The fracturing behavior of fiber-reinforced composites is often modeled using continuum damage mechanics-based approaches which commonly assume a linear softening damage law, i.e. a linearly decreasing stress with increasing strain. The objective of this paper is to assess the suitability of this assumption for composites and to systematically analyze the effect of the assumed shape of the softening damage law at material point, on the predicted fracturing behavior of the structure. The material considered is an epoxy/carbon-fiber twill woven composite. Numerical evaluations are conducted by predicting the strength size effect and progressive accumulation of damage in a structure and comparing with experimental measurements. Damage models with a wide range of shapes of softening laws are considered. These include linear, bilinear, trilinear, exponential, power law and sigmoidal. The effect of introducing a sudden drop in the damage law is also evaluated. All modeling is conducted via the crack band model (CBM), to ensure the mesh objectivity of results. It is found that despite using the right strength and fracture energy as input at the material point level, not all softening law shapes can accurately predict the strength size effect and post-peak softening. Especially the sudden drop feature leads to severe underprediction of strength. Bilinear softening shows the best combination of simplicity and accuracy, especially if formulated via the R-curve approach. Further insights are obtained by assessing the predicted fracture process zone size and fracture energy via the size effect method. Finally structure level predictions are made by considering plug initiated axial crushing of a cylindrical crushcan. The close ties between the shape of the material softening law and predicted process zone, and structural fracturing are revealed, and shown to be an important consideration in formulating damage models.
BažantZPOhBH (1983)
Crack band theory for fracture of concrete. Matériaux et Constructions16(3): 155–177.
5.
BažantZPPijaudier-CabotG (1989)
Measurement of characteristic length of nonlocal continuum. Journal of Engineering Mechanics115(4): 755–767.
6.
BažantZPPlanasJ (1997) Fracture and Size Effect in Concrete and Other Quasibrittle Materials.
vol.16.
Boca Raton, FL:
CRC press.
7.
CanerFCBažantZPHooverCG, et al. (2011)
Microplane model for fracturing damage of triaxially braided fiber-polymer composites. Journal of Engineering Materials and Technology133(2): 021024-1–021024-12.
8.
Cedolin L and Cusatis G. Cohesive fracture and size effect in concrete. In: Carpinteri A, Gambarova P, Ferro A, et al. (eds). Proceedings of the 6th int conf on fracture mechanics of concrete and concrete structures. London: Taylor and Francis; 2007.
9.
ChabocheJL (1988a)
Continuum damage mechanics: Part I – General concepts. Journal of Applied Mechanics55(1): 59–64.
10.
ChabocheJL (1988b)
Continuum damage mechanics: Part II – Damage growth, crack initiation, and crack growth. Journal of Applied Mechanics55(1): 65–72.
11.
DanielIMIshaiODanielIM, et al. (1994) Engineering Mechanics of Composite Materials.
vol.3.
New York:
Oxford University Press.
12.
DávilaCGRoseCACamanhoPP (2009)
A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites. International Journal of Fracture158(2): 211–223.
13.
De BorstRMuhlhausHB (1992)
Gradient-dependent plasticity: Formulation and algorithmic aspects. International Journal for Numerical Methods in Engineering35(3): 521–539.
14.
ElicesMPlanasJ (1993)
The equivalent elastic crack: 1. Load-Y equivalences. International Journal of Fracture61(2): 159–172.
15.
EskandariSPiresFMACamanhoPP, et al. (2019)
Analyzing the failure and damage of FRP composite laminates under high strain rates considering visco-plasticity. Engineering Failure Analysis101: 257–273.
16.
HeinrichCWaasA (2012) Investigation of progressive damage and fracture in laminated composites using the smeared crack approach. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, p.1537. Honolulu,: American Institute of Aeronautics and Astronautics.
17.
HooverCGBažantZP (2014)
Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests. International Journal of Fracture187(1): 133–143.
18.
HuguetCG (2017)
A continuum damage mechanics model for woven composites. Master’s Thesis, TU Delft Aerospace Engineering.
