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AbstractThe analysis of 3D braided composites is more difficult due to its complex microstructure. A new type of finite element method isdeveloped to predict the effective moduli and the local stress within 3D braided composites under the 3D mechanical loading. Toverify the present method, the material properties of undamaged 3D braided composites predicted in this paper are compared withthe previous work. To demonstrate this method, some examples are analyzed. 2003 Elsevier Ltd. All rights reserved.Keywords: 3D braided composites; Finite element method; Mechanical property; Cracking 1. IntroductionFiber-reinforced composites have excellent mechani-cal properties, such as high specific strength, high spe-cific stiffness, etc. In particular, laminated compositestructures have extensively been used where the in-planeproperties are important. However, laminated compos-ites have relatively poor mechanical properties in thethickness direction and are prone to interlaminar de-lamination. In an attempt to overcoming this difficulty,three-dimensional (3D) braided composites have beendeveloping in the past two decades. These materialshave better out-of-plane stiffness, strength and impactresistance and therefore have potential applications inthe aerospace, automobile and marine industries. As theapplication of 3D braided composites is becomingwider, a lot of models have been developed to analyze itsmechanical properties. Due to the complicated archi-tecture, these analyses are very challenging.In the past, most mechanical analyses of 3D braidedcomposites have been focused on their effective elasticmoduli. Ishikawa and Chou [1–4] proposed three typesof models (mosaic model, fiber-undulation model andbridging model) for the analysis of textile composites. These models are called classical models since the basicassumption of the classical lamination theory is valid forevery infinitesimal piece of repeating unit cell of thewoven-fabric region. Ma and coworkers [5,6] firststudied the effective elastic performance of 3D braidedcomposites by using the fiber interlock model and fiberinclination model. Whyte [7] developed the Fabric ge-ometry model’ by combining textile engineering meth-odology with a modified laminate theory.50295
Wang andWang [8] reported a mixed volume averaging techniqueto predict the mechanical behavior of 3D braidedcomposites. Naik and coworkers [9–11] developed ananalytical model in which the yarns of the braided fab-rics are pided into slices using parallel planes perpen-dicular to the fabric plane. Whitcomb and coworker[12–15] gave the stress distribution of woven compositesusing the global/local finite element method. Tang andPostle [16] discussed the nonlinear deformation of 3Dbraided composites by the finite element method. Huang[17,18] analyzed the elastic and inelastic behavior offabric laminates. Recently, Zeng et al. [19] presented adamage model to analyze the effective modulus of 3Dbraided composites with transverse cracking.However, there are few literatures on the local stressdistribution of 3D braided composites. The main pur-pose of the present work is to develop a simple andaccurate numerical model for calculating the local stressof 3D braided composites. In addition, the mechanicalproperties of damaged 3D braided composites are ana-lyzed in this paper. 2. Finite element model of 3D braided compositesThe 3D braided fiber construction is produced by abraiding technique which interlaces and orients theyarns by an orthogonal shedding motion, followed by acompacting motion in the braiding direction [20].Therefore, the orientation of the yarns in the braidedperform is controlled by the three orthogonal motions.The resultant perform is a continuous interwovenstructure composed of yarns oriented in various direc-tions. A unit cell structure is constructed based upon thefiber bundles oriented in four body diagonal directionsin a rectangular parallelepiped which is shown sche-matically in Fig. 1. It is assumed that dimensions of theunit cell are a, b and c in the x-, y- and z-directions,respectively. The 3D composite can be regarded as anassemblage of unit cells.A systematic variation of the 3D braided compositegeometry and the constituent elastic properties is ex-tremely difficult, time-consuming and expensive to carryout on real fabrics in practice. However, it is quite easyto implement in a model. For the conventional finiteelement method (FEM), the yarns and matrix aremodeled discretely. This is very complicated and difficultdue to its complex microstructure. In this study, the unitcell is pided into a number of rectangular subcells asshown in Fig. 2(a). This makes the analysis of braidedcomposites to become simpler. According to the mate-rial properties of the elements, three kinds of elementsare obtained shown as Fig. 2(b). The first is called theyarn element which only contains the yarn material. Thesecond is called the matrix element which only containsthe matrix material. The last is called the mixed elementwith both the yarn and the matrix. This discretizationmethod is simple and easy to implement. Subsequently,a finite element method is prescribed by using this dis-cretization method. Let ½K , fdg and fRg denote thestiffness matrix of the structure, the nodal degree offreedom and the total load of the structure, respectively.The load–displacement equation of the static elasticproblem can be stated as½K fdg¼fRgð1Þwhere fRg can be computed by fRg¼X MþNþLk¼1fregk ð2ÞHere, M, N and L is the number of yarn elements, matrixelements and mixed elements, respectively.From Eq. (2), fRg depends on the boundary condi-tion and load applied of elements, so solving Eq. (1) isequivalent to determining the stiffness matrix ½K .