A Multi Material Shell Model for the Mechanical Analysis of Triaxial Braided Composites

  • A. García-Carpintero
  • M. Herráez
  • J. Xu
  • C. S. Lopes
  • C. González


An efficient numerical methodology based on a multi material shell (MMS) approximation is proposed in this paper for the analysis of the mechanical behavior of triaxial braided composites subjected to tensile loads. The model is based on a geometrical description of the textile architecture of the material at the Gauss point level of a standard shell including the corresponding yarn geometrical parameters. The mechanical properties at the yarn level were determined from values reported in the literature or by means of micromechanical homogenization of unidirectional fiber reinforced composites. Simulations were carried out on single representative unit cell subjected to periodic boundary conditions and on multiple cell representative volume elements corresponding to the size of the standard width of a tensile specimen. The numerical results were compared with the stress-strain curves obtained experimentally as well as the damage mechanisms progression during deformation captured using radiographs performed on interrupted tests.


Computational modelling Finite element analysis (FEA) Damage mechanics Strength 


  1. 1.
    Dassault Systèmes: Abaqus 6.13 Documentation (2013)Google Scholar
  2. 2.
    A&P Technology: Q-ISO Braided Triaxial Fabric. http://www.braider.com/Products/QISO-Braided-Triaxial-Fabric.aspx (2016)
  3. 3.
    Ayranci, C., Carey, J.: 2D braided composites: A review for stiffness critical applications. Compos. Struct. 85(1), 43–58 (2008). doi:10.1016/j.compstruct.2007.10.004. http://linkinghub.elsevier.com/retrieve/pii/S0263822307002395 CrossRefGoogle Scholar
  4. 4.
    Barbero, E.J.: Finite Element Analysis of Composite Materials (2008)Google Scholar
  5. 5.
    Byun, J.H.: The analytical characterization of 2-D braided textile composites. Compos. Sci. Technol. 60 (5), 705–716 (2000). doi:10.1016/S0266-3538(99)00173-6. http://linkinghub.elsevier.com/retrieve/pii/S0266353899001736 CrossRefGoogle Scholar
  6. 6.
    Catalanotti, G., Xavier, J.: Measurement of the mode II intralaminar fracture toughness and R-curve of polymer composites using a modified Iosipescu specimen and the size effect law. Eng. Fract. Mech. 138(June 2016), 202–214 (2015). doi:10.1016/j.engfracmech.2015.03.005 CrossRefGoogle Scholar
  7. 7.
    Cater, C.R., Xiao, X., Goldberg, R.K., Kohlman, L.W.: Single ply and multi-ply braided composite response predictions using modified subcell approach. J. Aerosp. Eng. 28(5), 04014,117 (2015). doi:10.1061/(ASCE)AS.1943-5525.0000445 CrossRefGoogle Scholar
  8. 8.
    Chamis, C.: Mechanics of composite materials: past, present and future. J. Compos. Technol. Res. 11(1), 3–14Google Scholar
  9. 9.
    Cheng, J., Binienda, W.K.: Simplified braiding through integration points model for triaxially braided composites. J. Aerosp. Eng. 21(3), 152–161 (2008). doi:10.1061/(ASCE)0893-1321(2008)21:3(152).
  10. 10.
    Falzon, P., Herszbergb, I.: Mechanical performance of 2-D braided carbon / epoxy composites *. Compos. Sci. Technol. 3538(97), 253–265 (1998)CrossRefGoogle Scholar
  11. 11.
    Gerlach, R., Siviour, C.R., Petrinic, N., Wiegand, J.: Experimental characterisation and constitutive modelling of RTM-6 resin under impact loading. Polymer 49(11), 2728–2737 (2008). doi:10.1016/j.polymer.2008.04.018 CrossRefGoogle Scholar
  12. 12.
    González, C., LLorca, J.: Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling. Compos. Sci. Technol. 67(13), 2795–2806 (2007). doi:10.1016/j.compscitech.2007.02.001 CrossRefGoogle Scholar
