Computational Mechanics

, Volume 63, Issue 5, pp 999–1017 | Cite as

Effects of shape and misalignment of fibers on the failure response of carbon fiber reinforced polymers

  • Hossein Ahmadian
  • Ming Yang
  • Anand Nagarajan
  • Soheil SoghratiEmail author
Original Paper


An integrated computational framework is presented for the automated modeling and simulation of the failure response of carbon fiber reinforced polymers (CFRPs) with arbitrary-shaped, randomly-misaligned, embedded fibers. The proposed approach relies on a new packing/relocation-based reconstruction algorithm to synthesize realistic 3D representative volume elements (RVEs) of CFRP. A non-iterative mesh generation algorithm is then employed to create high-quality finite element models of each RVE. The failure response of CFRP is simulated using ductile and cohesive-contact damage models for the epoxy matrix and along fiber-matrix interfaces, respectively. In addition to studying the impact of fiber misalignments, this computational framework is employed to investigate the effect of cross-sectional geometry of fibers (circular versus oval shaped) on the strength, ductility, and toughness of CFRP subject to tensile and compressive loads applied transverse to the fibers direction.


Fiber reinforced composite Misalignment Cross-sectional geometry Damage Finite element 



This work has been supported by the Air Force Office of Scientific Research (AFOSR) under Grant Number FA9550-17-1-0350 and the Ohio State University Simulation Innovation and Modeling Center (SIMCenter) through support from Honda R&D Americas, Inc. The authors also acknowledge the allocation of computing time from the Ohio Supercomputer Center (OSC).


  1. 1.
    Freeman WT (1993) The use of composites in aircraft primary structure. Compos Eng 3(7):767–775Google Scholar
  2. 2.
    Morgan P (2005) Carbon fibers and their composites. CRC Press, Boca RatonGoogle Scholar
  3. 3.
    Chung D (2012) Carbon fiber composites. Butterworth-Heinemann, OxfordGoogle Scholar
  4. 4.
    Klier T, Linn J (2010) Corporate average fuel economy standards and the market for new vehicles. Resour Futur Discuss Pap 3(1):445–462Google Scholar
  5. 5.
    Buffiere JY, Maire E, Verdu C, Cloetens P, Pateyron M, Peix G, Baruchel J (1997) Damage assessment in an Al/SiC composite during monotonic tensile tests using synchrotron x-ray microtomography. Mater Sci Eng A 234:633–635Google Scholar
  6. 6.
    Kastner J, Harrer B, Degischer HP (2011) High resolution cone beam x-ray computed tomography of 3D-microstructures of cast Al-alloys. Mater Charact 62(1):99–107Google Scholar
  7. 7.
    Martin-Herrero J, Germain Ch (2007) Microstructure reconstruction of fibrous C/C composites from x-ray microtomography. Carbon 45(6):1242–1253Google Scholar
  8. 8.
    Sheidaei A, Baniassadi M, Banu M, Askeland P, Pahlavanpour M, Kuuttila N, Pourboghrat F, Drzal LT, Garmestani H (2013) 3-D microstructure reconstruction of polymer nano-composite using FIB-SEM and statistical correlation function. Compos Sci Technol 80:47–54Google Scholar
  9. 9.
    Ahmadian H, Liang B, Soghrati S (2017) An integrated computational framework for simulating the failure response of carbon fiber reinforced polymer composites. Comput Mech 60(6):1033–1055MathSciNetGoogle Scholar
  10. 10.
    Xu H, Dikin DA, Burkhart C, Chen W (2014) Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials. Comput Mater Sci 85:206–216Google Scholar
  11. 11.
    Xu H, Liu R, Choudhary A, Chen W (2015) A machine learning-based design representation method for designing heterogeneous microstructures. J Mech Des 137(5):051403Google Scholar
  12. 12.
    Beasley D, Martin RR, Bull DR (1993) An overview of genetic algorithms: part 1. Fundamentals. Univ Comput 15:58–58Google Scholar
  13. 13.
    Matouš K, Lepš M, Zeman J, Šejnoha M (2000) Applying genetic algorithms to selected topics commonly encountered in engineering practice. Comput Methods Appl Mech Eng 190(13):1629–1650zbMATHGoogle Scholar
  14. 14.
    Yeong CLY, Torquato S (1998) Reconstructing random media. Phys Rev E 57(1):495MathSciNetGoogle Scholar
  15. 15.
    Torquato S (2013) Random heterogeneous materials: microstructure and macroscopic properties, vol 16. Springer, BerlinzbMATHGoogle Scholar
  16. 16.
