Mechanics of Composite Materials

, Volume 55, Issue 1, pp 95–106 | Cite as

Predicting the Elastic Properties of 3D N-Directional Braided Composites Via a Theoretical Method

  • Y. HongEmail author
  • Y. Yan
  • F. Guo
  • X. Li
  • Z. Tian

The microstructure of 3D n-directional braided composites is established in this study. A theoretical method that considers 3D braided composites as assemblages of unidirectional composites is proposed to predict their elastic properties. A comparison of the predicted stiffness with experimental results showed their good agreement. The relationship between braiding parameters, including the braiding angle and fiber volume fraction, and the elastic constants is analyzed.


3D braided composites prediction elastic properties theoretical method 


  1. 1.
    B. Sun, R. Liu, and B. Gu, “Numerical simulation of three-point bending fatigue of four-step 3-D braided rectangular composite under different stress levels from unit-cell approach,” Comp. Mater. Sci., 65, 239-246 (2012).CrossRefGoogle Scholar
  2. 2.
    X. Chen and Z. Li, “Analysis of the dynamic response of 3D-braided rectangular plates on an elastic foundation,” Mech. Compos. Mater., 44, 607-622 (2008).CrossRefGoogle Scholar
  3. 3.
    X. Wu, J. Li, and R. Shenoi, “Measurement of braided preform permeability,” Compos. Sci. Technol., 66, 3064-3069 (2006).CrossRefGoogle Scholar
  4. 4.
    F. Ko and C. Pastore, “Structure and properties of an integrated 3-D fabric for structural composites,” Recent Advances in Composites in the United States and Japan, ASTM STP 864, J. R. Vinson and M. Taya, Eds., American Society for Testing and Materials, Philadelphia, 1985, pp. 428-439.CrossRefGoogle Scholar
  5. 5.
    Y. Wang and A. Wang, “Microstructure/property relationships in three-dimensionally braided fiber composites,” Compos. Sci. Technol., 53, 213-222 (1995).CrossRefGoogle Scholar
  6. 6.
    J. Ya, Z. Liu, and Y. Wang, “Micro-CT characterization on the meso-structure of three-dimensional full five-directional braided composite,” Appl. Compos. Mater., 24, 593-610 (2017).CrossRefGoogle Scholar
  7. 7.
    Z. Quan, Z. Larimore, X. Qin, J. Yu, M. Mirotznik, J. Byun, Y. Oh, and T. Chou, “Microstructural characterization of additively manufactured multi-directional preforms and composites via X-ray micro-computed tomography,” Compos. Sci. Technol., 131, 48-60 (2016).CrossRefGoogle Scholar
  8. 8.
    J. Yang, C. Ma, and T. Chou, “Fiber inclination model of three-dimensional textile structural composites,” J. Compos. Mater., 20, 472-484 (1986).CrossRefGoogle Scholar
  9. 9.
    C. Ma, J. Yang, and T. Chou, “Elastic stiffness of three-dimensional braided textile structural composites,” Composite Materials: Testing and Design (Seventh Conference), ASTM STP 893. J. M. Whitney, Ed., American Society for Testing and Materials, Philadelphia, 1986, pp. 404-421.CrossRefGoogle Scholar
  10. 10.
    D. Wu, “Three-cell model and 5D braided structural composites,” Compos. Sci. Technol., 56, 225-233 (1996).CrossRefGoogle Scholar
  11. 11.
    S. R. Kalidindi and E. Franco, “Numerical evaluation of isostrain and weighted-average models for elastic moduli of three-dimensional composites,” Compos. Sci. Technol., 57, 293-305 (1997).CrossRefGoogle Scholar
  12. 12.
    L. Chen, X. Tao, and C. Choy, “Mechanical analysis of 3-D braided composites by the finite multiphase element method,” Compos. Sci. Technol., 59, 2383-2391 (1999).CrossRefGoogle Scholar
  13. 13.
    D. Li, Z. Lu, L. Chen, L., and J. Li, “Microstructure and mechanical properties of three-dimensional five-directional braided composites,” Int. J. Solids Struct., 46, 3422-3432 (2009).Google Scholar
  14. 14.