  13. 13.
    Goyal, D., Whitcomb, J.D., Tang, X.: Validation of full 3D and equivalent tape laminate modeling of plasticity induced non-linearity in 2 × 2 braided composites. Compos. A: Appl. Sci. Manuf. 39(5), 747–760 (2008). doi:10.1016/j.compositesa.2008.02.007 CrossRefGoogle Scholar
  14. 14.
    Hallal, A., Younes, R., Fardoun, F.: Review and comparative study of analytical modeling for the elastic properties of textile composites. Compos. Part B 50, 22–31 (2013). doi:doi:10.1016/j.compositesb.2013.01.024 10.1016/j.compositesb.2013.01.024 CrossRefGoogle Scholar
  15. 15.
    Herráez, M., González, C., Lopes, C.S., Guzmán de Villoria, R., Llorca, J., Varela, T., Sánchez, J.: Computational micromechanics evaluation of the effect of fibre shape on the transverse strength of unidirectional composites: an approach to virtual materials design. Compos. Part A: Appl. Sci. Manuf. (2016). doi:10.1016/j.compositesa.2016.02.026 Google Scholar
  16. 16.
    Herráez, M., Mora, D., Naya, F., Lopes, C.S., González, C., Llorca, J.: Transverse cracking of cross-ply laminates: A computational micromechanics perspective 110, 196–204 (2015). doi:10.1016/j.compscitech.2015.02.008 10.1016/j.compscitech.2015.02.008
  17. 17.
    Hexcel: Datasheet HexFlow RTM6. Tech. rep. (2016)Google Scholar
  18. 18.
    Hexcel: Datasheet HexTow AS4C. Tech. rep. (2016)Google Scholar
  19. 19.
    Ivanov, D.S., Baudry, F., Van Den Broucke, B., Lomov, S.V., Xie, H., Verpoest, I.: Failure analysis of triaxial braided composite. Compos. Sci. Technol. 69 (9), 1372–1380 (2009). doi:doi:10.1016/j.compscitech.2008.09.013 10.1016/j.compscitech.2008.09.013. http://www.sciencedirect.com/science/article/pii/S0266353808003308
  20. 20.
    Kohlman, L.W.: Evaluation of test methods for triaxial braid composites and the development of a large multiaxial test frame for validation using braided tube specimens. Ph.D. thesis. Thesis submitted to The University of Akron (2012)Google Scholar
  21. 21.
    Littell, J.: The experimental and analytical characterization of the. Ph.D thesis (2008)Google Scholar
  22. 22.
    Littell, J.D.: Experimental and analytical characterization of the macromechanical response for triaxial braided composite materials NASA/CR—2013-215450 (December) (2013)Google Scholar
  23. 23.
    Littell, J.D., Binienda, W.K., Arnold, W.A., Roberts, G.D., Goldberg, R.K.: Effect of microscopic damage events on static and ballistic impact strength of triaxial braid composites. Compos. A: Appl. Sci. Manuf. 40(12), 1846–1862 (2009). doi:10.1016/j.compositesa.2009.08.001 CrossRefGoogle Scholar
  24. 24.
    Llorca, J., González, C., Molina-Aldareguía, J.M., Segurado, J., Seltzer, R., Sket, F., Rodríguez, M., Sádaba, S., Muñoz, R., Canal, L.P.: Multiscale modeling of composite materials: a roadmap towards virtual testing. Adv. Mater. (Deerfield Beach, Fla.) 23(44), 5130–47 (2011). doi:10.1002/adma.201101683. http://www.ncbi.nlm.nih.gov/pubmed/21971955
  25. 25.
    Lomov, S.V., Ivanov, D.S., Truong, T.C., Verpoest, I., Baudry, F., Vanden Bosche, K., Xie, H.: Experimental methodology of study of damage initiation and development in textile composites in uniaxial tensile test. Compos. Sci. Technol. 68(12), 2340–2349 (2008). doi:10.1016/j.compscitech.2007.07.005 CrossRefGoogle Scholar
  26. 26.
    Lomov, S.V., Ivanov, D.S., Verpoest, I., Zako, M., Kurashiki, T., Nakai, H., Hirosawa, S.: Meso-FE modelling of textile composites: Road map, data flow and algorithms. Compos. Sci. Technol. 67(9), 1870–1891 (2007). doi:10.1016/j.compscitech.2006.10.017 CrossRefGoogle Scholar
  27. 27.