    Ghosh S, Nowak Z, Lee K (1997) Quantitative characterization and modeling of composite microstructures by voronoi cells. Acta Mater 45(6):2215–2234Google Scholar
  17. 17.
    Fritzen F, Böhlke T (2011) Periodic three-dimensional mesh generation for particle reinforced composites with application to metal matrix composites. Int J Solids Struct 48(5):706–718zbMATHGoogle Scholar
  18. 18.
    Yu M, Zhu P, Ma Y (2013) Effects of particle clustering on the tensile properties and failure mechanisms of hollow spheres filled syntactic foams: a numerical investigation by microstructure based modeling. Mater Des 47:80–89Google Scholar
  19. 19.
    Soghrati S, Liang B (2016) Automated analysis of microstructural effects on the failure response of heterogeneous adhesives. Int J Solids Struct 81:250–261Google Scholar
  20. 20.
    Roberts AP (1997) Statistical reconstruction of three-dimensional porous media from two-dimensional images. Phys Rev E 56(3):3203Google Scholar
  21. 21.
    Jiang Z, Chen W, Burkhart C (2012) A hybrid approach to 3D porous microstructure reconstruction via Gaussian random field. In: ASME 2012 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers, pp 1033–1042Google Scholar
  22. 22.
    Sebdani MM, Baniassadi M, Jamali J, Ahadiparast M, Abrinia K, Safdari M (2015) Designing an optimal 3D microstructure for three-phase solid oxide fuel cell anodes with maximal active triple phase boundary length (TPBL). Int J Hydrog Energy 40(45):15585–15596Google Scholar
  23. 23.
    Kumar H, Briant CL, Curtin WA (2006) Using microstructure reconstruction to model mechanical behavior in complex microstructures. Mech Mater 38(8):818–832Google Scholar
  24. 24.
    Liu Y, Greene MS, Chen W, Dikin DA, Liu WK (2013) Computational microstructure characterization and reconstruction for stochastic multiscale material design. Comput Aided Des 45(1):65–76Google Scholar
  25. 25.
    Kumar NC, Matouš K, Geubelle PH (2008) Reconstruction of periodic unit cells of multimodal random particulate composites using genetic algorithms. Comput Mater Sci 42(2):352–367Google Scholar
  26. 26.
    Collins BC, Matous K, Rypl D (2010) Three-dimensional reconstruction of statistically optimal unit cells of multimodal particulate composites. Int J Multiscale Comput Eng 8(5):489–507Google Scholar
  27. 27.
    Shewchuk JR (2002) Delaunay refinement algorithms for triangular mesh generation. Comput Geom 22(1):21–74MathSciNetzbMATHGoogle Scholar
  28. 28.
    Yerry MA, Shephard MS (1984) Automatic three-dimensional mesh generation by the modified-octree technique. Int J Numer Methods Eng 20(11):1965–1990zbMATHGoogle Scholar
  29. 29.
    Shephard MS, Georges MK (1991) Automatic three-dimensional mesh generation by the finite octree technique. Int J Numer Methods Eng 32(4):709–749zbMATHGoogle Scholar
  30. 30.
    Lo SH (1985) A new mesh generation scheme for arbitrary planar domains. Int J Numer Methods Eng 21(8):1403–1426zbMATHGoogle Scholar
  31. 31.
    Lo SH (1991) Volume discretization into tetrahedra-II. 3D triangulation by advancing front approach. Comput Struct 39(5):501–511zbMATHGoogle Scholar
  32. 32.
    Babuska I, Melnek JM (1997) The partition of unity method. Int J Numer Methods Eng 40(4):727–758MathSciNetzbMATHGoogle Scholar
  33. 33.
    Oden TJ, Duarte CA, Zienkiewicz OC (1998) A new cloud-based hp finite element method. Comput Methods Appl Mech Eng 153(1–2):117–126MathSciNetzbMATHGoogle Scholar
  34. 34.
    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150zbMATHGoogle Scholar
  35. 35.
    Soghrati S (2014) Hierarchical interface-enriched finite element method: an automated technique for mesh-independent simulations. J Comput Phys 275:41–52MathSciNetzbMATHGoogle Scholar
  36. 36.
    Soghrati S, Ahmadian H (2015) 3D hierarchical interface-enriched finite element method: implementation and applications. J Comput Phys 299:45–55MathSciNetzbMATHGoogle Scholar
  37. 37.
    Lang C, Makhija D, Doostan A, Maute K (2014) A simple and efficient preconditioning scheme for heaviside enriched XFEM. Comput Mech 54(5):1357–1374MathSciNetzbMATHGoogle Scholar
  38. 38.