    D. Li, D. Fang, N. Jiang, and X. Yao, “Finite element modeling of mechanical properties of 3D five-directional rectangular braided composites,” Composites: Part B., 42, 1373-1385 (2011).CrossRefGoogle Scholar
  15. 15.
    M. Shokrieh and M. Mazloomi, “A new analytical model for calculation of stiffness of three-dimensional four-directional braided composites,” Compos. Struct., 94, 1005-1015 (2012).CrossRefGoogle Scholar
  16. 16.
    G. Fang, J. Liang, B. Wang, and Y. Wang, “Effect of interface properties on mechanical behavior of 3D four-directional braided composites with large braid angle subjected to uniaxial tension,” Appl. Compos. Mater., 18, 449-465 (2011).CrossRefGoogle Scholar
  17. 17.
    S. Tsai and H. Hahn, Introduction to composite materials, Lancaster: Technomic Publishing Co. (1980).Google Scholar
  18. 18.
    C. Chamis, “Simplified composite micromechanics equations for hygral, thermal and mechanical properties,” SAMPE Quarterly, 15, 41-55 (1984).Google Scholar
  19. 19.
    C. Chamis, “Mechanics of composite materials: past, present and future,” J. Compos. Technol. Res. ASTM, 11, 3-14 (1984).Google Scholar
  20. 20.
    R. Hill, “Theory of mechanical properties of fiber-strengthened materials,” J. Math. Phys., 12, 199-212 (1964).Google Scholar
  21. 21.
    Z. Hashin and B. Rosen, “The elastic moduli of fiber-reinforced materials”, J. Appl. Mech., 31, 223-232 (1964).CrossRefGoogle Scholar
  22. 22.
    R. Christensen and H. Lo, “Solutions for effective shear properties in three phase sphere and cylinder models,” J. Mech. Phys. Solids, 27, 315-330 (1979).CrossRefGoogle Scholar
  23. 23.
    Z. Huang, “A unified micromechanical model for the mechanical properties of two constituent composite materials, Part I: Elastic behavior,” J. Thermoplast. Compos., 13, 252-271 (2000).CrossRefGoogle Scholar
  24. 24.
    Z. Huang, “A unified micromechanical model for the mechanical properties of two constituent composite materials, Part II: Plastic behavior,” J. Thermoplast. Compos., 13, 344-362 (2000).CrossRefGoogle Scholar
  25. 25.
    Z. Huang, “A unified micromechanical model for the mechanical properties of two constituent composite materials, Part III: Strength behavior,” J. Thermoplast. Compos., 14, 54-69 (2001).CrossRefGoogle Scholar
  26. 26.
    Z. Huang, “Micromechanical prediction of ultimate strength of transversely isotropic fibrous composites,” Int. J. Solids Struct., 38, 4147-4172 (2001).CrossRefGoogle Scholar
  27. 27.
    Z. Huang, “Simulation of the mechanical properties of fibrous composites by bridging micromechanics model,” Composites: Part A., 32, 143-172 (2001).CrossRefGoogle Scholar
  28. 28.
    K. Xu and X. Qian, “A new analytical model on predicting the elastic properties of 3D full five-directional braided composites based on a multiunit cell model,” Composites: Part B., 83, 242-252 (2015).CrossRefGoogle Scholar
  29. 29.
    Z. Tian, Y. Yan, H. Luo, and Y. Hong, “Parameterized unit-cell models for stiffness performance analyses of threedimensional n-directional braided composites,” J. Reinf. Plast. Compos., 35, 1371-1386 (2016).CrossRefGoogle Scholar
  30. 30.
    K. Xu, X. Xu, and H. Wang, “Experimental investigation of the mechanical properties of 3D 6-directional composites,” Acta Mater. Compos. Sin., 22, 145-149 (2005) (in Chinese).Google Scholar
  31. 31.
    D. Zhang, X. Zhen, Y. Sun, and X. Fan, “Comparative investigation of mechanical properties between 3D braided and laminated composites,” J. Aeron. Mater., 35, 89-96 (2015) (in Chinese).Google Scholar
  32. 32.
    S. R. Kalidindi and A. Abusafieh, “Longitudinal and transverse moduli and strengths of low angle 3-D braided composites,” J. Compos. Mater., 30, 885-905 (1996).CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aeronautic Science and EngineeringBeihang UniversityBeijingChina

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