SIMULATION OF 3D OVERBRAIDING SOLUTIONS AND CHALLENGES
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1 SIMULATION OF 3D OVERBRAIDING SOLUTIONS AND CHALLENGES Guido Grave August Herzog Maschinenfabrik GmbH & Co. KG Am Alexanderhaus 160, D Oldenburg Karin Birkefeld, Tjark von Reden, Klaus Drechsler Faserverbundtechnologie, IFB Universität Stuttgart Pfaffenwaldring 31, Stuttgart, Germany { karin.birkefeld, von-reden, drechsler Yordan Kyosev, Anna Rathjens Niederrhein University of Applied Sciences, Dept. of Textile and Clothing Technology, Webschulstr. 31, Mönchengladbach, Germany yordan.kyosev@hs-niederrhein.de, Anna.Rathjens@gmx.de 1. Introduction Composite reinforcement parts usually have complex three-dimensional forms. Besides multilayer or specially designed woven and knitted fabrics, braided fabrics have their own application fields as reinforcements. In this work the attention is focused onto simulation of biaxial or triaxial overbraids. A short overview of the available tools is presented and some limits of these tools are discussed. In section 1 of the paper, the actual state of the radial braiding machines is presented. The machine equipment is very important factor during the building of the braided structure high quality structures can be produced only on a modern machine, where the parameters can be kept constant or if possible can be controlled to follow special law. Section 2 presents one very general approach of the structure simulation building the virtual structure simulating the production process using commercial FEM Software. Section 3 presents an alternative approach building the virtual structure, where the program with original algorithms, where the computations are kept as less as possible, but more process related knowledge is implemented in the program. In section 4 is discussed the way for the calculation of the elastic constants of the composite structure using the WiseTex package. Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
2 2. Braiding machines Complex forms can be efficiently covered by high performance filaments using the radial braiding machine. The braids have the important advantage in comparison to the other fabrics to allow large changes in the angle between the yarn systems (the braiding angle) and to fit on the mandrel without draping wrinkles. The modern over braiding machines uses normally computer controlled take up arm, where motion in each direction is possible (Fig.1). Fig. 1. Overbraiding of complex profile using robot for the take up For the cases, where closed loop parts or such with high curvature and sizes are covered, could be easier to split the radial braiding machine into two parts like presented at the fig. 2 b., in order to take out the expensive part. a b Fig. 2. Radial Braider RF 1/ , with set up for 64 braiding bobbins and threads. Most of the high performance fibers for composites are very sensitive to bending load. In order to minimize the loss of the tenacity (because of broken filaments) a Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
3 special carriers for carbon and glass are developed (Fig. 3). They are characterized with yarn guides with higher bending radius and special coatings, in order to reduce the friction and bending of the filaments. 3. Simulation of the braiding with FEM software Fig. 3. Carrier for carbon fibers Previous work on braiding simulation with FE has focused on 3D-Rotary braiding [5]. In this process, it has to be differentiated between the calculation of the bobbin-path on the machine and the FEsimulation of the braid. The control of a 3D-braidingmachine is such a complex process that it must be supported by special developed numerical software. 3D-braiding is a specialized variation in which a square array of horn gears is mounted on a flat plate. Each horn gear is gated separately. Switches are located between each pair of horn gears. These switches can transfer the bobbins form one horn gear to the next or keep them on one horn gear. Figure 4 shows the principle of a 3D-Braidingmachine. 3D-braid Take-up direction 0 -fibre insertion Bobbin Bobbin path Figure 4: Principle of 3D-Braidingmachine with bobbin way in dependence on switch stance Figure 5: Prototype of 3D-Braiding machine With this machine any optional movement of the bobbins in the working plate is possible. But also collisions of the bobbins could happen. Due to that the simulation of bobbin motion is necessary. Having the bobbin motion, the simulation of the braiding process and the building of the braided fabrics can start. For this the bobbin Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
4 motion law and the geometry of all elements like take up rollers, braiding rings, additional needles for control the braiding points are build as geometry, and the yarns between the take-up point and the bobbins are generated too. All these elements are discretized (meshed) into finite elements. During the FEM Simulation the software PAM Crash build automatically the system of differential equations about the nodes of the finite elements and check for the contact between them. The used elements are bar or membrane type with a typical length of two millimeters. Owing to the short length of the element in comparison to the length of a whole yarn a high number of elements arise. A length of 2 mm or less is necessary to get a realistic model of the braid. Also the pull-back-effect of the yarn was integrated in the simulation. These effects occur when a carrier moves