International Journal of Fracture

, Volume 208, Issue 1–2, pp 269–285 | Cite as

Effective simulation of the mechanics of longitudinal tensile failure of unidirectional polymer composites

  • Rodrigo P. Tavares
  • Fermin Otero
  • Albert Turon
  • Pedro P. Camanho
IUTAM Baltimore


An efficient computational model to simulate tensile failure of both hybrid and non-hybrid composite materials is proposed. This model is based on the spring element model, which is extended to a random 2D fibre packing. The proposed model is used to study the local stress fields around a broken fibre as well as the failure process in composite materials. The influence of fibre strength distributions and matrix properties on this process is also analysed. A detailed analysis of the fracture process and cluster development is performed and the results are compared with experimental results from the literature.


Composites Fracture Strength Numerical modelling 



The first author acknowledges the support of the Portuguese Government’s Fundação para a Ciência e Tecnologia, under the Grant SFRH/BD/115872/2016. The second gratefully acknowledges the funding of Project NORTE-01-0145-FEDER-000022 SciTech Science and Technology for Competitive and Sustainable Industries, cofinanced by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER). The last author gratefully acknowledges the funding of Project PTDC/EMS-PRO/4732/2014, cofinanced by Programa Operacional Competitividade e Internacionalização and Programa Operacional Regional de Lisboa, through Fundo Europeu de Desenvolvimento Regional (FEDER) and by National Funds through FCT—Fundação para a Ciência e Tecnologia. The authors would like to thank the support of Dr. Stephane Mahdi, Dr. Christian Weimer and Christian Metzner (AIRBUS).


