clustering on ductile fracture are studied by modeling a discrete set of randomly distributed clusters. Each cluster consists of four, equally-spaced, cylindrical voids. The spacing between the clusters is held constant while the spacing between the voids is varied. A Eulerian finite element program is used to numerically solve the boundary value problems. A salient feature of the previous investigations is that both the ultimate stress and the fracture strain are functions of the void distribution. In contrast, the ultimate stress remains constant while the fracture strain changes with the void cluster diameter in the current investigation.     

Void interaction and coalescence in polymeric materials

Beyond pressure-sensitivity, plastic deformation of glassy polymers exhibits intrinsic softening followed by progressive rehardening at large strains. This highly nonlinear stress–strain behavior is captured by a constitutive model introduced in this work. In the first part of the paper, we focus on void growth and coalescence in an axisymmetric representative material volume consisting of a single large void and a population of discrete microvoids. Our study shows that microvoid cavitation, enhanced by strain softening, accelerates the process of void coalescence resulting in brittle-like failure at lowered stresses and strains. Pressure-sensitivity also reduces stress-carrying capacity as well as influences the strain for void coalescence; plastic dilatancy effects are relatively milder. In the second part of the paper, we introduce a population of discrete spherical voids within a three-dimensional computational model to study void growth and damage ahead of a crack front. Our studies reveal a distinctive change in the deformed void shape from oblate to prolate when strain softening is followed by high rehardening at large plastic strains. By contrast, an extended strain softening regime promotes oblacity and facilitates multiple void interaction and their cooperative growth over large distances ahead of the crack front. This multi-void failure mechanism is exacerbated by pressure-sensitivity.