A Realistic 3-d Textile Geometric Model

Textile composites are widely used in automotive, naval, and aerospace industries. The variation of the topology of the textile structure will affect the performance of the composite. The yarn micro-geometry is determined by 1) the textile process, such as weaving, braiding, etc. and 2) the composite forming process, such as vacuum bagging, resin transfer molding, etc. In this paper, we present a method to predict fiber distribution by simulating the textile deformation under the textile process and the vacuum bagging process. The fiber-level distribution is then transformed into the yarnbased description by the yarn-surface smoothing method. Further, each yarn was subdivided into multiple parametric volumes for the three-dimensional stress analysis. INTRODUCTION Textile composites are widely used in automotive, naval, and aerospace industries. The tailoring of textile reinforcement structures for advanced composites has mainly focused on achieving high modulus and high strength. However, the progressive damage failure is one of the most common failures in their applications and it is dependent upon textile fabric geometry. The variation of the topology of the textile structure could affect the performance of the composite. Cox and Flanagan reported that irregularity of yarn geometry and undulation has a modest effect on the average elastic module but a strong effect on the strength [1]. The strength, notch sensitivity, and delaminating resistance all require detailed modeling of yarn geometry. To optimize an accurate damage prediction method, we should consider the realistic yarn geometry instead of the idealized one. The study of detailed yarn topology is an effective way to optimize the design of textile reinforcement. The detailed textile geometry is determined by textile processes, forming processes, and ultimately the resin transfer molding (RTM) process. Since a yarn consists of a bundle of fibers, the distribution of fibers determines the yarn geometry. For each fiber, its position and undulation are the results of balanced forces applied on the fiber, such as fiber tension, inter-fiber compression, inter-fiber friction, and external compacting force. Three main approaches have been applied for representing the yarn geometry: a) Idealized yarn architecture approximation. It has been used by many researchers. It can predict mechanical properties of a textile composite with a certain degree of accuracy. However, it may not be suitable for progressive damage analysis, since the initiation and growth of a crack always depends on the local detailed yarn geometry. The general application of this method is limited in structural analysis. It treats the structural component as a homogeneous material [2-5]. b) The realistic yarn geometry approach. It is a relatively new technology. Lomov, et al. measured yarn geometry in the free state and its behavior in the loading state, and then employed an algorithm of conformal mapping to predict fiber distribution in a textile composite. The assumption of constant cross section leads the yarn interpenetration. To solve this problem, yarn is twisted to reduce the intersection [6]. Zhou and Wang [7] developed a multi-chain digital element model to predict distribution of fibers during the textile process. This method calculated all individual fibers’ positions subject to loads by solving the equilibrium equations. This approach leads to only small interpenetration, which may occur in the process of smoothing the digital chain boundaries into yarn boundaries. However, the effects of the composite forming process on the fabric geometry have not been investigated yet. c) The third approach is 3-D digital image reconstruction. This approach determines the description of textile architecture based on image reconstruction techniques. The images from an optical microscope or other sources can be segmented into objective constituents and reconstructed into 3-D geometries [8,9]. Since images are scanned from the experiment directly, the geometry generated based on these images presents a real description of the textile architecture. In this paper, we focus on how to predict the textile geometry with the applied compacting force. Multi-chain Digital Element In 2000, Sun and Wang developed a concept of the digital element to predict the yarn path by simulating the textile processing [10]. In their approach, each yarn was modeled as a frictionless pin-connected rod element, which is defined as a “digital element” (Figure 1.a). However, the method can only obtain the approximate yarn path not the yarn geometry, because the yarn was modeled as a rod with rigid properties in the transverse direction. Since then, Zhou and Wang continued to work on the yarn geometry issue by defining each yarn as an assembly of multiple digital chains, called “multi-chain digital element” [7]. Each digital chain is represented as a bundle of fibers instead of a yarn. Therefore, by examining the final distribution of these chains, one can predict the realistic yarn geometry. In reality, a yarn consists of thousands of discrete fibers. The bonding force between fibers in the yarn is very weak compared with the fiber’s transverse rigidity. Therefore, when the load is applied on the yarn, the individual fiber should be forced to move out of its original position instead of being deformed in the transverse direction, as shown in Figure 1.b. The following assumptions were made: 1) Only fiber tensile deformation in the axial direction was considered; 2) No deformation exists in the fiber transverse direction; 3) Fiber curvature is achieved by bending the joint between the two neighboring elements; and 4) The final yarn geometry is determined by the fiber’s distributions at each cross section. The stiffness matrix of the multi-chain digital element is similar to the 3-D truss element with extra constant stiffness at each joint pin. The contact stiffness was carefully redefined after each relaxation step to mimic the entangled fibers. Physically, a yarn is composed of hundreds or thousands of fibers. A direct representation of each fiber as a digital chain is not feasible. The following steps are taken to increase the efficiency of the modeling. 1) A far smaller amount of digital chains is used here to represent individual yarn, while each chain represents a bundle of real fibers. From comparison of simulations and experimental observations, the authors found that the 19 digital-chain yarn model is sufficient in numerical simulation to predict micro-geometries [11]. 2) In the multi-chain digital element approach, a new static relaxation method has replaced the step-by-step textile process method in the original digital element approach. Initial yarn architecture is established based upon known fabric information from literature, measurement, and database. The yarns are discretized into multiple digital chains. The nonequilibrium force induced to each node is calculated and then relaxed. Compared to the step-by-step textile method, less than 10% computer resource is required to generate the same fabric [11]. The stiffness of the digital element can be written as: where E is the modulus of the yarn, L is the length of the digital element and A is the area of the cross section. ∆ is a small perturbation for the support stiffness, which is necessary to be added to the element stiffness matrix to avoid singularity. Because of the assumption that the digital element can only support the tension, the global stiffness matrix may become singular if any two neighboring digital elements are aligned as a straight line. The digital element’s length/diameter ratio is recommended as smaller than 0.75. The contact stiffness matrix can be written as: where kn, ks are the compression stiffness coefficient and the lateral stiffness, respectively. Sliding occurs when s n F F = μ . The lateral stiffness becomes zero. Contact element stiffness matrix can thus be written as [5]: