A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.
Cite this paper
W. Ma and D. Yin, "3D Braided Material Based on Space Group R
3 Symmetry," Materials Sciences and Applications
, Vol. 4 No. 12, 2013, pp. 773-779. doi: 10.4236/msa.2013.412098
 A. P. Mouritz, M. K. Bannister, P. J. Falzon, et al., “Review of Applications for Advanced Three-Dimensional Fibre Textile Composites,” Composites: Part A, Vol. 30, No. 12, 1999, pp. 1445-1461. http://dx.doi.org/10.1016/S1359-835X(99)00034-2
 X. M. Wang and Y. F. Xing, “Developments in Research on 3D Braided Composites,” Acta Aeronautica Et Astronautica Sinica, Vol. 31, No. 5, 2010, pp. 914-927.
 Y. Q. Wang and A. S. D. Wang, “Spatial Distribution of Yarns and Mechanical Properties in 3D Braided Tubular Composites,” Applied Composite Materials, Vol. 4, 1997, pp. 121-132
 W. Zhang, X. Ding and Y. L. Li, “Calculation and Design of Parameters for Four-step 3D Braided Preform with Complex Rectangular Cross Sections,” Journal of Industrial Textiles, Vol. 38, No. 2, 2008, pp. 139-150. http://dx.doi.org/10.1177/1528083707087838
 Y. Sun, J. L. Li and L. Chen, “Topology Optimization of the Fiber Microstructure of 3D Multidirectional Braided Composites,” Journal of Textile Research, Vol. 28, No. 10, 2007, pp. 46-48.
 K. Xu and X. W. Xu, “Microstructure Model of 3D 5-Directional Rectangular Braided Composites,” Journal of Nanjing University of Aeronautics & Astronautics, Vol. 40, No. 2, 2008, pp. 168-172.
 J. C. Li and L. Chen, “Parameterized Unit Cell of 3-D Five-Directional Braided Composites,” Journal of Tianjin Polytechnic University, Vol. 27, No. 5, 2008, pp. 1-3.
 J. Y. Liu and L. Chen, “Microstructure of 3D Six-Directional Braided Preforms,” Journal of Tianjin Polytechnic University, Vol. 25, No. 6, 2006, pp. 5-8.
 D. S. Li, Z. X. Lu and L. Chen, “Microstructure Analysis of 3-Dimensional 7-Directional Braided Structure,” Acta Materiae Compositae Sinica, Vol. 23, No. 1, 2006, pp. 135-141.
 J. L. Li and Y. Sun, “Microstructure of the Two-Step Rectangle 3D Braided Composites,” Acta Materiae Compositae Sinica, Vol. 19, No. 4, 2002, pp. 69-75.
 W. Feng, W. S. Ma, “Group Theory Analysis of Braided Geometry Structures,” Chinese Science Bulletin, Vol. 50, No. 21, 2005, pp. 2529-2533.
 W.-S. Ma, J.-X. Zhu, Y. Jiang and C.-K. Yang, “3D Braided Geometric Structures Derived by Space Groups,” Journal of Materials Science & Engineering, Vol. 28, No. 5, 2010, pp. 653-657,687.
 R. H. Wang and K. X. Guo, “Crystallographic Symmetry Group,” Science Press, Beijing, 1990, p. 207.
 W. S. Ma and X. Z. Ren, Chinese Science Bulletin (Chinese Version), Vol. 56, 2011, pp. 598-603. http://dx.doi.org/10.1360/972010-1937
 F. K. Ko and C. M. Pastore, “Structure and Properties of Integrated 3D Fabric for Structural Composites,” American Society for Testing Material, 1985, pp. 428-439.
 C. L. Ma, J. M. Yang and T. W. Chou, “Elastic Stiffness of Three-dimensional Braided Textile Structural Composites,” American Society for Testing Material, 1986, pp. 404-421.
 J. M. Yang, C. L. Ma and T. W. Chou, “Fiber Inclination Model of Three-Dimensional Textile Structural Composites,” Journal of Composite Materials, Vol. 20, No. 5, 1986, pp. 472-484. http://dx.doi.org/10.1177/002199838602000505
 G. W. Du, T. W. Chou and P. Popper, “Analysis of Three-Dimensional Textile Preforms for Multidirectional Reinforcement of Composites,” Journal of Materials Science, Vol. 26, No. 13, 1991, pp. 3438-3448. http://dx.doi.org/10.1007/BF00557129
 G. W. Du and F. K. Ko, “Unit Cell Geometry of 3-D Braided Structures,” Journal of Reinforced Plastics and Composites, Vol. 12, No. 7, 1993, pp. 752-768. http://dx.doi.org/10.1177/073168449301200702