Skip to main content

Numerical Analysis of Free-Edge Effect on Size-Influenced Mechanical Properties of Single-Layer Triaxially Braided Composites


The mechanical properties of triaxially braided composites under transverse loads are found to be size-dependent, due to the presence of free-edge effect. Numerical studies of the mechanical behaviors of straight-sided coupon specimens and an infinitely large plate under both axial and transverse tension loads were conducted using a meso-scale finite element model. The numerical model correlates well with experimental results, successfully capturing the free-edge warping phenomena under transverse tension. Free-edge effect is observed as out-of-plane warping, and it can be correlated to the premature damage initiation in the affected area. The numerical results characterize the impact of free-edge effects on the global stress–strain response and local failure mechanisms. By conducting dimensional analysis, the relationships of effective stiffness and strength against specimen width are quantified using Weibull equations. The results of this study indicate that the free-edge effect is an inherent behavior of braided architecture. The free-edge effect produces significantly reduced transverse tension modulus and strength measurements.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14


  1. 1.

    Zweben, C.: Designer’s corner: Is there a size effect in composites? Composites 25, 451–454 (1994)

    Article  Google Scholar 

  2. 2.

    Wagner, H.D.: Statistical concepts in the study of fracture properties of fibres and composites. In: Friedrich, K. (ed.) Application of Fracture Mechanics to Composite Materials, pp. 39–77. Elsevier, North-Holland (1989)

    Chapter  Google Scholar 

  3. 3.

    Wisnom, M., Atkinson, J., Jones, M.: Reduction in compressive strain to failure with increasing specimen size in pin-ended buckling tests. Compos. Sci. Technol. 57, 1303–1308 (1997)

    Article  Google Scholar 

  4. 4.

    Wisnom, M.R.: Size effects in tensile, compressive and interlaminar failure of unidirectional composites. In: Simitses, G.J. (ed.) Analysis and Design Issues for Modern Aerospace Vehicles- 1997, pp. 67–77. American Society of Mechanical, New York (1997)

    Google Scholar 

  5. 5.

    Bullock, R.: Strength ratios of composite materials in flexure and in tension. J. Compos. Mater. 8, 200–206 (1974)

    Article  Google Scholar 

  6. 6.

    Camponeschi, E., Gillespie, J., Wilkins, D.: Kink-band failure analysis of thick composites in compression. J. Compos. Mater. 27, 471–490 (1993)

    Article  Google Scholar 

  7. 7.

    Wisnom, M.R.: The effect of specimen size on the bending strength of unidirectional carbon fibre-epoxy. Compos. Struct. 18, 47–63 (1991)

    Article  Google Scholar 

  8. 8.

    Wisnom, M.: Size effects in the testing of fibre-composite materials. Compos. Sci. Technol. 59, 1937–1957 (1999)

    Article  Google Scholar 

  9. 9.

    O’Brien, T.K.: Characterization of delamination onset and growth in a composite laminate. In: Reifsnider, K.L. (ed.) Damage in Composite Materials, ASTM STP775, pp. 140–167. American Society for Testing and Materials, Ann Arbor, MI (1982)

  10. 10.

    Daniel, I., Whitney, J., Pipes, R.: Experimental mechanics of fiber reinforced composite materials. Exp. Tech. 7, 25 (1983)

    Article  Google Scholar 

  11. 11.

    Herakovich, C.T.: Influence of layer thickness on the strength of angle-ply laminates. J. Compos. Mater. 16, 216–227 (1982)

    Article  Google Scholar 

  12. 12.

    Mittelstedt, C., Becker, W.: Interlaminar stress concentrations in layered structures: Part I-a selective literature survey on the free-edge effect since 1967. J. Compos. Mater. 38, 1037–1062 (2004)

    Article  Google Scholar 

  13. 13.

    Sun, C., Zhou, S.: Failure of quasi-isotropic composite laminates with free-edges. J. Reinf. Plast. Compos. 7, 515–557 (1988)

    Article  Google Scholar 

  14. 14.

    Pipes, R.B., Pagano, N.J.: Interlaminar stresses in composite laminates under uniform axial extension. J. Compos. Mater. 4, 538–548 (1970)

    Google Scholar 

  15. 15.

    Rose, C.A., Herakovich, C.T.: An approximate solution for interlaminar stresses in composite laminates. Compos. Eng. 3, 271–285 (1993)

    Article  Google Scholar 

  16. 16.

    Tahani, M., Nosier, A.: Free-edge stress analysis of general cross-ply composite laminates under extension and thermal loading. Compos. Struct. 60, 91–103 (2003)

    Article  Google Scholar 

  17. 17.