    Belytschko T, Gracie R, Ventura G (2009) A review of extended/generalized finite element methods for material modeling. Model Simul Mater Sci Eng 17(4):043001Google Scholar
  39. 39.
    Hobbiebrunken T, Hojo M, Adachi T, De Jong C, Fiedler B (2006) Evaluation of interfacial strength in CF/epoxies using FEM and in-situ experiments. Compos Part A Appl Sci Manuf 37(12):2248–2256Google Scholar
  40. 40.
    Yang L, Yan Y, Liu Y, Ran Z (2012) Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression. Compos Sci Technol 72(15):1818–1825Google Scholar
  41. 41.
    Totry E, González C, LLorca J (2008) Failure locus of fiber-reinforced composites under transverse compression and out-of-plane shear. Compos Sci Technol 68(3):829–839zbMATHGoogle Scholar
  42. 42.
    Davila CG, Camanho PP, Rose CA (2005) Failure criteria for FRP laminates. J Compos Mater 39(4):323–345Google Scholar
  43. 43.
    Hinton MJ, Kaddour AS, Soden PD (2004) Failure criteria in fibre reinforced polymer composites: the world-wide failure exercise. Elsevier, New YorkGoogle Scholar
  44. 44.
    Romanowicz M (2010) Progressive failure analysis of unidirectional fiber-reinforced polymers with inhomogeneous interphase and randomly distributed fibers under transverse tensile loading. Compos Part A Appl Sci Manuf 41(12):1829–1838Google Scholar
  45. 45.
    Canal LP, Segurado J, LLorca J (2009) Failure surface of epoxy-modified fiber-reinforced composites under transverse tension and out-of-plane shear. Int J Solids Struct 46(11):2265–2274zbMATHGoogle Scholar
  46. 46.
    Tang Z, Wang C, Yu Y (2015) Failure response of fiber-epoxy unidirectional laminate under transverse tensile/compressive loading using finite-volume micromechanics. Compos Part B Eng 79:331–341Google Scholar
  47. 47.
    Melro AR, Camanho PP, Pires FMA, Pinho ST (2013) Micromechanical analysis of polymer composites reinforced by unidirectional fibres: part II-micromechanical analyses. Int J Solids Struct 50(11):1906–1915Google Scholar
  48. 48.
    Soni G, Singh R, Mitra M, Falzon BG (2014) Modelling matrix damage and fibre-matrix interfacial decohesion in composite laminates via a multi-fibre multi-layer representative volume element (M\(^{2}\)RVE). Int J Solids Struct 51(2):449–461Google Scholar
  49. 49.
    Bienias J, Debski H, Surowska B, Sadowski T (2012) Analysis of microstructure damage in carbon/epoxy composites using FEM. Comput Mater Sci 64:168–172Google Scholar
  50. 50.
    Romanowicz M (2012) A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension. Comput Mater Sci 51(1):7–12Google Scholar
  51. 51.
    Totry E, González C, LLorca J (2008) Prediction of the failure locus of c/peek composites under transverse compression and longitudinal shear through computational micromechanics. Compos Sci Technol 68(15):3128–3136Google Scholar
  52. 52.
    Yang L, Wu Z, Cao Y, Yan Y (2015) Micromechanical modelling and simulation of unidirectional fibre-reinforced composite under shear loading. J Reinf Plast Compos 34(1):72–83Google Scholar
  53. 53.
    Kim TJ, Park CK (1998) Flexural and tensile strength developments of various shape carbon fiber-reinforced lightweight cementitious composites. Cement Concr Res 28(7):955–960Google Scholar
  54. 54.
    Park SJ, Seo MK, Shim HB, Rhee KY (2004) Effect of different cross-section types on mechanical properties of carbon fibers-reinforced cement composites. Mater Sci Eng A 366(2):348–355Google Scholar
  55. 55.
    Xu Z, Li J, Wu X, Huang Y, Chen L, Zhang G (2008) Effect of kidney-type and circular cross sections on carbon fiber surface and composite interface. Compos Part A Appl Sci Manuf 39(2):301–307Google Scholar
  56. 56.
    Liu X, Wang R, Wu Z, Liu W (2012) The effect of triangle-shape carbon fiber on the flexural properties of the carbon fiber reinforced plastics. Mater Lett 73:21–23Google Scholar
  57. 57.
    Agnese F, Scarpa F (2014) Macro-composites with star-shaped inclusions for vibration damping in wind turbine blades. Compos Struct 108:978–986Google Scholar
  58. 58.
    Herráez M, González C, Lopes CS, de Villoria RG, LLorca J, Varela T, Sánchez J (2016) 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 91:484–492Google Scholar
  59. 59.
