Abstract
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.
Similar content being viewed by others
References
Freeman WT (1993) The use of composites in aircraft primary structure. Compos Eng 3(7):767–775
Morgan P (2005) Carbon fibers and their composites. CRC Press, Boca Raton
Chung D (2012) Carbon fiber composites. Butterworth-Heinemann, Oxford
Klier T, Linn J (2010) Corporate average fuel economy standards and the market for new vehicles. Resour Futur Discuss Pap 3(1):445–462
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 234:633–635
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):99–107
Martin-Herrero J, Germain Ch (2007) Microstructure reconstruction of fibrous C/C composites from x-ray microtomography. Carbon 45(6):1242–1253
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 80:47–54
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):1033–1055
Xu H, Dikin DA, Burkhart C, Chen W (2014) Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials. Comput Mater Sci 85:206–216
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):051403
Beasley D, Martin RR, Bull DR (1993) An overview of genetic algorithms: part 1. Fundamentals. Univ Comput 15:58–58
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):1629–1650
Yeong CLY, Torquato S (1998) Reconstructing random media. Phys Rev E 57(1):495
Torquato S (2013) Random heterogeneous materials: microstructure and macroscopic properties, vol 16. Springer, Berlin
Ghosh S, Nowak Z, Lee K (1997) Quantitative characterization and modeling of composite microstructures by voronoi cells. Acta Mater 45(6):2215–2234
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):706–718
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 47:80–89
Soghrati S, Liang B (2016) Automated analysis of microstructural effects on the failure response of heterogeneous adhesives. Int J Solids Struct 81:250–261
Roberts AP (1997) Statistical reconstruction of three-dimensional porous media from two-dimensional images. Phys Rev E 56(3):3203
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 1033–1042
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):15585–15596
Kumar H, Briant CL, Curtin WA (2006) Using microstructure reconstruction to model mechanical behavior in complex microstructures. Mech Mater 38(8):818–832
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):65–76
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):352–367
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):489–507
Shewchuk JR (2002) Delaunay refinement algorithms for triangular mesh generation. Comput Geom 22(1):21–74
Yerry MA, Shephard MS (1984) Automatic three-dimensional mesh generation by the modified-octree technique. Int J Numer Methods Eng 20(11):1965–1990
Shephard MS, Georges MK (1991) Automatic three-dimensional mesh generation by the finite octree technique. Int J Numer Methods Eng 32(4):709–749
Lo SH (1985) A new mesh generation scheme for arbitrary planar domains. Int J Numer Methods Eng 21(8):1403–1426
Lo SH (1991) Volume discretization into tetrahedra-II. 3D triangulation by advancing front approach. Comput Struct 39(5):501–511
Babuska I, Melnek JM (1997) The partition of unity method. Int J Numer Methods Eng 40(4):727–758
Oden TJ, Duarte CA, Zienkiewicz OC (1998) A new cloud-based hp finite element method. Comput Methods Appl Mech Eng 153(1–2):117–126
Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150
Soghrati S (2014) Hierarchical interface-enriched finite element method: an automated technique for mesh-independent simulations. J Comput Phys 275:41–52
Soghrati S, Ahmadian H (2015) 3D hierarchical interface-enriched finite element method: implementation and applications. J Comput Phys 299:45–55
Lang C, Makhija D, Doostan A, Maute K (2014) A simple and efficient preconditioning scheme for heaviside enriched XFEM. Comput Mech 54(5):1357–1374
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):043001
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):2248–2256
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):1818–1825
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):829–839
Davila CG, Camanho PP, Rose CA (2005) Failure criteria for FRP laminates. J Compos Mater 39(4):323–345
Hinton MJ, Kaddour AS, Soden PD (2004) Failure criteria in fibre reinforced polymer composites: the world-wide failure exercise. Elsevier, New York
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):1829–1838
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):2265–2274
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 79:331–341
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):1906–1915
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):449–461
Bienias J, Debski H, Surowska B, Sadowski T (2012) Analysis of microstructure damage in carbon/epoxy composites using FEM. Comput Mater Sci 64:168–172
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):7–12
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):3128–3136
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):72–83
Kim TJ, Park CK (1998) Flexural and tensile strength developments of various shape carbon fiber-reinforced lightweight cementitious composites. Cement Concr Res 28(7):955–960