    Bar-Yoseph, P., Ben-David, D.: Free-edge effects in unsymmetrically laminated composite plates. Compos. Struct. 30, 13–23 (1995)

    Article  Google Scholar 

  18. 18.

    Bauld, N.R., Goree, J.G., Tzeng, L.S.: A comparison of finite-difference and finite-element methods for calculating free-edge stresses in composites. Comput. Struct. 20, 897–914 (1985)

    Article  Google Scholar 

  19. 19.

    Pipes, R.B.: Boundary layer effects in composite laminates. Fibre Sci. Technol. 13, 49–71 (1980)

    Article  Google Scholar 

  20. 20.

    Esquej, R., Castejon, L., Lizaranzu, M., Carrera, M., Miravete, A., Miralbes, R.: A new finite element approach applied to the free-edge effect on composite materials. Compos. Struct. 98, 121–129 (2013)

    Article  Google Scholar 

  21. 21.

    Berbinau, P., Wolff, E.G.: Analytical model for prediction of microbuckling initiation in composite laminates. In: Scott, M.L. (ed.) Proceeding of 11th International Conference on Composite Material, pp. 807–817. Gold Coast, Queensland Australia (1997)

  22. 22.

    Littell, J.D., Binienda, W.K., Roberts, G.D., Goldberg, R.K.: Characterization of damage in triaxial braided composites under tensile loading. J. Aerosp. Eng. 22, 270–279 (2009)

    Article  Google Scholar 

  23. 23.

    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. The University of Akron, Akron (2012)

    Google Scholar 

  24. 24.

    Macander, A.B., Crane, R.M., Camponeschi, E.T.: Fabrication and mechanical properties of multidimensionally (XD) braided composite materials. In: Whitney, J.M. (ed.) Composite Materials Testing and Design, ASTM STP893, pp. 422–445. American Society for Testing and Materials, Philadelphia, PA (1986)

  25. 25.

    Pickett, A.K., Fouinneteau, M.: Material characterisation and calibration of a meso-mechanical damage model for braid reinforced composites. Compos. Part A 37, 368–377 (2007)

    Article  Google Scholar 

  26. 26.

    Kohlman, L.W., Bail, J.L., Roberts, G.D., Salem, J.A., Martin, R.E., Binienda, W.K.: A notched coupon approach for tensile testing of braided composites. Compos. Part A 43, 1680–1688 (2012)

    Article  Google Scholar 

  27. 27.

    Zhang, C., Binienda, W.K., Kohlman, L.W., Goldberg, R.K.: Meso-scale failure modeling of single layer triaxially braided composite using finite element method. Compos. Part A 58, 36–46 (2014)

    Article  Google Scholar 

  28. 28.

    Li, X., Binienda, W.K., Goldberg, R.K.: Finite-element model for failure study of two-dimensional triaxially braided composite. J. Aerosp. Eng. 24, 170–180 (2010)

    Article  Google Scholar 

  29. 29.

    Hashin, Z., Rotem, A.: A fatigue failure criterion for fiber reinforced materials. J. Compos. Mater. 7, 448–464 (1973)

    Article  Google Scholar 

  30. 30.

    Simulia Dassault Systems Corporation: Abaqus 6.11 Documentation, Providence (2011)

  31. 31.

    Zhang, C., Binienda, W.K., Kohlman, L.W.: Analytical and numerical analysis on elastic behavior of triaxial braided composites. J. Aerosp. Eng. (2013). doi:10.1061/(ASCE)AS.1943-5525.0000369

    Google Scholar 

  32. 32.

    Kueh, A.B.H.: Size-influenced mechanical isotropy of singly-plied triaxially woven fabric composites. Compos. Part A 57, 76–87 (2014)

    Article  Google Scholar 

  33. 33.

    Cater, C.R., Xiao, X., Goldberg, R.K., Kohlman, L.W.: Improved subcell model for the prediction of braided composite response. In: Proceeding of 54th AIAA/ASME/ASCE/AHS/ASC Structures, structure dynamics and materials conference, pp. 1628. American Institute of Aeronautics and Astronautics, Boston, Massachusetts (2013)

  34. 34.

    Bazant, Z.P., Chen, E.P.: Scaling of structural failure. Appl. Mech. Rev. 50, 593–627 (1997)

    Article  Google Scholar 

  35. 35.

    Weibull, W.: A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293–297 (1951)

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Chao Zhang.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zhang, C., Binienda, W.K. Numerical Analysis of Free-Edge Effect on Size-Influenced Mechanical Properties of Single-Layer Triaxially Braided Composites. Appl Compos Mater 21, 841–859 (2014).

Download citation


  • Triaxially braided composites
  • Free-edge effect
  • Mechanical properties
  • Finite element analysis (FEA)
  • Damage mechanics