    Pathan MV, Tagarielli VL, Patsias S (2017) Effect of fibre shape and interphase on the anisotropic viscoelastic response of fibre composites. Compos Struct 162:156–163Google Scholar
  60. 60.
    Yang L, Liu X, Wu Z, Wang R (2016) Effects of triangle-shape fiber on the transverse mechanical properties of unidirectional carbon fiber reinforced plastics. Compos Struct 152:617–625Google Scholar
  61. 61.
    Jelf PM, Fleck NA (1992) Compression failure mechanisms in unidirectional composites. J Compos Mater 26(18):2706–2726Google Scholar
  62. 62.
    Czabaj MW, Riccio ML, Whitacre WW (2014) Numerical reconstruction of graphite/epoxy composite microstructure based on sub-micron resolution x-ray computed tomography. Compos Sci Technol 105:174–182Google Scholar
  63. 63.
    Hillig WB (1994) Effect of fibre misalignment on fracture behaviour of fibre-reinforced composites. J Mater Sci 29(4):899–920Google Scholar
  64. 64.
    Knibbs RH, Morris JB (1974) The effects of fibre orientation on the physical properties of composites. Composites 5(5):209–218Google Scholar
  65. 65.
    Swift DG (1975) Elastic moduli of fibrous composites containing misaligned fibres. J Phys D Appl Phys 8(3):223Google Scholar
  66. 66.
    Budiansky B, Fleck NA (1993) Compressive failure of fibre composites. J Mech Phys Solids 41(1):183–211Google Scholar
  67. 67.
    Kyriakides S, Arseculeratne R, Perry EJ, Liechti KM (1995) On the compressive failure of fiber reinforced composites. Int J Solids Struct 32(6–7):689–738zbMATHGoogle Scholar
  68. 68.
    Bednarcyk BA, Aboudi J, Arnold SM (2014) The effect of general statistical fiber misalignment on predicted damage initiation in composites. Compos Part B Eng 66:97–108Google Scholar
  69. 69.
    Li Y, Stier B, Bednarcyk B, Simon JW, Reese S (2016) The effect of fiber misalignment on the homogenized properties of unidirectional fiber reinforced composites. Mech Mater 92:261–274Google Scholar
  70. 70.
    Liu D, Fleck NA, Sutcliffe MPF (2004) Compressive strength of fibre composites with random fibre waviness. J Mech Phys Solids 52(7):1481–1505zbMATHGoogle Scholar
  71. 71.
    Basu S, Waas AM, Ambur DR (2006) Compressive failure of fiber composites under multi-axial loading. J Mech Phys Solids 54(3):611–634zbMATHGoogle Scholar
  72. 72.
    Gutkin R, Pinho ST, Robinson P, Curtis PT (2011) A finite fracture mechanics formulation to predict fibre kinking and splitting in CFRP under combined longitudinal compression and in-plane shear. Mech Mater 43(11):730–739Google Scholar
  73. 73.
    Yokozeki T, Ogasawara T, Ishikawa T (2005) Effects of fiber nonlinear properties on the compressive strength prediction of unidirectional carbon-fiber composites. Compos Sci Technol 65(14):2140–2147Google Scholar
  74. 74.
    Pimenta S, Gutkin R, Pinho ST, Robinson P (2009) A micromechanical model for kink-band formation: part ii: analytical modelling. Compos Sci Technol 69(7):956–964Google Scholar
  75. 75.
    Numayr KS, Al Rjoub YS (2013) Two analogous methods for estimating the compressive strength of fibrous composites. Compos Part B Eng 50:290–296Google Scholar
  76. 76.
    Pimenta S, Gutkin R, Pinho ST, Robinson P (2009) A micromechanical model for kink-band formation: part i: experimental study and numerical modelling. Compos Sci Technol 69(7):948–955Google Scholar
  77. 77.
    Zhou HW, Yi HY, Gui LL, Dai GM, Peng RD, Wang HW, Mishnaevsky L (2013) Compressive damage mechanism of GFRP composites under off-axis loading: experimental and numerical investigations. Compos Part B Eng 55:119–127Google Scholar
  78. 78.
    Gutkin R, Pinho ST, Robinson P, Curtis PT (2010) Micro-mechanical modelling of shear-driven fibre compressive failure and of fibre kinking for failure envelope generation in CFRP laminates. Compos Sci Technol 70(8):1214–1222Google Scholar
  79. 79.
    Bai X, Bessa MA, Melro AR, Camanho PP, Guo L, Liu WK (2015) High-fidelity micro-scale modeling of the thermo-visco-plastic behavior of carbon fiber polymer matrix composites. Compos Struct 134:132–141Google Scholar
  80. 80.