19.
IrwinG (1958) Fracture, Elasticity and Plasticity. In: Encyclopaedia of Physics.
vol. 6.
Heidelberg, Germany:
Springer-Verlag, pp.551–590.
20.
JainJRGhoshS (2009)
Damage evolution in composites with a homogenization-based continuum damage mechanics model. International Journal of Damage Mechanics18(6): 533–568.
21.
JirasekMRolshovenSGrasslP (2004)
Size effect on fracture energy induced by non-locality. International Journal for Numerical and Analytical Methods in Geomechanics28(78): 653–670.
22.
KachanovLM (1986) Introduction to Continuum Damage Mechanics.
vol.10.
Berlin, Germany:
Springer Science & Business Media.
23.
KimKTBažantZPYuQ (2013)
Non-uniqueness of cohesive-crack stress-separation law of human and bovine bones and remedy by size effect tests. International Journal of Fracture181(1): 67–81.
24.
KiraneK (2014)
Fatigue, fracture and size effect in particulate and fabric composites: constitutive modeling, theory and experiments. PhD Thesis, Northwestern University, USA.
25.
KiraneKSalviatoMBažantZP (2016a)
Microplane-triad model for elastic and fracturing behavior of woven composites. Journal of Applied Mechanics83(4): 041006.
26.
KiraneKSalviatoMBažantZP (2016b)
Microplane triad model for simple and accurate prediction of orthotropic elastic constants of woven fabric composites. Journal of Composite Materials50(9): 1247–1260.
27.
KoloorSTaminM (2018)
Mode-II interlaminar fracture and crack-jump phenomenon in CFRP composite laminate materials. Composite Structures204: 594–606.
28.
KoloorSKhosravaniMRHamzahR, et al. (2018)
FE model-based construction and progressive damage processes of FRP composite laminates with different manufacturing processes. International Journal of Mechanical Sciences141: 223–235.
29.
LapczykIHurtadoJA (2007)
Progressive damage modeling in fiber-reinforced materials. Composites Part A: Applied Science and Manufacturing38(11): 2333–2341.
30.
LiXGaoWLiuW (2019)
A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation. International Journal of Damage Mechanics28(9): 1299–1322.
31.
LiuPZhengJ (2010)
Recent developments on damage modeling and finite element analysis for composite laminates: A review. Materials & Design31(8): 3825–3834.
32.
McGregorCVaziriRXiaoX (2010)
Finite element modelling of the progressive crushing of braided composite tubes under axial impact. International Journal of Impact Engineering37(6): 662–672.
33.
MaimíPCamanhoPPMayugoJ, et al. (2007)
A continuum damage model for composite laminates, Part I: Constitutive model. Mechanics of Materials39(10): 897–908.
34.
MaimíPMayugoJCamanhoP (2008)
A three-dimensional damage model for transversely isotropic composite laminates. Journal of Composite Materials42(25): 2717–2745.
35.
MamalisARobinsonMManolakosD, et al. (1997)
Crashworthy capability of composite material structures. Composite Structures37(2): 109–134.
36.
MareauCMorelF (2019)
A continuum damage mechanics-based approach for the high cycle fatigue behavior of metallic polycrystals. International Journal of Damage Mechanics28(6): 838–856.
37.
MatzenmillerALublinerJTaylorR (1995)
A constitutive model for anisotropic damage in fiber-composites. Mechanics of Materials20(2): 125–152.
38.
MeyerPWaasA (2016)
FEM predictions of damage in continuous fiber ceramic matrix composites under transverse tension using the crack band method. Acta Materialia102: 292–303.
39.
OkabeTOnoderaSKumagaiY, et al. (2018)
Continuum damage mechanics modeling of composite laminates including transverse cracks. International Journal of Damage Mechanics27(6): 877–895.
40.
OnoderaSOkabeT (2020)
Analytical model for determining effective stiffness and mechanical behavior of polymer matrix composite laminates using continuum damage mechanics. International Journal of Damage Mechanics29(10): 1512–1542.