    Lopes, C., Camanho, P., Gürdal, Z., Tatting, B.: Progressive failure analysis of tow-placed, variable-stiffness composite panels. Int. J. Solids Struct. 44(25), 8493–8516 (2007). doi:doi:10.1016/j.ijsolstr.2007.06.029 10.1016/j.ijsolstr.2007.06.029 CrossRefGoogle Scholar
  28. 28.
    Naik, R., Ifju, P., Masters, J.E.: Effect of fibre architecture parameters on defromation fields and elastic moduli of 2-D braided composites, vol. 28 (1994)Google Scholar
  29. 29.
    Naik, R.A.: Failure analysis of woven and braided fabric reinforced composites. J. Compos. Mater. 29 (17), 2334–2363 (1995). doi:10.1177/002199839502901706 CrossRefGoogle Scholar
  30. 30.
    Naya, F., González, C., Lopes, C., Van der Veen, S., Pons, F.: Computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects. Compos. A: Appl. Sci. Manuf. 92, 146–157 (2017). doi:10.1016/j.compositesa.2016.06.018
  31. 31.
    Pablo, L., González, C., Segurado, J., Llorca, J.: Intraply fracture of fiber-reinforced composites: Microscopic mechanisms and modeling. Compos. Sci. Technol. 72(11), 1223–1232 (2012). doi:10.1016/j.compscitech.2012.04.008 CrossRefGoogle Scholar
  32. 32.
    Quek, S.C., Waas, A.M., Shahwan, K.W., Agaram, V.: Analysis of 2D triaxial flat braided textile composites. Int. J. Mech. Sci. 45(6-7), 1077–1096 (2003). doi:10.1016/j.ijmecsci.2003.09.003. http://www.sciencedirect.com/science/article/pii/S0020740303001632 CrossRefGoogle Scholar
  33. 33.
    Roberts, G.D., Goldberg, R.K., Binienda, W.K., Arnold, W.A., Littell, J., Kohlman, L.W.: Characterization of triaxial braided composite material properties for impact simulation. NASA Technical Report (September), 41 (2009)Google Scholar
  34. 34.
    Sherburn, M.: Geometric and mechanical modelling of textiles. Ph.D. thesis. Thesis submited to The University of Nottingham (2007)Google Scholar
  35. 35.
    Sket, F., Enfedaque, A., Alton, C., González, C., Molina-Aldareguia, J., Llorca, J.: Automatic quantification of matrix cracking and fiber rotation by X-ray computed tomography in shear-deformed carbon fiber-reinforced laminates. Compos. Sci. Technol. 90, 129–138 (2014). doi:doi:10.1016/j.compscitech.2013.10.022 CrossRefGoogle Scholar
  36. 36.
    Totry, E., Molina-Aldareguía, J.M., González, C., LLorca, J.: Effect of fiber, matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites. Compos. Sci. Technol. 70(6), 970–980 (2010). doi:10.1016/j.compscitech.2010.02.014. http://linkinghub.elsevier.com/retrieve/pii/S0266353810000734 CrossRefGoogle Scholar
  37. 37.
    Verpoest, I., Lomov, S.V.: Virtual textile composites software WiseTex: Integration with micro-mechanical, permeability and structural analysis. Compos. Sci. Technol. 65 (15), 2563–2574 (2005). doi:10.1016/j.compscitech.2005.05.031 CrossRefGoogle Scholar
  38. 38.
    Xiao, X., Kia, H.G., Gong, X.J.: Strength prediction of a triaxially braided composite. Compos. A: Appl. Sci. Manuf. 42(8), 1000–1006 (2011). doi:10.1016/j.compositesa.2011.04.003 CrossRefGoogle Scholar
  39. 39.
    Zebdi, O., Boukhili, R., Trochu, F.: An inverse approach based on laminate theory to calculate the mechanical properties of braided composites. J. Reinf. Plast. Compos. 28(23), 2911–2930 (2009). doi:10.1177/0731684408094063 CrossRefGoogle Scholar
  40. 40.
    Zhang, C., Binienda, W.K., Goldberg, R.K., Kohlman, L.W.: A Meso-scale failure modeling of single layer triaxial braided composite using finite element method. Compos. Part A 58, 36–46 (2014). doi:10.1016/j.compositesa.2013.11.009 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.IMDEA Materials InstituteMadridSpain
  2. 2.Department of Materials ScienceMadridSpain

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