from the edge to the middle of the machine. Figure 6: Simulation of 3D-Braid with membrane elements The trails show a good interaction of the yarns and that the contact between the yarns seems to function well. In Figure 6 the simulation of a rectangular braid is shown. It is possible to make an analysis of the yarn path in the braid. Also it is possible to use the yarn-paths to generate a mezo-mechanical model for stiffness and failure analyses. Used for 3D- Braiding process simulation, this way can be used for radial braiding too, if the bobbin path is adjusted suitably and the braiding rings are included in order to get proper geometry in the braiding zone. 4. Simulation through the emulation of the braiding process Other possible way to generate the structure of the braid in the computer is to calculate the yarn paths and yarn crossing points using the motion law of the horn gears and the local geometry in the braiding zone. This approach uses the same idea to simulate the braiding process, but is more fast then the FEM and at the same Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
5 time have more limitations. The approach is faster, because the calculations of the contact between the yarns are based on the checking contact between the whole yarn pieces, and not between the short elements (Fig. 7). Because of this the computational time for the contact detection is reduced significantly. The disadvantage is, that if someone have to change the type of the machine (i.e. putting a braiding needle in the braiding zone), more adjustments in the program are required. a b Fig. 7. Potential contact places a) between two yarns, presented as line segments there is only one check required; b between two yarns, meshed with small segments, check between each segment pairs are required. The algorithm for simulation of over braiding includes check of the contact between the yarn and the mandrel surface, too. If the mandrel has rotational symmetry, then the checks are more simplified and the programs run faster. An Implementation of such algorithms, as presented in [4] or [7] is developed in Matlab and is based on the geometry, presented on Fig. 8. The algorithms differ from these presented in [1] in the presentation of the mandrel surface here it is presented as line segment and not as surface. Fig. 8. Geometry of the overbraiding process The advantage of this simulation principle is in its speed. But this method reach its limit, if closed braids have to be simulated, where the yarn cross section changes significantly under the influence of the contact forces. On Fig. 9a is presented a photo of a braided sample, where the take up speed is adjusted for the three regions so, that the braiding angle to remain constant. On the Fig. 9b are presented the yarn Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
6 of the simulated same fabrics, using the Matlab implementation of the method, described in this section. a b Fig. 9. Braided sample with adjusted take up speed and the simulated one. In order to use this information about the yarn axis for calculation at the unit cell level, the information about the yarn cross section is required. As one can see on Fig. 9a, the yarns at the left hand side of the sample have quite higher width in comparison to the yarns in the left hand side, where the structure is more compact. A measurement of all the widths of the yarns at different diameters for this sample was done with the accuracy of 0.1 mm (Fig. 10). 5 4,5 4 Width, mm 3,5 3 2,5 D=50 D=42 D=34 D=25 2 1,5 1 Yarn Number Fig. 10. Width of the yarn cross section for sample from Fig. 9.a. The diagram shows that the yarn cross section changes depending on the diameter of the mandrel, but very high variations between the yarns at the same diameter can be found. This is because the carbon multifilaments are without any twist, and the single filaments change their local positions according to the load. Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
7 The same measurement was repeated for a second sample, braided with constant take up speed, presented on Fig. 11. Fig. 11. Braided sample with constant take up speed of m/s This sample have two characteristic areas on the left side, the part with the smaller diameter is closed braid, where the yarns, going into the same direction are in strong contact. The left hand side with the higher diameter is an open braid, where the yarns, having the same direction do not contact and because of this their cross section is not influenced. This is visible on the results on the Fig. 12, where the yarn width at the larger diameter (D=50mm) is higher then yarn width at the same diameter but at the closed fabrics, presented on Fig ,5 4 Width, mm 3,5 3 2,5 D=50 D=42 D=34 D=25 2 1, Yarn Number Fig. 12. Width of the yarn cross section in for the sample 11. These changes in the yarn diameter can not currently be calculated using the simulation algorithm, presented in this section. The yarn axis information can be used Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