  1. Argon AS (1974) Statistical aspects of fracture, chap 4. In: Broutman LJ (ed) Composite materials: fatigue and fracture, vol 5. Academic Press, New York, pp 153–190Google Scholar
  2. Batdorf SB (1982) Tensile strength of unidirectionally reinforced composites—I. J Reinf Plast Compos 1(2):153–164. CrossRefGoogle Scholar
  3. Batdorf S, Ghaffarian R (1982) Tensile strength of unidirectionally reinforced composites—II. J Reinf Plast Compos 1(2):165–176. CrossRefGoogle Scholar
  4. Beyerlein IJ, Phoenix S (1996) Statistics for the strength and size effects of microcomposites with four carbon fibers in epoxy resin. Compos Sci Technol 56(1):75–92. CrossRefGoogle Scholar
  5. Cox HL (2002) The elasticity and strength of paper and other fibrous materials. Br J Appl Phys 3(3):72–79. CrossRefGoogle Scholar
  6. Curtin WA (1991) Theory of mechanical properties of ceramic-matrix composites. J Am Ceram Soc 74(11):2837–2845. CrossRefGoogle Scholar
  7. Curtin WA (2000) Tensile strength of fiber-reinforced composites: III. Beyond the traditional Weibull model for fiber strengths. J Compos Mater 34(15):1301–1332CrossRefGoogle Scholar
  8. Curtin WA, Takeda N (1998) Tensile strength of fiber-reinforced composites: I. Model and effects of local fiber geometry. J Compos Mater 32(22):2042–2059CrossRefGoogle Scholar
  9. Czél G, Jalalvand M, Wisnom MR, Czigány T (2017) Design and characterisation of high performance, pseudo-ductile all-carbon/epoxy unidirectional hybrid composites. Compos Part B Eng 111:348–356. CrossRefGoogle Scholar
  10. DeJong MJ, Hendriks MA, Rots JG (2008) Sequentially linear analysis of fracture under non-proportional loading. Eng Fract Mech 75(18):5042–5056. CrossRefGoogle Scholar
  11. Delaunay B (1934) Sur la sphere vide. Izv Akad Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk 7(793–800):1–2Google Scholar
  12. Fukuda H (1985) Stress concentration factors in unidirectional composites with random fiber spacing. Compos Sci Technol 22(2):153–163. CrossRefGoogle Scholar
  13. Gulino R, Phoenix SL (1991) Weibull strength statistics for graphite fibres measured from the break progression in a model graphite/glass/epoxy microcomposite. J Mater Sci 26(11):3107–3118. CrossRefGoogle Scholar
  14. Harlow DG, Phoenix SL (1978) The chain-of-bundles probability model for the strength of fibrous materials I: analysis and conjectures. J Compos Mater 12(2):195–214. CrossRefGoogle Scholar
  15. Hedgepeth JM, Dyke PV (1967) Local stress concentrations in imperfect filamentary composite materials. J Compos Mater 1(3):294–309. CrossRefGoogle Scholar
  16. Hedgepeth JM, Van Dyke P (1967) Local stress concentrations in imperfect filamentary composite materials. J Compos Mater 1(3):294–309. CrossRefGoogle Scholar
  17. Kelly A, Tyson W (1965) Tensile properties of fibre-reinforced metals: copper/tungsten and copper/molybdenum. J Mech Phys Solids 13(6):329–350. CrossRefGoogle Scholar
  18. Lamon J (2007) Mécanique de la rupture fragile et de l’endommagement: approches statistiques et probabilistes. Études en mécanique des matériaux et des structures, Hermes Science Publications.
  19. Landis CM, McMeeking RM (1999) A shear-lag model for a broken fiber embedded in a composite with a ductile matrix. Compos Sci Technol 59(3):447–457. CrossRefGoogle Scholar
  20. Madhukar MS, Drzal LT (1991) Fiber-matrix adhesion and its effect on composite mechanical properties: II. Longitudinal (0) and transverse (90) tensile and flexure behavior of graphite/epoxy composites. J Compos Mater 25(8):958–991. CrossRefGoogle Scholar
  21. Melro AR, Camanho PP, Pinho ST (2008) Generation of random distribution of fibres in long-fibre reinforced composites. Compos Sci Technol 68(9):2092–2102. CrossRefGoogle Scholar
  22. Mishnaevsky L, Brøndsted P (2009) Micromechanisms of damage in unidirectional fiber reinforced composites: 3D computational analysis. Compos Sci Technol 69(7–8):1036–1044. CrossRefGoogle Scholar
  23. Nishikawa M, Okabe T, Takeda N (2008) Determination of interface properties from experiments on the fragmentation process in single-fiber composites. Mater Sci Eng A 480(1–2):549–557. CrossRefGoogle Scholar
  24. Okabe T, Sekine H, Ishii K, Nishikawa M, Takeda N (2005) Numerical method for failure simulation of unidirectional fiber-reinforced composites with spring element model. Compos Sci Technol 65(6):921–933. CrossRefGoogle Scholar