    Naya F, Herráez M, Lopes CS, González C, Van der Veen S, Pons F (2017) Computational micromechanics of fiber kinking in unidirectional FRP under different environmental conditions. Compos Sci Technol 144:26–35Google Scholar
  81. 81.
    Soghrati S, Nagarajan A, Liang B (2017) Conforming to interface structured adaptive mesh refinement: new technique for the automated modeling of materials with complex microstructures. Finite Elem Anal Des 125:24–40Google Scholar
  82. 82.
    Nagarajan A, Soghrati S (2018) Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation. Comput Mech. MathSciNetzbMATHGoogle Scholar
  83. 83.
    Yang M, Nagarajan A, Liang B, Soghrati S (2018) New algorithms for virtual reconstruction of heterogenous microstructures. Comput Methods Appl Mech Eng 338:275–298Google Scholar
  84. 84.
    Hill R (1985) On the micro-to-macro transition in constitutive analyses of elastoplastic response at finite strain. In: Mathematical proceedings of the Cambridge philosophical society, vol 98. Cambridge University press, pp 579–590Google Scholar
  85. 85.
    Kouznetsova V, Geers MGD, Brekelmans WAM (2002) Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. Int J Numer Methods Eng 54(8):1235–1260zbMATHGoogle Scholar
  86. 86.
    Terada K, Hori M, Kyoya T, Kikuchi N (2000) Simulation of the multi-scale convergence in computational homogenization approaches. Int J Solids Struct 37(16):2285–2311zbMATHGoogle Scholar
  87. 87.
    Inglis HM, Geubelle PH, Matouš Kl (2008) Boundary condition effects on multiscale analysis of damage localization. Philos Mag 88(16):2373–2397Google Scholar
  88. 88.
    Hooputra H, Gese H, Dell H, Werner H (2004) A comprehensive failure model for crashworthiness simulation of aluminium extrusions. Int J Crashworthiness 9(5):449–464Google Scholar
  89. 89.
    Sadowski T, Golewski P, Kneć M (2014) Experimental investigation and numerical modelling of spot welding-adhesive joints response. Compos Struct 112:66–77Google Scholar
  90. 90.
    de Souza Neto EA, Peric D, Owen DRJ (2011) Computational methods for plasticity: theory and applications. Wiley, HobokenGoogle Scholar
  91. 91.
    Hillerborg A, Modéer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6(6):773–781Google Scholar
  92. 92.
    Prantl A, Ruzicka J, Spaniel M, Moravec M, Dzugan J, Konopík Pl (2013) Identification of ductile damage parameters. In: SIMULIA community conference, Vienna, AustriaGoogle Scholar
  93. 93.
    Safaei M, Sheidaei A, Baniassadi M, Ahzi S, Mashhadi MM, Pourboghrat F (2015) An interfacial debonding-induced damage model for graphite nanoplatelet polymer composites. Comput Mater Sci 96:191–199Google Scholar
  94. 94.
    Minnicino MA, Santare MH (2012) Modeling the progressive damage of the microdroplet test using contact surfaces with cohesive behavior. Compos Sci Technol 72(16):2024–2031Google Scholar
  95. 95.
    Lee HG, Brandyberry M, Tudor A, Matouš K (2009) Three-dimensional reconstruction of statistically optimal unit cells of polydisperse particulate composites from microtomography. Phys Rev E 80(6):061301Google Scholar
  96. 96.
    Fiedler B, Hojo M, Ochiai S, Schulte K, Ando M (2001) Failure behavior of an epoxy matrix under different kinds of static loading. Compos Sci Technol 61(11):1615–1624Google Scholar
  97. 97.
    Au C, Büyüköztürk O (2006) Peel and shear fracture characterization of debonding in FRP plated concrete affected by moisture. J Compos Constr 10(1):35–47Google Scholar
  98. 98.
    Horie K, Hiromichi M, Mita I (1976) Bonding of epoxy resin to graphite fibres. Fibre Sci Technol 9(4):253–264Google Scholar
  99. 99.
    Lau D, Büyüköztürk O, Buehler MJ (2012) Characterization of the intrinsic strength between epoxy and silica using a multiscale approach. J Mater Res 27(14):1787–1796Google Scholar
  100. 100.
    de Almeida SFM, Neto ZSN (1994) Effect of void content on the strength of composite laminates. Compos Struct 28(2):139–148Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Integrated Systems EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.Department of Mechanical and Aerospace EngineeringThe Ohio State UniversityColumbusUSA
  3. 3.Department of Mechanical and Aerospace Engineering, Department of Materials Science and EngineeringThe Ohio State UniversityColumbusUSA

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