8 for the generation of 3D yarn information, if the cross section is given, but it has to be taken from some other place. In contrary, the FEM Model, presented in Section 3 could be able to model the changes in the yarn cross section, if the proper material model for the yarns is selected. Since the multifilament yarn consists of thousand of single filaments, they do not represent continuous material and because of this, only some approximations of behavior of the cross section can be done. 5. Unit cell simulation for braided material A unit cell simulation of a braided material is a common method for the determination of its mechanical properties. Unit cells are the smallest weaving pattern units, in which the internal geometry of a textile structure can be described. Besides the information about the characteristic textile pattern, information about yarn spacing and yarn sections is necessary to create a unit cell for simulation purposes. Gaining internal geometry of a braid Figure 13: Micrograph of a biaxial briaded material (IFB) With simulation of the overbraiding process as it is presented, the paths of the yarns in a braided material become obvious. This is an important step towards geometrical description of the braided material, because information about the weaving pattern and spacing of yarns is available. In a second step, the measurement of the yarn sections in the component or specimen is necessary, to get a full description of the internal geometry of a unit cell. This can be done via optical measurement on the surface for the braiding angle and measurements of the thickness. An alternative for the definition of the internal geometry of a braided material is the measurement of yarn sections in micrographs. Approaches for the homogenization of the unit cell After the process of defining the internal geometry of a braid, the mechanical properties can be calculated with different kind of techniques. First of all, there is the FE analysis, where the yarns and the matrix are meshed and analyzed very detailed. This method is e. g. used to predict internal failure of the composite structure. The disadvantage of a FE approach is the time consuming pre-processing and calculation process. Other methods of homogenization base on an Eshelby analytical-numerical Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
9 approach [2]and are much faster than FE methods. For the prediction of stiffness of a composite material, their accuracy is sufficient. Figure 14: Geometry of a biaxial braid from WiseTex The homogenisation of the unit cells can be performed with the WiseTex software package developed by KU Leuven [8], see Fig. 14. This software is an integrated textile pre-processor for the description of the internal geometry and mechanical behaviour of textile structures. The unit cell can be homogenised in the software TexComp. In TexComp, several homogenisation techniques, e.g. Mori-Tanaka scheme, are available. 6. Conclusions As presented in section 3, the simulation of the over braided structures is possible using the explicit FEM commercial software. This way is connected with larger computational time, requires knowledge about the braiding process and the FEM, but does not require special programming skills from the user. The method can implement some interactions between the yarns, but for proper representation, suitable element type (3D) and its material model for in the lateral direction is required. The other alternative could be to model each single filament, which is not effective strategy for the today s computational resources. The alternative approach where mesh free simulation program is created from scratch is quicker, because for the contact detection quite less contact searches are required. The current implementation in Matlab allows representation of the yarn axes, but the position of these axes does not consider the forces between the neighbor yarns and because of this the geometry is not enough accurate. Both of the approaches can lead to more accurate models, if the yarn cross section changes under influence of the local forces are implemented. As alternative to the simulation, the information for the cross section can be taken from micro-cuts. Then the prediction of the mechanical properties with Eshbey Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
10 model, implemented in TexComp allows speeding up of the design process of composites, minimizing the number of trials go get proper structure. References [1]. Akkerman, R. & Rodríguez, B. H. V. (2006), 'Braiding Simulation for RTM Preforms''TEXCOMP 8'. [2]. Huysmans, G.; Verpoest, I. & Houtte, P. V. ( ), 'Eshelby Models applied to woven fabric composites: A benchmark study', ttp:// [3]. Ko, F.; Pastore, C. & Head, C. A. (1988), Handbook of Industrial Braiding, Atkins and Pearce. [4]. Kyosev, Y.; Brücken, A.; A.Tillmanns & Büssgen, A. (2008), Modeling of the geometry and numerical calculation of the elasticity parameters of 3D braided shapes, in S. Advani & J. Gillespie, ed.,'texcomp9 - Recent Advances in Textile Composites', pp [5]. Langer, H.; Pickett, A.; Obolenski, B.; Schneider, H.; Schneider, M. & Jacobs, E. (2000), 'Computer Controlled, Automated Manufacture of 3D-Braids for Composites''Euromat'. [6]. Lomov, S. V.; Parnas, R. S.; Gosh, S. B.; Verpoest, I. & Nakai, A. (2002), 'Experimental and theoretical characterization of the geometry of twodimensionalbraided fabrics', Textile Research Journal 72, No. 8. [7]. Rawal, A.; Potluri, P. & Steele, C. (2005), 'Geometrical Modeling of the yarn paths in three-dimensional braided structures', J. of Industrial Textiles 35, [8]. Verpoest, I. & S.V.Lomov (2005), 'Virtual textile composites software Wisetex: integration with micro-mechanical, permeability and structural analysis.', Composites Science and Technology 65(15-16), Second World Conference on 3D Fabrics and their Applications, Greenville 6-7 April
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