  25. Okabe T, Ishii K, Nishikawa M, Takeda N (2007) Prediction of tensile strength of unidirectional CFRP composites. J Jpn Soc Compos Mater 33(December 2014):205–212. CrossRefGoogle Scholar
  26. Otero F, Oller S, Martinez X, Salomón O (2015) Numerical homogenization for composite materials analysis. Comparison with other micro mechanical formulations. Compos Struct 122:405–416. CrossRefGoogle Scholar
  27. Padgett WJ, Durham SD, Mason AM (1995) Weibull analysis of the strength of carbon fibers using linear and power law models for the length effect. J Compos Mater 29(14):1873–1884CrossRefGoogle Scholar
  28. Pimenta S (2015) Fibre failure modelling, chap 25. In: Camanho PP, Hallet SR (eds) Numerical modelling of failure in advanced composite materials. Woodhead Publishing, CambridgeGoogle Scholar
  29. Rots JG, Invernizzi S (2004) Regularized sequentially linear saw-tooth softening model. Int J Numer Anal Methods Geomech 28(78):821–856. CrossRefGoogle Scholar
  30. Scott A, Mavrogordato M, Wright P, Sinclair I, Spearing S (2011) In situ fibre fracture measurement in carbonepoxy laminates using high resolution computed tomography. Compos Sci Technol 71(12):1471–1477. CrossRefGoogle Scholar
  31. Scott AE, Sinclair I, Spearing SM, Thionnet A, Bunsell AR (2012) Damage accumulation in a carbon/epoxy composite: comparison between a multiscale model and computed tomography experimental results. Compos Part A Appl Sci Manuf 43(9):1514–1522. CrossRefGoogle Scholar
  32. Swolfs Y, Gorbatikh L, Romanov V, Orlova S, Lomov SV, Verpoest I (2013a) Stress concentrations in an impregnated fibre bundle with random fibre packing. Compos Sci Technol 74(0):113–120. CrossRefGoogle Scholar
  33. Swolfs Y, Gorbatikh L, Verpoest I (2013b) Stress concentrations in hybrid unidirectional fibre-reinforced composites with random fibre packings. Compos Sci Technol 85:10–16.
  34. Swolfs Y, Gorbatikh L, Verpoest I (2014) Fibre hybridisation in polymer composites: a review. Compos Part A Appl Sci Manuf 67(0):181–200.
  35. Swolfs Y, McMeeking RM, Verpoest I, Gorbatikh L (2015a) Matrix cracks around fibre breaks and their effect on stress redistribution and failure development in unidirectional composites. Compos Sci Technol 108(0):16–22.
  36. Swolfs Y, Morton H, Scott A, Gorbatikh L, Reed P, Sinclair I, Spearing S, Verpoest I (2015b) Synchrotron radiation computed tomography for experimental validation of a tensile strength model for unidirectional fibre-reinforced composites. Compos Part A Appl Sci Manuf 77:106–113.
  37. Tanaka F, Okabe T, Okuda H, Kinloch IA, Young RJ (2014) Factors controlling the strength of carbon fibres in tension. Compos Part A Appl Sci Manuf 57(0):88–94. CrossRefGoogle Scholar
  38. Tavares RP, Melro AR, Bessa MA, Turon A, Liu WK, Camanho PP (2016) Mechanics of hybrid polymer composites: analytical and computational study. Comput Mech 57(3):405–421. CrossRefGoogle Scholar
  39. Thionnet A, Chou HY, Bunsell A (2014) Fibre break processes in unidirectional composites. Compos Part A Appl Sci Manuf 65(0):148–160. CrossRefGoogle Scholar
  40. Toyama N, Takatsubo J (2004) An investigation of non-linear elastic behavior of CFRP laminates and strain measurement using Lamb waves. Compos Sci Technol 64(16):2509–2516. CrossRefGoogle Scholar
  41. Watanabe J, Tanaka F, Okuda H, Okabe T (2014) Tensile strength distribution of carbon fibers at short gauge lengths. Adv Compos Mater 23(5–6):535–550. CrossRefGoogle Scholar
  42. Watson AS, Smith RL (1985) An examination of statistical theories for fibrous materials in the light of experimental data. J Mater Sci 20(9):3260–3270. CrossRefGoogle Scholar
  43. Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech Trans ASME 58(7):1001–1010Google Scholar
  44. Xia ZH, Curtin WA (2001) Multiscale modeling of damage and failure in aluminum-matrix composites. Compos Sci Technol 61(15):2247–2257. CrossRefGoogle Scholar
  45. Xing J, Liu XR, Chou TW (1985) Dynamic stress concentration factors in unidirectional composites. J Compos Mater 19(3):269–275. CrossRefGoogle Scholar
  46. Zweben C (1968) Tensile failure of fiber composites. AIAA J 6(68):2325–2331. CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.DEMec, Faculdade de EngenhariaUniversidade do PortoPortoPortugal
  2. 2.AMADE, Polytechnic SchoolUniversity of GironaGironaSpain
  3. 3.INEGIPortoPortugal

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