Abstract
In this paper nonlinear cohesive fracture models with cohesive parameters and laminar elasticity typical of polymer composites are used to study the initiation and propagation of a transverse intra-ply crack that is coupled to possible delaminations at the ply interfaces in a [0/90/0°] laminate. The evolution of the transverse crack is found to be more complex than previously described, involving initial growth, growth along the ply in a tunneling mode, and expansion across the thickness of the ply in a plane strain mode. For the coupled crack system, two failure modes are distinguished: (1) complete tunneling propagation of the transverse crack before any delamination occurs, followed by delamination initiation and propagation; and (2) simultaneous propagation of the transverse and delaminations cracks. The former process is always stable, is favored by large values of the mode II to mode I toughness ratio and low values of the cohesive strength, and is predicted to be the prevalent failure sequence for polymer composites. The latter process is often unstable, because it tends to occur when the cohesive strength is so high that the stress for initiating the transverse crack exceeds the stress required for its tunneling propagation. The nonlinear fracture models provide a unified description of the entire process of initiation and crack propagation. If the delamination cracks are modeled by linear elastic fracture mechanics, substantially inaccurate predictions result for the onset of delamination cracking and for the tunneling crack initiation from a pre-existing flaw.
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References
Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45: 601–620
Borg R, Nilsson L et al (2004) Simulating DCB, ENF, and MMB experiments using shell elements and a cohesive zone model. Composites Sci Technol 64: 269–278
Camanho PP, Davila CG et al (2003) Numerical simulation of mixed-mode progressive delamination in composite materials. J Composite Mater 37: 1415–1438
Camanho PP, Davila CG et al (2006) Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear. Composite Part A: Appl Sci Manufacturing 37: 165–176
Case SW, Reifsnider KL (1999) MRLife 12 theory manual—composite materials. Materials Response Group, Virginia Polytechnical Institute and State University
Cavalli MN, Thouless MD (2001) The effect of damage nucleation on the toughness of an adhesive joint. J Adhesion 76: 75–92
Chang KY, Liu S et al (1991) Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings. J Composite Mater 25: 274–301
Cottrell AH (1963) Mechanics of fracture. Tewksbury symposium on fracture, University of Melbourne, Melbourne, Australia
Cox BN, Marshall DB (1996) Crack initiation in fiber-reinforced brittle laminates. J Am Ceram Soc 79: 1181–1188
Cox BN, Yang QD (2006) In quest of virtual tests for structural composites. Science 314: 1102–1107
Davila CG, Camanho PP et al (2005) Failure criteria for FPR laminates. J Composite Mater 39: 323–345
Dollar A, Steif PS (1991) The branched crack problem revisited. J Appl Mech 58: 584–586
Geers MGD (1999) Enhanced solution control for physically and geometrically nonlinear problems. Part II—comparative performance analysis. Int J Numer Methods Eng 46: 205–230
Gonzalez C, LLorca J (2006) Multiscale modeling of fracture in fiber-reinforced composites. Acta Materialia 54: 4171– 4181
Hallett S, Wisnom MR (2006) Numerical investigation of progressive damage and the effect of layup in notched tensile tests. J Composites Mater 40: 1229–1245
Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 193: 3523–3540
He M-Y, Hutchinson JW (1989) Crack deflection at an interface between dissimilar materials. Int J Solids Struct 25: 1053–1067
Hillerborg A, Modeer M et al (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res 6: 773–782
Ho S, Suo Z (1993) Tunneling cracks in constraint layers. ASME J Appl Mech 60: 890–894
Hoiseth K, Qu J (2003) Cracking paths at the ply interface in a cross-ply laminate. Composites Part B 34: 437–445
Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. Adv Appl Mech 29: 63–191
Iarve EV, Mollenhauer D et al (2005) Theoretical and experimental investigation of stress redistribution in open-hole composite laminates due to damage accumulation. Composites: Part A 36: 163–171
Ling DS, Fang XJ et al (2010) Nonlinear fracture analysis of delamination crack jumps in laminated composites. J Aerospace Eng (in press)
Ling DS, Yang QD et al (2009) An augmented finite element method for modeling arbitrary discontinuities in composite materials. Inter J Fract 156: 53–73