41.
OucifCVoyiadjisGZKattanPI, et al. (2019)
Investigation of the super healing theory in continuum damage and healing mechanics. International Journal of Damage Mechanics28(6): 896–917.
42.
PanYTianFZhongZ (2018)
A continuum damage-healing model of healing agents based self-healing materials. International Journal of Damage Mechanics27(5): 754–778.
43.
PandeyVSinghIMishraB, et al. (2019)
Creep crack simulations using continuum damage mechanics and extended finite element method. International Journal of Damage Mechanics28(1): 3–34.
44.
PinedaEJWaasAM (2013)
Numerical implementation of a multiple-ISV thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates. International Journal of Fracture182(1): 93–122.
45.
Polanco-LoriaMSϕrensenS (1995)
Damage evolution laws for concrete – A comparative study. In: Proceedings of FRAMCOS-2, F. H. Wittmann (Ed) Fracture Mechanics of Concrete Structures1027–1036.
46.
ReinerJFeserTSchuelerD, et al. (2019)
Comparison of two progressive damage models for studying the notched behavior of composite laminates under tension. Composite Structures207: 385–396.
47.
SalviatoMChauVTLiW, et al. (2016a)
Direct testing of gradual post peak softening of fracture specimens of fiber composites stabilized by enhanced grip stiffness and mass. Journal of Applied Mechanics83(11): 111003.
48.
SalviatoMKiraneKAshariSE, et al. (2016b)
Experimental and numerical investigation of intra-laminar energy dissipation and size effect in two-dimensional textile composites. Composites Science and Technology135: 67–75.
49.
Simulia (2017) ABAQUS User’s Manual, Version 2017.
Dassault Systemes Simulia Corp.,
Providence, RI, USA.
50.
SlobbeAHendriksMRotsJ (2013)
Systematic assessment of directional mesh bias with periodic boundary conditions: Applied to the crack band model. Engineering Fracture Mechanics109: 186–208.
51.
TalrejaR (1985)
A continuum mechanics characterization of damage in composite materials. Proceedings of the Royal Society of London A: Mathematical and Physical Sciences399(1817): 195–216.
52.
TaniguchiNNishiwakiTHirayamaN, et al. (2009)
Dynamic tensile properties of carbon fiber composite based on thermoplastic epoxy resin loaded in matrix-dominant directions. Composites Science and Technology69(2): 207–213.
53.
Van Der MeerFSluysL (2009)
Continuum models for the analysis of progressive failure in composite laminates. Journal of Composite Materials43(20): 2131–2156.
54.
VoyiadjisGZKattanPI (2019)
Fundamental aspects for characterization in continuum damage mechanics. International Journal of Damage Mechanics28(2): 200–218.
55.
WangWLiuY (2019)
Continuum damage mechanics-based analysis of creep-fatigue interaction behavior in a turbine rotor. International Journal of Damage Mechanics28(3): 455–477.
56.
WecharatanaMShahSP (1983)
Predictions of nonlinear fracture process zone in concrete. Journal of Engineering Mechanics109(5): 1231–1246.
57.
WilliamsKVVaziriRPoursartipA (2003)
A physically based continuum damage mechanics model for thin laminated composite structures. International Journal of Solids and Structures40(9): 2267–2300.
58.
XueJKiraneK (2019)
Strength size effect and post-peak softening in textile composites analyzed by cohesive zone and crack band models. Engineering Fracture Mechanics212: 106–122.
59.
YunKWangZHeL, et al. (2018)
A damage model based on the introduction of a crack direction parameter for FRP composites under quasi-static load. Composite Structures184: 388–399.
60.
ZhongSGuoLLuH, et al. (2015)
A continuum damage model for three-dimensional woven composites and finite element implementation. Composite Structures128: 1–9.
61.
ZobeiryN (2010)
Extracting the strain-softening response of composites using full-field displacement measurement. PhD Thesis, University of British Columbia.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
