Abstract
This paper explains previous studies addressing the onset crack or matrix crack in composite materials and presents a brief history of this field for the understanding of readers. Next, the analytic criterion and periodic unit cell analysis are compared for thermosetting or thermoplastic matrices. For both matrix resins, comparisons show that the Tsai-Hill criterion obviously cannot reproduce the results obtained from the periodic unit cell analysis, and the Hashin and Christensen criteria may give an appropriate failure envelope. Furthermore, macroscopic yielding and nonlinear deformation occur due to the plastic deformation of matrix resin before the failure. Thus it is appropriate to consider the elastoplastic or viscoplastic behavior of matrix resin. For thermoplastic resin, macroscopic yielding and nonlinear deformation occur due to the viscoplastic deformation of matrix resin much before its failure. Hence nonlinear deformation including creep may be more important than failure for thermoplastic resin.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Ashby MF (2011) Materials selection in mechanical design, 4th edn. Elsevier/Butterworth-Heinemann, Oxford
Asp LE, Berglund LA, Talreja R (1996a) A criterion for crack initiation in glassy polymers subjected to a composite-like stress state. Compos Sci Technol 56:1291–1301
Asp LE, Berglund LA, Talreja R (1996b) Prediction of matrix-initiated transverse failure in polymer composites. Compos Sci Technol 56:1089–1097
Azzi VD, Tsai SW (1965) Anisotropic strength of composites. Exp Mech 5:283–288
Bathe KJ (1996) Finite element procedures. Prentice Hall, New Jersey
Bazant ZP, Pijaudier-Cabot G (1988) Nonlocal continuum damage, localization instability and convergence. Trans ASME J Appl Mech 55:287–293
Camanho PP, Arteiro A, Melro AR, Catalanotti G, Vogler M (2015) Three-dimensional invariant-based failure criteria for fibre-reinforced composites. Int J Solids Struct 55:92–107
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 46:2265–2274
Christensen RM (1997) Stress based yield/failure criteria for fiber composites. Int J Solids Struct 34(5):529–543
Christensen RM (2005) Mechanics of composite materials. Dover, New York
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
Gosse JH, Christensen S (2001) Strain invariant failure criteria for polymers in composite materials. In: 19th AIAA applied aerodynamics conference, AIAA, 1184
Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part i - yield criteria and flow rules for porous ductile media. Trans ASME J Eng Mater Technol 99:2–15
Hashin Z (1980) Failure criteria for unidirectional fiber composites. Trans ASME J Appl Mech 47:329–334
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 A Appl Sci Manuf 37(12):2248–2256
Huang Y, Xu L, Ha SK (2012) Prediction of three-dimensional composite laminate response using micromechanics of failure. J Compos Mater 46:2431–2442
Kobayashi S, Tomii D, Shizawa K (2004) A modelling and simulation on failure prediction of ductile polymer based on craze evolution and annihilation. Trans Jpn Soc Mech Eng Ser A 70(694):810–817
LLorca J, González C, Molina-Aldareguía JM, Segurado J, Seltzer R, Sket F, Rodríguez M, Sádaba S, Muñoz R, Canal LP,(2011) Multiscale modeling of composite materials: a roadmap towards virtual testing. Adv Mater 23:5130–5147
Matsuda T, Ohno N, Tanaka H, Shimizu T (2002) Homogenized in-plane elastic-viscoplastic behavior of long fiber-reinforced laminates. JSME Int J Ser A Solid Mech Mater Eng 45(4):538–544
Melro AR, Camanho PP, Pires FMA, Pinho ST (2013) Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I—Constitutive modelling. Int J Solids Struct 50:1897–1905
Murakami D, Kobayashi S, Torigaki T, Shizawa K (2002) A thermomechanical modeling and simulation of viscoplastic large deformation behavior for polymeric materials : 1st report, non-coaxiality of constitutive equation originated in strain rate dependence. Trans Jpn Soc Mech Eng Ser A 68(668):674–681
Murakami S (2012) Continuum damage mechanics: a continuum mechanics approach to the analysis of damage and fracture. Springer, New York
Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32(6):461–490
Nishikawa M (2008) Multiscale modeling for the microscopic damage and fracture of fiber-reinforced plastic composites. Dr eng. thesis, The University of Tokyo, Tokyo
Ohno N, Okumura D, Noguchi H (2002) Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation. J Mech Phys Solids 50(5):1125–1153
Okabe T (2015) Recent studies on numerical modelling of damage progression in fibre-reinforced plastic composites. Mech Eng Rev 2(1):1–11
Okabe T, Nishikawa M, Toyoshima H (2011) A periodic unit-cell simulation of fiber arrangement dependence on the transverse tensile failure in unidirectional carbon fiber reinforced composites. Int J Solids Struct 48(20):2948–2959
Okabe T, Imamura H, Sato Y, Higuchi R, Koyanagi J, Talreja R (2015) Experimental and numerical studies of initial cracking in CFRP cross-ply laminates. Compos A Appl Sci Manuf 68:81–89
Okumura D, Ohno N, Noguchi H (2004) Elastoplastic microscopic bifurcation and post-bifurcation behavior of periodic cellular solids. J Mech Phys Solids 52(3):641–666
Pagano NJ, Schoeppner GA, Kim R, Abrams FL (1998) Steady-state cracking and edge effects in thermo-mechanical transverse cracking of cross-ply laminates. Compos Sci Technol 58(11):1811–1825
Peirce D, Shih CF, Needleman A (1984) A tangent modulus method for rate dependent solids. Comput Struct 18(5):875–887
Sato Y, Okabe T, Higuchi R, Yoshioka K (2014) Multiscale approach to predict crack initiation in unidirectional off-axis laminates. Adv Compos Mater 23(5–6):461–475
Totry E, González C, LLorca J (2008) Failure locus of fiber-reinforced composites under transverse compression and out-of-plane shear. Compos Sci Technol 68:829–839
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 68:3128–3136
Tsai SW, Wu EM (1971) A general theory of strength for anisotropic materials. J Compos Mater 5:58–80
Tvergaard V (1982) On localization in ductile materials containing spherical voids. Int J Fract 18(4):237–252
Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169
Tvergaard V, Needleman A (1995) Effects of nonlocal damage in porous plastic solids. Int J Solids Struct 32(8–9):1063–1077
Wang ASD, Kishore NN, Li CA (1985) Crack development in graphite-epoxy cross-ply laminates under uniaxial tension. Compos Sci Technol 24:1–31
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Okabe, T., Kumagai, Y., Higuchi, R., Nishikawa, M. (2015). Onset of Matrix Cracking in Fiber Reinforced Polymer Composites: A Historical Review and a Comparison Between Periodic Unit Cell Analysis and Analytic Failure Criteria. In: Altenbach, H., Matsuda, T., Okumura, D. (eds) From Creep Damage Mechanics to Homogenization Methods. Advanced Structured Materials, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-19440-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-19440-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19439-4
Online ISBN: 978-3-319-19440-0
eBook Packages: EngineeringEngineering (R0)