Lu T-J (1996) Crack branching in all-oxide composites. J Am Ceram Soc 79(1): 266–274
Massabò R, Cox BN (1999) Concepts for bridged mode II delamination cracks. J Mech Phys Solids 47: 1265–1300
McCartney LN (2003) Physically based damage models for laminated composites. J Mater: Design Appl 217(3): 163– 199
Mergheim J, Kuhl E et al (2005) A finite element method for the computational modeling of cohesive cracks. Int J Numerical Methods Eng 63: 276–289
Mergheim J, Kuhl E et al (2007) Towards the algorithmic treatment of 3D strong discontinuities. Commun Numer Methods Eng 23: 97–108
Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fracture Mech 69: 813–833
Parmigiani J, Thouless MD (2006) The roles of toughness and cohesive strength on crack deflection at interfaces. J Mech Phys Solids 54: 266–287
Rice JR (1980) The mechanics of earthquake rupture. In: Dziewonski AM, Boschi E (eds) Proceedings of the International School of Physics “Enrico Fermi”, Course 781979, Physics of the Earth’s Interior, Italian Physical Society and North-Holland Publ Co, pp 555–649
Shahwan KW, Waas AM (1997) Non-self-similar decohesion along a finite interface of unilaterally constrained delaminations. Proc Royal Soc London A 453: 515–550
Song SJ, Waas AM (1994) Energy-based mechanical model for mixed mode failure of laminated composites. J Eng Mater Technol 116: 512–516
Spearing SM, Beaumont PWR (1992) Fatigue amage mechanics of composite materials. I: experimental measurement of damage and post-fatigue properties. Composites Sci Technol 44: 159–168
Suiker ASJ, Fleck NA (2004) Crack tunneling and plane strain delamination in layered solids. Int J Fracture 125: 1–32
Talreja R (2006) Mulitscale modeling in damage mechanics of composite materials. J Mater Sci 41: 6800–6812
Tay T-E (2003) Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001. Appl Mech Rev 56(1): 1–32
Thouless MD, Yang QD (2001) Measurement and analysis of the fracture properties of adhesive joints. In: Dillard DA, Pocious AV, Chaudhury M (eds) The Mechanics of adhesion, vol 1. Elsevier Science, Amsterdam, The Netherlands, pp 235–271
Turon A, Camanho PP et al (2005) A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mech Mater 38: 1072–1089
Tvergaard V, Hutchinson JW (1993) The influence of plasticity on the mixed-mode interface toughness. J Mech Phys Solids 41: 1119–1135
Van de Meer FP, Sluys LJ (2008) Continuum models for the analysis of progressive failure in composite laminates. J Composite Mater (in press)
Verhoosel CV, Remmers JJC, Gutierrez MA (2008) A dissipation-based arc-length method for robust simulation of brittle and ductile failure. Int J Numer Methods Eng 77: 1290–1321
Wang ASD (1984) Fracture mechanics of sublaminate cracks in composite materials. Composite Technol Rev 6: 45–62
Wang ASD, Crossman FW (1982) Fracture mechanics of transverse cracks and edge delamination in graphite-epoxy composite laminates. AFOSR Report: 167p.
Wang JS, Suo Z (1990) Experimental determination of interfacial toughness using Brazil-nut-sandwich. Acta Metallurgica 38: 1279–1290
Xia ZC, Carr RR et al (1993) Transverse cracking in fiber- reinforced brittle matrix, cross-ply laminates. Acta Met Mater 41(8): 2365–2376
Xia ZC, Hutchinson JW (1994) Matrix cracking of cross-ply ceramic composites. Acta Met Mater 42(6): 1933– 1945
Yang B (2002) Examination of free edge crack nucleation of around an open hole in composite laminates. Int J Fracture 115: 173–191
Yang QD, Cox BN (2005) Cohesive models for damage evolution in laminated composites. Int J Fracture 133(2): 107–137
Yang QD, Cox BN et al (2006) Fracture and length scales in human cortical bone: the necessity of Nonlinear Fracture Models. Biomaterials 27: 2095–2113
Yang QD, Fang XJ, Shi JX, Lua J (2010) An improved cohesive element for shell delamnation analysis. Int J Numer Methods Eng (in press)
Yang QD, Thouless MD (2001) Mixed mode fracture of plastically-deforming adhesive joints. Int J Fracture 110: 175–187
Ye T, Suo Z et al (1992) Thin film cracking and the roles of substrate and interface. Int J Solids Struct 29: 2639– 2648
Zhang Y, Wang S (2009) Buckling, post-buckling and delamination propagation in debonded composite laminates. Part I: Theoretical development. Composite Struct 88: 121–130
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Zhou, Z.Q., Fang, X.J., Cox, B.N. et al. The evolution of a transverse intra-ply crack coupled to delamination cracks. Int J Fract 165, 77–92 (2010). https://doi.org/10.1007/s10704-010-9506-5
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DOI: https://doi.org/10.1007/s10704-010-9506-5