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):348–355
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):301–307
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 73:21–23
Agnese F, Scarpa F (2014) Macro-composites with star-shaped inclusions for vibration damping in wind turbine blades. Compos Struct 108:978–986
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 91:484–492
Pathan MV, Tagarielli VL, Patsias S (2017) Effect of fibre shape and interphase on the anisotropic viscoelastic response of fibre composites. Compos Struct 162:156–163
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 152:617–625
Jelf PM, Fleck NA (1992) Compression failure mechanisms in unidirectional composites. J Compos Mater 26(18):2706–2726
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 105:174–182
Hillig WB (1994) Effect of fibre misalignment on fracture behaviour of fibre-reinforced composites. J Mater Sci 29(4):899–920
Knibbs RH, Morris JB (1974) The effects of fibre orientation on the physical properties of composites. Composites 5(5):209–218
Swift DG (1975) Elastic moduli of fibrous composites containing misaligned fibres. J Phys D Appl Phys 8(3):223
Budiansky B, Fleck NA (1993) Compressive failure of fibre composites. J Mech Phys Solids 41(1):183–211
Kyriakides S, Arseculeratne R, Perry EJ, Liechti KM (1995) On the compressive failure of fiber reinforced composites. Int J Solids Struct 32(6–7):689–738
Bednarcyk BA, Aboudi J, Arnold SM (2014) The effect of general statistical fiber misalignment on predicted damage initiation in composites. Compos Part B Eng 66:97–108
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 92:261–274
Liu D, Fleck NA, Sutcliffe MPF (2004) Compressive strength of fibre composites with random fibre waviness. J Mech Phys Solids 52(7):1481–1505
Basu S, Waas AM, Ambur DR (2006) Compressive failure of fiber composites under multi-axial loading. J Mech Phys Solids 54(3):611–634
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):730–739
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):2140–2147
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):956–964
Numayr KS, Al Rjoub YS (2013) Two analogous methods for estimating the compressive strength of fibrous composites. Compos Part B Eng 50:290–296
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):948–955
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 55:119–127
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):1214–1222
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 134:132–141
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 144:26–35
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 125:24–40
Nagarajan A, Soghrati S (2018) Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation. Comput Mech. https://doi.org/10.1007/s00466-018-1560-2
Yang M, Nagarajan A, Liang B, Soghrati S (2018) New algorithms for virtual reconstruction of heterogenous microstructures. Comput Methods Appl Mech Eng 338:275–298
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 579–590
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):1235–1260
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):2285–2311
Inglis HM, Geubelle PH, Matouš Kl (2008) Boundary condition effects on multiscale analysis of damage localization. Philos Mag 88(16):2373–2397
Hooputra H, Gese H, Dell H, Werner H (2004) A comprehensive failure model for crashworthiness simulation of aluminium extrusions. Int J Crashworthiness 9(5):449–464
Sadowski T, Golewski P, Kneć M (2014) Experimental investigation and numerical modelling of spot welding-adhesive joints response. Compos Struct 112:66–77
de Souza Neto EA, Peric D, Owen DRJ (2011) Computational methods for plasticity: theory and applications. Wiley, Hoboken
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):773–781
Prantl A, Ruzicka J, Spaniel M, Moravec M, Dzugan J, Konopík Pl (2013) Identification of ductile damage parameters. In: SIMULIA community conference, Vienna, Austria
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 96:191–199
Minnicino MA, Santare MH (2012) Modeling the progressive damage of the microdroplet test using contact surfaces with cohesive behavior. Compos Sci Technol 72(16):2024–2031
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):061301
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):1615–1624
Au C, Büyüköztürk O (2006) Peel and shear fracture characterization of debonding in FRP plated concrete affected by moisture. J Compos Constr 10(1):35–47
Horie K, Hiromichi M, Mita I (1976) Bonding of epoxy resin to graphite fibres. Fibre Sci Technol 9(4):253–264
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):1787–1796
de Almeida SFM, Neto ZSN (1994) Effect of void content on the strength of composite laminates. Compos Struct 28(2):139–148
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ahmadian, H., Yang, M., Nagarajan, A. et al. Effects of shape and misalignment of fibers on the failure response of carbon fiber reinforced polymers. Comput Mech 63, 999–1017 (2019). https://doi.org/10.1007/s00466-018-1634-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-018-1634-1